IMPROVEMENT OF AUTOPHAGY OR INCREASE IN LONGEVITY BY ADMINISTRATION OF UROLITINES OR THEIR PRECURSORS

Abstract

The present invention relates to methods, compounds, and compositions useful for increasing autophagy and promoting longevity. The methods, compounds, and compositions relate to urolithins and urolithin precursors and their use. Certain urolithins are represented by Formula I, while certain urolithin receptors are represented by Formula IV. The urolithin may be urolithin A, urolithin B, urolithin C, or urolithin D. The urolithin precursor may be ellagic acid or an ellagitannin. The methods include in vivo, ex vivo, and in vitro uses of the compounds and compositions.

Description

IMPROVEMENT OF AUTOPHAGY OR INCREASE OF LONGEVITY BY ADMINISTRATION OF UROLITINS OR PRECURSORS THEREOF CROSS REFERENCE TO RELATED APPLICATIONS This application claims the benefit of priority to Provisional Patent Application No. 61 / 791,137, filed on March 15, 2013; US Provisional Patent Application No. 61 / 712,886, filed October 12, 2012; and US Provisional Patent Application No. 61 / 665,137, filed June 27, 2012. BACKGROUND OF THE INVENTION Autophagy is a pathway of lysosomal degradation in both animals and plants that is essential for development, differentiation, homeostasis, and survival. In animals, autophagy primarily serves as an adaptive mechanism to protect organisms against various pathologies, including infection, cancer, neurodegeneration, heart disease, and aging. The repertoire of routine maintenance functions performed by autophagy includes clearance of defective proteins and organelles, prevention of accumulation of abnormal protein aggregates, and clearance of intracellular pathogens. The autophagy pathway is only capable of degrading entire organelles, such as mitochondria, peroxisomes, and endoplasmic reticulum. Multiple reports indicate that proteins required for autophagy induction, such as sirtuin 1, have reduced expression in aged tissues; Autophagy levels have been shown to decrease with age. Reduced levels of autophagy have also been associated with obesity, diabetes, cancer, neurodegenerative diseases, cardiovascular disease, osteoarthritis, and age-related macular degeneration. A number of compounds that stimulate autophagy have been identified, including rapamycin, resveratrol, metformin, spermidine and glucosamine. Urolithins are metabolites derived from ellagic acid and ellagitannin produced, for example, by mammalian colonic microflora, including human colonic microflora. Urolithins are known to have anti-oxidant activity. BRIEF DESCRIPTION OF THE INVENTION One aspect of the invention is a method for increasing autophagy in an animal, which comprises the step of administering to an animal in need thereof an effective amount of a urolithin or a precursor thereof, thereby increasing autophagy in the animal. animal. One aspect of the invention is a method of increasing longevity in an animal, which comprises the step of administering to an animal in need thereof an effective amount of a urolithin or a precursor thereof, thereby increasing the longevity of the animal. . MA / a / ¿U¿¿ / UU l ¿04 One aspect of the invention is a method for increasing autophagy in a cell, comprising the step of contacting a cell with an effective amount of a urolithin or a precursor thereof, thereby increasing autophagy in the cell. One aspect of the invention is a method of increasing the longevity of a cell, which comprises the step of contacting a cell with an effective amount of a urolithin or a precursor thereof, thereby increasing the longevity of the cell. One aspect of the invention is a method for increasing the autophagy of eukaryotic cells in vitro, which comprises the step of contacting the eukaryotic cells in vitro with an effective amount of a urolithin or a precursor thereof, thereby increasing the Autophagy in eukaryotic cells in vitro. One aspect of the invention is a method for increasing the longevity of eukaryotic cells in vitro, which comprises the step of contacting the eukaryotic cells in vitro with an effective amount of a urolithin or a precursor thereof, thereby increasing the longevity of eukaryotic cells in vitro. One aspect of the invention is a composition comprising a urolithin or a precursor thereof; and a compound selected from the group consisting of rapamycin, resveratrol, metformin, and spermidine. One aspect of the invention is a compound of Formula II Formula II iviAazuzzuu / ¿04 where X1, X2, X3, X4, X5, X6, X7, and X8 are independently selected from the group consisting of H and OH; and provided that the compound is not a compound of Formula II wherein X1, X2, X3, X4, X5, X6, X7, and X8 are H; X1 is OH, and X2, X3, X4, X5, X6, X7, and X8 are H; X2 is OH, and X1, X3, X4, X5, X6, X7, and X8 are H (urolithin B); X3 is OH, and X1, X2, X4, X5, X6, X7, and X8 are H; X4 is OH, and X1, X2, X3, X5, X6, X7, and X8 are H; X5 is OH, and X1, X2, X3, X4, X6, X7, and X8 are H; X6 is OH, and X1, X2, X3, X4, X5, X7, and X8 are H; X7 is OH, and X1, X2, X3, X4, X5, X6, and X8 are H; Χ8 is OH, and X1, X2, X3, X4, X5, X6, and X7 are H; X1 and X2 are OH, and X3, X4, X5, X6, X7, and X8 are H; X1 and X5 are OH, and X2, X3, X4, X6, X7, and X8 are H; X1 and X7 are OH, and X2, X3, X4, X5, X6, and X8 are H; X1 and X8 are OH, and X2, X3, X4, X5, X6, and X7 are H; X2 and X3 are OH, and X1, X4, X5, X6, X7, and X8 are H; X2 and X4 are OH, and X1, X3, X5, X6, X7, and X8 are H; X2 and X5 are OH, and X1, X3, X4, X6, X7, and X8 are H; X2 and X6 are OH, and X1, X3, X4, X5, X7, and X8 are H (urolithin A); X2 and X7 are OH, and X1, X3, X4, X5, X6, and X8 are H; X3 and X4 are OH, and X1, X2, X5, X6, X7, and X8 are H; X3 and X5 are OH, and X1, X2, X4, X6, X7, and X8 are H; X3 and X6 are OH, and X1, X2, X4, X5, X7, and X8 are H; X5 and X6 are OH, and X1, X2, X3, X4, X7, and X8 are H; X5 and X8 are OH, and X1, X2, X3, X4, X6, and X7 are H; X6 and X7 are OH, and X1, X2, X3, X4, X5, and X8 are H; Χ1, X2, and X5 are OH, and X3, X4, X6, X7, and X8 are H; Χ1, X2, and X6 are OH, and X3, X4, X5, X7, and X8 are H; Χ1, X5, and X8 are OH, and X2, X3, X4, X6, and X7 are H; X2, X4, and X6 are OH, and X1, X3, X5, X7, and X8 are H; X2, X4, and X7 are OH, and X1, X3, X5, X6, and X8 are H; X2, X6, and X7 are OH, and X1, X3, X4, X5, and X8 are H (urolithin C); X2, X6, and X8 are OH, and X1, X3, X4, X5, and X7 are H; X2, X7, and X8 are OH, and X1, X3, X4, X5, and X6 are H; X1, X2, X5, and X6 are OH, and X3, X4, X7, and X8 are H; X1, X2, X5, and X7 are OH, and X3, X4, X6, and X8 are H; X1, X2, X6, and X7 are OH, and X3, X4, X5, and X8 are H (urolithin D); X1, X6, X7, and X8 are OH, and X2, X3, X4, and X5 are H; X2, X3, X6, and X7 are OH, and X1, X4, X5, and X8 are H; X2, X4, X5, and X8 are OH, and X1, X3, X6, and X7 are H; X2, X4, X6, and X7 are OH, and X1, X3, X5, and X8 are H; X1, X2, X4, X5, and X7 are OH, and X3, X6, and X8 are H; X1, X2, X6, X7, and X8 are OH, and X3, X4, and X5 are H; and X1, X2, X3, X6, X7, and X8 are OH, and X4 and X5 are H. One aspect of the invention is a compound of Formula III IVIA / a / ZUZZ / UU / ¿04 ΜΛ / a / ZUZZ / UU l ¿04 where R1, R2, R3, R4, R5, R6, R7, and R8 are independently selected from the group consisting of H and OR; R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide; and provided that the compound is not a compound of Formula III wherein R1, R2, R3, R4, R5, R6, R7, and R8 are H; R1 is OR, and R2, R3, R4, R5, R6, R7, and R8 are H; R2 is OR, and R1, R3, R4, R5, R6, R7, and R8 are H; R3 is OR, and R1, R2, R4, R5, R6, R7, and R8 are H; R4 is OR, and R1, R2, R3, R5, R6, R7, and R8 are H; R5 is OR, and R1, R2, R3, R4, R6, R7, and R8 are H; R6 is OR, and R1, R2, R3, R4, R5, R7, and R8 are H; R7 is OR, and R1, R2, R3, R4, R5, R6, and R8 are H; R8 is OR, and R1, R2, R3, R4, R5, R6, and R7 are H; R1 and R2 are OR, and R3, R4, R5, R6, R7, and R8 are H; R1 and R5 are OR, and R2, R3, R4, R6, R7, and R8 are H; R1 and R7 are OR, and R2, R3, R4, R5, R6, and R8 are H; R1 and R8 are OR, and R2, R3, R4, R5, R6, and R7 are H; R2 and R3 are OR, and R1, R4, R5, R6, R7, and R8 are H; R2 and R4 are OR, and R1, R3, R5, R6, R7, and R8 are H; R2 and R5 are OR, and R1, R3, R4, R6, R7, and R8 are H; R2 and R6 are OR, and R1, R3, R4, R5, R7, and R8 are H; R2 and R7 are OR, and R1, R3, R4, R5, R6, and R8 are H; R2 and R8 are OR, and R1, R3, R4, R5, R6, and R7 are H; R3 and R4 are OR, and R1, R2, R5, R6, R7, and R8 are H; R3 and R5 are OR, and R1, R2, R4, R6, R7, and R8 are H; R3 and R6 are OR, and R1, R2, R4, R5, R7, and R8 are H; R3 and R7 are OR, and R1, R2, R4, R5, R6, and R8 are H; R3 and R8 are OR, and R1, R2, R4, R5, R6, and R7 are H; R4 and R8 are OR, and R1, R2, R3, R5, R6, and R7 are H; R5 and R6 are OR, and R1, R2, R3, R4, R7, and R8 are H; R5 and R7 are OR, and R1, R2, R3, R4, R6, and R8 are H; R5 and R8 are OR, and R1, R2, R3, R4, R6, and R7 are H; R6 and R7 are OR, and R1, R2, R3, R4, R5, and R8 are H; R6 and R8 are OR, and R1, R2, R3, R4, R5, and R7 are H; R1, R2, and R3 are OR, and R4, R5, R6, R7, and R8 are H; R1, R2, and R5 are OR, and R3, R4, R6, R7, and R8 are H; R1, R2, and R6 are OR, and R3, R4, R5, R7, and R8 are H; R1, R2, and R8 are OR, and R3, R4, R5, R6, and R7 are H; R1, R5, and R8 are OR, and R2, R3, R4, R6, and R7 are H; R1, R7, and R8 are OR, and R2, R3, R4, R5, and R6 are H; R2, R3, and R4 are OR, and R1, R5, R6, R7, and R8 are H; R2, R4, and R6 are OR, and R1, R3, R5, R7, and R8 are H; R2, R4, and R7 are OR, and R1, R3, R5, R6, and R8 are H; R2, R5, and R8 are OR, and R1, R3, R4, R6, and R7 are H; R2, R6, and R7 are OR, and R1, R3, R4, R5, and R8 are H; R2, R6, and R8 are OR, and R1, R3, R4, R5, and R7 are H; R2, R7, and R8 are OR, and R1, R3, R4, R5, and R6 are H; R3, R5, and R8 are OR, and R1, R2, R4, R6, and R7 are H; R3, R7, and R8 are OR, and R1, R2, R4, R5, and R6 are H; R6, R7, and R8 are OR, and R1, R2, R3, R4, and R5 are H; R1, R2, R5, and R6 are OR, and R3, R4, R7, and R8 are H; R1, R2, R5, and R7 are OR, and R3, R4, R6, and R8 are H; R1, R2, R6, and R7 are OR, and R3, R4, R5, and R8 are H; R1, R6, R7, and R8 are OR, and R2, R3, R4, and R5 are H; R2, R3, R4, and R6 are OR, and R1, R5, R7, and R8 are H; R2, R3, R5, and R7 are OR, and R1, R4, R6, and R8 are H; R2, R3, R6, and R7 are OR, and R1, R4, R5, and R8 are H; R2, R4, R5, and R8 are OR, and R1, R3, R6, and R7 are H; R2, R4, R6, and R7 are OR, and R1, R3, R5, and R8 are H; R2, R5, R6, and R7 are OR, and R1, R3, R4, and R8 are H; R2, R6, R7, and R8 are OR, and R1, R3, R4, and R5 are H; R1, R2, R4, R5, and R7 are OR, and R3, R6, and R8 are H; R1, R2, R6, R7, and R8 are OR, and R3, R4, and R5 are H; R2, R3, R4, R5, and R7 are OR, and R1, R6, and R8 are H; R2, R3, R6, R7, and R8 are OR, and R1, R4, and R5 are H; MA / a / ¿U¿¿ / UU l ¿04 R2, R4, R6, R7, and R8 are OR, and R1, R3, and R5 are H; R2, R5, R6, R7, and R8 are OR, and R1, R3, and R4 are H; R1, R2, R3, R6, R7, and R8 are OR, and R4 and R5 are H; R2, R3, R4, R6, R7, and R8 are OR, and R1 and R5 are H; and R2, R4, R5, R6, R7, and R8 are OR, and R1 and R3 are H. One aspect of the invention is a compound of Formula Vl ¿04 where X9, X10, X11, X12, X13, and X14 are independently selected from the group consisting of H and OH; and provided that the compound is not a compound of Formula V wherein X9, X10, X11, X12, X13, and X14 are H; X10 is OH, and X9, X11, X12, X13, and X14 are H; X9 and X12 are OH, and X10, X11, X13, and X14 are H; X9 and X13 are OH, and X10, X11, X12, and X14 are H; X9 and X14 are OH, and X10, X11, X12, and X13 are H; X10 and X13 are OH, and X9, X11, X12, and X14 are H; X10, X11, and X13 are OH, and X9, X12, and X14 are H; X9, X10, X12, and X14 are OH, and X11 and X13 are H; X9, X10, X13, and X14 are OH, and X11 and X12 are H (ellagic acid); X9, X10, X11, X13, and X14 are OH, and X12 is H; and X9, X10, X11, X12, X13, and X14 are OH. One aspect of the invention is a compound of Formula VI EITHER Formula VI where R9, R10, R11, R12, R13, and R14 are independently selected from the group consisting of H and OR; R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide; and provided that the compound is not a compound of Formula VI wherein R9, R10, R11, R12, R13, and R14 are H; R10 is OR, and R9, R11, R12, R13, and R14 are H; R9 and R12 are OR, and R10, R11, R13, and R14 are H; R9 and R13 are OR, and R10, R11, R12, and R14 are H; R9 and R14 are OR, and R10, R11, R12, and R13 are H; R10 and R13 are OR, and R9, R11, R12, and R14 are H; R9, R10, and R13 are OR, and R11, R12, and R14 are H; R9, R10, and R14 are OR, and R11, R12, and R13 are H; R10, R11, and R13 are OR, and R9, R12, and R14 are H; R9, R10, R12, and R13 are OR, and R11 and R14 are H; R9, R10, R12, and R14 are OR, and R11 and R13 are H; R9, R10, R13, and R14 are OR, and R11 and R12 are H; R10, R11, R12, and R13 are OR, and R9 and R14 are H; R9, R10, R11, R12, and R13 are OR, and R14 is H; R9, R10, R11, R13, and R14 are OR, and R12 is H; and R9, R10, R11, R12, R13, and R14 are OR. One aspect of the invention is a composition comprising a first compound; and a second compound selected from the group consisting of rapamycin, resveratrol, metformin, and spermidine, wherein the first compound is a compound of any of Formulas II, III, V, or VI. One aspect of the invention is a method of increasing autophagy in a cell, comprising contacting the cell with an effective amount of a compound of any of Formulas II, III, V, or VI, thereby increasing autophagy. in the cell. One aspect of the invention is a method of increasing longevity in an animal, comprising administering to an animal in need thereof an effective amount of a compound of any of Formulas II, III, V, or VI, thereby increasing the longevity of the animal. One aspect of the invention is a method for increasing the longevity of eukaryotic cells in vitro, which comprises contacting the eukaryotic cells in vitro with an effective amount of a compound of any of Formulas II, III, V, or VI, of thereby increasing the longevity of eukaryotic cells in vitro. MA / a / ¿U¿¿ / UU f ¿04 BRIEF DESCRIPTION OF THE FIGURES Figure 1 is a schematic diagram representing four stages of macroautophagy: induction and nucleation, expansion, fusion, and degradation. The proteins involved in each stage are indicated above each stage. The role of p62 and LC3 is explained schematically, thus, p62 helps transport cellular material into the autophagosome by binding to LC3. Figure 2 represents structural formulas for urolithin A (UA), ellagic acid (EA), telimagrandin (TL), punicalagin (PA), and punicalin (PB). Figure 3 represents ellagic acid (EA) and its metabolites, urolithin D (UD), urolithin C (UC), urolithin A (UA), and urolithin B (UB), which are produced by the intestinal microflora in mammals, which They include humans. Figure 4 is a set of five graphs representing the effect of ellagic acid and urolithin A, B, C, and D on the lifespan of C. elegans. Test agents were present at 50 μΜ in DMSO. DMSO, dimethyl sulfoxide, was the control and vehicle for the test agents. Figure 5 is a series of graphs depicting the longevity of native-type C. elegans growing in the presence of urolithin A, at the concentrations shown. Figure 6A-6F is a set of six graphs representing lifespan analyzes of indicated and wild-type C. elegans mutant strains grown in the absence (black) or presence (gray) of urolithin A, at 50 μΜ. Figure 7 is a bar graph depicting the effect of urolithin A on mitochondria in C. elegans muscle. The transgenic C. elegans strain SJ4103 displays fluorescence due to muscle-specific expression of green fluorescent protein (GFP) which is directed to the mitochondrial membrane. The presence of mitochondria in C. elegans muscle is shown by an increase in fluorescence. The results are expressed as mean ± SEM. *, p = 0.0014 (Student's t-test). Figures 8A - 8D is a line graph and three bar graphs depicting the effect of urolithin A (UA) on basal and uncoupled respiration in young (one day old) and old (ten days old) C. elegans. ). Figure 8A represents basal and uncoupled respiration (FCCP) in 10-day-old control worms treated with 0.1% DMSO and ten-day-old worms treated with 30 μΜ urolithin A in 0.1% DMSO. Figure 8B represents the representative area under the curve (AUC) of uncoupled respiration (FCCP) in ten-day-old control worms treated with vehicle (0.1% DMSO) or 30 μΜ urolithin A in 0.1% DMSO. The results are expressed as mean ± SEM. *, p < 0.05 (Student's t-test). Oxygen consumption rate, OCR. Figure 8C represents the comparison of basal respiration between one-day-old and ten-day-old worms treated with vehicle (0.1% DMSO). The figure IVIA / a / ¿U¿¿ / UU / ¿04 8D represents the comparison of basal respiration between one-day and ten-day-old worms treated with UA (30 μΜ). Figure 9A is a group of three confocal images depicting the effect of urolithin A on the induction of autophagy in C. elegans. Figure 9B is a corresponding dot plot depicting the effect of urolithin A on autophagy induction. p < 0.001 (Student's t-test). Figures 10A - 10C is a set of three graphs representing survival curves, showing the effect of RNAi knockdown of vps-34 and bec-1 on the longevity phenotype induced by urolithin A treatment in C. elegans . Both inhibitions of vps-34 (Figure 10B) and bec-1 (Figure 10C) completely suppress the lifespan phenotype observed in worms treated with urolithin A (50 μΜ) and fed the empty vector (Figure 10A). Survival analyzes were performed using the Kaplan Meier method and the significance of differences between survival curves was calculated using the log-rank test. p < 0.001 (log rank test). Figure 11 is a series of graphs demonstrating the effects of urolithin A (UA), urolithin B (UB), urolithin C (UC) and urolithin D (UD) treatment on pharyngeal pumping in C. elegans worms after 7 and 14 days of treatment. (* p < 0.05; ** p < 0.01; *** p < 0.001) Figure 12 are three line graphs demonstrating the effects of ellagic acid (EA), urolithin A (UA), and urolithin B (UB) treatment on mortality in young C. elegans worms on days 1, 3, 5, and 8 from the treatment. (* p< 0.05; “ p<0.01; ***p<0.001) Figure 13 is a series of images demonstrating the mobility time path traces of C. elegans after treatment with ellagic acid (EA), urolithin A (UA), urolithin B (UB), urolithin C (UC) and Urolithin D (UD) on days 8, 14 and 16 of treatment. Figure 14 is a Western blot of ModeK cells, an intestinal epithelial cell line, demonstrating the effect of urolithin A treatment on the autophagy marker LC3-II / LC3-I ratio, p62, and on the ρ ratio. -ΑΜΡΚα / ΑΜΡΚα. The bar graph demonstrates the quantified fold increase in the ratio of LC3-II to LC3-I, and the ratio of p-AMPKa to AMPKo levels observed in the western, ctl, and control stains. Figure 15 is a Western blot of primary mouse hepatocytes, demonstrating the effect of urolithin A treatment on the autophagy marker LC3-II / LC3-I ratio, p62, and on the ρ-ΑΜΡΚα / ΑΜΡΚα ratio. The bar graph demonstrates the quantified fold increase in the ratio of LC3-II to LC3-I, and the ratio of p-AMPKa to AMPKa levels observed in the western, ctl, and control stains. Figure 16 is a Western blot of C2C12 mouse myocytes, demonstrating the effect of urolithin A treatment on the autophagy marker LC3-II / LC3-I ratio, p62, and on the ρ-ΑΜΡΚα / ΑΜΡΚα ratio. The bar graph shows the times of increase IVIA / a / ZUZZ / UU / ¿04 quantified in the ratio of LC3-II to LC3-I, and the ratio of p-AMPKa to AMPKa levels observed in the western, ctl, and control stains. Figure 17 is a Western blot of human primary myoblasts, demonstrating the effect of urolithin A treatment on the autophagy marker LC3-II / LC3-I ratio, p62, and on the ρ-ΑΜΡΚα / ΑΜΡΚα ratio. The bar graph demonstrates the quantified fold increase in the ratio of LC3-II to LC3-I levels observed in Western blots. Ctrl, control. Figure 18 is a Western blot of primary human aortic endothelial cells, demonstrating the effect of urolithin A treatment on the ratio of autophagy marker LC3-H / LC3-I and p62 protein. The bar graph demonstrates the quantified fold increase in the ratio of LC3-H to LC3-I levels observed in Western blots. Ctrl, control. Figure 19 is a Western blot of livers isolated from untreated control mice and mice administered urolithin A, at a dose of 55 mg / kg / day mixed in food. Urolithin A treatment increases the ratio of autophagy marker LC3II / LC3-I, decreased p62, and increased ratio of ρ-ΑΜΡΚα / ΑΜΡΚα. The bar graph demonstrates the quantified fold increase in the ratio of LC3-II to LC3-I, and the ratio of p-AMPKa to AMPKa levels observed in the western, ctl, and control stains. Figure 20 is a graph depicting the effect of orally consumed urolithin A at 55 mg / kg / day on the motor activity of C57BL / 6J mice. Treated young mice increase their spontaneous voluntary running on a running wheel by at least 25% over the five-day period investigated. Figure 21 is a bar graph depicting the effect of orally consumed urolithin A on running in aged C57BL / 6J mice. Figure 22 is a graph depicting the effect of orally consumed urolithin A on grip resistance in aged C57BL / 6J mice. Figure 23 is a pair of graphs depicting the effect of orally consumed urolithin A on ambulation and rearing in aged C57BL / 6J mice. HFD, high fat diet; UA, urolithin A. Figure 24 is a Western blot of skeletal muscle isolated from untreated control mice aged on high-fat diet (HFD), and from aged mice on high-fat diet administered with urolithin A (UA) at a dose of 50 mg / kg. kg / day mixed in feed. Treatment with urolithin A increases the ratio of autophagy marker LC3II / LC3-I and decreases p62 levels. The bar graph demonstrates the quantified fold increase in the ratio of LC3-II to LC3-I levels observed in Western blots. Ctrl, control. Figure 25 shows the effect of urolithin A (UA) on autophagy in C2C12 myoblasts. Myoblasts incubated for 24 hours with increased doses of UA show a dose response, with an increase in autophagy because the concentration of UA was elevated (10 μΜ, 50 μΜ and 100 μΜ), which was demonstrated by the change in increase in the Histogram depicting levels of LC3-B cells, a marker of autophagy, compared to untreated controls. Figure 26 shows the effect of urolithin A (UA), urolithin B (UB), urolithin C (UC), and urolithin D (UD) on autophagy in C2C12 cells. Myoblasts incubated with UA, UB, UC, or UD at 100 μΜ experience an increase in autophagy as demonstrated by the change in the histogram representing the levels of LC3-B cells compared to untreated controls. Figure 27 represents twenty-five compounds of the invention. Figure 28 depicts predictive synthetic routes to the compounds in Figure 27. DETAILED DESCRIPTION OF THE INVENTION Summary Autophagy is a process by which cells break down their own components, recycling amino acids and other building blocks that can be reused. Such degradation is carried out by lysosomal acid hydrolases. It is a tightly regulated process that plays an important role in the growth, development, and homeostasis of normal cells, helping to maintain a balance between the synthesis, degradation, and subsequent recycling of cellular products. It is a primary mechanism by which starving cells can reallocate nutrients from less essential processes to more essential processes. During nutrient starvation, increased levels of autophagy lead to the breakdown of non-vital components and the release of nutrients, ensuring that vital processes can continue. Mutant yeast cells that have reduced autophagic capacity perish rapidly under nutrient-deficient conditions. A gene known as Atg7 has been implicated in nutrient-mediated autophagy, and studies in mice have shown that starvation-induced autophagy was impaired in Atg7-deficient mice. Komatsu M et al. (2005) J Cell Biol. 169:425-434. Autophagy degrades damaged organelles, cell membranes, and proteins. Autophagy failure is thought to be an important factor in the accumulation of cellular damage and, therefore, aging. Three types of autophagy can be distinguished, depending on the trajectory along which cellular components are delivered to lysosomes: macroautophagy, microautophagy, and chaperone-mediated autophagy (CMA). Macroautophagy Macroautophagy involves the degradation of long-lived proteins and entire cellular organelles through a multi-step process (Figure 1). Macroautophagy begins with the formation of a double-stratified insulation membrane (phagophore) around the molecules and / or organelles to be degraded. The phagophore engulfs the cytosolic components and seals around the contents, forming an autophagosome. Eventually, the autophagosome fuses with a lysosome, enveloping it into an autophagolysome (or autolysome) where lysosomal hydrolases digest the cargo. Microautophagy involves the direct sequestration of cytosolic components through invaginations or arm-like projections of the lysosomal membrane. Microautophagy can serve to renew long-lived proteins; however, the significance and regulation of this type of autophagy remains poorly understood. Finally, chaperone-mediated autophagy is a highly selective process dedicated to the degradation of soluble cytosolic proteins. Microtubule-associated protein 1A / 1B-light chain 3 (LC3), a mammalian homologue of yeast Atg8, is a soluble protein with a molecular mass of approximately 17 kDa which is ubiquitously distributed in mammalian tissues and cultured cells. It is processed immediately after its synthesis by Atg4B, a cysteine ​​protease, which exposes the C-terminal glycine residue (LC3-I). During autophagy, autophagosomes engulf cytoplasmic components, including cytosolic proteins and organelles. Concomitantly, a cytosolic form of LC3 (LC3-I) is conjugated to phosphatidylethanolamine (PE) to form and conjugate LC3-PE (LC3-II), which is sequestered to autophagosomal membranes (Figure 1). p62, also known as sequestosome-1, was identified as a novel pattern of atypical protein kinase Cs (aPKCs) and is a ubiquitously expressed cellular protein. p62 is known to have domains that interact with and bind ubiquitinated proteins, and has been identified as a component of inclusion bodies observed in human diseases, especially neurodegenerative diseases (e.g., Alzheimer's disease, Parkinson's disease, amyotrophic lateral sclerosis ) as well as in liver diseases. p62 has also been identified as an LC3 interacting protein and it has been shown that an 11 amino acid sequence in mouse p62 serves to recognize the LC3 protein. As seen in Figure 1, LC3 binds to p62 and transports it (and any of the ubiquitinated proteins or cellular components that bind to them) into the autophagosome, where it is degraded. Consequently, one of the hallmarks of autophagy is an increase in the LC3-II / LC3-I ratio with a concomitant decrease in the level of cellular p62. Of the three types of autophagy described, macroautophagy is the best characterized in mammalian cells. Starvation is the strongest stimulus of macroautophagy. During nutrient starvation, macroautophagy breaks down cellular components, generating amino acids, fatty acids, and carbohydrates, which can be used for energy production and for the synthesis of essential cellular molecules. Macroautophagy is also involved in specific cytosolic rearrangements during embryogenesis and postnatal development. Furthermore, macroautophagy is induced during viral or bacterial infections, in hypoxia, and under various stress conditions, including radiation exposure and generation of increased reactive oxygen species (ROS). Under these circumstances, macroautophagy is essential for the maintenance of cellular homeostasis by promoting the removal of damaged components. However, impairments in macroautophagy induce premature aging and shorten lifespan in several organisms, including C. elegans, yeast, and Drosophila. Hars ES et al. (2007) Autophagy 3:93-95; Matéele M et al. (2010) PLoS Genet. 6:e1000921; Lee JH et al. (2010) Science 327:1223-1228. Conversely, upregulation of macroautophagy is proposed to be a primary mechanism underlying the lifespan extension properties of calorie restriction. Toth ML et al. (2008) Autophagy 4:330-338; Morselli E et al. (2010) Cell Death Dis. 1;e10. More than 35 Atg proteins (related to AuTophaGia) have been identified in yeast and mammals; However, the precise role that each Atg protein plays during autophagy is not yet fully established. As illustrated in Figure 1, the process of macroautophagy can be divided into discrete stages, that is, induction and nucleation, expansion, fusion, and degradation. The induction phase is mediated by the ULK1-Atg13-FIP200 kinase complex. The regulation of the nucleation step, which consists of the recruitment of Atg proteins to the phagophore assembly site, is not yet fully understood. However, vacuolar protein sorting-34 (Vps34), a class III phosphatidylinositol-3-kinase (PI3K), is required for this stage. Vps34 associates with Beclinl, the mammalian homolog of yeast Atg6, and subsequently recruits Atg14 and Vps15 (p150) to the preautophagosomal structure. Phagophore membrane elongation and expansion requires two ubiquitin-like conjugation systems involving Atg12 (conjugated to Atg5) and Atg8 / microtubule-associated protein 1 light chain-3 (LC3, conjugated to phosphatidyl ethanolamine), along with other Atg proteins such as Atg9 and Atg16. Autophagosome fusion with a lysosome depends on the canonical cell fusion machinery consisting of the Rab-SNARE (Soluble Netylmaleimide Sensitive Factor-Associating Protein REceptor) system and requires the presence of lysosomal membrane-associated protein-2. (LAMP-2) and the gene associated with resistance to UV radiation (UVRAG). Finally, digestion of the cargo is performed by lysosomal hydrolases, followed by transport of degraded components into the cytoplasm by lysosomal efflux transporters such as Atg22. With respect to the regulation of macroautophagy, mTOR, the mammalian target of rapamycin, is considered to be a major checkpoint, linking the cellular nutritional status with the level of ongoing autophagy. Under nutrient-rich conditions, mTOR is active and inhibits the ULK1-Atg13-FIP200 complex required for the induction of macroautophagy. Energy deprivation leads to inactivation of mTOR and stimulation of AMP-activated protein kinase (AMPK), both of which induce macroautophagy. AMPK functions as an energy-sensitive kinase and is activated by increases in the cellular AMP to ATP ratio. Under such circumstances, AMPK promotes autophagy by directly activating ULK1 and relieving mTOR-mediated inhibition of macroautophagy. Macroautophagy can be selectively directed toward the removal of particular targets, for example, peroxisomes (pexophagy), endoplasmic reticulum (reticulophagy), intracellular lipids (lipophagy), ribosomes (ribophagy), and intracellular pathogens (xenopathy). Likewise, mitochondria can be selectively targeted for degradation through macroautophagy (mitophagy). Mitophagy: A Specialized Form of Macroautophagy Mitophagy is a highly selective process that can promote the elimination of dysfunctional or unnecessary mitochondria. Wang K et al. (2011) Autophagy 7:297-300. The loss of mitochondrial membrane potential (Δψm) represents a major activator of mitophagy. However, laser-induced photodamage of selected mitochondria within living hepatocytes results in rapid dissipation of Δψm, followed by rapid removal of depolarized mitochondria through mitophagy. Furthermore, oxidative damage can lead to the formation of asymmetric daughter mitochondria characterized by different Δψm, with autophagy specifically targeting mitochondria with lower Δψm. Apart from the degradation of damaged mitochondria under stress conditions, mitophagy is essential for mitochondrial utilization in the basal state and during cellular differentiation, such as the maturation of reticulocytes into mature red blood cells. Research into the molecular regulation of mitophagy has revealed specific mitophagy proteins. Parkin and Pinkl are thought to play important roles in the selective degradation of damaged mitochondria, at least under certain circumstances. Parkin is a cytosolic E3-ubiquitin ligase that is selectively recruited to dysfunctional mitochondria and assists in their removal by mitophagy. Narenda D (2008) J Cell Biol. 183:795-803. Pinkl is imported into healthy mitochondria through a Δψm-dependent process and is degraded by presenilin-associated rhomboid-like protease (PARL). Matsuda N et al. (2010) J Cell Biol. 189:211-221. Dissipation of Δψm results in the accumulation of Pinkl on the mitochondrial surface, leading to the recruitment of Parkin, which ubiquitinates other membrane proteins, including the voltage-gated anion channel (VDAC). Ubiquitin-tagged mitochondria are proposed to be directly targeted to autophagic vacuoles through the interaction of ubiquitinated proteins with the autophagosomal marker LC3 (Atg8). Furthermore, Parkin can ubiquitinate the mitochondrial membrane and B cell lymphoma-2 apoptosis regulatory protein (Bcl-2), thereby de-repressing Beclin 1. Recent evidence also suggests that opening of the mitochondrial permeability transition pore (mPTP) may be required for the selective removal of damaged mitochondria. The opening of the mPTP causes a sudden increase in the permeability of the inner membrane to solutes with molecular weight up to 1500 Da. This results in mitochondrial depolarization, activation of mitochondrial ATPase (i.e., ATP synthase operating in reverse), and swelling and rupture of the outer membrane. The loss of Δψm subsequent to the permeability transition directs individual mitochondria for degradation. Loss of Δψm and activation of macroautophagy are prevented by cyclosporin A, an inhibitor of cyclophilin D component of mPTP. Furthermore, starvation fails to induce macroautophagy in cyclophilin-D-deficient murine cardiomyocytes, while autophagy is enhanced even under fed conditions in cardiac cells from mice overexpressing cyclophilin D. Nicotinamide-dependent sirtuinα-3 deacetylase (SIRT3) adenine dinucleotide (NAD)-, appears to be critically involved in the control of mPTP by modulation of cyclophilin D. Similar to mPTP, the apoptotic proteins Bnip3 (Bcl-2 and adenovirus E1B 19 kDa interacting protein-3) and Nix (Nip3-like protein X) are thought to activate selective mitophagy through mitochondrial depolarization. However, Bnip3 can induce mitophagy by competitively disrupting the inhibitory interaction between Bcl-2 and Beclinl. Finally, Nix associates with mitochondrial membranes and interacts directly with LC3 (Atg8). Although the molecular regulation of mitophagy has not yet been fully elucidated, the mTOR / AMPK pathway is proposed to be a major checkpoint. AMPK, in addition to stimulating mitochondrial clearance through autophagy, enhances the activity of sirtuin-1 (SIRT1) and its downstream target PGC-1a, resulting in the stimulation of mitochondrial biogenesis. Therefore, through AMPK activity, mitophagy and mitochondrial biogenesis are coordinately regulated, maintaining a healthy and functional mix of mitochondria in the cell. Lipophagy is a recently recognized alternative pathway of lipid metabolism in which intracellular lipid droplets of triglycerides and cholesterol are taken up by autophagosomes and delivered to lysosomes for degradation by acidic hydrolases, thereby releasing free fatty acids. Lipophagy, therefore, functions to regulate intracellular lipid stores, cellular levels of free lipids, such as fatty acids, and energy homeostasis. Xenophagy is a recently recognized defense mechanism against several types of intracellular pathogens, including Mycobacterium tuberculosis, Salmonella typhimurium, Legionella pneumophila, Brucella species, Chlamydia species, Coxiella burnetti, Listeria monocytogenes, Shigella flexneri, Rickettsia species, Mycobacterium marinum, Burkholderia species, and Francisella tularensis. Microautophagy involves lysosomes directly engulfing the cytoplasm by invagination, protrusion, or septation of the lysosomal limiting membrane. Chaperone-mediated autophagy Chaperone-mediated autophagy (CMA) refers only to those proteins that have a consensus peptide sequence that can be recognized by the binding of a co-chaperone / chaperone complex containing hsc70. The CMA chaperone / substrate complex then moves to lysosomes, where it is recognized by the CMA receptor lysosome-associated membrane protein type 2a (LAMP-2A). The protein is unfolded and translocated across the lysosome membrane assisted by lysosomal hsc70 on the other side. Thus, CMA substrates are translocated across the lysosomal membrane on a one-by-one basis, while in macroautophagy and microautophagy, the substrates are engulfed and sequestered in volume. However, CMA degrades only certain proteins and not organelles. Exemplary Therapeutic Indications for Increased Autophagy The compounds, compositions, and methods of the invention can be used to treat and prevent any of the following therapeutic indications for increased autophagy. Autophagy Protects Organisms from Metabolic Stress Nutrient starvation, growth factor suppression, and hypoxia can induce metabolic stress leading to the induction of autophagy and the regeneration of free amino acids and fatty acids. These can be recycled cell autonomously and used for 1) de novo synthesis of proteins important in the stress response, and 2) supplying the TCA cycle to maintain ATP function. The importance of this process is demonstrated by the inability of mice and C. elegans deficient in ATG proteins important for autophagy to resist starvation. Thus, a critical role for autophagy is the mobilization of intracellular energy resources to meet the organism's and cellular demand for metabolic substrates. Autophagy Induction for Heart Treatment Cardiomyocyte function and survival critically depend on the presence of basal levels of cardiomyocyte autophagy. Autophagic recycling of damaged cellular components under nutrient-rich conditions constitutes a primary means of organelle and protein quality control, ridding the cell of dysfunctional organelles and defective proteins (e.g., unfolded or oxidized). This fact is highlighted by the observation that abrogation of autophagic pathways in the adult heart by conditional inactivation of either the Atg5 or Atg7 genes activates rapid-onset cardiac hypertrophy, left ventricular dilation, and decreased cardiac output. Danon disease, a condition marked by severe progressive myopathy, arises from defective function of autophagosomes with lysosomes. In early cardiac development, disruption of Atg5 causes in utero defects and embryonic lethality. At the other end of the age spectrum, the age-related decline in autophagic clearance efficiency likely contributes to the progressive accumulation of defective proteins and organelles which ultimately lead to functional decline over time. Normal aging is associated with loss of cardiac function primarily due to impaired relaxation during diastole. Variant calorie restriction (CR) formulations may prolong lifespan and improve LV diastolic function; The fundamental mechanisms are believed to be the induction of autophagy. Together, these facts highlight the life-sustaining role for cardiomyocyte autophagy as a mechanism of organelle and protein survival and quality control. Autophagy May Improve Skeletal Muscle Function in Setting Muscle Atrophy Skeletal muscle adapts its capacity to levels of load and use. A central aspect of this adaptation is the regulation of fiber remodeling through the degeneration or regeneration of muscle fibers. In the absence of muscle activity, muscle atrophy occurs, resulting in decreased muscle capacity. This atrophy has been shown to occur due to increased levels of oxidative stress in disused muscle. Attenuation of this oxidative stress could lead to decreased atrophy. The process of autophagy, and in particular mitophagy, are important in the separation of damaged mitochondria and reduce the effects of increased oxidative stress on the capacity for muscle function. Failure of the autophagy process has been shown to be an important contributing factor to muscle disuse atrophy, failing to remove damaged mitochondria. This decrease in mitochondrial utilization leads to an accumulation of dysfunctional organs and subsequent muscle damage. Preservation of Autophagy Function During Aging May Improve Sarcopenia Skeletal muscle atrophy and impaired muscle endurance represent a major health problem and can occur as a consequence of immobilization, disuse, injury, starvation, and aging. In particular, advanced age is inevitably accompanied by the loss of muscle mass and resistance. This condition, known as aging sarcopenia, has significant effects on individual health and impacts the severity of frailty. However, poor muscular endurance is highly predictive of disability and mortality, and general weakness often results in loss of independent living, thereby affecting individual quality of life and imposing a high burden on care expenditures. of the greeting. Aside from aging, skeletal muscle can undergo significant atrophy after disuse. Sarcopenia is characterized by a gradual loss of muscle proteins. The size of stable post-mitotic tissues, such as cardiac and skeletal muscles, is regulated by protein utilization, and skeletal muscle is influenced by a balance between protein synthesis and degradation and contractile protein utilization. A key factor influencing the development of sarcopenia is the imbalance between the rates of protein synthesis and degradation. Protein degradation in skeletal muscle cells is essentially mediated by the activity of two highly conserved pathways: the autophagic lysosomal pathway and the ubiquitinproteasome pathway. Recent studies have shown that the impaired autophagy seen in ATG7 null muscles is characterized by muscle atrophy, weakness, and features of myofiber degeneration. Consequently, autophagy has been found to be essential for myofiber maintenance and for the separation of damaged proteins and altered organelles. Autophagy, which is activated when skeletal muscle is under nutritional stress (such as metabolic stress), plays a role in the catabolic condition and in the degradation of macromolecules and organelles. Catabolic pathways are accelerated during exercise to supply energy and substrates to the muscle for continued contractions. It has been well established that glucose and (relatively small) amino acid oxidation rates are increased during endurance exercise, and increased energy consumption is probably required to induce autophagy. It has been shown that autophagy is required for myofiber maintenance and for the separation of damaged proteins and altered organelles. Mild exercise has been shown to improve muscle function and decrease the decline in muscle function observed in sarcopenia. These positive benefits are at least in part due to an exercise-induced improvement in the autophagy process. In aged mice, the autophagy proteins LC3-II, Beclin-1, ATG7, and MuRF-1 significantly decrease with age in muscle. However, mice undergoing a treatment regimen during the aging process show a significantly attenuated decrease in these autophagy proteins. In overweight older women, mild exercise has been shown to increase the transcript levels of the autophagy regulators LCB3, Atg7, and LAMP-2 and thus improve the autophagy process. Thus, the preservation of autophagy may play an important role in the IVIA / a / ¿U¿¿ / UU l ¿04 Skeletal myocyte homeostasis and optimal mitochondrial utilization in aged muscle. An age-related attenuation of autophagy has been shown and results in decreased efficiency of protein degradation and separation of damaged organelles. A decrease in proteolytic activity has been considered responsible, at least in part, for the accumulation of damaged cellular components in almost all tissues of aging organisms. Improving Autophagy as a Therapeutic Target for Degenerative Muscle Diseases Muscular dystrophies are a group of hereditary, genetic muscle diseases characterized by defects in muscle proteins. These defects result in progressive skeletal muscle damage accompanied by myofiber necrosis and chronic local inflammation, leading to replacement of myofibers by adipose and connective tissue. In Duchenne muscular dystrophy (DMD), the most severe form of these diseases, progressive and continuous skeletal muscle damage leads to complete paralysis and death of patients, usually from cardiac and / or respiratory failure. The therapeutic protocols currently in use, based on corticosteroid administration, provide some delay in the progression of the disease, but are associated with severe side effects. Therapies that replace corticosteroids or at least can act as corticosteroid-reducing drugs are thus being actively pursued, and biological mechanisms relevant to skeletal muscle homeostasis are being explored, in order to identify new targets. Autophagy is emerging as an important process that limits muscle damage. Inhibition / alteration of autophagy contributes to myofiber degeneration leading to the accumulation of abnormal organelles. Mutations that inactivate Jumpy, a phosphatase that counteracts VPS34 activation for autophagosome formation and reduces autophagy, are associated with centronuclear myopathy. This observation suggests that unbalanced autophagy is pathogenic in muscle degeneration. Similarly, hyperactivation of Akt as a consequence of muscle-specific suppression of the mammalian target of rapamycin (mTOR), leads to inhibition of autophagy and a muscle phenotype resembling one observed in muscular dystrophy. The validity of autophagy modulation as a therapeutic strategy has been shown in a mouse model of Ulrich myopathy characterized by defective autophagy and accumulation of dysfunctional organelles. Forced reactivation of autophagy in these animals provides a beneficial therapeutic response. In vivo and ex vivo analyzes have shown that autophagy is defective in both human (DMD) and mouse (MDX) muscular dystrophy and that such a defect contributes to the MA / a / ¿U¿¿ / UU f ¿04 pathogenesis of the disease. Muscle biopsies from DMD patients have been shown to have significantly lower levels of LC3 II and significant accumulation of p62, a protein known to be incorporated into autophagosomes and efficiently degraded, relative to tissues from unaffected, control individuals. . A low protein diet has been shown in mice to lead to a prolonged induction of autophagy. In DMD mice fed a low-protein diet, an induction of autophagy leads to improvement and management in disease progression. Significant improvements in muscle function have been observed with improved whole body tension, reduced muscle fibrosis, decreased collagen disposition, reduced accumulation of damaged organelles, and reduced apoptosis of muscle fibers. This demonstrates that autophagy induction is an important homeostatic mechanism that is altered in dystrophic muscles and indicates that novel therapeutic procedures targeting autophagy reactivation may serve as a valuable strategy to reduce muscle damage in DMD. Autophagy Protects the Liver from Oxidative Stress and Disease During liver diseases such as cancer and cirrhosis, the liver can become hypoxic. This process has been shown to induce an autophagy process, which is inhibited resulting in increased apoptosis of liver cells. In α1-antitrypsin deficiency, the most common genetic cause of human liver disease, there is significant chronic inflammation and eventual carcinogenesis. In this disease, a point mutation occurs in α1-antitrypsin Z (ATZ) leading to inappropriate folding and accumulation of aggregates. Deletion of ATG5 in liver cell lines leads to an accumulation of the mutant ATZ protein, demonstrating the important role for autophagy in reducing the impact of liver disease. Autophagy is Important in Limiting Isguemic Reperfusion Injury With advancing age, patients are more likely to acquire primary and secondary liver malignancies that are amenable to surgical resection and transplantation. Although elderly patients can be treated surgically, the aged liver has significantly diminished reparative capacity after the reperfusion injury and ischemia associated with these operations. Ischemic preconditioning is the only promising strategy for improving the outcome of liver surgery, but its beneficial effects are limited to young patients. To date, no therapeutic strategy can suppress age-dependent ischemia and reperfusion injury. A reduction in autophagy has been observed in old cells subjected to severe stress such as ischemia followed by reperfusion. Studies have shown that by overexpression of autophagy genes in aged mouse livers, autophagy was increased and hepatocyte cell survival was increased after ischemia and reperfusion. Consequently, defective autophagy has been shown to be a causal mechanism for age-dependent hepatic ischemia-reperfusion injury and that improvement of autophagy has been shown to offer therapeutic benefit and reduce age-mediated hepatic ischemia-reperfusion injury. . Autophagy in Intestinal Epithelial Cells as a Therapeutic Target The intestinal epithelium interacts directly with a diverse community of bacteria that includes benign commensals, opportunistic pathogens, and open pathogens, and consequently is the first line of defense against bacterial invasion of host tissues. One means that the epithelial cells used to defend themselves include secreting antimicrobial proteins. Unfortunately, there are some intestinal pathogens, including Salmonella tyhpimurium or opportunistically invasive commensal bacteria, such as Enterococcus faecalis, which can bypass this first line of defense and enter epithelial cells. Autophagy has been shown to be essential for the recognition and degradation of intracellular pathogens, acting as an innate barrier to infection. In cell culture, autophagy has been shown to limit the replication of certain bacterial species. It has been shown through genetic studies of inflammatory bowel disease (IBD) that autophagy plays an important role in intestinal immune homeostasis. IBD is a chronic inflammatory bowel disease that arises from dysregulated interactions with resident microbiota. Recently, polymorphisms in genes in the autophagic pathway have been shown to be linked to Crohn's Disease (CD). Crohn's Disease is a chronic form of IBD that can affect any part of the gastrointestinal system, but is usually found in the colon or terminal ileus. The average onset is at 27 years of age in humans, and is usually present throughout the normal lifespan of individuals. It is characterized by severe colitis, strictures, and perianal fistulas, typically requiring surgery. The chronic inflammatory process characteristic of CD requires intensive interaction between intestinal epithelial cells and immune competent cells. In CD, there is an exaggerated immune response to the gut microbiota, characterized by an abnormal increase in Th17 cells, which play a major role in autoimmunity, and a downregulation of Treg cells important for controlling the immune response. It has recently been shown that intestinal epithelial cell autophagy is essential for mammalian intestinal defense against invasive bacteria. Autophagy in epithelial cells protects against the spread of invasive bacteria. Following oral infection with the invasive pathogen Salmonella typhimurium as well as Enterococcus ΜΛ / a / ZUZZ / UU f ¿04 faecalis, mouse epithelial cells activate autophagy as a consequence of exposure to these pathogens. Autophagy was also shown to be critical for limiting the extra-intestinal dispersal of S. typhimurium. This indicates that autophagy is a key epithelial cell-autonomous mechanism of antibacterial defense that protects against the dissemination of intestinal bacteria. The present invention provides the know-how to use compounds that include urolithiasis and its precursors as autophagy enhancers for administration to and treatment of individuals with inflammatory bowel disease (IBD) or Crohn's Disease (CD) and in need of increasing the levels of autophagy in your intestinal epithelial cells in order to treat either IBD or CD. Autophagy is Important in Cardiac Muscle Aging The effects of autophagy induction on improved outcome for ischemic injury and muscle maintenance make it especially relevant for cardiac muscle maintenance and protection from injury. Cardiac muscle suffers a progressive decline in mitochondrial function, similar to that observed in skeletal muscle, resulting in an increase in reactive oxygen species, as well as an increase in the accumulation of defective organelles. The separation of these damaged organelles by autophagy is important for the maintenance of cardiac muscle function. As autophagy declines with age, promoting autophagy may serve to protect heart muscle function. The cardiac muscle is also strongly exposed to ischemic events during cardiac infarctions. The level of cardiac muscle damage that these ischemic events produce is strongly dependent on the cells' ability to mount an effective autophagy response to separate damaged organelles. In aged animals, a defective autophagy response leads to increased cardiac muscle damage after ischemic events. Thus, the promotion of autophagy during these acute events could serve to protect cardiac muscle from damage. Autophagy is Important in the Inflammatory Process Due to the role of autophagy in the separation of defective organelles, a defect in this process leads to an accumulation of cellular debris and the induction of apoptosis. Autophagy also plays an important role in defending the body against microbial pathogens by inducing their degradation. Additionally, autophagy plays an important role in trafficking events that activate adaptive and innate immunity. Autophagic removal of apoptotic bodies is critical to prevent danger signals that could lead to an inflammatory response. In an impaired autophagy response, where apoptotic clearance is not efficient, the resulting induction of inflammation could overcome tolerance to self-antigens leading to immune diseases such IVIA / a / ZUZZ / UU / ¿04 as systemic lupus erythematosus. In this way, the induction of autophagy could serve to reduce inflammatory responses and the development of autoimmune diseases. Applications of Autophagy for the Treatment of Liver Disorders A number of characteristics of hepatocytes and the liver as a whole make this organ particularly dependent on autophagy. The liver is preferably unique in its regenerative properties in that while hepatocytes are normally in a quiescent state, they retain the ability to rapidly enter the cell cycle when there is loss of liver tissue due to injury or surgical removal. The lack of cellular utilization makes hepatocytes particularly vulnerable to the effects of altered autophagy, since long-lived cells accumulate high levels of damaged organelles, protein aggregates, etc. which are normally separated by autophagy. This leads to cellular injury and potentially transformation. Hepatocellular Lipid Metabolism The liver serves as the second largest repository of stored lipids in the body after adipose tissue. Hepatocytes are an important cellular store for neutral lipids in the form of glycides (TGs) and cholesterol esters contained in specialized organelles called lipid droplets (LD). Autophagy mediates the breakdown of intracellular LD stores through the process of lipophagy. This allows hepatocytes to rapidly mobilize their lipid stores in times of metabolic need. Loss of hepatocyte autophagy leads to a marked increase in hepatic cholesterol and TG content, indicating that lipophagy limits lipid accumulation by the liver in vivo. Also, lipophagy controls cellular energy homeostasis by providing free fatty acids (FFA) from the breakdown of TGs, which subsequently trigger cellular ATP generation and mitochondrial β-oxidation. The autophagosomal protein LC3, critical for autophagosome membrane formation, has been shown to associate with LDs. Autophaoia Protects Against Liver Diseases SERPINA1 / a1-anti-tñpsin deficiency (ATD) is the most common genetic cause of human liver disease in children. This disease is caused by homozygosity for the SERPINA1 / a1 -antitrypsin Z allele SERPINA1-Z, a point mutation, which makes the hepatic secretory glycoprotein SERPINA1 prone to unfolding, polymerization and aggregation. The mutant SERPINA1-Z protein accumulates in hepatocytes and SERPINA1 levels found in blood and body fluids are reduced to 10-15% of those normally observed. Accumulation of mutant SERPINA1 -Z in the endoplasmic reticulum (ER) of hepatocytes leads to liver damage through a gain of function. It has been shown that intracellular degradation of SERPINA1-Z aggregates and polymers involves the autophagic pathway. MA / a / 2U22 / UU f 204 The drug carbamazepine, known to induce autophagy, was recently shown to be effective in the mouse and cell-based model of ATD. Carbamazepine increases autophagic degradation of SERPINA1-Z in cultured cells and when orally provided to the PiZ mouse model of ATD, reduces hepatic SERPINA1-Z load. Additionally, inducing autophagy reduces liver fibrosis. Consequently, drugs that enhance autophagy are attractive candidates for improving the liver disease that develops in some patients with ATD. The present invention provides the knowledge of using compounds that include urolithin and its precursors as autophagy enhancers for the treatment of individuals with ATD and the need to increase the levels of autophagy in their liver and hepatocytes in order to reduce their liver toxicity. Autophagy Protects Against Non-Alcoholic Fatty Liver Disease Non-alcoholic fatty liver disease (NAFLD) is an important component of metabolic syndrome along with obesity and diabetes. NAFLD encompasses a spectrum of liver abnormalities ranging from simple fatty liver or steatosis to fatty liver with hepatocellular damage and inflammation, known as nonalcoholic steatohepatitis (NASH). NAFLD is now the most prevalent liver disease in the United States and is estimated to account for approximately 75% of all chronic liver diseases. The most important role of autophagy in hepatic liver disease might be to regulate the process of excessive lipid accumulation. Indeed, mice with a hepatocyte-specific knockout of Atg7, a protein required for autophagy, consuming a high-fat diet led to a marked increase in liver TGs and cholesterol content, showing that autophagy defects can induce hepatic steatosis. When considering NASH, while its exact causes are unknown, free fatty acid (FFA)-induced lipotoxicity has been implicated in the mechanisms of hepatocellular injury of this disease. Evidence points to the fact that hepatocyte autophagy provides cells with more resistance to FFA injury. Autophagy is an attractive therapeutic target for the treatment and prevention of both NAFLD and NASH. Therapeutic intervention to increase autophagy may reverse not only the hepatic manifestations of NAFLD, including hepatocellular steatosis and injury, but also some of the underlying metabolic abnormalities of the disease through its effects on insulin resistance. Additionally, treatment by increasing autophagy may prevent common end-stage complications of NAFLD, such as hepatocellular carcinoma. The present invention provides knowing how to use compounds that include urolithins and their precursors as autophagy enhancers for the treatment of individuals with NAFLD and ivixazuzzuu / ¿04 in need of increasing the levels of autophagy in their liver and hepatocytes in order to treat these conditions. Autophagy Protects Against Alcoholic Liver Disease Alcoholic liver disease (ALD) is a leading cause of chronic liver disease, and like NALD, it has a broad spectrum of pathogenic features, ranging from steatosis to severe acute alcoholic hepatitis, fibrosis, cirrhosis, and hepatocellular carcinoma. Autophagy has been shown to play a role in the treatment of ALD. For example, induction of autophagy by rapamycin administration significantly suppresses alcohol-induced steatosis. Also, a common feature of chronic alcohol abuse is the formation of hepatic protein aggregates known as Mallory-Denk bodies, which are cytosolic inclusion bodies enriched in Krt8 / keratin 8 and Krt18 and proteins including ubiquitin. Rapamycin treatment significantly reduces the number of Mallory-Denk bodies in KRT8 transgenic mice treated with proteasome inhibitor. Consequently, improving hepatic autophagy is an attractive target for ameliorating alcohol-induced liver disease. The present invention provides knowing how to use compounds that include urolithins and their precursors as autophagy enhancers for the treatment of individuals with ALD and in need of increasing the levels of autophagy in their liver and hepatocytes in order to treat this condition. Autophagy Protects Against Drug-Induced Liver Injury Most drugs are metabolized and detoxified in the liver, making the liver the primary target for drug damage. Liver injury due to drugs is a common cause for withdrawal of approved drugs from the market, and drug-induced hepatotoxicity is thought to be responsible for more than half of acute cases of liver failure. Acetaminophen, also known as paracetamol and N-acetyl-paminophenol (APAP), is a widely used analgesic and antipyretic drug and is also the most common source of severe drug-induced hepatotoxicity. At therapeutic levels APAP is safe, but overdosage leads to toxicity primarily due to its reactive metabolite, N-acetyl-p-benzoquinone mine (NAPQI). NAPQI can deplete hepatic stores of glutathione (GSH), an intracellular antioxidant. After GSH depletion, NAPQI is known to react with cellular proteins as well as mitochondrial proteins to form protein adducts. These APAP-induced mitochondrial protein adducts can then lead to mitochondrial damage and subsequent necrosis. When autophagy is enhanced with rapamycin, APAP-induced necrosis is significantly inhibited, both in cultured primary hepatocytes and mouse livers. Treatment with rapamycin two hours after APAP administration has been seen to significantly improve APAP-induced liver injury, even though APAP metabolism and hepatic GSH depletion have already occurred. This is particularly important since patients at risk for hepatotoxicity from acute APAP overdose do not receive medical care until they are past the metabolic phase. Consequently, pharmacological intervention aimed at enhancing autophagy retains potential therapeutic benefit for individuals at risk for APAP hepatotoxicity following overdose. The present invention provides the knowledge of using compounds that include urolithins and their precursors as autophagy enhancers for the treatment of individuals at risk of hepatotoxicity due to the side effects of the drug and in need of increasing the levels of autophagy in their liver and hepatocytes with the in order to treat or prevent potential drug toxicity. Autofac / ia is Important in Limiting Reperfusion Injury / Isguemia Ischemia / reperfusion (I / R) injury is a causal factor contributing to morbidity and mortality. The vulnerability of the liver to l / R injury is a major obstacle to liver resection and transplant surgery where reperfusion after sustained ischemia is inevitable during hepatectomy and vascular reconstruction. Mitochondrial dysfunction is known to be one of the critical downstream events leading to l / R-mediated cell death. Autophagy separates dysfunctional or abnormal mitochondria to ensure optimal cellular function and survival. With insufficient or impaired mitophagy, cells accumulate damaged mitochondria, which subsequently leads to uncontrolled ROS formation, mitochondrial DNA mutation, energy failure, and ultimately cell death. Consequently, the failure of mitophagy to remove a small number of damaged mitochondria during l / R may have a significant impact on hepatocellular function and viability. Mitophagy is essential for liver function and survival after l / R injury. While minimizing l / R injury plays an important role in the outcome of transplanted young livers, aged livers are even more susceptible to the negative impact of l / R injury. In the case of aged livers, hepatocytes fail to respond to l / R stress and upregulate their endogenous protective autophagy response. Similar to young livers after prolonged ischemia, aged livers after short-term ischemia accumulate dysfunctional mitochondria, undergo mitochondrial permeability transition, and lose their viability soon after reperfusion. Methods to enhance autophagy, which include preischemic nutrient depletion and overexpression of pro-autophagy genes ATG7 or BECN1, lead to suppression of mitochondrial permeability transition and increase hepatocyte survival after reperfusion. This indicates that treatments with agents that induce autophagy in the liver will offer protection during an I / R situation and help minimize cellular injury. Such treatments are applicable in situations of transplantation of both young and aged livers. Treatments may involve: (i) pre-treatments of liver tissue ex vivo by perfusion of the liver with a solution containing an autophagy inducer; (i) treatment of the liver donor with an autophagy inducer; or (III) treatment of the liver vessel prior to, during the operation and / or immediately after the surgical intervention. Of course, these treatment modalities can be applied individually or in any combination (for example: 1 and 2; 2 and 3; 1 and 3; 1,2, and 3). The present invention provides know-how to use compounds including urolithins and their precursors as autophagy enhancers for the treatment of individuals and their livers, which may be at risk of I / R injury. These compounds can be provided orally or parenterally to the donor or recipient, or provided in a preconditioning solution that can be applied to the resected liver tissue. Autophagy and Osteoarthritis Osteoarthritis (OA) is the most common joint pathology related to aging and is characterized by the degradation of the cartilage extracellular matrix (ECM) and reduced cartilage cellularity. Changes in articular cartilage appear to be critical in the initiation and progression of OA. Chondrocytes are the only cell population of adult articular cartilage. The ability of adult articular chondrocytes to regenerate normal cartilage matrix architecture is limited and declines with aging, due to cell death and abnormal sensitivity to anabolic stimuli. Articular cartilage is characterized by a very low rate of cellular utilization and it has been shown that autophagy plays an important role in chondrocyte cellular function and survival. Indeed, autophagy is a constitutively active and protective process for the maintenance of cartilage homeostasis. Studies have shown both in joint aging and OA in humans and mice, that there is a reduction in the expression of autophagy regulators, which was accompanied by an increase in chondrocyte apoptosis. Compromised autophagy is thought to contribute to the development of OA. It has been shown that treatment with the compound rapamycin, a known inducer of autophagy, has been able to increase LC activation in cartilage in an animal model of OA and consequently reduce the severity of articular cartilage degradation. In the present invention, urolithins and their precursors have been shown to increase autophagy levels in tissues after oral consumption, making them ideal candidates for the treatment and reduction of the severity of osteoarthritis in young and aged animals and mammals. Metabolic Syndrome, Diabetes, v Obesity The compounds and methods of the invention are useful in the treatment and prevention of metabolic syndrome, type 2 diabetes mellitus, and obesity. As used herein, the term “metabolic syndrome” refers to a combination of medical disorders that, when occurring together, increase the risk of developing cardiovascular disease and diabetes. It affects one in five people in the United States and the prevalence increases with age. Some studies have shown the prevalence in the United States to be an estimated 25% of the population. According to the International Diabetes Foundation (2006) global consensus definition, metabolic syndrome is central obesity plus any two of the following: • Elevated triglycerides: > 150 mg / dL (1.7 mmol / L), or specific treatment for this lipid abnormality; • Reduced HDL Cholesterol: < 40 mg / dL (1.03 mmol / L) in males, < 50 mg / dL (1.29 mmol / L) in females, or specific treatment for this lipid abnormality; • Elevated blood pressure: systolic BP > 130 or diastolic BP > 85 mm Hg, or treatment for previously diagnosed hypertension; and • Elevated fasting plasma glucose: (FPG) >100 mg / dL (5.6 mmol / L), or previously diagnosed type 2 diabetes. Autofac / ia and Neurodegenerative Diseases In neurodegenerative diseases, brain tissue accumulates in autophagosomes, demonstrating an increase in autophagy, which in model organisms has been shown to have a protective effect. It plays an important role in the separation of unfolded proteins that accumulate as a result of severe neurodegenerative diseases. These include proteins that have polyQ repeats as seen in Huntington's diseases and spinocerebellar ataxia, mutant α-synucleins involved in Parkinson's, as well as tau aggregates. Inactivation of ATG genes important in autophagy in C. elegans results in increased aggregate formation and toxicity of PolyQ proteins. In Alzheimer's Disease the autophagy process is altered as a result of a defect in autophagosomal maturation that could be an important reason for the accumulation of aggregates. In contrast, induction of autophagy by rapamycin in both Drosophila and mouse models of polyQ disease protects these animals from neurotoxicity. These results demonstrate that autophagy induction may have a protective role in neuronal cells against neurodegeneration. MA / a / 2U22 / UU f 204 which affect the brain and other parts of the central nervous system; and (b) those which affect other organs or tissues around the body. Examples of amyloid-related diseases which fall under these two categories are listed in the next two sections; However, many other examples of rare, inherited amyloid-related diseases are known, which are not included here, and additional forms of amyloid-related disease are likely being discovered in the future. Neurodegenerative Diseases Associated with Amyloidosis Many different neurodegenerative diseases are associated with the unfolding and aggregation of a specific protein or peptide in a particular part of the brain, or elsewhere in the central nervous system, depending on the specific disease. Examples of such diseases follow. Various forms of Alzheimer's disease (AD), as well as Down syndrome, hereditary cerebral hemorrhage with amyloidosis (HCHWA, Dutch type), cerebral amyloid angiopathy, and possibly also mild cognitive impairment and other forms of dementia, are associated with aggregation. of a 40 / 42 residue peptide called β-amyloid, Αβ(Ι-40) or Αβ(Ι42), which forms insoluble amyloid fibers and plaques in the cerebral cortex, hippocampus or elsewhere in the brain, depending on the disease specific. Alzheimer's disease is also associated with the formation of neurofibrillary tangles due to the aggregation of a hyperphosphorylated protein called tau, which also occurs in frontotemporal dementia (Pick's disease). Parkinson's disease (PD), dementia with Lewy bodies (DLB), and multiple system atrophy (MSA), are associated with the aggregation of a protein called asynuclein, which results in the formation of soluble inclusions called Lewy bodies. Huntington's disease (HD), spinal bulbar muscular atrophy (SBMA, also known as Kennedy disease), dentatorubral pallidoluyian atrophy (DRPLA), different forms of spinocerebellar ataxia (SCA, types 1,2, 3, 6 and 7), and possibly several other heritable neurodegenerative diseases are associated with the aggregation of various proteins and peptides containing abnormally expanded glutamine repeats (extended polyglutamine tracts). Creutzfeldt-Jakob disease (CJD), bovine spongiform encephalopathy (BSE) in cows, scrapie in sheep, kuru, Gerstmann-Straussler-Scheinker disease (GSS), fatal familial insomnia, and possibly other forms of transmissible encephalopathies are associated with auto -propagation unfolding and aggregation of prion proteins. Amyotrophic lateral sclerosis (ALS), and possibly also some other forms of motor neuron disease (MND), are associated with the aggregation of a protein called superoxide dismutase. IVIASZUZZUU / ¿04 Familial British dementia (FBD) and familial Danish dementia (FDD), respectively, are associated with the degradation of the ABri and ADan peptide sequences derived from the BRI protein. Hereditary brain hemorrhage with amyloidosis (HCHWA, Icelandic type) is associated with the aggregation of a protein called cystatin C. Systemic Diseases Associated with Amyloidosis In addition to the neurodegenerative diseases listed above, a wide variety of degenerative or aging-related diseases are associated with the unfolding and aggregation of a particular protein or peptide in various other tissues around the body (i.e., outside the brain). Examples of such diseases follow. Type II diabetes mellitus (also known as adult-onset diabetes, or non-insulin-dependent diabetes mellitus) is associated with the aggregation of a 37-residue peptide called islet amyloid polypeptide (IAPP, or “amylin”), which forms insoluble deposits that are associated with the progressive destruction of insulin-producing β-cells in the islets of Langerhans within the pancreas. Dialysis-related amyloidosis (DRA) and prosthetic amyloid are associated with the aggregation of a protein called β-microglobulin, either in bones, joints, and tendons in DRA, which develops during prolonged periods of hemodialysis, or within the prostate in the case of prostatic amyloid. Primary systemic amyloidosis, systemic AL amyloidosis, and myeloma-associated amyloidosis are associated with the aggregation of immunoglobulin light chain (or in some cases immunoglobulin heavy chain) into insoluble amyloid deposits, which gradually accumulate in several major organs such as such as the liver, kidneys, heart and gastrointestinal tract (Gl). AA reactive systemic amyloidosis, secondary systemic amyloidosis, familial Mediterranean fever, and chronic inflammatory disease are associated with the aggregation of serum amyloid A protein, which forms insoluble amyloid deposits that accumulate in major organs such as the liver, kidneys, and kidneys. spleen. Senile systemic amyloidosis (SSA), familial amyloid polyneuropathy (FAP), and familial amyloid cardiomyopathy (FAC) are associated with the unfolding and aggregation of different mutants of the protein transthyretin (TTR), which forms insoluble inclusions in various organs and tissues such as the heart (especially in FAC), peripheral nerves (especially in FAP) and gastrointestinal tract (Gl). Another form of familial amyloid polyneuropathy (FAP, type II) is associated with the aggregation of apolipoprotein Al in peripheral nerves. Familial visceral amyloidosis and hereditary nonneuropathic systemic amyloidosis are associated with the unfolding and aggregation of various lysozyme mutants, which form insoluble deposits in major organs such as the liver, kidneys, and spleen. IVIA / a / ZUZZ / UU / ¿04 Finnish hereditary systemic amyloidosis is associated with the aggregation of a protein called gelsolin in the eyes (particularly in the cornea). Fibrinogen α-chain amyloidosis is associated with the aggregation of the fibrinogen A α chain, which forms insoluble amyloid deposits in various organs, such as the liver and kidney. Insulin-related amyloidosis occurs due to aggregation of insulin at the injection site in diabetics. Medullary thyroid carcinoma is associated with calcitonin aggregation in surrounding tissues. Isolated atrial amyloidosis is associated with aggregation of atrial natriuretic peptide (ANP) in the heart. Various forms of cataracts are associated with the aggregation of γ-crystalline proteins in the lenses of the eyes. Autophagy and Endothelial Cell Function and Associated Disease Endothelial Cell Dysfunction Global endothelial cell dysfunction occurs in several diverse diseases such as diabetes, hypertension, chronic kidney disease, and atherosclerosis. In these diseases endothelial cell dysfunction is thought to occur as a result of stress-induced premature senescence (SIPS). SIPS is characterized by subverted autophagy and lysosomal dysfunction, with the accumulation of autolysosomal vacuoles. Endothelial cell dysfunction also occurs as a result of aging with an increased incidence of cardiovascular disease. This increase in cellular dysfunction correlates with a decrease in autophagy. In older humans, the expression of autophagy markers in arterial endothelial cells was impaired by 50% (P < 0.05) and was associated with a 30% (P < 0.05) reduction in arterial endothelium-dependent dilation (EDD). Similarly, in control C57BL / 6 mice aging was associated with a 40% decrease (P < 0.05) in arterial markers of autophagy and a 25% reduction (P < 0.05) in EDD, demonstrating that impaired autophagy It is a cause of age-related arterial dysfunction. In old mice, treatment with the autophagy-enhancing agent trehalose, restored expression of autophagy markers, rescued NO-mediated EDD by reducing oxidative stress, and normalized inflammatory cytokine expression. The present invention provides the knowledge of using compounds that include urolithins and their precursors as autophagy enhancers for the treatment of individuals who have health conditions linked to endothelial cell dysfunction and in need thereof. Endothelial cell injury IVIA / a / ¿U¿¿ / UU f ¿04 Endothelial cell injury can occur as a result of disease processes such as sickle cell anemia or thalassemia in which pathologically high levels of iron and heme release can occur. Severe skeletal muscle damage as well as cardiac ischemic injury results in the release of the heme protein, myoglobin, which also results in endothelial cell injury. This damage to vascular endothelial cells can lead to vascular dysfunction and an increase in cardiovascular complications. Endothelial cell injury caused by heme toxicity is associated with a progressive decrease in the endothelial cell mitochondrial membrane potential, leading to apoptosis. Micro- and macro-vascular complications are commonly seen in diabetic patients, and endothelial dysfunction contributes to the development and progression of complications. Abnormal functions in endothelial cells lead to increased vascular tension and atherosclerosis, followed by systemic hypertension as well as increased incidence of ischemia and stroke in diabetic patients. Mitochondrial dysfunction appears to be central to vascular endothelial dysfunction. Enhanced mitochondrial fission and / or attenuated fusion lead to mitochondrial fragmentation and breakdown of physiological endothelial function. Abnormal mitochondrial biogenesis and disturbance of mitochondrial autophagy increase the accumulation of damaged mitochondria, such as weak or irreversibly depolarized mitochondria, and facilitate cell death. Increased mitochondrial ROS production and Ca2+ payload in mitochondria not only cause maladaptive effect on endothelial function, but are also potentially detrimental to cell survival. Endothelial cell injury can also result from cardiac procedures such as angioplasty, bypass surgery, and valve replacement. Upregulation of autophagy should lead to a reduction in injury to associated endothelial cells. Strategies that increase autophagy could have clear therapeutic potential. The present invention provides know-how to use compounds including urolithins and their precursors as autophagy enhancers for the treatment of individuals who have healthy conditions linked to endothelial cell injury resulting from disease processes such as diabetes, sickle cell anemia, or thalassemia, as well as protect endothelial cells from the most acute effects of severe muscle injury. Autophagy and Cancer Autophagy and cancer have similar regulatory trajectories, with several tumor suppressor genes such as PTEN, TSC1 and TSC2 leading to upstream inhibition of TOR signaling, leading to stimulation of autophagy. Additionally, the autophagy protein, Beclinl, has been identified as a tumor suppressor eliminated in WIA / a / ZUZ4UU f ¿04 many human cancers. These results demonstrate that autophagy plays an important role in tumor suppression. Aging By far the largest risk factor for neurodegenerative diseases, such as Alzheimer's disease (AD), Parkinson's disease (PD), and amyotrophic lateral sclerosis (ALS), is aging. Mitochondria have been thought to contribute to aging through the accumulation of mitochondrial DNA (mtDNA) mutations and pure reproduction of reactive oxygen species (ROS). Although most mitochondrial proteins are encoded by the nuclear genome, the mitochondria contain many copies of their own DNA. Human mtDNA is a circular molecule of 16,569 base pairs that encodes 13 polypeptide components of the respiratory chain, as well as the rRNAs and tRNAs necessary to support intramitochondrial protein synthesis using its own genetic code. Inherited mutations in mtDNA are known to cause a variety of diseases, most of which affect the brain and muscles – tissues with high energy requirements. It has been hypothesized that somatic mtDNA mutations acquired during aging contribute to the physiological decline that occurs with aging and age-related neurodegeneration. It is well established that mtDNA accumulates mutations with aging, especially large-scale deletions and point mutations. In the control region of mtDNA, point mutations at specific sites can accumulate to high levels in certain tissues: T414G in cultured fibroblasts, A189G and T408A in muscle, and C150T in white blood cells. However, these control region “hot spots” have not yet been observed in the brain. Point mutations in individual nucleotides appear to occur at low levels in the brain, although the total level may be high. Using a polymerase chain reaction (PCR)-cloning-sequencing strategy, the average level of point mutations in two protein-coding regions of brain mtDNA from elderly subjects was found to be ~2 mutations per 10 kb. . Noncoding regions, which may be under less selection pressure, potentially accumulate two to four times as much. The accumulation of these deletions and point mutations with aging correlates with the decline in mitochondrial function. For example, a negative correlation has been found between brain cytochrome oxidase activity and increased point mutation levels in a cytochrome oxidase (CO1) gene. Pure ROS production is another important mechanism by which mitochondria are thought to contribute to aging. Mitochondria contain multiple electron carriers capable of producing ROS, as well as an extensive network of antioxidant defenses. Mitochondrial attacks, which include oxidative damage itself, can cause an imbalance between ROS production and removal, resulting in the production of MA / a / 2U22 / UU f 204 Pure ROS. The importance of pure mitochondrial ROS production for aging is supported by observations that enhancing mitochondrial antioxidant defenses can increase longevity. In Drosophila, overexpression of the mitochondrial antioxidant enzymes manganese superoxide dismutase (MnSOD) and methionine sulfoxide reductase prolongs lifespan. This strategy is most successful in short-lived strains of Drosophila, and has no effect in already long-lived strains. However, it has recently been shown that overexpression of catalase experimentally targeted to the mitochondria increases lifespan in an already long-lived mouse strain. Improving Activity During Aging Activity in animals is largely activated by the circardial rhythm and is synchronized to the environment. Breaking the circardial rhythm or desynchronization with the environment can lead to an increase in nighttime wakefulness or daytime naps. Normal aging is accompanied by decline in locomotor activity, altered cicardial rhythms, as well as altered sleep and food absorption patterns. These effects lead to a decrease in alertness and alertness, decreasing in the elderly, leading to an increase in nighttime wakefulness, as well as an increase in daytime naps. Activity patterns may also be altered in a similar way by disease, such as Alzheimer's disease. Age-dependent changes in activity rhythms are also observed in other animals, for example, rats, hamsters, mice and dogs, with an increase in fragmentation and a decrease in synchronization with the environment. These age-dependent cicardial alterations have been linked to the degeneration of the suprachiasmatic nuclei of the hypothalamus. Sleep disturbance, in both animals and rodents, has been shown to contribute to age-dependent cognitive dysfunction. Increasing disruption of cicardial rhythms is accompanied by a gradual decline in motor activity with age in several species, including humans, mice, monkeys, and dogs. Of particular interest, the daytime activity of older dogs (>10 years of age) declines compared to middle-aged and young dogs. These changes in activity can be monitored by devices proposed to measure activity, for example, by means of an accelerometer or using motion sensing cameras. Many of the alterations seen in aging as a result of decreased activity are also observed in younger populations where cultural trends have resulted in decreased activity, accompanied by increased caloric absorption, leading to epidemic obesity. The resulting caloric imbalance has led to an increase in several disease conditions such as type 2 diabetes, colon cancer, and metabolic syndrome, as well as mental health problems. Several prospective cohort studies and meta-analyses in humans have shown that physical inactivity is associated with an elevated risk for the development of metabolic syndrome, type 2 diabetes, hypertension, coronary artery disease, stroke, and cardiovascular disease. Both humans and animals, particularly dogs, could benefit from the present invention and its ability to improve activity during the youth and aging periods of life. In one embodiment, the urolithin or precursor could increase the activity of the recipient, human or animal. In yet another embodiment, the increase in activity is an increase by 1% up to 100%. For example, activity can be increased by 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, or 10%. In certain modalities, the increase in activity is an increase of 510%, 10-15%, 15-20%, 20-25%, 25-30%, 30-35%, 35-40%, 40-45%, 45-50%, 50-55%, 55-60%, 60-65%, 65-70%, 70-75%, 75-80%, 80-85%, 85-90%, 90-95%, and 95-100%. In one embodiment, treatment by urolithin or a precursor thereof could increase activity and lead to a reduction in risk of metabolic syndrome. In one embodiment, treatment by urolithin or a precursor thereof could increase activity and lead to a reduction in the risk of type 2 diabetes. In one embodiment, treatment by urolithin or a precursor thereof could increase activity and lead to a reduction in the risk of hypertension, coronary artery disease, stroke, and cardiovascular disease. In one embodiment, treatment by urolithin or a precursor thereof could increase activity and improve cognitive function. Mood Disorders The compounds and methods of the invention are useful for treating a mood disorder (also known as an affective disorder). As used herein, a “mood disorder” refers to a disturbance in emotional state, as set forth in the Diagnostic and Statistical Manual of Mental Disorders, published by the American Psychiatric Association. Mood disorders include but are not limited to major depression, postpartum depression, dysthymia, and bipolar disorder. In one embodiment, the mood disorder is major depression. The compounds and methods of the invention are useful for treating or preventing a stress-related or stress-induced mood disorder. As used herein, a “stress-related or stress-induced mood disorder” refers to a disturbance in emotional state that is induced or related to stress. Such mood disorders are sometimes referred to as reactive mood disorders and are being distinguished from other mood disorders, for example, so-called organic mood disorders. The compounds and methods of the invention are useful for treating an anxiety disorder. As used herein, an “anxiety disorder” refers to a dysfunctional state of fear and anxiety, for example, fear and anxiety that is out of proportion to a stressful situation or the anticipation of a stressful situation. In one embodiment, a disorder of MA / a / 2U22 / UU f 204 anxiety is any or a combination of generalized anxiety disorder, panic disorder, panic disorder with agoraphobia, agoraphobia, social anxiety disorder, obsessive-compulsive disorder, and post-traumatic stress disorder . In one embodiment, an anxiety disorder is any or a combination of generalized anxiety disorder, obsessive-compulsive disorder, panic disorder, post-traumatic stress disorder, and social anxiety disorder. In one embodiment, an anxiety disorder is generalized stress disorder. In one embodiment, an anxiety disorder is post-traumatic stress disorder. In one embodiment, an anxiety disorder is a stress-induced anxiety disorder. The compounds and methods of the invention are useful for treating or preventing a stress-related or stress-induced anxiety disorder. As used herein, a “stress-related or stress-induced anxiety disorder” refers to a dysfunctional state of fear and anxiety that is induced or related to stress. Such anxiety disorders are sometimes referred to as reactive anxiety disorders and are being distinguished from other anxiety disorders, for example, so-called organic anxiety disorders. For the purposes of this invention, each of the above diseases or conditions is associated with, or characterized by, reduced or diminished autophagy, or could benefit from increased autophagy, and therefore could benefit from the administration of urolithins and their precursors. . Table 1 summarizes some of the cell types affected by autophagy and the beneficial effects of autophagy on these cells. Table 1. Health Benefits of Increased Autophagy Cell Type Condition Improved by Autophagy All cells • Maintenance of amino acid combination during starvation • Anti-aging • Tumor suppression • Separation of intracellular microbes • Separation of protein aggregates Neurons • Prevention of neurodegeneration • Relief of symptoms related to neurodegeneration • Separation of protein aggregates Ancinar cells of the pancreas • Improved outcome in acute pancreatitis MA / a / ¿U¿¿ / UU l ¿04 Smooth muscle cells • Improved outcome in various cardiac conditions such as heart disease, cardiac hypertrophy, left ventricular dilation, Danon disease • Relief of cardiomyopathy resulting from diabetes • Prevention of cardiac deterioration with age • Improved outcome of heart injury ischemia / reperfusion • Protection of cells from ischemia and hypoxic conditions resulting from myocardial function • Improved cardiac performance • Improved left ventricular diastolic function • Improvement in blood pressure • Protection of cells during cardiac procedures such as angioplasty, bypass, valve replacement Intestinal epithelial cells • Improvement of immune response to intracellular bacteria; Crohn's disease; inflammatory bowel disease (IBD) Podocytes in kidney • Resistance of podocytes to injury, which can be caused by the following diseases: minimal change disease, focal segmental glomerulosclerosis, diabetic nephropathy, membrane glomerulopathy, lupus nephritis, and glomerular disease experimental MA / a / ¿U¿¿ / UU l ¿04 Skeletal muscle cells • Protection against glucose intolerance, leptin resistance, high cholesterol and triglycerides in high-fat diets • Improved muscle function • Reduction in sarcopenia • Improved balance and coordination • Improvement in muscle endurance • Increase in mass muscle • Reduction in muscle atrophy • Improvement in muscle endurance • Improved outcome for muscular dystrophy • Improved muscle recovery after exercise • Protection against muscle damage Liver tissue • Cleavage of mutant alpha-antitrypsin • Improved outcome in liver disease nonalcoholic fatty liver disease (NAFLD), nonalcoholic steatohepatitis (NASH), and alcoholic liver disease (ALD) Hepatic hepatocytes • Protection against glucose intolerance, leptin resistance, triglycerides, and high cholesterol in high-fat diets • Treatment of obesity and diabetes type II • Improved outcome of ischemia / reperfusion injury • Protection against drug-induced liver injury • Protection of liver tissue Pancreatic beta cells • Protection against glucose intolerance, leptin resistance, high cholesterol and triglycerides in high-fat diets MA / a / ¿U¿¿ / UU l ¿04 Adipocytes • Protection against glucose intolerance, leptin resistance, high cholesterol and triglycerides in high-fat diets • Treatment of obesity and type II diabetes Endouelial cells • Improves endothelial cell dysfunction which can occur as a result of diabetes, hypertension, chronic kidney disease, atherosclerosis and aging • Protects against endothelial cell injury resulting from disease processes such as diabetes, sickle cell anemia or thalassemia, as well as severe muscle injury • Protection of cells from ischemia and hypoxic conditions resulting from myocardial function • Improved angiogenesis • Protection of cells during cardiac procedures such as angioplasty, bypass, valve replacement Chondrocytes / cartilage • Reduction in osteoarthritis in joints Osteoblasts • Improved tissue mineral density • Increased bone strength Epithelial cells Lens • Reduction in age-related cataracts Retinal cells Ganglion cell layer Inner nuclear layer Outer nuclear layer Retinal pigment epithelial cells • Reduction in age-related macular degeneration • Protection from diabetic retinopathy ΜΛ / a / ZUZZ / UU f ¿04 Retinal photopreceptors • Improved outcome of infraocular inflammation or uveitis • Reduction in photoreceptor injury from uveitis Glaucomatous Tissue • Reduction in glaucomatous neurodegeneration Keratinocytes • Treatment of intracellular skin infections, warts, psoriasis • Protection of the skin from environmental insults, i.e. , UV light, anti-aging • Reduction of skin injury from excessive lipid oxidation commonly observed in aged and diseased skin Lung cells • Separation of protein aggregates in lung cells • Improved outcome of pulmonary emphysema caused by antitrypsin-od • Disorder chronic obstructive pulmonary Alveolar macrophages • Improved outcome for chronic obstructive pulmonary disease Airway epithelial cells • Reduction in protein aggregates in cystic fibrosis • Improved separation of aggresomes that accumulate the mutant cystic fibrosis transmembrane conductance regulator (CFTR) protein ) • Improved outcome for human idiopathic pulmonary fibrosis Immune cells • Reduction of autoimmune disorders • Improved immune response to pathogen infection Exemplary Compound of the Invention Compounds of the invention include certain urolithins and precursors thereof. These compounds can be used to practice any of the methods herein, including but not limited to increasing autophagy or longevity, and for the treatment or prevention of the various diseases and conditions described herein. In certain embodiments, the invention relates to urolithins. As used herein, a “urolithin” refers to a compound of Formula I: EITHER Formula I where R1, R2, R3, R4, R5, R6, R7, and R8 are independently selected from the group consisting of H and OR; and R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide. As used herein, the term “alkyl” refers to a saturated or unsaturated, cyclic or non-cyclic, branched or straight chain aliphatic hydrocarbon radical containing carbon atoms. Representative saturated straight chain alkyls include methyl, ethyl, n-propyl, n-butyl, n-pentyl, n-hexyl, and the like; while saturated branched alkyls include isopropyl, sec-butyl, isobutyl, tere-butyl, isopentyl, and the like. Representative saturated cyclic alkyls include cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, and the like; while unsaturated cyclic alkyls include cyclopentenyl and cyclohexenyl, and the like. Unsaturated alkyls contain at least one double or triple bond between adjacent carbon atoms (referred to as an “alkenyl” or “alkynyl,” respectively). Representative branched and straight chain alkenyls include ethyleneyl, propylenyl, 1-butenyl, 2-butenyl, isobutylenyl, 1-pentenyl, 2-pentenyl, 3-methyl-1-butenyl, 2-methyl-2-butenyl, 2,3-dimethyl -butenyl, and the like; while representative branched and straight chain alkynyls include acetylenyl, propynyl, 1-butynyl, 2-butynyl, 1-pentynyl, 2-pentynyl, 3-methyl-1-butynyl, and the like. As used herein, the term "aryl" refers to a hydrocarbon ring system radical comprising hydrogen, 6 to 10 carbon atoms and at least one aromatic ring. For purposes of this invention, the aryl radical may be a monocyclic, bicyclic, tricyclic or tetracyclic ring system, which may include fused or bridged ring systems. Aryl radicals include, but are not limited to, aryl radicals derived from aceantrylene, acenaphthylene, acephenantrylene, anthracene, azulene, benzene, chrysene, fluoranthene, fluorene, as-indacene, s-indacene, indane, indene, naphthalene, phenalene, phenanthrene , pleiadene, pyrene, and triphenylene. Unless otherwise specifically stated in the specification, the term "aryl" or the prefix "ar" (such as in "aralkyl"), is meant to include aryl radicals that are optionally substituted. As used herein, the term “monosaccharide” refers to a simple sugar of the Formula (CH2O)n. Monoscarides can be ring or straight chain systems, and can include a sucrose unit of the Formula —CH(OH)—C(=O)—. Examples of monosaccharides include erythrose, threose, ribose, arabinose, xylose, lyxose, allose, altrose, glucose, mannose, gulose, idose, galactose, thallose, erythulose, ribulose, xiulose, psychose, fructose, sorbose, tagatose, erytropentulose, threopentulose, glycerotetrulose, glucopyranose, fructofuranose. In certain embodiments, monosaccharide refers to glucopyranose. As used herein, the term "oligosaccharide" refers to a saccharide consisting of at least two, up to 10 glycosidically linked monosaccharide units, preferably 2 to 8 monosaccharide units, more preferably 2 to 7 monosaccharide units. , and even more preferably from 2 to 6 monosaccharide units or from 2 to 5 monosaccharide units. The term "substituted" as used herein (for example, in the context of a substituted heterocyclyl or substituted aryl) means that at least one hydrogen atom is replaced with a substituent. “Substituents within the context of this invention include halogen, hydroxy, oxo, cyano, nitro, amino, thioxo, amino, alkylamino, dialkylamino, alkyl, alkoxy, alkylthio, haloalkyl, aryl, aralkyl, heteroaryl, heteroarylalkyl, heterocycle and heterocycloalkyl, as well as -NRaRb, -NRaC(=O)Rb, -NRaC(=O)NRaNRb, NRaC(=O)ORb -NRaSO2Rb, -C(=O)Ra, -C(=O)ORa, -C( =O)NRaRb, -OC(=O)NRaRb, -ORa, -SRa, -SORa, -S(=O)2Ra, -OS(=O)2Ra, -S(=O)2ORa, =NSO2Ra and - SO2NRaRb. In the above, Ra and Rb in this context may be the same or different and independently hydrogen, alkyl, haloalkyl, cycloalkyl, aryl, aralkyl, heterocyclyl. Furthermore, the above substituents may further be substituted with one or more of the above substituents. In one embodiment, the urolithin is urolithin A. In one embodiment, the urolithin is urolithin B. In one embodiment, the urolithin is urolithin C. In one embodiment, the urolithin is urolithin D. In one embodiment, a “urolithin” refers to any one or a combination of urolithin A, urolithin B, urolithin C, and urolithin D (see, for example, Figure 2 and Figure 3). In one embodiment, a urolithin is urolithin A, urolithin B, urolithin C, urolithin D, or any combination of urolithin A, urolithin B, urolithin C, and urolithin D. In one embodiment, a urolithin is urolithin A, urolithin B, urolithin C, or any combination of urolithin A, urolithin B, and urolithin C. In one embodiment, a urolithin is urolithin A, urolithin B, or a combination of urolithin A and urolithin B. In one embodiment, a urolithin is urolithin A. MA / a / 2U22 / UU 1204 In one embodiment, a urolithin is provided as an isolated urolithin, for example, isolated from a natural source or prepared by total synthesis. Isolated urolithins can be synthesized de novo. See Examples 1-4. In one embodiment, a urolithin is provided as a purified urolithin. In one embodiment, a “urolithin” as used herein is or may include glucuronated, methylated, or sulfated urolithin. In certain embodiments, the invention relates to a compound of Formula II IVIA3ZUZZUU / ¿04 Formula II where X1, X2, X3, X4, X5, X6, X7, and X8 are independently selected from the group consisting of H and OH; with the proviso that the compound is not a compound of Formula II wherein X1, X2, X3, X4, X5, X6, X7, and X8 are H; X1 is OH, and X2, X3, X4, X5, X6, X7, and X8 are H; X2 is OH, and X1, X3, X4, X5, X6, X7, and X8 are H (urolithin B); X3 is OH, and X1, X2, X4, X5, X6, X7, and X8 are H; X4 is OH, and X1, X2, X3, X5, X6, X7, and X8 are H; X5 is OH, and X1, X2, X3, X4, X6, X7, and X8 are H; X6 is OH, and X1, X2, X3, X4, X5, X7, and X8 are H; X7 is OH, and X1, X2, X3, X4, X5, X6, and X8 are H; X8 is OH, and X1, X2, X3, X4, X5, X6, and X7 are H; X1 and X2 are OH, and X3, X4, X5, X6, X7, and X8 are H; X1 and X5 are OH, and X2, X3, X4, X6, X7, and X8 are H; X1 and X7 are OH, and X2, X3, X4, X5, X6, and X8 are H; X1 and X8 are OH, and X2, X3, X4, X5, X6, and X7 are H; X2 and X3 are OH, and X1, X4, X5, X6, X7, and X8 are H; X2 and X4 are OH, and X1, X3, X5, X6, X7, and X8 are H; X2 and X5 are OH, and X1, X3, X4, X6, X7, and X8 are H; X2 and X6 are OH, and X1, X3, X4, X5, X7, and X8 are H (urolithin A); X2 and X7 are OH, and X1, X3, X4, X5, X6, and X8 are H; X3 and X4 are OH, and X1, X2, X5, X6, X7, and X8 are H; X3 and X5 are OH, and X1, X2, X4, X6, X7, and X8 are H; Χ3 and Χ6 are OH, and Χ1, X2, X4, X5, X7, and X8 are H; X5 and X6 are OH, and X1, X2, X3, X4, X7, and X8 are H; X5 and X8 are OH, and X1, X2, X3, X4, X6, and X7 are H; X6 and X7 are OH, and X1, X2, X3, X4, X5, and X8 are H; Χ1, X2, and X5 are OH, and X3, X4, X6, X7, and X8 are H; Χ1, X2, and X6 are OH, and X3, X4, X5, X7, and X8 are H; Χ1, X5, and X8 are OH, and X2, X3, X4, X6, and X7 are H; X2, X4, and X6 are OH, and X1, X3, X5, X7, and X8 are H; X2, X4, and X7 are OH, and X1, X3, X5, X6, and X8 are H; X2, X6, and X7 are OH, and X1, X3, X4, X5, and X8 are H (urolithin C); X2, X6, and X8 are OH, and X1, X3, X4, X5, and X7 are H; X2, X7, and X8 are OH, and X1, X3, X4, X5, and X6 are H; X1, X2, X5, and X6 are OH, and X3, X4, X7, and X8 are H; X1, X2, X5, and X7 are OH, and X3, X4, X6, and X8 are H; X1, X2, X6, and X7 are OH, and X3, X4, X5, and X8 are H (urolithin D); X1, X6, X7, and X8 are OH, and X2, X3, X4, and X5 are H; X2, X3, X6, and X7 are OH, and X1, X4, X5, and X8 are H; X2, X4, X5, and X8 are OH, and X1, X3, X6, and X7 are H; X2, X4, X6, and X7 are OH, and X1, X3, X5, and X8 are H; X1, X2, X4, X5, and X7 are OH, and X3, X6, and X8 are H; X1, X2, X6, X7, and X8 are OH, and X3, X4, and X5 are H; either X1, X2, X3, X6, X7, and X8 are OH, and X4 and X5 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least two of X1, X2, X3, X4, X5, X6, X7, and X8 are OH. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least three of X1, X2, X3, X4, X5, X6, X7, and X8 are OH. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least four of X1, X2, X3, X4, X5, X6, X7, and X8 are OH. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least five of X1, X2, X3, X4, X5, X6, X7, and X8 are OH. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least six of X1, X2, X3, X4, X5, X6, X7, and X8 are OH. MA / a / 2U22 / UU 1204 In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least seven of X1, X2, X3, X4, X5, X6, X7, and X8 are OH. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X1, X2, X3, X4, X5, X6, X7, and X8 are OH. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X1 and X3 are OH; and X2, X4, X5, X6, X7, and X8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X1 and X4 are OH; and X2, X3, X5, X6, X7, and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X1 and X6 are OH; and X2, X3, X4, X5, X7, and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X2 and X8 are OH; and X1, X3, X4, X5, X6, and X7 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X3 and X7 are OH; and X1, X2, X4, X5, X6, and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X3 and X8 are OH; and X1, X2, X4, X5, X6, and X7 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X4 and X5 are OH; and X1, X2, X3, X6, X7, and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X4 and X6 are OH; and X1, X2, X3, X5, X7, and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X4 and X7 are OH; and X1, X2, X3, X5, X6, and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X4 and X8 are OH; and X1, X2, X3, X5, X6, and X7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X5 and X7 are OH; and X1, X2, X3, X4, X6, and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X6 and X8 are OH; and X1, X2, X3, X4, X5, and X7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X7 and X8 are OH; and X1, X2, X3, X4, X5, and X6 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein Χ1, X2, and X3 are OH; and X4, X5, X6, X7, and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein Χ1, X2, and X4 are OH; and X3, X5, X6, X7, and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein Χ1, X2, and X7 are OH; and X3, X4, X5, X6, and X8 are H. MA / a / 2U22 / UU 1204 In certain embodiments, the invention mentioned above, where Χ1, X2, In certain embodiments, the invention mentioned above, where Χ1, X3, In certain embodiments, the invention mentioned above, where Χ1, invention mentioned above, where Χ1, X3, In certain embodiments, the invention mentioned above, where Χ1, X3, In certain embodiments, the invention mentioned above, where Χ1, where Χ1, X4, In certain embodiments, the invention mentioned above, where Χ1, In certain embodiments, the invention mentioned above, where Χ1, X5, In certain embodiments, the invention mentioned above, where Χ1, X5, In certain embodiments, the invention mentioned above, where Χ1, invention mentioned above, where Χ1, X6, In certain embodiments, the invention mentioned above, where Χ1, X7, In certain embodiments, the invention mentioned above, where where X2, X3, In certain embodiments, the invention mentioned above, where X2, X3, refers to any of the compounds and X8 are OH; and X3, X4, X5, X6, and X7 are H. refers to any of the compounds and X4 are OH; and X2, X5, X6, X7, and X8 are H. refers to any of the compounds and X5 are OH; and X2, X4, X6, X7, and X8 are H. refers to any of the compounds and X6 are OH; and X2, X4, X5, X7, and X8 are H. refers to any of the compounds and X7 are OH; and X2, X4, X5, X6, and X8 are H. refers to any of the compounds and X8 are OH; and X2, X4, X5, X6, and X7 are H. refers to any of the compounds and X5 are OH; and X2, X3, X6, X7, and X8 are H. refers to any of the compounds and X6 are OH; and X2, X3, X5, X7, and X8 are H. refers to any of the compounds and X7 are OH; and X2, X3, X5, X6, and X8 are H. refers to any of the compounds and X8 are OH; and X2, X3, X5, X6, and X7 are H. refers to any of the compounds and X6 are OH; and X2, X3, X4, X7, and X8 are H. refers to any of the compounds and X7 are OH; and X2, X3, X4, X6, and X8 are H. refers to any of the compounds and X7 are OH; and X2, X3, X4, X5, and X8 are H. refers to any of the compounds and X8 are OH; and X2, X3, X4, X5, and X7 are H. refers to any of the compounds and X8 are OH; and X2, X3, X4, X5, and X6 are H. refers to any of the compounds and X4 are OH; and X1, X5, X6, X7, and X8 are H. refers to any of the compounds and X5 are OH; and X1, X4, X6, X7, and X8 are H. refers to any of the compounds and X6 are OH; and X1, X4, X5, X7, and X8 are H. iviAazuzzuu / ¿04 In certain embodiments, the invention mentioned above, where X2, X3, In certain embodiments, the invention mentioned above, where X2, X3, In certain embodiments, the invention mentioned above, where X2, invention mentioned above, where X2, X4, In certain embodiments, the invention mentioned above, where X2, X5, In certain embodiments, the invention mentioned above, where where X2, X5, In certain embodiments, the invention mentioned above, where X3, X4, In certain embodiments, the invention mentioned above, where X3, In certain embodiments, the invention mentioned above, where X3, X4, In certain embodiments, the invention mentioned above, where X3, X5, In certain embodiments, the invention mentioned above, where X3, invention mentioned above, where X3, X5, In certain embodiments, the invention mentioned above, where X3, X6, In certain embodiments, the invention mentioned above, where where X3, X7, In certain embodiments, the invention mentioned above, where X4, X5, refers to any of the compounds and X7 are OH; and X1, X4, X5, X6, and X8 are H. refers to any of the compounds and X8 are OH; and X1, X4, X5, X6, and X7 are H. refers to any of the compounds and X5 are OH; and X1, X3, X6, X7, and X8 are H. refers to any of the compounds and X8 are OH; and X1, X3, X5, X6, and X7 are H. refers to any of the compounds and X6 are OH; and X1, X3, X4, X7, and X8 are H. refers to any of the compounds and X7 are OH; and X1, X3, X4, X6, and X8 are H. refers to any of the compounds and X8 are OH; and X1, X3, X4, X6, and X7 are H. refers to any of the compounds and X5 are OH; and X1, X2, X6, X7, and X8 are H. refers to any of the compounds and X6 are OH; and X1, X2, X5, X7, and X8 are H. refers to any of the compounds and X7 are OH; and X1, X2, X5, X6, and X8 are H. refers to any of the compounds and X8 are OH; and X1, X2, X5, X6, and X7 are H. refers to any of the compounds and X6 are OH; and X1, X2, X4, X7, and X8 are H. refers to any of the compounds and X7 are OH; and X1, X2, X4, X6, and X8 are H. refers to any of the compounds and X8 are OH; and X1, X2, X4, X6, and X7 are H. refers to any of the compounds and X7 are OH; and X1, X2, X4, X5, and X8 are H. refers to any of the compounds and X8 are OH; and X1, X2, X4, X5, and X7 are H. refers to any of the compounds and X8 are OH; and X1, X2, X4, X5, and X6 are H. refers to any of the compounds and X6 are OH; and X1, X2, X3, X7, and X8 are H. MA / a / 2U22 / UU 1204 In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X4, X5, and X7 are OH; and X1, X2, X3, X6, and X8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X4, X5, and X8 are OH; and X1, X2, X3, X6, and X7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X4, X6, and X7 are OH; and X1, X2, X3, X5, and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X4, X6, and X8 are OH; and X1, X2, X3, X5, and X7 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X4, X7, and X8 are OH; and X1, X2, X3, X5, and X6 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X5, X6, and X7 are OH; and X1, X2, X3, X4, and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X5, X6, and X8 are OH; and X1, X2, X3, X4, and X7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X5, X7, and X8 are OH; and X1, X2, X3, X4, and X6 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X6, X7, and X8 are OH; and X1, X2, X3, X4, and X5 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X1, X2, X3, and X4 are OH; and X5, X6, X7, and X8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X1, X2, X3, and X5 are OH; and X4, X6, X7, and X8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X1, X2, X3, and X6 are OH; and X4, X5, X7, and X8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X1, X2, X3, and X7 are OH; and X4, X5, X6, and X8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X1, X2, X3, and X8 are OH; and X4, X5, X6, and X7 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X1, X2, X4, and X5 are OH; and X3, X6, X7, and X8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X1, X2, X4, and X6 are OH; and X3, X5, X7, and X8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X1, X2, X4, and X7 are OH; and X3, X5, X6, and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X1, X2, X4, and X8 are OH; and X3, X5, X6, and X7 are H. iviAazuzzuu / ¿04 In certain embodiments, the invention is mentioned above, where X1, X2, X5, In certain embodiments, the invention is mentioned above, where X1, X2, X7, In certain embodiments, the invention is mentioned above, where X1, X3, X4, In certain embodiments, the invention is mentioned above, where X1, X3, X4, In certain embodiments, the invention is mentioned above, where X1, X3, X4, In certain embodiments, the invention is mentioned above, where X1, X3, X5, In certain embodiments, the invention is mentioned above, where X1, wherein X1, X3, X5, In certain embodiments, the invention is mentioned above, wherein X1, are mentioned above, where X1, X3, X7, In certain embodiments, the invention is mentioned above, where X1, X4, In certain embodiments, the invention is mentioned above, where X1, X4, X5, In certain embodiments, the invention is mentioned above, where X1, X4, X6, refers to any of the compounds and X8 are OH; and X3, X4, X6, and X7 are H. refers to any of the compounds and X8 are OH; and X3, X4, X5, and X7 are H. refers to any of the compounds and X8 are OH; and X3, X4, X5, and X6 are H. refers to any of the compounds and X5 are OH; and X2, X6, X7, and X8 are H. refers to any of the compounds and X6 are OH; and X2, X5, X7, and X8 are H. refers to any of the compounds and X7 are OH; and X2, X5, X6, and X8 are H. refers to any of the compounds and X8 are OH; and X2, X5, X6, and X7 are H. refers to any of the compounds and X6 are OH; and X2, X4, X7, and X8 are H. refers to any of the compounds and X7 are OH; and X2, X4, X6, and X8 are H. refers to any of the compounds and X8 are OH; and X2, X4, X6, and X7 are H. refers to any of the compounds and X7 are OH; and X2, X4, X5, and X8 are H. refers to any of the compounds and X8 are OH; and X2, X4, X5, and X7 are H. refers to any of the compounds and X8 are OH; and X2, X4, X5, and X6 are H. refers to any of the compounds and X6 are OH; and X2, X3, X7, and X8 are H. refers to any of the compounds and X7 are OH; and X2, X3, X6, and X8 are H. refers to any of the compounds and X8 are OH; and X2, X3, X6, and X7 are H. refers to any of the compounds and X7 are OH; and X2, X3, X5, and X8 are H. refers to any of the compounds and X8 are OH; and X2, X3, X5, and X7 are H. IVIASZUZZUU / ¿04 In certain embodiments, the invention mentioned above, where Χ1, X4, In certain embodiments, the invention mentioned above, where Χ1, X5, In certain embodiments, the invention mentioned above, where Χ1, invention mentioned above, where Χ1, X5, In certain embodiments, the invention mentioned above, where X2, X3, In certain embodiments, the invention mentioned above, where where X2, X3, In certain embodiments, the invention mentioned above, where X2, X3, In certain embodiments, the invention mentioned above, where X2, In certain embodiments, the invention mentioned above, where X2, X3, In certain embodiments, the invention mentioned above, where X2, X3, In certain embodiments, the invention mentioned above, where X2, invention mentioned above, where X2, X4, In certain embodiments, the invention mentioned above, where X2, X4, In certain embodiments, the invention mentioned above, where where X2, X4, In certain embodiments, the invention mentioned above, where X2, X5, refers to any of the compounds X7, and and X2, X3, X5, and X6 are H. refers to any of the compounds X6, and X7 are OH; and X2, X3, X4, and X8 are H. refers to any of the compounds X6, and X8 are OH; and X2, X3, X4, and X7 are H. refers to any of the compounds X7, and X8 are OH; and X2, X3, X4, and X6 are H. refers to any of the compounds X4, and X5 are OH; and X1, X6, X7, and X8 are H. refers to any of the compounds X4, and X6 are OH; and X1, X5, X7, and X8 are H. refers to any of the compounds X4, and X7 are OH; and X1, X5, X6, and X8 are H. refers to any of the compounds X4, and X8 are OH; and X1, X5, X6, and X7 are H. refers to any of the compounds X5, and X6 are OH; and X1, X4, X7, and X8 are H. refers to any of the compounds X5, and X7 are OH; and X1, X4, X6, and X8 are H. refers to any of the compounds X5, and X8 are OH; and X1, X4, X6, and X7 are H. refers to any of the compounds X6, and X8 are OH; and X1, X4, X5, and X7 are H. refers to any of the compounds X7, and X8 are OH; and X1, X4, X6, and X7 are H. refers to any of the compounds X5, and X6 are OH; and X1, X3, X7, and X8 are H. refers to any of the compounds X5, and X7 are OH; and X1, X3, X6, and X8 are H. refers to any of the compounds X6, and X8 are OH; and X1, X3, X5, and X7 are H. refers to any of the compounds X7, and X8 are OH; and X1, X3, X5, and X6 are H. refers to any of the compounds X6, and X7 are OH; and X1, X3, X4, and X8 are H. iviAazuzzuu / ¿04 In certain embodiments, the invention is mentioned above, where X2, X5, X6, In certain embodiments, the invention is mentioned above, where X2, X6, X7, In certain embodiments, the invention is mentioned above, where X3, X4, X5, In certain embodiments, the invention is mentioned above, where X3, X4, wherein X3, X4, X5, In certain embodiments, the invention is mentioned above, wherein X3, X4, are mentioned above, where X3, X4, X7, In certain embodiments, the invention is mentioned above, where X3, In certain embodiments, the invention is mentioned above, where X3, X5, X7, In certain embodiments, the invention is mentioned above, where X3, X6, X6, In certain embodiments, the invention is mentioned above, where X4, X5, X6, In certain embodiments, the invention is mentioned above, where X4, X6, X7, In certain embodiments, the invention is mentioned above, where X5, X6, X7, refers to any of the compounds and X8 are OH; and X1, X3, X4, and X7 are H. refers to any of the compounds and X8 are OH; and X1, X3, X4, and X6 are H. refers to any of the compounds and X8 are OH; and X1, X3, X4, and X5 are H. refers to any of the compounds and X6 are OH; and X1, X2, X7, and X8 are H. refers to any of the compounds and X7 are OH; and X1, X2, X6, and X8 are H. refers to any of the compounds and X8 are OH; and X1, X2, X6, and X7 are H. refers to any of the compounds and X7 are OH; and X1, X2, X5, and X8 are H. refers to any of the compounds and X8 are OH; and X1, X2, X5, and X7 are H. refers to any of the compounds and X8 are OH; and X1, X2, X5, and X6 are H. refers to any of the compounds and X7 are OH; and X1, X2, X4, and X8 are H. refers to any of the compounds and X8 are OH; and X1, X2, X4, and X7 are H. refers to any of the compounds and X8 are OH; and X1, X2, X4, and X6 are H. refers to any of the compounds and X8 are OH; and X1, X2, X4, and X5 are H. refers to any of the compounds and X7 are OH; and X1, X2, X3, and X8 are H. refers to any of the compounds and X8 are OH; and X1, X2, X3, and X7 are H. refers to any of the compounds and X8 are OH; and X1, X2, X3, and X6 are H. refers to any of the compounds and X8 are OH; and X1, X2, X3, and X5 are H. refers to any of the compounds and X8 are OH; and X1, X2, X3, and X4 are H. IVIAaZUZZUU / ¿04 In certain embodiments, the invention is mentioned above, where X1, X2, X3, In certain embodiments, the invention is mentioned above, where X1, X2, X3, In certain embodiments, the invention is mentioned above, where X1, X2, X3, In certain embodiments, the invention is mentioned above, where X1, X2, where X1, X2, X3, In certain embodiments, the invention is mentioned above, where X1, X2, are mentioned above, where X1, X2, X3, In certain embodiments, the invention is mentioned above, where X1, In certain embodiments, the invention is mentioned above, where X1, X2, X4, In certain embodiments, the invention is mentioned above, where X1, X2, X4, In certain embodiments, the invention is mentioned above, where X1, X2, X4, In certain embodiments, the invention is mentioned above, where X1, X2, X5, In certain embodiments, the invention is mentioned above, where X1, X2, X5, refers to any of the compounds and X6, X7, and X8 are H. refers to any of the compounds X4, and X6 are OH; and X5, X7, and X8 are H. refers to any of the compounds X4, and X7 are OH; and X5, X6, and X8 are H. refers to any of the compounds X4, and X8 are OH; and X5, X6, and X7 are H. refers to any of the compounds X5, and X6 are OH; and X4, X7, and X8 are H. refers to any of the compounds X5, and X7 are OH; and X4, X6, and X8 are H. refers to any of the compounds X5, and X8 are OH; and X4, X6, and X7 are H. refers to any of the compounds X6, and X7 are OH; and X4, X5, and X8 are H. refers to any of the compounds X6, and X8 are OH; and X4, X5, and X7 are H. refers to any of the compounds X7, and X8 are OH; and X4, X5, and X6 are H. refers to any of the compounds X5, and X6 are OH; and X3, X7, and X8 are H. refers to any of the compounds X5, and X8 are OH; and X3, X6, and X7 are H. refers to any of the compounds X6, and X7 are OH; and X3, X5, and X8 are H. refers to any of the compounds X6, and X8 are OH; and X3, X5, and X7 are H. refers to any of the compounds X7, and X8 are OH; and X3, X5, and X6 are H. refers to any of the compounds X6, and X7 are OH; and X3, X4, and X8 are H. refers to any of the compounds X6, and X8 are OH; and X3, X4, and X7 are H. refers to any of the compounds X7, and X8 are OH; and X3, X4, and X6 are H. iviAazuzzuu / ¿04 In certain embodiments, the invention mentioned above, where Χ1, X3, In certain embodiments, the invention mentioned above, where Χ1, X3, In certain embodiments, the invention mentioned above, where Χ1, invention mentioned above, where Χ1, X3, In certain embodiments, the invention mentioned above, where Χ1, X3, In certain embodiments, the invention mentioned above, where Χ1, where Χ1, X3, In certain embodiments, the invention mentioned above, where Χ1, In certain embodiments, the invention mentioned above, where Χ1, X4, In certain embodiments, the invention mentioned above, where Χ1, X4, In certain embodiments, the invention mentioned above, where Χ1, invention mentioned above, where Χ1, X4, In certain embodiments, the invention mentioned above, where Χ1, X5, In certain embodiments, the invention mentioned above, where where X2, X3, In certain embodiments, the invention mentioned above, where X2, X3, refers to any of the compounds X4, and X2, X7, and X8 are H. refers to any of the compounds X4, X5, and X7 are OH; and X2, X6, and X8 are H. refers to any of the compounds X4, X5, and X8 are OH; and X2, X6, and X7 are H. refers to any of the compounds X4, X6, and X7 are OH; and X2, X5, and X8 are H. refers to any of the compounds X4, X6, and X8 are OH; and X2, X5, and X7 are H. refers to any of the compounds X4, X7, and X8 are OH; and X2, X5, and X7 are H. refers to any of the compounds X5, X6, and X7 are OH; and X2, X4, and X8 are H. refers to any of the compounds X5, X6, and X8 are OH; and X2, X4, and X7 are H. refers to any of the compounds X5, X7, and X8 are OH; and X2, X4, and X6 are H. refers to any of the compounds X6, X7, and X8 are OH; and X2, X4, and X5 are H. refers to any of the compounds X5, X6, and X7 are OH; and X2, X3, and X8 are H. refers to any of the compounds X5, X6, and X8 are OH; and X2, X3, and X7 are H. refers to any of the compounds X5, X7, and X8 are OH; and X2, X3, and X6 are H. refers to any of the compounds X6, X7, and X8 are OH; and X2, X3, and X6 are H. refers to any of the compounds X6, X7, and X8 are OH; and X2, X3, and X4 are H. refers to any of the compounds X4, X5, and X6 are OH; and Χ1, X7, and X8 are H. refers to any of the compounds X4, X5, and X7 are OH; and Χ1, X6, and X8 are H. refers to any of the compounds X4, X5, and X8 are OH; and Χ1, X6, and X7 are H. MA / a / ¿U¿¿ / UU l ¿04 In certain embodiments, the invention is mentioned above, where X2, X3, X4, In certain embodiments, the invention is mentioned above, where X2, X3, X4, In certain embodiments, the invention is mentioned above, where X2, X3, X5, In certain embodiments, the invention is mentioned above, where X2, X3, wherein X2, X3, X5, In certain embodiments, the invention is mentioned above, wherein X2, X3, are mentioned above, where X2, X4, X5, In certain embodiments, the invention is mentioned above, where X2, X4, embodiments, the invention is mentioned above, where X2, X5, X6, In certain embodiments, the invention is mentioned above, where X3, X4, X5, In certain embodiments, the invention is mentioned above, where X3, X4, X5, In certain embodiments, the invention is mentioned above, where X3, X5, X6, In certain embodiments, the invention is mentioned above, where X4, X5, X6, refers to any of the compounds X6, and and Χ1, X5, and X8 are H. refers to any of the compounds X6, and X8 are OH; and Χ1, X5, and X7 are H. refers to any of the compounds X7, and X8 are OH; and Χ1, X5, and X6 are H. refers to any of the compounds X6, and X7 are OH; and Χ1, X4, and X8 are H. refers to any of the compounds X6, and X8 are OH; and Χ1, X4, and X7 are H. refers to any of the compounds X7, and X8 are OH; and Χ1, X4, and X6 are H. refers to any of the compounds X7, and X8 are OH; and Χ1, X4, and X5 are H. refers to any of the compounds X6, and X7 are OH; and Χ1, X3, and X8 are H. refers to any of the compounds X6, and X8 are OH; and Χ1, X3, and X7 are H. refers to any of the compounds X7, and X8 are OH; and Χ1, X3, and X6 are H. refers to any of the compounds X7, and X8 are OH; and Χ1, X3, and X5 are H. refers to any of the compounds X7, and X8 are OH; and Χ1, X3, and X5 are H. refers to any of the compounds X6, and X7 are OH; and Χ1, X2, and X8 are H. refers to any of the compounds X6, and X8 are OH; and Χ1, X2, and X7 are H. refers to any of the compounds X7, and X8 are OH; and Χ1, X2, and X6 are H. refers to any of the compounds X7, and X8 are OH; and Χ1, X2, and X5 are H. refers to any of the compounds X7, and X8 are OH; and Χ1, X2, and X4 are H. refers to any of the compounds X7, and X8 are OH; and Χ1, X2, and X3 are H. IVIASZUZZUU / ¿04 In certain embodiments, the invention is mentioned above, where X1, X2, X3, In certain embodiments, the invention is mentioned above, where X1, X2, X3, In certain embodiments, the invention is mentioned above, where X1, X2, X3, In certain embodiments, the invention is mentioned above, where X1, where X1, X2, X3, In certain embodiments, the invention is mentioned above, where X1, X2, are mentioned above, where X1, X2, X3, In certain embodiments, the invention is mentioned above, where X1, In certain embodiments, the invention is mentioned above, where X1, X2, X4, In certain embodiments, the invention is mentioned above, where X1, X2, X5, In certain embodiments, the invention is mentioned above, where X1, X3, X4, In certain embodiments, the invention is mentioned above, where X1, X3, X4, In certain embodiments, the invention is mentioned above, where X1, X3, X4, refers to any of the compounds X4, and X7 and X8 are H. refers to any of the compounds X4, X5, and X7 are OH; and X6 and X8 are H. refers to any of the compounds X4, X5, and X8 are OH; and X6 and X7 are H. refers to any of the compounds X4, X6, and X7 are OH; and X5 and X8 are H. refers to any of the compounds X4, X6, and X8 are OH; and X5 and X7 are H. refers to any of the compounds X4, X7, and X8 are OH; and X5 and X6 are H. refers to any of the compounds X5, X6, and X7 are OH; and X4 and X8 are H. refers to any of the compounds X5, X6, and X8 are OH; and X4 and X7 are H. refers to any of the compounds X5, X7, and X8 are OH; and X4 and X6 are H. refers to any of the compounds X5, X6, and X7 are OH; and X3 and X8 are H. refers to any of the compounds X5, X6, and X8 are OH; and X3 and X7 are H. refers to any of the compounds X5, X7, and X8 are OH; and X3 and X6 are H. refers to any of the compounds X6, X7, and X8 are OH; and X3 and X5 are H. refers to any of the compounds X6, X7, and X8 are OH; and X3 and X4 are H. refers to any of the compounds X5, X6, and X7 are OH; and X2 and X8 are H. refers to any of the compounds X5, X6, and X8 are OH; and X2 and X7 are H. refers to any of the compounds X5, X7, and X8 are OH; and X2 and X6 are H. refers to any of the compounds X6, X7, and X8 are OH; and X2 and X5 are H. MA / a / 2U22 / UU 1204 In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X1, X3, X5, X6, X7, and X8 are OH; and X2 and X4 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X1, X4, X5, X6, X7, and X8 are OH; and X2 and X3 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X2, X3, X4, X5, X6, and X7 are OH; and X1 and X8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X2, X3, X4, X5, X6, and X8 are OH; and X1 and X7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X2, X3, X4, X5, X7, and X8 are OH; and X1 and X6 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X2, X3, X4, X6, X7, and X8 are OH; and X1 and X5 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X2, X3, X5, X6, X7, and X8 are OH; and X1 and X4 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X2, X4, X5, X6, X7, and X8 are OH; and X1 and X3 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X3, X4, X5, X6, X7, and X8 are OH; and X1 and X2 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X1, X2, X3, X4, X5, X6, and X7 are OH; and X8 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X1, X2, X3, X4, X5, X6, and X8 are OH; and X7 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X1, X2, X3, X4, X5, X7, and X8 are OH; and X6 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X1, X2, X3, X4, X6, X7, and X8 are OH; and X5 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X1, X2, X3, X5, X6, X7, and X8 are OH; and X4 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X1, X2, X4, X5, X6, X7, and X8 are OH; and X3 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X1, X3, X4, X5, X6, X7, and X8 are OH; and X2 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X2, X3, X4, X5, X6, X7, and X8 are OH; and X1 is H. In certain embodiments, the invention relates to a compound of Formula III IVIAaZUZZUU / ¿04 where R1, R2, R3, R4, R5, R6, R7, and R8 are independently selected from the group consisting of H and OR; R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide; and provided that the compound is not a compound of Formula III wherein R1, R2, R3, R4, R5, R6, R7, and R8 are H; R1 is OR, and R2, R3, R4, R5, R6, R7, and R8 are H; R2 is OR, and R1, R3, R4, R5, R6, R7, and R8 are H; R3 is OR, and R1, R2, R4, R5, R6, R7, and R8 are H; R4 is OR, and R1, R2, R3, R5, R6, R7, and R8 are H; R5 is OR, and R1, R2, R3, R4, R6, R7, and R8 are H; R6 is OR, and R1, R2, R3, R4, R5, R7, and R8 are H; R7 is OR, and R1, R2, R3, R4, R5, R6, and R8 are H; R8 is OR, and R1, R2, R3, R4, R5, R6, and R7 are H; R1 and R2 are OR, and R3, R4, R5, R6, R7, and R8 are H; R1 and R5 are OR, and R2, R3, R4, R6, R7, and R8 are H; R1 and R7 are OR, and R2, R3, R4, R5, R6, and R8 are H; R1 and R8 are OR, and R2, R3, R4, R5, R6, and R7 are H; R2 and R3 are OR, and R1, R4, R5, R6, R7, and R8 are H; R2 and R4 are OR, and R1, R3, R5, R6, R7, and R8 are H; R2 and R5 are OR, and R1, R3, R4, R6, R7, and R8 are H; R2 and R6 are OR, and R1, R3, R4, R5, R7, and R8 are H; R2 and R7 are OR, and R1, R3, R4, R5, R6, and R8 are H; R2 and R8 are OR, and R1, R3, R4, R5, R6, and R7 are H; R3 and R4 are OR, and R1, R2, R5, R6, R7, and R8 are H; R3 and R5 are OR, and R1, R2, R4, R6, R7, and R8 are H; R3 and R6 are OR, and R1, R2, R4, R5, R7, and R8 are H; R3 and R7 are OR, and R1, R2, R4, R5, R6, and R8 are H; R3 and R8 are OR, and R1, R2, R4, R5, R6, and R7 are H; R4 and R8 are OR, and R1, R2, R3, R5, R6, and R7 are H; R5 and R6 are OR, and R1, R2, R3, R4, R7, and R8 are H; R5 and R7 are OR, and R1, R2, R3, R4, R6, and R8 are H; R5 and R8 are OR, and R1, R2, R3, R4, R6, and R7 are H; R6 and R7 are OR, and R1, R2, R3, R4, R5, and R8 are H; R6 and R8 are OR, and R1, R2, R3, R4, R5, and R7 are H; R1, R2, and R3 are OR, and R4, R5, R6, R7, and R8 are H; R1, R2, and R5 are OR, and R3, R4, R6, R7, and R8 are H; R1, R2, and R6 are OR, and R3, R4, R5, R7, and R8 are H; R1, R2, and R8 are OR, and R3, R4, R5, R6, and R7 are H; R1, R5, and R8 are OR, and R2, R3, R4, R6, and R7 are H; R1, R7, and R8 are OR, and R2, R3, R4, R5, and R6 are H; R2, R3, and R4 are OR, and R1, R5, R6, R7, and R8 are H; R2, R4, and R6 are OR, and R1, R3, R5, R7, and R8 are H; R2, R4, and R7 are OR, and R1, R3, R5, R6, and R8 are H; R2, R5, and R8 are OR, and R1, R3, R4, R6, and R7 are H; R2, R6, and R7 are OR, and R1, R3, R4, R5, and R8 are H; R2, R6, and R8 are OR, and R1, R3, R4, R5, and R7 are H; R2, R7, and R8 are OR, and R1, R3, R4, R5, and R6 are H; R3, R5, and R8 are OR, and R1, R2, R4, R6, and R7 are H; R3, R7, and R8 are OR, and R1, R2, R4, R5, and R6 are H; R6, R7, and R8 are OR, and R1, R2, R3, R4, and R5 are H; R1, R2, R5, and R6 are OR, and R3, R4, R7, and R8 are H; R1, R2, R5, and R7 are OR, and R3, R4, R6, and R8 are H; R1, R2, R6, and R7 are OR, and R3, R4, R5, and R8 are H; R1, R6, R7, and R8 are OR, and R2, R3, R4, and R5 are H; R2, R3, R4, and R6 are OR, and R1, R5, R7, and R8 are H; R2, R3, R5, and R7 are OR, and R1, R4, R6, and R8 are H; R2, R3, R6, and R7 are OR, and R1, R4, R5, and R8 are H; R2, R4, R5, and R8 are OR, and R1, R3, R6, and R7 are H; R2, R4, R6, and R7 are OR, and R1, R3, R5, and R8 are H; R2, R5, R6, and R7 are OR, and R1, R3, R4, and R8 are H; R2, R6, R7, and R8 are OR, and R1, R3, R4, and R5 are H; R1, R2, R4, R5, and R7 are OR, and R3, R6, and R8 are H; R1, R2, R6, R7, and R8 are OR, and R3, R4, and R5 are H; IVIASZUZZUU / ¿04 R2, R3, R4, R5, and R7 are OR, and R1, R6, and R8 are H; R2, R3, R6, R7, and R8 are OR, and R1, R4, and R5 are H; R2, R4, R6, R7, and R8 are OR, and R1, R3, and R5 are H; R2, R5, R6, R7, and R8 are OR, and R1, R3, and R4 are H; R1, R2, R3, R6, R7, and R8 are OR, and R4 and R5 are H; R2, R3, R4, R6, R7, and R8 are OR, and R1 and R5 are H; and R2, R4, R5, R6, R7, and R8 are OR, and R1 and R3 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least two of R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least three of R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least four of R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least five of R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least six of R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least seven of R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R1 and R3 are OR; and R2, R4, R5, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R1 and R4 are OR; and R2, R3, R5, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R1 and R6 are OR; and R2, R3, R4, R5, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R4 and R5 are OR; and R1, R2, R3, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R4 and R6 are OR; and R1, R2, R3, R5, R7, and R8 are H. ΜΛ / a / ZUZZ / UU f ¿04 In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R4 and R7 are OR; and R1, R2, R3, R5, R6, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R7 and R8 are OR; and R1, R2, R3, R4, R5, and R6 are H. MA / a / 2U22 / UU 1204 In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, wherein R1, R3, In certain embodiments, the invention mentioned above, wherein R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, in where R1, R3, In certain embodiments, the invention mentioned above, where R1, R4, In certain embodiments, the invention mentioned above, where R1, R4, In certain embodiments, the invention mentioned above, where R1, R4, In certain embodiments, the invention mentioned above, where R1, R4, In certain embodiments, the invention mentioned above, where R1, R5, In certain embodiments, the invention mentioned above, where R1, R5, In certain embodiments, the invention mentioned above, wherein R1, R6, In certain embodiments, the invention mentioned above, wherein R1, R6, In certain embodiments, the invention mentioned above, where R2, R3, refers to any of the compounds and R4 are OR; and R3, R5, R6, R7, and R8 are H. refers to any of the compounds and R7 are OR; and R3, R4, R5, R6, and R8 are H. refers to any of the compounds and R4 are OR; and R2, R5, R6, R7, and R8 are H. refers to any of the compounds and R5 are OR; and R2, R4, R6, R7, and R8 are H. refers to any of the compounds and R6 are OR; and R2, R4, R5, R7, and R8 are H. refers to any of the compounds and R7 are OR; and R2, R4, R5, R6, and R8 are H. refers to any of the compounds and R8 are OR; and R2, R4, R5, R6, and R7 are H. refers to any of the compounds and R5 are OR; and R2, R3, R6, R7, and R8 are H. refers to any of the compounds and R6 are OR; and R2, R3, R5, R7, and R8 are H. refers to any of the compounds and R7 are OR; and R2, R3, R5, R6, and R8 are H. refers to any of the compounds and R8 are OR; and R2, R3, R5, R6, and R7 are H. refers to any of the compounds and R6 are OR; and R2, R3, R4, R7, and R8 are H. refers to any of the compounds and R7 are OR; and R2, R3, R4, R6, and R8 are H. refers to any of the compounds and R7 are OR; and R2, R3, R4, R5, and R8 are H. refers to any of the compounds and R8 are OR; and R2, R3, R4, R5, and R7 are H. refers to any of the compounds and R5 are OR; and R1, R4, R6, R7, and R8 are H. In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, wherein R2, R4, In certain embodiments, the invention mentioned above, wherein R2, R4, In certain embodiments, the invention mentioned above, where R2, R5, In certain embodiments, the invention mentioned above, in where R2, R5, In certain embodiments, the invention mentioned above, where R3, R4, In certain embodiments, the invention mentioned above, where R3, R4, In certain embodiments, the invention mentioned above, where R3, R4, In certain embodiments, the invention mentioned above, where R3, R4, In certain embodiments, the invention mentioned above, where R3, R5, In certain embodiments, the invention mentioned above, where R3, R5, In certain embodiments, the invention mentioned above, wherein R3, R6, In certain embodiments, the invention mentioned above, wherein R3, R6, In certain embodiments, the invention mentioned above, wherein R4, R5, In certain embodiments, the invention mentioned above, in where R4, R5, In certain embodiments, the invention mentioned above, where R4, R5, refers to any of the compounds and R6 are OR; and R1, R4, R5, R7, and R8 are H. refers to any of the compounds and R7 are OR; and R1, R4, R5, R6, and R8 are H. refers to any of the compounds and R8 are OR; and R1, R4, R5, R6, and R7 are H. refers to any of the compounds and R5 are OR; and R1, R3, R6, R7, and R8 are H. refers to any of the compounds and R8 are OR; and R1, R3, R5, R6, and R7 are H. refers to any of the compounds and R6 are OR; and R1, R3, R4, R7, and R8 are H. refers to any of the compounds and R7 are OR; and R1, R3, R4, R6, and R8 are H. refers to any of the compounds and R5 are OR; and R1, R2, R6, R7, and R8 are H. refers to any of the compounds and R6 are OR; and R1, R2, R5, R7, and R8 are H. refers to any of the compounds and R7 are OR; and R1, R2, R5, R6, and R8 are H. refers to any of the compounds and R8 are OR; and R1, R2, R5, R6, and R7 are H. refers to any of the compounds and R6 are OR; and R1, R2, R4, R7, and R8 are H. refers to any of the compounds and R7 are OR; and R1, R2, R4, R6, and R8 are H. refers to any of the compounds and R7 are OR; and R1, R2, R4, R5, and R8 are H. refers to any of the compounds and R8 are OR; and R1, R2, R4, R5, and R7 are H. refers to any of the compounds and R6 are OR; and R1, R2, R3, R7, and R8 are H. refers to any of the compounds and R7 are OR; and R1, R2, R3, R6, and R8 are H. refers to any of the compounds and R8 are OR; and R1, R2, R3, R6, and R7 are H. iviAazuzzuu / ¿04 In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R4, R6, and R7 are OR; and R1, R2, R3, R5, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R4, R6, and R8 are OR; and R1, R2, R3, R5, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R4, R7, and R8 are OR; and R1, R2, R3, R5, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R5, R6, and R7 are OR; and R1, R2, R3, R4, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R5, R6, and R8 are OR; and R1, R2, R3, R4, and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R5, R7, and R8 are OR; and R1, R2, R3, R4, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R1, R2, R3, and R4 are OR; and R5, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R1, R2, R3, and R5 are OR; and R4, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R1, R2, R3, and R6 are OR; and R4, R5, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R1, R2, R3, and R7 are OR; and R4, R5, R6, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R1, R2, R3, and R8 are OR; and R4, R5, R6, and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R1, R2, R4, and R5 are OR; and R3, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R1, R2, R4, and R6 are OR; and R3, R5, R7, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R1, R2, R4, and R7 are OR; and R3, R5, R6, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R1, R2, R4, and R8 are OR; and R3, R5, R6, and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R1, R2, R5, and R8 are OR; and R3, R4, R6, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R1, R2, R6, and R8 are OR; and R3, R4, R5, and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R1, R2, R7, and R8 are OR; and R3, R4, R5, and R6 are H. IVIAaZUZZUU / ¿04 In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, wherein R1, R3, In certain embodiments, the invention mentioned above, wherein R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, in where R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, where R1, R4, In certain embodiments, the invention mentioned above, where R1, R4, In certain embodiments, the invention mentioned above, where R1, R4, In certain embodiments, the invention mentioned above, wherein R1, R4, In certain embodiments, the invention mentioned above, wherein R1, R4, In certain embodiments, the invention mentioned above, where R1, R4, In certain embodiments, the invention mentioned above, in where R1, R5, In certain embodiments, the invention mentioned above, where R1, R5, refers to any of the compounds R4, and R5 are OR; and R2, R6, R7, and R8 are H. refers to any of the compounds R4, and R6 are OR; and R2, R5, R7, and R8 are H. refers to any of the compounds R4, and R7 are OR; and R2, R5, R6, and R8 are H. refers to any of the compounds R4, and R8 are OR; and R2, R5, R6, and R7 are H. refers to any of the compounds R5, and R6 are OR; and R2, R4, R7, and R8 are H. refers to any of the compounds R5, and R7 are OR; and R2, R4, R6, and R8 are H. refers to any of the compounds R5, and R8 are OR; and R2, R4, R6, and R7 are H. refers to any of the compounds R6, and R7 are OR; and R2, R4, R5, and R8 are H. refers to any of the compounds R6, and R8 are OR; and R2, R4, R5, and R7 are H. refers to any of the compounds R7, and R8 are OR; and R2, R4, R5, and R6 are H. refers to any of the compounds R5, and R6 are OR; and R2, R3, R7, and R8 are H. refers to any of the compounds R5, and R7 are OR; and R2, R3, R6, and R8 are H. refers to any of the compounds R5, and R8 are OR; and R2, R3, R6, and R7 are H. refers to any of the compounds R6, and R7 are OR; and R2, R3, R5, and R8 are H. refers to any of the compounds R6, and R8 are OR; and R2, R3, R5, and R7 are H. refers to any of the compounds R7, and R8 are OR; and R2, R3, R5, and R6 are H. refers to any of the compounds R6, and R7 are OR; and R2, R3, R4, and R8 are H. refers to any of the compounds R6, and R8 are OR; and R2, R3, R4, and R7 are H. MA / a / 2U22 / UU 1204 In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R1, R5, R7, and R8 are OR; and R2, R3, R4, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R2, R3, R4, and R5 are OR; and R1, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R2, R3, R4, and R7 are OR; and R1, R5, R6, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R2, R3, R4, and R8 are OR; and R1, R5, R6, and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R2, R3, R5, and R6 are OR; and R1, R4, R7, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R2, R3, R5, and R8 are OR; and R1, R4, R6, and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R2, R3, R6, and R8 are OR; and R1, R4, R5, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R2, R3, R7, and R8 are OR; and R1, R4, R6, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R2, R4, R5, and R6 are OR; and R1, R3, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R2, R4, R5, and R7 are OR; and R1, R3, R6, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R2, R4, R6, and R8 are OR; and R1, R3, R5, and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R2, R4, R7, and R8 are OR; and R1, R3, R5, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R2, R5, R6, and R8 are OR; and R1, R3, R4, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R2, R5, R7, and R8 are OR; and R1, R3, R4, and R6 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R3, R4, R5, and R6 are OR; and R1, R2, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R3, R4, R5, and R7 are OR; and R1, R2, R6, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R3, R4, R5, and R8 are OR; and R1, R2, R6, and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R3, R4, R6, and R7 are OR; and R1, R2, R5, and R8 are H. IVIA3ZUZZUU / ¿04 In certain embodiments, the invention mentioned above, where R3, R4, In certain embodiments, the invention mentioned above, where R3, R4, 5 In certain embodiments, the invention mentioned above, where R3, R5, In certain embodiments, the invention mentioned above, wherein R3, R5, In certain embodiments, the invention mentioned above, wherein R3, R5, In certain embodiments, the invention mentioned above, wherein R3, R6, In certain embodiments, the invention mentioned above , where R4, R5, 15 In certain embodiments, the invention mentioned above, where R4, R5, In certain embodiments, the invention mentioned above, where R4, R5, In certain embodiments, the invention mentioned above, where R4 , R6, In certain embodiments, the invention mentioned above, where R5, R6, In certain embodiments, the invention mentioned above, where R1, R2, 25 In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, wherein R1, R2, In certain embodiments, the invention mentioned above, wherein R1, R2, In certain embodiments, the invention mentioned above, wherein R1, R2, In certain embodiments, the invention mentioned above, wherein R1, R2, 35 In certain embodiments, the invention mentioned above, wherein R1, R2, refers to any of the compounds R6, and R8 are OR; and R1, R2, R5, and R7 are H. refers to any of the compounds R7, and R8 are OR; and R1, R2, R5, and R6 are H. refers to any of the compounds R6, and R7 are OR; and R1, R2, R4, and R8 are H. refers to any of the compounds R6, and R8 are OR; and R1, R2, R4, and R7 are H. refers to any of the compounds R7, and R8 are OR; and R1, R2, R4, and R6 are H. refers to any of the compounds R7, and R8 are OR; and R1, R2, R4, and R5 are H. refers to any of the compounds R6, and R7 are OR; and R1, R2, R3, and R8 are H. refers to any of the compounds R6, and R8 are OR; and R1, R2, R3, and R7 are H. refers to any of the compounds R7, and R8 are OR; and R1, R2, R3, and R6 are H. refers to any of the compounds R7, and R8 are OR; and R1, R2, R3, and R5 are H. refers to any of the compounds R7, and R8 are OR; and R1, R2, R3, and R4 are H. refers to any of the compounds R3, R4, and R5 are OR; and R6, R7, and R8 are H. refers to any of the compounds R3, R4, and R6 are OR; and R5, R7, and R8 are H. refers to any of the compounds R3, R4, and R7 are OR; and R5, R6, and R8 are H. refers to any of the compounds R3, R4, and R8 are OR; and R5, R6, and R7 are H. refers to any of the compounds R3, R5, and R6 are OR; and R4, R7, and R8 are H. refers to any of the compounds R3, R5, and R7 are OR; and R4, R6, and R8 are H. refers to any of the compounds R3, R5, and R8 are OR; and R4, R6, and R7 are H. iviAazuzzuu / ¿04 In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, wherein R1, R2, In certain embodiments, the invention mentioned above, wherein R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, in where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, wherein R1, R3, In certain embodiments, the invention mentioned above, wherein R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, in where R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, refers to any of the compounds R3, R6, and R7 are OR; and R4, R5, and R8 are H. refers to any of the compounds R3, R6, and R8 are OR; and R4, R5, and R7 are H. refers to any of the compounds R3, R7, and R8 are OR; and R4, R5, and R6 are H. refers to any of the compounds R4, R5, and R6 are OR; and R3, R7, and R8 are H. refers to any of the compounds R4, R5, and R8 are OR; and R3, R6, and R7 are H. refers to any of the compounds R4, R6, and R7 are OR; and R3, R5, and R8 are H. refers to any of the compounds R4, R6, and R8 are OR; and R3, R5, and R7 are H. refers to any of the compounds R4, R7, and R8 are OR; and R3, R5, and R6 are H. refers to any of the compounds R5, R6, and R7 are OR; and R3, R4, and R8 are H. refers to any of the compounds R5, R6, and R8 are OR; and R3, R4, and R7 are H. refers to any of the compounds R5, R7, and R8 are OR; and R3, R4, and R6 are H. refers to any of the compounds R4, R5, and R6 are OR; and R2, R7, and R8 are H. refers to any of the compounds R4, R5, and R7 are OR; and R2, R6, and R8 are H. refers to any of the compounds R4, R5, and R8 are OR; and R2, R6, and R7 are H. refers to any of the compounds R4, R6, and R7 are OR; and R2, R5, and R8 are H. refers to any of the compounds R4, R6, and R8 are OR; and R2, R5, and R7 are H. refers to any of the compounds R4, R7, and R8 are OR; and R2, R5, and R7 are H. refers to any of the compounds R5, R6, and R7 are OR; and R2, R4, and R8 are H. ΜΛ / a / ZUZZ / UU f ¿04 In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, where R1, R4, In certain embodiments, the invention mentioned above, where R1, R4, In certain embodiments, the invention mentioned above, where R1, R4, In certain embodiments, the invention mentioned above, in where R1, R4, In certain embodiments, the invention mentioned above, where R1, R5, In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, wherein R2, R3, In certain embodiments, the invention mentioned above, wherein R2, R3, In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, in where R2, R4, In certain embodiments, the invention mentioned above, where R2, R4, refers to any of the compounds R5, R6, and R8 are OR; and R2, R4, and R7 are H. refers to any of the compounds R5, R7, and R8 are OR; and R2, R4, and R6 are H. refers to any of the compounds R6, R7, and R8 are OR; and R2, R4, and R5 are H. refers to any of the compounds R5, R6, and R7 are OR; and R2, R3, and R8 are H. refers to any of the compounds R5, R6, and R8 are OR; and R2, R3, and R7 are H. refers to any of the compounds R5, R7, and R8 are OR; and R2, R3, and R6 are H. refers to any of the compounds R6, R7, and R8 are OR; and R2, R3, and R6 are H. refers to any of the compounds R6, R7, and R8 are OR; and R2, R3, and R4 are H. refers to any of the compounds R4, R5, and R6 are OR; and R1, R7, and R8 are H. refers to any of the compounds R4, R5, and R8 are OR; and R1, R6, and R7 are H. refers to any of the compounds R4, R6, and R7 are OR; and R1, R5, and R8 are H. refers to any of the compounds R4, R6, and R8 are OR; and R1, R5, and R7 are H. refers to any of the compounds R4, R7, and R8 are OR; and R1, R5, and R6 are H. refers to any of the compounds R5, R6, and R7 are OR; and R1, R4, and R8 are H. refers to any of the compounds R5, R6, and R8 are OR; and R1, R4, and R7 are H. refers to any of the compounds R5, R7, and R8 are OR; and R1, R4, and R6 are H. refers to any of the compounds R5, R6, and R7 are OR; and R1, R3, and R8 are H. refers to any of the compounds R5, R6, and R8 are OR; and R1, R3, and R7 are H. MA / a / 2U22 / UU 1204 In certain embodiments, the invention mentioned above, where R2, R4, In certain embodiments, the invention mentioned above, where R3, R4, In certain embodiments, the invention mentioned above, where R3, R4, In certain embodiments, the invention mentioned above, wherein R3, R4, In certain embodiments, the invention mentioned above, wherein R3, R4, In certain embodiments, the invention mentioned above, where R3, R5, In certain embodiments, the invention mentioned above, in where R4, R5, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, wherein R1, R2, In certain embodiments, the invention mentioned above, wherein R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, in where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, refers to any of the compounds R5, R7, and R8 are OR; and R1, R3, and R6 are H. refers to any of the compounds R5, R6, and R7 are OR; and R1, R2, and R8 are H. refers to any of the compounds R5, R6, and R8 are OR; and R1, R2, and R7 are H. refers to any of the compounds R5, R7, and R8 are OR; and R1, R2, and R6 are H. refers to any of the compounds R6, R7, and R8 are OR; and R1, R2, and R5 are H. refers to any of the compounds R6, R7, and R8 are OR; and R1, R2, and R4 are H. refers to any of the compounds R6, R7, and R8 are OR; and R1, R2, and R3 are H. refers to any of the compounds R3, R4, R5, and R6 are OR; and R7 and R8 are H. refers to any of the compounds R3, R4, R5, and R7 are OR; and R6 and R8 are H. refers to any of the compounds R3, R4, R5, and R8 are OR; and R6 and R7 are H. refers to any of the compounds R3, R4, R6, and R7 are OR; and R5 and R8 are H. refers to any of the compounds R3, R4, R6, and R8 are OR; and R5 and R7 are H. refers to any of the compounds R3, R4, R7, and R8 are OR; and R5 and R6 are H. refers to any of the compounds R3, R5, R6, and R7 are OR; and R4 and R8 are H. refers to any of the compounds R3, R5, R6, and R8 are OR; and R4 and R7 are H. refers to any of the compounds R3, R5, R7, and R8 are OR; and R4 and R6 are H. refers to any of the compounds R4, R5, R6, and R7 are OR; and R3 and R8 are H. refers to any of the compounds R4, R5, R6, and R8 are OR; and R3 and R7 are H. IVIASZUZZUU / ¿04 In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, In certain embodiments, the invention mentioned above, wherein R1, R3, In certain embodiments, the invention mentioned above, wherein R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, in where R1, R3, In certain embodiments, the invention mentioned above, where R1, R3, In certain embodiments, the invention mentioned above, where R1, R4, In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, where R2, R3, In certain embodiments, the invention mentioned above, wherein R3, R4, In certain embodiments, the invention mentioned above, wherein R1, R2, In certain embodiments, the invention mentioned above, wherein R1, R2, In certain embodiments, the invention mentioned above, in where R1, R2, In certain embodiments, the invention mentioned above, where R1, R2, refers to any of the compounds R4, R5, R7, and R8 are OR; and R3 and R6 are H. refers to any of the compounds R4, R6, R7, and R8 are OR; and R3 and R5 are H. refers to any of the compounds R5, R6, R7, and R8 are OR; and R3 and R4 are H. refers to any of the compounds R4, R5, R6, and R7 are OR; and R2 and R8 are H. refers to any of the compounds R4, R5, R6, and R8 are OR; and R2 and R7 are H. refers to any of the compounds R4, R5, R7, and R8 are OR; and R2 and R6 are H. refers to any of the compounds R4, R6, R7, and R8 are OR; and R2 and R5 are H. refers to any of the compounds R5, R6, R7, and R8 are OR; and R2 and R4 are H. refers to any of the compounds R5, R6, R7, and R8 are OR; and R2 and R3 are H. refers to any of the compounds R4, R5, R6, and R7 are OR; and R1 and R8 are H. refers to any of the compounds R4, R5, R6, and R8 are OR; and R1 and R7 are H. refers to any of the compounds R4, R5, R7, and R8 are OR; and R1 and R6 are H. refers to any of the compounds R5, R6, R7, and R8 are OR; and R1 and R4 are H. refers to any of the compounds R5, R6, R7, and R8 are OR; and R1 and R2 are H. refers to any of the compounds R3, R4, R5, R6, and R7 are OR; and R8 is H. refers to any of the compounds R3, R4, R5, R6, and R8 are OR; and R7 is H. refers to any of the compounds R3, R4, R5, R7, and R8 are OR; and R6 is H. refers to any of the compounds R3, R4, R6, R7, and R8 are OR; and R5 is H. iviAazuzzuu / ¿04 In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R1, R2, R3, R5, R6, R7, and R8 are OR; and R4 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R1, R2, R4, R5, R6, R7, and R8 are OR; and R3 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R1, R3, R4, R5, R6, R7, and R8 are OR; and R2 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R2, R3, R4, R5, R6, R7, and R8 are OR; and R1 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R is H. As used herein, the term “urolithin precursor” refers to ellagic acid and any ellagitannin capable of being converted to one or more urolithins upon administration to an animal. In certain embodiments, a “urolithin precursor” is a compound of Formula IV: where Formula IV MA / a / 2U22 / UU 1204 R9, R10, R11, R12, R13, and R14 are independently selected from the group consisting of H and OR; and R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide. In certain embodiments, the invention relates to a compound of Formula V EITHER EITHER Formula V where X9, X10, X11, X12, X13, and X14 are independently selected from the group consisting of H and OH; and provided that the compound is not a compound of Formula V wherein X9, X10, X11, X12, X13, and X14 are H; X10 is OH, and X9, X11, X12, X13, and X14 are H; X9 and X12 are OH, and X10, X11, X13, and X14 are H; X9 and X13 are OH, and X10, X11, X12, and X14 are H; X9 and X14 are OH, and X10, X11, X12, and X13 are H; X10 and X13 are OH, and X9, X11, X12, and X14 are H; X10, X11, and X13 are OH, and X9, X12, and X14 are H; X9, X10, X12, and X14 are OH, and X11 and X13 are H; X9, X10, X13, and X14 are OH, and X11 and X12 are H (ellagic acid); X9, X10, X11, X13, and X14 are OH, and X12 is H; and X9, X10, X11, X12, X13, and X14 are OH. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least one of X9, X10, X11, X12, X13, and X14 is OH. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least two of X9, X10, X11, X12, X13, and X14 are OH. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least three of X9, X10, X11, X12, X13, and X14 are OH. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least four of X9, X10, X11, X12, X13, and X14 are OH. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein five of X9, X10, X11, X12, X13, and X14 are OH. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9 is OH; and X10, X11, X12, X13, and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X11 is OH; and X9, X10, X12, X13, and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9 and X10 are OH; and X11, X12, X13, and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9 and X11 are OH; and X10, X12, X13, and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X10 and X11 are OH; and X9, X12, X13, and X14 are H. iviAazuzzuu / ¿04 In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X10 and X12 are OH; and X9, X11, X13, and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X11 and X12 are OH; and X9, X10, X13, and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9, X10, and X11 are OH; and X12, X13, and X14 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X9, X10, and X12 are OH; and X11, X13, and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9, X10, and X13 are OH; and X11, X12, and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9, X10, and X14 are OH; and X11, X12, and X13 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9, X11, and X12 are OH; and X10, X13, and X14 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X9, X11, and X13 are OH; and X10, X12, and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9, X11, and X14 are OH; and X10, X12, and X13 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X9, X12, and X13 are OH; and X10, X11, and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X10, X11, and X12 are OH; and X9, X13, and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9, X10, X11, and X12 are OH; and X13 and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9, X10, X11, and X13 are OH; and X12 and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9, X10, X11, and X14 are OH; and X12 and X13 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9, X10, X12, and X13 are OH; and X11 and X14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9, X11, X12, and X13 are OH; and X10 and X14 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein X9, X11, X12, and X14 are OH; and X10 and X13 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X10, X11, X12, and X13 are OH; and X9 and X14 are H. iviAazuzzuu / ¿04 In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9, X10, X11, X12, and X13 are OH; and X14 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein X9, X10, X11, X12, and X14 are OH; and X13 is H. In certain embodiments, the invention relates to a compound of Formula VI Formula VI MA / a / 2U22 / UU 1204 where R9, R10, R11, R12, R13, and R14 are independently selected from the group consisting of H and OR; R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide; and provided that the compound is not a compound of Formula VI wherein R9, R10, R11, R12, R13, and R14 are H; R10 is OR, and R9, R11, R12, R13, and R14 are H; R9 and R12 are OR, and R10, R11, R13, and R14 are H; R9 and R13 are OR, and R10, R11, R12, and R14 are H; R9 and R14 are OR, and R10, R11, R12, and R13 are H; R10 and R13 are OR, and R9, R11, R12, and R14 are H; R9, R10, and R13 are OR, and R11, R12, and R14 are H; R9, R10, and R14 are OR, and R11, R12, and R13 are H; R10, R11, and R13 are OR, and R9, R12, and R14 are H; R9, R10, R12, and R13 are OR, and R11 and R14 are H; R9, R10, R12, yR14sonOR, yR11 yR13sonH; R9, R10, R13, and R14 are OR, and R11 and R12 are H; R10, R11, R12, and R13 are OR, and R9 and R14 are H; R9, R10, R11, R12, and R13 are OR, and R14 is H; R9, R10, R11, R13, and R14 are OR, and R12 is H; and R9, R10, R11, R12, R13, and R14 are OR. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least one of R9, R10, R11, R12, R13, and R14 is OR. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least two of R9, R10, R11, R12, R13, and R14 are OR. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least three of R9, R10, R11, R12, R13, and R14 are OR. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein at least four of R9, R10, R11, R12, R13, and R14 are OR. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein five of R9, R10, R11, R12, R13, and R14 are OR. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R9 is OR; and R10, R11, R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R11 is OR; and R9, R10, R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R9 and R10 are OR; and R11, R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R9 and R11 are OR; and R10, R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R10 and R11 are OR; and R9, R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R10 and R12 are OR; and R9, R11, R13, and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R11 and R12 are OR; and R9, R10, R13, and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R9, R10, and R11 are OR; and R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R9, R10, and R12 are OR; and R11, R13, and R14 are H. In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R9, R11, and R12 are OR; and R10, R13, and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R9, R11, and R13 are OR; and R10, R12, and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R9, R11, and R14 are OR; and R10, R12, and R13 are H. MA / a / ¿U¿¿ / UU l ¿04 In certain embodiments, the invention relates to any of the aforementioned compounds, wherein R9, R12, and R13 are OR; and R10, R11, and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R10, R11, and R12 are OR; and R9, R13, and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R9, R10, R11, and R12 are OR; and R13 and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R9, R10, R11, and R13 are OR; and R12 and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R9, R10, R11, and R14 are OR; and R12 and R13 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R9, R11, R12, and R13 are OR; and R10 and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R9, R11, R12, and R14 are OR; and R10 and R13 are H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R9, R10, R11, R12, and R14 are OR; and R13 is H. In certain embodiments, the invention relates to any of the above-mentioned compounds, wherein R is H. In one embodiment, a urolithin precursor is punicalagin (PA). In one embodiment, a urolithin precursor is punicalin (PB). See, for example, Figure 2. In one embodiment, a urolithin precursor is ellagic acid (EA). In one embodiment, a urolithin precursor is provided as an isolated urolithin precursor, for example, isolated from a natural food source or prepared by total synthesis. Isolated urolithin precursors are usually purified from natural sources or synthesized de novo; some urolithin precursors, including EA, are commercially available from suppliers, such as Sigma Aldrich. Also in accordance with the invention, urolithin precursors also include natural foods that contain ellagitannins and ellagic acid, especially natural foods that are rich in ellagitannins, ellagic acid, or both ellagitannins and ellagic acid. Such foods include without limitation certain berries, grapes, pomegranates, rose hips, and nuts. In one embodiment, the natural food is pomegranate. Additionally, urolithin precursors include foods and beverages processed from such natural foods. The processed food may take any form, including, for example, jellies, gelatins, preserves, pastes, spreads, juices, wines, extracts, concentrates and the like. In one embodiment, the processed food is pomegranate juice. In one embodiment, a urolithin precursor is provided as an extract, for example, a fruit extract. In one embodiment, a urolithin precursor is provided as a concentrate, for example, a fruit concentrate or fruit juice concentrate. In one embodiment, the urolithin precursor is an isolated urolithin precursor. In one embodiment, the urolithin precursor is a purified urolithin precursor. In one embodiment, the urolithin precursor is selected from the group consisting of ellagic acid, an ellagitannin, and any combination thereof. In one embodiment, the urolithin precursor is ellagic acid. In one embodiment, the urolithin precursor is an ellagitannin. In one embodiment, ellagitannin is selected from the group consisting of castalagin, castalin, casuarictin, chebulagic acid, chebulinic acid, gemin D, grandinin, pedunculagin, punicalagin, punicalin, roburin A, strychtin, telimagrandin I, telimagrandin II, terflavin A, terflavin B, tergalagin, Lambertianin C, Sanguiina H-6, Sanguiina H-10, and vescalagin. Ellagitannins Among the more than 500 hydrolyzable tannins so far characterized, ellagitannins, which produce ellagic acid after hydrolysis, constitute the largest group; the remaining group is gallotannins (galloylglucoses). Ellagitannins include; (1) monomeric ellagitannins, (2) C-glycosidic ellagitannins with an open-chain glucose core, (3) condensates of C-glycosidic tannins with flavan-3-ol (tannin complex), (4) oligomers which are produced through intermolecular C-0 or C-C bonds between monomers, and (5) other ellagitannins. Unlike condensed tannins that are widely dispersed throughout the plant kingdom, ellagitannins have been found only in dicotyledonous angiosperms. Among the plant families rich in ellagitannins are Myrtaceae, Lythraceae, Onagraceae, Melastomataceae, and Combretaceae. These families belong to the order Mirtales in accordance with the plant classification systems of New Engler, Cronquist, and APGII (angiosperm phylogeny group). Ellagitannins are characterized by the presence of one or more hexahydroxydiphenoyl (HHDP) unit(s) in a glucopyranose core. The HHDP group is biosynthetically formed through intramolecular, oxidative C-C bond formation between neighboring galloyl groups in galloylglucoses. They are easily hydrolyzed, either enzymatically or with acid, to release a stable ellagic acid such as the dilactone form of hexahydroxydiphenoic acid. In addition to the HHDP group, other constituent acyl units in ellagitannins include a galloyl group and HHDP metabolites such as valoneoyl, dehydrohexahydroxydiphenoyl (DHHDP), and chebuloyl groups. Referring to Table 2, variations in the number and position of these acyl units in the glucose core provide a variety of analogues such as telimagrandin I (1), and II (2), pedunculagin (6), casuarictin (7) , chebulagic acid (14), and chebulinic acid (15). MA / a / ¿U¿¿ / UU f ¿04 Table 2· Representative Monomeric Elaqitanins IVIAaZUZZUU / ¿04 Key Name Structure 1 Tolimagrandina I Rl= OH; R2 = R3= G OH HO^J^ COOCH. HO and V and ΟΟΟ'^Τ'Α-' u\ HC·5^ OH 01.2 2 Telimagrandina II Rl= ( / )-0G; R2= R3= G 3 Strethinin Rl= (βί-OG; R2= R3= H 4 Gemin D Rl= OH; R2= H; R3= G 5 4,6-(S)-HHDP glucose Rl= OH; R2= R3= H 6 Pedunculagin Rl= OH; R2= R3= (S)-HHDP r3oh2c r2o \ \ \ 1 c° co H°—0 y—ζ # 0H HO OHHO OH 7 Casuarictin Rl= (P)-OG; R2 = R3= (S)-HHDP 8 2,3-(S)-HHDP glucose Rl= OH; R2= R3= H 9 Punicalagin Rl= R2= (S)-HHDP OH J— COOÍH, H0 Y 1 2 jOL» \ Ηυ T Ί \ H0x OH V>-coo n or HO' 'γ OH 10 Punicalin Rl= R2= H 11 Tergalagin Rl= R2= T 12 Terflavin A Rl= R2= (S)-HHDP i ..«V ™ .1 XI / “ [ Γ 0 OR1 HC Y OH 13 Terflavin B Rl= R2= H Table 3. Representative Natural Sources of Monomeric Elaqitanins 1-15 Plant Source Ellagitanin Monomers Found in Mirtales T rapaceae Trapa japonica 1, 4, 6, 7 Melastomataceae 6, 7 Bredia tuberculata 3,7 Heterocentron roseum 3, 7 Melastoma malabathricum 3, 6, 7 M. normale 3, 6, 7 Tibouchina semidecandra 6, 7, 8 Myrtaceae Callistemon lanceolatus 4, 6, 8 Eucalyptus alba 1, 4, 6, 8 E. consideniana 1, 3, 4, 6 E. globulus 1 E. rostrata 1 E. viminalis 1, 2, 4, 6 Myrtus communis 1,2 Pimenta dioica 2, 3, 5, 6 Syzyqium aqueum 2, 6, 7 S. aromaticum 1,2, 3, 4, 7 Onagraceae Epilobium angustifolium 1, 3, 4, 6 Oenothera erytrosapala 1,4 O. laciniata 1 O. tetraptera 1,2, 4 Combretaceae Combretum glutinosum 8, 9, 10 C. molle 9, 10 Quisqualis indica 1,2, 6,8,9, 10 Terminalia arborea 8, 9, 10, 14, 15 T. arjuna 8, 9, 10 T brachystemma 9 T calamansanai 1,2, 8, 9, 10 T. catappa 1,8, 9, 10, 11, 12, 13, 14, 15 T chebula 9, 10, 12, 13, 14, 15 T citrine 9, 14 T macroptera 8, 9, 12, 13 T. myriocarpa 8, 9 T. triflora 10 Punicaceae Púnica granatum 1,3, 6, 8, 9, 10 IVIAaZUZZUU / ¿04 C-Glycosidic ellagitannins have been found in many plant families including Lythraceae, Myrtaceae, Combretaceae, Melastomataceae, and Punicaceae, as well as Fagaceae, Betulaceae, Casuarinaceae, Rosaceae, Theaceae, and Elaeagnaceae. They are categorized into two types: castalagin type, which contains a flavogalloyl unit that participates in the C-glycosidic bond, such as castalagin (16) and its C-1 epimer, vescalagin (18), and casuarinin type, which contain a HHDP unit, such as casuarinine (20) and stachyurin (21). Table 4· Representative C-Glycosidic Ellagitaninsase IVIAaZUZZUU / ¿04 No Name Code Structure 16 Castalagina Rl = H; R2=OH; R3= R4 = (S)-HHDP r4oh2c OR3 17 Castalina Rl = R3= R4 = H ; R2 = OH \ o' CO \ xR2 / R 18 19 Vescalagin Grandinina Rl = OH; R2=H; R3= R4= (S)-HHDP Rl = L; R2=H; R3= R4 = (S)-HHDP R2= OH; R3= G OH hoA 21 Stachyuri na Rl = OH; R2=H; R3 = G, COOCH? HC | V. 22 Casuariina Rl = R3= H; R2= OH I II \ 23 5- desgaloiestaqu iuri na Rl = OH; R2 = R3= H 1 '' 9 0H JO 29 Lagerstroemina Rl= H; R2= OH; R3= Val / X / \ HO OHHO OH 24 Punicacortein A Rl = R4 = H; R2= OH; R3= G FtOHjC ^-OR HO \ Λ 25 Epi- Punicacortein A Rl= OH; R2= R4= H; R3= G C A / X \ p CO cc á-1 <r2 r1No Name Code Structure 26 Punicacortein B Rl= R3= H; R2= OH; R4= G 27 Punicacor thein C Rl= H; R2= OH J—COOCH-. HO \ XCH AJA A Aoh no ϊ π / \~ R2 HO. x aG, (S)-HHDP, and Val have the same meanings as in Table 2. Table 5 presents a representative list of natural sources of C-glycosidic ellagitannins 16-28. Table 5. Representative Natural Sources of C-Glycosidic Ellagitanins 16-28 Family Plant species Ellagitanins C-Glycosidics Found in Mirtales Combretaceae Anogeis sus acuminata 16, 17, 18, 19 Amogeis sus leiocarpus 16 Lumnitzera racemos a 16 Termina lía arjuna 16, 20, 22 Termina lia macroptera 27 Terminalía arborea 28 Thíloa glaucocarpa 16, 18 , 20, 21 Lythraceae Lagerstroemia flos reginea 16, 18, 20, 21, 22, 23, 24, 29 Lagerstroemia speciosa 16, 18, 19, 29 Melastomataceae Osbeckia chinensis 20, 22, 25 Tíbouchina semidecandra 16, 18, 20 Myrtaceae Callistemon lanceolatus 20 Eucalyptus alba 21, 22 Eugenia granais 16, 18 Kunzea ambigua 20 Melaleuca squarrosa 20, 21 Pimenta dioica 16, 18, 20, 22 Siphoneugena densifiora Syzygium agueum 16, 20 16, 18, 19 Syzygium aromaticum 20, 22 Punicácese Púnica granatum 20, 22, 25, 26, 27, 28 Trapaceae Trapa japonica 20 Tannin complexes (flavono-elagitanins) are characterized by a unique C-C condensed structure of C-glycosidic tannins (vescalagin type or stachyurin type) with flavan-3-ol (catechin or epicatechin). Unlike C-glycosidic tannins, these tannins have been found in a preferably limited number of plant species belonging to the families Combretaceae, Myrtaceae, Melastomataceae, Fagaceae, and Theaceae. Table 6 presents a representative list of ellagitannin complexes. Table 6 Representative Elaqitanin Complexes Acutisimin A Guayavina A Guayavina B Guavina A Guavina C Guavina D Malabatrin A Malabatrin E Malabatrin F Mongolicain A Mongolicain B Psidinin A Psidinin B Psidinin C Stenophylanine A Oligomeric ellagitannins are common among many plant families including Fagaceae, Rosaceae, Coriariaceae, Onagraceae, Melastomataceae, Myrtaceae, and Lythraceae. This class of tannins is divided into three subgroups based on structural characteristics: (1) oligomers containing a valoneoyl group or its equivalent, formed by intermolecular C-0 bonds between an HHDP group and a galloyl group of a neighboring monomer ; (2) macrocyclic oligomers formed by two C-O bonds; and (3) Cglycosidic tannin oligomers produced by C-C intermolecular bond formation between C-1 of one monomer and the aromatic ring of another. Table 7 presents a representative list of oligomeric ellagitannins. Table 7· Representative Oligomeric Elaqitanins C-Glycosidic Ellagitannin Dimers from Combretaceae Anogeisinin Anogeisusin A Anogeisusin B Castamolinin Other Ellagitannin Oligomers Alienanine B Benzylcation Casuarictin Casuglaunin B Cowaniina IVIAaZUZZUU / ¿04 Cufiina D1 Cufiina D2 Eugeniflorin D1 Eugeniflorin D2 Melasquanin A Melasquanin B Melasquanin C Melasquanin D Melastoflorin A Melastoflorin B Melastoflorin C Melastoflorin D Nobotanin B Nobotanin E Nobotanin F Nobotanin K Oenothein A Oenothein B Oenoterin T1 Oenoterin T2 Pterocaryanin C Reginan A Reginan B Reginan C Reginan D stachyurin Woodfordina C Woodfordina D Table 8 provides a representative list of other ellagitannins. Table 8. Other Representative Elaqitanins Acalifidine D1 Agrimonin Ascorgeraniin (Elaeocarpusine) Camellia tannin A Cameliatannin B Cameliatannin E Cameliatanina F iviAazuzzuu / ¿04 Cameliin B Coriariin A Dehydrogeraniin Eucalbanin B Eucalbanin C Euphorbine E Eurobustin C Furosinin Gemina A Geraniin Geraniinic Acid B Geraniinic Acid C Heterophilin E Hyrtelin A Hyrtelin B Hyrtelin O Laevigatin B Laevigatin C Laevigatin E Liquidambina Melastoflorin A Philantusiin A Philantusiin B Philantusin C Potentiline Putranjivain A Repandusinic Acid Rosenin A Rosenin B Rugosin D Rugosin E Rugosin F Rugosin G Tamarixin ina A Tamarixinin B Tamarixinin C Terquebine MA / a / 2U22 / UU 1204 Trapanin B Table 9 provides yet another representative list of ellagitannins, including known natural sources for some of them. Table 9. Representative Ellagitanins MA / a / 2U22 / UU 1204 Name Source(s) 2-0-galoyl-punicalina Casaurictlna Rhu tree, plant Estaquirus Castalagina & Vecalagina Pomegranate bark Castali na Casuarictina T. japonica Casuar!ina Leaves of the Bañaba tree Casuarinina Leaves of the Bañaba tree Casuari nina Granada Chebulagic acid T. chebula Chebulinic acid T. chebula Corilagin Granada Cornusiina A Cornusiina C Cornusiina E Epipunicacorteina A Leaves of the Bañaba tree Phlosin B Leaves of the Bañaba tree Unfortunately, most ellagitannins are poorly absorbed by the human intestine. However, a number of ellagitannin-derived metabolites are absorbed by the human intestine, including certain metabolites ultimately formed in the intestine by commensal microorganisms (i.e., intestinal microflora). Ellagitannins release ellagic acid under physiological conditions in vivo, and ellagic acid is then gradually metabolized by intestinal microflora in the intestine to produce urolithin A (UA), urolithin B, urolithin C, and urolithin D. Once the metabolites are absorbed, they are further metabolized to produce urolithin glucuronides and / or sulfates, to give a combination of metabolites secreted into the bile. Ellagic acid is normally found in relatively low amounts in plant tissues. Ellagic acid is thought to be derived from ellagitannins, which when broken down form hexahydroxydiphenic acid, which is spontaneously converted to ellagic acid. Some additional sources of ellagic acid are shown in Table 10. Table 10. Representative Sources of Ellagic Acid MA / a / 2U22 / UU f 204 Fruit Amount Acai 55.4 + 1.39 mg / L of fresh pulp Umbu 314 mg / 100 g dry weight (commercial) Camu-camu 490 mg / 100 g dry weight Cagaita 289 mg / 100 g dry weight (commercial) Aracá 262 mg / 100 g dry weight 218 mg / 100 g dry weight (commercial) Cambuci 240 mg / 100 g dry weight 512 mg / 100 g dry weight (commercial) Muscat grapes 219 mg / 100 g dry weight The fruits of the pomegranate (Púnica granatum) are ancient medicinal foods which have been used for centuries in popular medicine. They are consumed fresh and as juices, which is an excellent source of ellagitannins and ellagic acid. Ellagitannins in pomegranate fruit juice and peel include punicalin, punicalagin, corilagin, casuarinin, terminalin / galagildilactone, pedunculagin, telimagrandin, granatin A, and granatin B. Other parts of the pomegranate plant contain additional ellagitannins, including punicafolin, punicacortein A, punicacortein B, punicacortein C, punicacortein D, and punigluconin. Commercial juices contain galagyl-type ellagitannins, which include punicalagin isomers (1500-1900 mg / L), undefined hydrolyzable tannins (400-500 mg / L), and ellagic acid and its glycosides (120-260 mg / L). Gil et al. (2000) J. Agríe. Food Chem 48:4581-4589. Punicalagins, ellagitannins in which galagic and ellagic acids are linked to a glucose molecule, are abundant in pomegranate peel. Isomers of punicalagin and ellagic acid derivatives are not present in aril juice, but during industrial juice processing they are extracted from the shell membrane surrounding the arils and released in large quantities into the juice. Urolithins are metabolites of ellagic acid, punicalagin (PA), punicalin (PB), telimagrandin (TL), and other ellagitannins. Ellagic acid (EA) is abundant in pomegranate juice. Gil et al. (2000) J. Agríe. Food Chem 48:4581-4589. Ellagitannin telimagrandin (TL) has previously been isolated from pomegranate and other plants. The structural formulas for UA, PA, PB, EA, and TL are presented in Figure 2. As mentioned above, ellagitannins are generally not absorbed in the intestine. Preferably, they release EA in the intestine, which is poorly absorbed in the stomach and small intestine. EA is extensively metabolized by unidentified bacteria in the intestinal lumen to produce urolithins. Microbial metabolism begins in the small intestine and the first metabolites produced retain four phenolic hydroxyls (urolithin D, four hydroxyl groups), and these are further metabolized throughout the intestinal tract to remove hydroxyl units that lead to urolithin C (three hydroxyls). , urolithin A (two hydroxyls) and B (one hydroxyl) in the distal parts of the colon (Figure 3). The absorbed metabolites are conjugated with glucuronic acid (one or two units), and / or methyl ethers (when other ortho-dihydroxyl groups are present). Urolithin A and B conjugates are the main metabolites detected in plasma and urine, although some trihydroxy derivatives (hydroxyl-UA) or EA-dimethyl ether glucuronide have also been detected in smaller quantities. Tetrahydroxy-urolithins, trihydroxy-urolithins, and EA derivatives are generally not detected in peripheral plasma, but are absorbed in the small intestine and transported to the liver where they are further metabolized and excreted with bile to the small intestine, establishing a circulation. enterohepatic that is responsible for the relatively long life of urolithins in plasma and urine. In addition to natural food sources, many roles have emerged in the biosynthesis, isolation, and biological activity of tannins, especially ellagitannins, over the past twenty years. Accessing pure ellagitannins by isolation from natural sources can be cumbersome and provide only relatively small amounts of pure natural products. See, for example, Okuda et al., (1982) Chem Pharm Bull. 30:4230-4233; Okuda et al. (1982) Chem Pharm Bull. 30:234-4236. It is therefore notable that methods for the total synthesis of many ellagitannins are known. See, for example, MA / a / ¿U¿¿ / UU f ¿04 Khanbabaee, K., Strategies for the synthesis of ellagitannins, In: Chemistry and Biology of Ellagitannins, Ed. S. Quideau, World Scientific Publishing, Singapore, 2009, pp. 152-202, which include references cited therein. Methods to Increase Autophagy, Increase Longevity, and Treat or Prevent Diseases and Disorders Using Urolithins and Related Compounds In certain embodiments, the invention provides methods for increasing or improving autophagy, both in vivo and in vitro, methods for increasing longevity, and methods for treating or preventing various diseases and conditions using urolithins and precursors thereof. In particular embodiments, a disease or disorder treated or prevented in accordance with the present invention is a disease or disorder associated with reduced autophagy, or which could benefit from increased autophagy, including but not limited to any of the conditions and diseases described herein. One aspect of the invention is a method of treating or preventing a disease or condition associated with, or characterized by, reduced or decreased autophagy, or which could benefit from increased autophagy. The method includes the step of administering to a subject in need thereof a therapeutically effective amount of a urolithin or precursor thereof. In particular embodiments, any of the urolithins or precursors thereof described herein may be used to practice any aspect of the invention. As used herein, unless the context makes otherwise clear, "treats", and similar words such as "treatment", "treated", "treat", etc., indicate a procedure to obtain beneficial results or desired, including clinical outcomes. Treatment may optionally involve either reducing or alleviating symptoms of the disease or condition, or slowing the progression of the disease or condition. In some modalities, treatment is achieved by reducing the duration of the disease or condition. Administration of a compound described herein may, in some embodiments, treat one or more of such symptoms. As used herein, unless the context makes otherwise clear, "prevents", and similar words such as "prevention", "prevented", "prevent", etc., indicate a procedure to prevent, inhibit or reduce the likelihood of the onset or recurrence of a disease or condition. It also refers to preventing, inhibiting, or reducing the probability of the appearance or recurrence of the symptom of a disease or condition, or optionally a procedure to delay the onset or recurrence of a disease or condition or delay the appearance or recurrence of the symptoms of a disease or condition. an illness or condition. As used herein, “prevents” and similar words also include reducing the intensity, effect, symptoms, or burden of a disease or condition prior to the onset or recurrence of the disease or condition. MA / a / ¿U¿¿ / UU f ¿04 One aspect of the invention is a method for increasing autophagy in a cell, which comprises the step of contacting a cell with an effective amount of a urolithin or a precursor thereof to increase autophagy in the cell. In particular embodiments, the cell is present within a subject, for example, a mammal. Furthermore, the invention includes a method for increasing autophagy in a cell, wherein the cell is present in a subject, for example, a mammal, comprising the step of providing the subject with an effective amount of a urolithin or a precursor of the itself to increase autophagy in the cell. One aspect of the invention is a method for increasing autophagy in a cell, which comprises the step of contacting a cell with an effective amount of a urolithin, or a precursor thereof, to increase autophagy in the cell. In particular embodiments, a urolithin is a compound having a structure set forth in Formula I, Formula II, or Formula III, including any of the specific compounds of Formula II or Formula III described herein. An "effective amount" as used herein refers to an amount that is sufficient to achieve or realize a desired or specified biological effect. For example, an effective amount of a urolithin to increase autophagy in a cell is an amount of a urolithin that is sufficient to increase autophagy in the cell. An increase in autophagy in a cell can be measured using any assay suitable for measuring autophagy. For example, autophagy formation can be determined using the fluorescent dye monodansylcadaverine (MDC) (Sigma-Aldrich, 30432). This dye selectively labels autophagic vacuoles. Biederbick A et al. (1995) Eur. J. Cell. Biol. 66:3-14. Autophagy can also be determined by examining the change in the ratio of proteins involved in autophagy, such as LC3-II to LC3-I, for example, using Western blot analysis. With such a method, an increase in the LC3-II / LC3-I ratio in a treated cell above the baseline LC3-II / LC3-I ratio of untreated cells could be considered as an increase in autophagy. Examination of other protein levels such as p62 may also aid in confirmation. For the purposes of calculating the percentage (%) increase in autophagy in a cell, the ratio of LC3-II / LC3I at baseline (Ratio B) and the ratio of LC3-II / LC3-I during treatment ( Relationship T) can be used. The percentage (%) increase can be determined mathematically, for example, by the Formula 100x[((T Ratio)-(B Ratio)) / (B Ratio)]. Autophagy is said to be increased in a cell if it is measurably greater than autophagy is, or could be present in an untreated or placebo control cell. In one embodiment, autophagy is said to be increased in a cell if it is greater by a statistically significant amount or degree than autophagy is, or could be, present in an untreated or placebo control cell. In certain embodiments, the increase in autophagy is an increase of at least 5%, at least 10%, at least 15%, at least 20%, at least 25%, at least 30%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, at least 90%, at least 100%, at least 150%, at least 200%, at least 300%, at least 400%, at least 500%, at least 600%, at least 700%, at least 800%, at least 900%, at least 1,000% or greater than 1,000%, compared to the level of autophagy present in an untreated cell or a cell treated with a placebo. In certain embodiments, the increase in autophagy is an increase of 5-500%, 10500%, 15-500%, 20-500%, 25-500%, 30-500%, 40-500%, 50-500% , 60-500%, at least 70-500%, 80-500%, 90-500%, 100-500%, 150-500%, 200-500%, 300-500%, OR 400-500%, 51,000%, 10-500%, 15-1,000%, 20-1,000%, 25-1,000%, 30-1,000%, 40-1,000%, 50-1,000%, 601,000%, at least 70-1,000%, 80-1,000%, 90-1000%, 100-1000%, 150-1000%, 200-1000%, 300-1000%, 400-1000%, 500-1000%, 600-1000%, 700-1000%, 800-1000% or 900-1,000%, compared to the level of autophagy present in an untreated cell or a cell treated with a placebo. In one embodiment, autophagy is mitophagy. In one embodiment, urolithin is an isolated urolithin. In one embodiment, the urolithin is a purified urolithin. In one embodiment, urolithin is selected from the group consisting of urolithin A, urolithin B, urolithin C, urolithin D, and any combination thereof. In one embodiment, the urolithin is urolithin A. In one embodiment, the urolithin is urolithin B. In one embodiment, the urolithin is urolithin C. In one embodiment, the urolithin is urolithin D. In certain embodiments, urolithin is a compound of Formula I, Formula II, or Formula III, which includes any of the specific compounds of these formulas described herein. In one embodiment, the urolithin precursor is an isolated urolithin precursor. In one embodiment, the urolithin precursor is a purified urolithin precursor. In certain embodiments, the urolithin precursor is a compound of Formula IV, Formula V, or Formula VI, which includes any of the specific compounds of these formulas described herein. In one embodiment, the urolithin precursor is selected from the group consisting of ellagic acid, an ellagitannin, and any combination thereof. In one embodiment, the urolithin precursor is ellagic acid. In one embodiment, the urolithin precursor is an ellagitannin. In one embodiment, ellagitannin is selected from the group consisting of castalagin, castalin, casuarictin, chebulagic acid, chebulinic acid, gemin D, ΜΛ / a / ZUZZ / UU l ¿04 grandinine, pedunculagin, punicalagin, punicalin, roburin A, strychtin, telimagrandin I, telimagrandin II, terflavin A, terflavin B, tergalagin, Lambertianin C, Sanguiina H-6, Sanguiina H-10, and vescalagin. In one embodiment, the cell is selected from the group consisting of: embryonic stem cells, induced pluripotent stem cells, adult stem cells, differentiated cells, blood cells, hematopoietic cells, epithelial cells, exocrine cells, endocrine cells, connective tissue cells, adipose cells, bone cells, smooth muscle cells, striated muscle cells, nerve cells, sensory cells, cardiac cells, liver cells, gastric cells, intestinal cells, lung cells, kidney cells, and germ cells . In one embodiment, the cell is selected from the group consisting of: endothelial cells, cells of the central and peripheral nervous system (neurons (all types) and glial cells (microglia, astroglia and oligodendrocytes, Schwann cells), keratinocytes ( skin cells), retinal cells, immune cells, also hair cells and follicular stem cells, and cancer stem cells. In certain embodiments, the cells are embryonic stem cells. In certain embodiments, the cells are induced pluripotent stem cells. In certain embodiments, the cells are induced pluripotent stem cells. embodiments, the cells are adult stem cells. In certain embodiments, the cells are hematopoietic stem cells. In certain embodiments the cells are cancer cells. In certain embodiments, the cells are present in an isolated organ or block of organs, such as a organ or block of organs harvested by transplantation or maintained ex vivo In certain embodiments, the cells are present in a tissue or slice of tissue. In various embodiments, cells are contacted with urolithin or precursor thereof in vivo, ex vivo, or in vitro. One aspect of the invention is a method for increasing longevity in an animal, which comprises the step of administering to an animal in need thereof an effective amount of a urolithin or a precursor thereof to increase autophagy in the animal, of this way increasing the longevity of the animal. The term "longevity" as used herein in reference to the longevity of an animal refers to the lifespan of an individual organism. Although longevity can be measured in an individual organism, it is common to measure and compare average or median of populations of individual organisms. For example, longevity can be measured and compared as mean survival in an experimental treatment group and an appropriately selected placebo or untreated control group. Longevity can also be considered in populations of individuals affected with a health condition in need of autophagy. Treatment of such individuals should increase their longevity compared to their untreated counterparts. In one embodiment, longevity is actual longevity. In one embodiment, longevity is actuarial longevity. iviAazuzzuu / ¿04 The term "longevity" as used herein with reference to the longevity of eukaryotic cells in vitro refers to the lifespan of an individual cell. Although longevity can be measured for an individual cell, it is common to measure and compare longevity mean or median of individual cell populations. For example, longevity can be measured and compared in terms of mean survival in an experimental treatment group and an appropriately selected placebo or untreated control group. The term “longevity” is also used refers to the useful life of a cell that is subjected to certain metabolic stress. In one embodiment, the metabolic stresses are due to nutrient starvation, growth factor suppression, or hypoxia. For example, the treatment of metabolically stressed cells by a urolithin or a precursor, either directly in vitro, ex vivo or in vivo by administration to a subject, could lead to an increase in the longevity of these metabolically stressed cells and in the case of ex vivo and in vivo treatment, increased longevity of these metabolically stressed cells could improve the function of tissues which they comprise. In one embodiment, longevity is said to be increased when it is at least 5 percent longer than the untreated control. In several specific embodiments, longevity is said to increase when it is at least 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 , 23, 24, 25, 26, 27, 28, 29, 30, 31,32, 33, 34, 35, 36, 37, 38, 39, 40, 41,42, 43, 44, 45, 46, 47 , 48, 49, or 50 percent longer than the untreated control. In certain embodiments, longevity is increased by at least 10 percent compared to the untreated control. In certain embodiments, longevity is increased by at least 20 percent compared to the untreated control. In certain embodiments, longevity is increased by at least 30 percent compared to the untreated control. In certain embodiments, longevity is increased by at least 40 percent compared to the untreated control. In certain embodiments, longevity is increased by at least 50 percent compared to the untreated control. In one embodiment, longevity is said to be increased when it is at least 5 percent longer than the placebo control. In several specific embodiments, longevity is said to increase when it is at least 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 , 23, 24, 25, 26, 27, 28, 29, 30, 31,32, 33, 34, 35, 36, 37, 38, 39, 40, 41,42, 43, 44, 45, 46, 47 , 48, 49, or 50 percent longer than the placebo control. In certain modalities, longevity is increased by at least 10 percent compared to the placebo control. In certain modalities, longevity is increased by at least 20 percent compared to the placebo control. In certain modalities, longevity is increased by at least 30 percent compared to the placebo control. In certain modalities, longevity is increased by at least 40 percent compared to the placebo control. In certain modalities, longevity is increased by at least 50 percent compared to the placebo control. In one embodiment, longevity is said to increase the longer it is, by a statistically significant difference, compared to the untreated control. In one embodiment, the statistical significance of the difference is p s 0.05. In one embodiment, the statistical significance of the difference is p < 0.01. In one embodiment, the statistical significance of the difference is p < 0.005. In one embodiment, the statistical significance of the difference is p < 0.001. In one embodiment, longevity is said to increase the longer it is, by a statistically significant difference, compared to the placebo control. In one embodiment, the statistical significance of the difference is p s 0.05. In one embodiment, the statistical significance of the difference is p < 0.01. In one embodiment, the statistical significance of the difference is p < 0.005. In one embodiment, the statistical significance of the difference is p < 0.001. An animal is any multicellular eukaryote that belongs to the kingdom Animalia. In one embodiment an animal is an invertebrate, for example a nematode (e.g., C. elegans) or a fruit fly (e.g., D. melanogaster). In one embodiment, an animal is a vertebrate, for example a fish or a mammal. In one embodiment, an animal is a mammal. In one embodiment, an animal is a primate. In one embodiment, an animal is a human. In certain embodiments, an animal is a domestic animal, such as a dog or cat. In certain embodiments, an animal is livestock, such as a horse, cow, or sheep. In one embodiment, urolithin is an isolated urolithin. In one embodiment, the urolithin is a purified urolithin. In one embodiment, urolithin is selected from the group consisting of urolithin A, urolithin B, urolithin C, urolithin D, and any combination thereof. In one embodiment, the urolithin is urolithin A. In one embodiment, the urolithin is urolithin B. In one embodiment, the urolithin is urolithin C. In one embodiment, the urolithin is urolithin D. In certain embodiments, urolithin is a compound of Formula I, Formula II, or Formula III, which includes any of the specific compounds of these formulas described herein. In one embodiment, the urolithin precursor is an isolated urolithin precursor. In one embodiment, the urolithin precursor is a purified urolithin precursor. In certain embodiments, the urolithin precursor is a compound of Formula IV, Formula V, or Formula VI, which includes any of the specific compounds of these formulas described herein. In one embodiment, the urolithin precursor is selected from the group consisting of ellagic acid, an ellagitannin, and any combination thereof. MA / a / ¿U¿¿ / UU f ¿04 In one embodiment, the urolithin precursor is ellagic acid. In one embodiment, the urolithin precursor is an ellagitannin. In one embodiment, ellagitannin is selected from the group consisting of castalagin, castalin, casuarictin, chebulagic acid, chebulinic acid, gemin D, grandinin, pedunculagin, punicalagin, punicalin, roburin A, strychtin, telimagrandin I, telimagrandin II, terflavin A, terflavin B, tergalagin, Lambertianin C, Sanguiina H-6, Sanguiina H-10, and vescalagin. One aspect of the invention is a method for increasing the longevity of eukaryotic cells in vitro, the method comprises the step of contacting the eukaryotic cells in vitro with an effective amount of a urolithin to increase autophagy in the cells, thereby increasing the longevity of eukaryotic cells in vitro. In accordance with the invention, urolithins can be used as a cell culture reagent to help promote the growth and preservation of cells and tissues in culture. It is believed that urolithin has the potential to keep primary cells and tissues alive for prolonged periods of time, which means that it could be used for a wide range of in vitro applications including: (i) routine cell culture in laboratories. investigation of cell lines, primary cells of any origin (i.e., recently isolated from humans or animals); and (i) tissues or organs that are maintained in culture. For both cells and tissues maintained in culture, these could also have in vitro diagnostic applications as well as therapeutic applications, such as: tissue expansion, protection during transport (for transplantation in humans), for cell therapy applications using primary cells which need to be frozen in storage, so they can be part of a special solution for cell freezing. The invention includes a method for culturing or preserving cells or tissues, comprising growing or culturing the cells or tissues in a culture medium comprising a urolithin. Cell culture media suitable for culturing and growing various cells and tissues are known in the art and are commercially available. Urolithins and precursors thereof may also find use as positive controls when tested for autophagy and improved mitochondrial function in a cell, tissue or organism. For example, a urolithin can be used separately or included as part of a kit useful for examining mitochondrial function or longevity-related pathways such as the mTOR pathway. In one embodiment, autophagy is mitophagy. In one embodiment, urolithin is an isolated urolithin. In one embodiment, the urolithin is a purified urolithin. In one embodiment, urolithin is selected from the group consisting of urolithin A, urolithin B, urolithin C, urolithin D, and any combination thereof. In one embodiment, the urolithin is urolithin A. In one embodiment, the urolithin is urolithin B. In one embodiment, the urolithin is urolithin C. In one embodiment, the urolithin is urolithin D. In certain embodiments, urolithin is a compound of Formula I, Formula II, or Formula III, which includes any of the specific compounds of these formulas described herein. In one embodiment, the urolithin precursor is an isolated urolithin precursor. In one embodiment, the urolithin precursor is a purified urolithin precursor. In certain embodiments, the urolithin precursor is a compound of Formula IV, Formula V, or Formula VI, which includes any of the specific compounds of these formulas described herein. In one embodiment, the urolithin precursor is selected from the group consisting of ellagic acid, an ellagitannin, and any combination thereof. In one embodiment, the urolithin precursor is ellagic acid. In one embodiment, the urolithin precursor is an ellagitannin. In one embodiment, ellagitannin is selected from the group consisting of castalagin, castalin, casuarictin, chebulagic acid, chebulinic acid, gemin D, grandinin, pedunculagin, punicalagin, punicalin, roburin A, strychtin, telimagrandin I, telimagrandin II, terflavin A, terflavin B, tergalagin, Lambertianin C, Sanguiina H-6, Sanguiina H-10, and vescalagin. In one embodiment, the eukaryotic cells are eukaryotic cells in primary culture. In one embodiment, the eukaryotic cells are part of a cell line. In one embodiment, the eukaryotic cells are selected from the group consisting of: embryonic stem cells, induced pluripotent stem cells, adult stem cells, differentiated cells, blood cells, hematopoietic cells, epithelial cells, exocrine cells, endocrine cells. , connective tissue cells, adipose cells, bone cells, smooth muscle cells, striated muscle cells, nerve cells, sensory cells, cardiac cells, liver cells, gastric cells, intestinal cells, lung cells, kidney cells, and cells germinal. In certain embodiments, the cells are embryonic stem cells. In certain embodiments, the cells are induced pluripotent stem cells. In one embodiment, the cell is selected from the group consisting of: endothelial cells, cells of the central and peripheral nervous system (neurons (all types) and glial cells (microglia, astroglia and oligodendrocytes, Schwann cells), keratinocytes ( skin cells), retinal cells, immune cells, also hair cells and follicular stem cells, and cancer stem cells. In certain embodiments, the cells are adult stem cells. In certain embodiments, the cells are hematopoietic stem cells. In certain embodiments, the cells are hematopoietic stem cells. modalities the cells are cancer cells. In certain embodiments, the cell is present in an isolated tissue or organ or portion or sample thereof. In certain embodiments, the cells are present in an isolated organ or organ block, such as an organ or organ block harvested by transplant or maintained ex vivo. In certain embodiments, the cells are present in a tissue or slice of tissue. In particular embodiments, the cell is present in a primary culture, i.e., a "primary cell." As used herein, "primary culture" refers to cells cultured directly from a tissue or subject. In one embodiment, a primary culture includes two or more types of cells. In one embodiment, a primary culture includes a single type of cell, for example, endothelial cells. Cells in primary culture can often have only a limited number of passages or divisions. In particular embodiments, the cell is present in a cell line. As used herein, a "cell line" refers to an established, immortalized and genetically homogeneous population of cells derived from a eukaryotic animal and maintained in vitro. In one embodiment, a cell line is derived from a mammal. In one embodiment, a cell line is derived from a mammal. In another embodiment, a cell line is derived from a human. Cell lines of many types are available from a number of commercial suppliers, including, for example, the American Type Culture Collection (ATCC), Manassas, Virginia. In certain embodiments, the invention relates to a method of increasing autophagy in a cell, comprising contacting the cell with an effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, thereby increasing autophagy in the cell. In certain embodiments, the invention relates to any of the methods mentioned above, wherein autophagy is mitophagy. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin A. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin B. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin C. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin D. MA / a / 2U22 / UU f 204 In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is ellagic acid. In certain embodiments, the invention relates to any of the aforementioned methods, wherein the cell is selected from the group consisting of: embryonic stem cells, induced pluripotent stem cells, adult stem cells, differentiated cells, cells of the blood, hematopoietic cells, epithelial cells, exocrine cells, endocrine cells, connective tissue cells, adipose cells, bone cells, smooth muscle cells, striated muscle cells, nerve cells, sensory cells, cardiac cells, liver cells, cells gastric cells, intestinal cells, lung cells, kidney cells, and germ cells. In certain embodiments, the invention relates to a method of increasing longevity in an animal, comprising administering to an animal in need thereof an effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, thus increasing the longevity of the animal. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin A. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin B. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin C. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin D. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is ellagic acid. In certain embodiments, the invention relates to any of the aforementioned methods, wherein the animal is a mammal. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the mammal is a human. In certain embodiments, the invention relates to a method for increasing the longevity of eukaryotic cells in vitro, which comprises contacting the eukaryotic cells in vitro with an effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, thereby increasing the longevity of eukaryotic cells in vitro. IVIA / a / ¿U¿¿ / UU f ¿04 In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin A. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin B. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin C. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin D. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is ellagic acid. In certain embodiments, the invention relates to any of the aforementioned methods, wherein the eukaryotic cells are eukaryotic cells in primary culture. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the eukaryotic cells are part of a cell line. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the eukaryotic cells are cells selected from the group consisting of: embryonic stem cells, induced pluripotent stem cells, adult stem cells, differentiated cells, blood, hematopoietic cells, epithelial cells, exocrine cells, endocrine cells, connective tissue cells, adipose cells, bone cells, smooth muscle cells, striated muscle cells, nerve cells, sensory cells, cardiac cells, liver cells , gastric cells, intestinal cells, lung cells, kidney cells, and germ cells. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the eukaryotic cells are cells selected from the group consisting of: embryonic stem cells, induced pluripotent stem cells, and adult stem cells. In certain embodiments, the invention relates to a method of increasing autophagy in a cell, comprising contacting the cell with an effective amount of a compound of Formula I, thereby increasing autophagy in the cell; where the compound of Formula I is EITHER Formula I MA / a / 2U22 / UU 1204 where 100 R1, R2, R3, R4, R5, R6, R7, and R8 are independently selected from the group consisting of H and OR; and R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide. In certain embodiments, the invention relates to any of the methods mentioned above, wherein autophagy is mitophagy. In certain embodiments, the invention relates to any of the aforementioned methods, wherein the cell is selected from the group consisting of: embryonic stem cells, induced pluripotent stem cells, adult stem cells, differentiated cells, cells of the blood, hematopoietic cells, epithelial cells, exocrine cells, endocrine cells, connective tissue cells, adipose cells, bone cells, smooth muscle cells, striated muscle cells, nerve cells, sensory cells, cardiac cells, liver cells, cells gastric cells, intestinal cells, lung cells, kidney cells, and germ cells. In certain embodiments, the invention relates to a method of increasing longevity in an animal, comprising administering to an animal in need thereof an effective amount of a compound of Formula I, thereby increasing the longevity of the animal, wherein the compound of Formula I is IVIA / a / ZUZZ / UU í ¿04 Formula I where R1, R2, R3, R4, R5, R6, R7, and R8 are independently selected from the group consisting of H and OR; and R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide. In certain embodiments, the invention relates to any of the aforementioned methods, wherein the animal is a mammal. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the mammal is a human. In certain embodiments, the invention relates to a method for increasing the longevity of eukaryotic cells in vitro, which comprises bringing the cells into contact 101 eukaryotic cells in vitro with an effective amount of a compound of Formula I, thereby increasing the longevity of eukaryotic cells in vitro, wherein the compound of Formula I is MA / a / 2U22 / UU 1204 where R1, R2, R3, R4, R5, R6, R7, and R8 are independently selected from the group consisting of H and OR; and R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide. In certain embodiments, the invention relates to any of the aforementioned methods, wherein the eukaryotic cells are eukaryotic cells in primary culture. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the eukaryotic cells are part of a cell line. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the eukaryotic cells are cells selected from the group consisting of: embryonic stem cells, induced pluripotent stem cells, adult stem cells, differentiated cells, blood, hematopoietic cells, epithelial cells, exocrine cells, endocrine cells, connective tissue cells, adipose cells, bone cells, smooth muscle cells, striated muscle cells, nerve cells, sensory cells, cardiac cells, liver cells , gastric cells, intestinal cells, lung cells, kidney cells, and germ cells. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the eukaryotic cells are cells selected from the group consisting of: embryonic stem cells, induced pluripotent stem cells, and adult stem cells. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R3, R4, R5, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein at least one of R1, R2, R3, R4, R5, R6, R7, and R8 is OR. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein at least two of R1, R2, R3, R4, R5, R6, R7, and R8 are OR. 102 In certain embodiments, the Invention relates to any of the aforementioned methods, where at least three of R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein at least four of R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein at least five of R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein at least six of R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein at least seven of R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the Invention relates to any of the methods mentioned above, where R1, R2, R3, R4, R5, R6, R7, and R8 are OR. In certain embodiments, the invention relates to any of the methods mentioned above, where R1 is OR; and R2, R3, R4, R5, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the methods mentioned above, where R2 is OR; and R1, R3, R4, R5, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the methods mentioned above, where R3 is OR; and R1, R2, R4, R5, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R4 is OR; and R1, R2, R3, R5, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R5 is OR; and R1, R2, R3, R4, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R6 is OR; and R1, R2, R3, R4, R5, R7, and R8 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R7 is OR; and R1, R2, R3, R4, R5, R6, and R8 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R8 is OR; and R1, R2, R3, R4, R5, R6, and R7 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R1 and R2 are OR; and R3, R4, R5, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1 and R3 are OR; and R2, R4, R5, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R1 and R4 are OR; and R2, R3, R5, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1 and R5 are OR; and R2, R3, R4, R6, R7, and R8 are H. iviAazuzzuu / ¿04 In certain embodiments, the invention above, wherein R1 and R6 are OR; In certain embodiments, the invention above, wherein R1 and R7 are OR; In certain embodiments, the invention above, wherein R1 and R8 are OR; In certain embodiments, the invention above, wherein R2 and R3 are OR; In certain embodiments, the invention above, wherein R2 and R4 are OR; In certain embodiments, the invention above, wherein R2 and R5 are OR; In certain embodiments, the invention above, wherein R2 and R6 are OR; In certain embodiments, the invention above, wherein R2 and R7 are OR; In certain embodiments, the invention above, wherein R2 and R8 are OR; In certain embodiments, the invention above, wherein R3 and R4 are OR; In certain embodiments, the invention above, wherein R3 and R5 are OR; In certain embodiments, the invention above, wherein R3 and R6 are OR; In certain embodiments, the invention above, wherein R3 and R7 are OR; In certain embodiments, the invention above, wherein R3 and R8 are OR; In certain embodiments, the invention above, wherein R4 and R5 are OR; In certain embodiments, the invention above, wherein R4 and R6 are OR; In certain embodiments, the invention above, wherein R4 and R7 are OR; In certain embodiments, the invention above, wherein R4 and R8 are OR; 103 refers to any of the mentioned methods and R2, R3, R4, R5, R7, and R8 are H. refers to any of the mentioned methods and R2, R3, R4, R5, R6, and R8 are H. refers to any of the mentioned methods and R2, R3, R4, R5, R6, and R7 are H. refers to any of the mentioned methods and R1, R4, R5, R6, R7, and R8 are H. refers to any of the mentioned methods and R1, R3, R5, R6, R7, and R8 are H. refers to any of the mentioned methods and R1, R3, R4, R6, R7, and R8 are H. refers to any of the mentioned methods and R1, R3, R4, R5, R7, and R8 are H. refers to any of the mentioned methods and R1, R3, R4, R5, R6, and R8 are H. refers to any of the mentioned methods and R1, R3, R4, R5, R6, and R7 are H. refers to any of the mentioned methods and R1, R2, R5, R6, R7, and R8 are H. refers to any of the mentioned methods and R1, R2, R4, R6, R7, and R8 are H. refers to any of the mentioned methods and R1, R2, R4, R5, R7, and R8 are H. refers to any of the mentioned methods and R1, R2, R4, R5, R6, and R8 are H. refers to any of the mentioned methods and R1, R2, R4, R5, R6, and R7 are H. refers to any of the mentioned methods and R1, R2, R3, R6, R7, and R8 are H. refers to any of the mentioned methods and R1, R2, R3, R5, R7, and R8 are H. refers to any of the mentioned methods and R1, R2, R3, R5, R6, and R8 are H. refers to any of the mentioned methods and R1, R2, R3, R5, R6, and R7 are H. IVIA3ZUZZUU / ¿04 In certain embodiments, the invention above, wherein R5 and R6 are OR; In certain embodiments, the invention above, wherein R5 and R7 are OR; In certain embodiments, the invention above, wherein R5 and R8 are OR; In certain embodiments, the invention above, wherein R6 and R7 are OR; In certain embodiments, the invention above, wherein R6 and R8 are OR; In certain embodiments, the invention above, wherein R7 and R8 are OR; In certain embodiments, the invention above, where R1, R2, and R3 are In certain embodiments, the invention above, where R1, R2, and R4 are In certain embodiments, the invention above, where R1, R2, and R5 are In certain embodiments, the invention above, where R1, R2, and R6 are In certain embodiments, the invention above, where R1, R2, and R7 are In certain embodiments, the invention above, where R1, R2, and R8 are In certain embodiments, the invention above, where R1, R3, and R4 are In certain embodiments, the invention above, where R1, R3, and R5 are In certain embodiments, the invention above, where R1, R3, and R6 are In certain embodiments, the invention above, where R1, R3, and R7 are In certain embodiments, the invention above, where R1, R3, and R8 are are In certain embodiments, the invention above, where R1, R4, and R5 are 104 refers to any of the mentioned methods and R1, R2, R3, R4, R7, and R8 are H. refers to any of the mentioned methods and R1, R2, R3, R4, R6, and R8 are H. refers to any of the mentioned methods and R1, R2, R3, R4, R6, and R7 are H. refers to any of the mentioned methods and R1, R2, R3, R4, R5, and R8 are H. refers to any of the mentioned methods and R1, R2, R3, R4, R5, and R7 are H. refers to any of the mentioned methods and R1, R2, R3, R4, R5, and R6 are H. refers to any of the methods mentioned OR; and R4, R5, R6, R7, and R8 are H. refers to any of the methods mentioned OR; and R3, R5, R6, R7, and R8 are H. refers to any of the methods mentioned OR; and R3, R4, R6, R7, and R8 are H. refers to any of the methods mentioned OR; and R3, R4, R5, R7, and R8 are H. refers to any of the methods mentioned OR; and R3, R4, R5, R6, and R8 are H. refers to any of the methods mentioned OR; and R3, R4, R5, R6, and R7 are H. refers to any of the methods mentioned OR; and R2, R5, R6, R7, and R8 are H. refers to any of the methods mentioned OR; and R2, R4, R6, R7, and R8 are H. refers to any of the methods mentioned OR; and R2, R4, R5, R7, and R8 are H. refers to any of the methods mentioned OR; and R2, R4, R5, R6, and R8 are H. refers to any of the methods mentioned OR; and R2, R4, R5, R6, and R7 are H. refers to any of the methods mentioned OR; and R2, R3, R6, R7, and R8 are H. IVIAaZUZZUU / ¿04 In certain embodiments, the invention above, where R1, R4, and R6 are In certain embodiments, the invention above, where R1, R4, and R7 are In certain embodiments, the invention above, where R1, R4, and R8 are In certain embodiments, the invention above, where R1, R5, and R6 are In certain embodiments, the invention above, where R1, R5, and R7 are In certain embodiments, the invention above, where R1, R5, and R8 are In certain embodiments, the invention above, where R1, R6, and R7 are In certain embodiments, the invention above, where R1, R6, and R8 are In certain embodiments, the invention above, where R1, R7, and R8 are In certain embodiments, the invention above, where R2, R3, and R4 are In certain embodiments, the invention above, where R2, R3, and R5 are In certain embodiments, the invention above, where R2, R3, and R6 are In certain embodiments, the invention above, where R2, R3, and R7 are In certain embodiments, the invention above, where R2, R3, and R8 are In certain embodiments, the invention above, where R2, R4, and R5 are In certain embodiments, the invention above, where R2, R4, and R6 are In certain embodiments, the invention above, where R2, R4, and R7 are In certain embodiments, the invention above, where R2, R4, and R8 are 105 refers to any of the mentioned OR methods; and R2, R3, R5, R7, and R8 are H. refers to any of the methods mentioned OR; and R2, R3, R5, R6, and R8 are H. refers to any of the methods mentioned OR; and R2, R3, R5, R6, and R7 are H. refers to any of the methods mentioned OR; and R2, R3, R4, R7, and R8 are H. refers to any of the methods mentioned OR; and R2, R3, R4, R6, and R8 are H. refers to any of the methods mentioned OR; and R2, R3, R4, R6, and R7 are H. refers to any of the methods mentioned OR; and R2, R3, R4, R5, and R8 are H. refers to any of the methods mentioned OR; and R2, R3, R4, R5, and R7 are H. refers to any of the methods mentioned OR; and R2, R3, R4, R5, and R7 are H. refers to any of the methods mentioned OR; and R1, R5, R6, R7, and R8 are H. refers to any of the methods mentioned OR; and R1, R4, R6, R7, and R8 are H. refers to any of the methods mentioned OR; and R1, R4, R5, R7, and R8 are H. refers to any of the methods mentioned OR; and R1, R4, R5, R6, and R8 are H. refers to any of the methods mentioned OR; and R1, R4, R5, R6, and R7 are H. refers to any of the methods mentioned OR; and R1, R3, R6, R7, and R8 are H. refers to any of the methods mentioned OR; and R1, R3, R5, R7, and R8 are H. refers to any of the methods mentioned OR; and R1, R3, R5, R6, and R8 are H. refers to any of the methods mentioned OR; and R1, R3, R5, R6, and R7 are H. ΜΛ / a / ZUZZ / UU l ¿04 In certain embodiments, the invention above, where R2, R5, and R6 are In certain embodiments, the invention above, where R2, R5, and R7 are In certain embodiments, the invention above, where R2, R5, and R8 are In certain embodiments, the invention above, where R2, R6, and R7 are In certain embodiments, the invention above, where R2, R6, and R8 are In certain embodiments, the invention above, where R2, R7, and R8 are In certain embodiments, the invention above, where R3, R4, and R5 are In certain embodiments, the invention above, where R3, R4, and R6 are In certain embodiments, the invention above, where R3, R4, and R7 are In certain embodiments, the invention above, where R3, R4, and R8 are In certain embodiments, the invention above, where R3, R5, and R6 are In certain embodiments, the invention above, where R3, R5, and R7 are In certain embodiments, the invention above, where R3, R5, and R8 are In certain embodiments, the invention above, where R3, R6, and R7 are In certain embodiments, the invention above, where R3, R6, and R8 are In certain embodiments, the invention above, where R3, R7, and R8 are In certain embodiments, the invention above, where R4, R5, and R6 are In certain embodiments, the invention above, where R4, R5, and R7 are 106 refers to any of the mentioned OR methods; and R1, R3, R4, R7, and R8 are H. refers to any of the methods mentioned OR; and R1, R3, R4, R6, and R8 are H. refers to any of the methods mentioned OR; and R1, R3, R4, R7, and R8 are H. refers to any of the methods mentioned OR; and R1, R3, R4, R5, and R8 are H. refers to any of the methods mentioned OR; and R1, R3, R4, R5, and R7 are H. refers to any of the methods mentioned OR; and R1, R3, R4, R5, and R6 are H. refers to any of the methods mentioned OR; and R1, R2, R6, R7, and R8 are H. refers to any of the methods mentioned OR; and R1, R2, R5, R7, and R8 are H. refers to any of the methods mentioned OR; and R1, R2, R5, R6, and R8 are H. refers to any of the methods mentioned OR; and R1, R2, R5, R6, and R7 are H. refers to any of the methods mentioned OR; and R1, R2, R4, R7, and R8 are H. refers to any of the methods mentioned OR; and R1, R2, R4, R6, and R8 are H. refers to any of the methods mentioned OR; and R1, R2, R4, R6, and R7 are H. refers to any of the methods mentioned OR; and R1, R2, R4, R5, and R8 are H. refers to any of the methods mentioned OR; and R1, R2, R4, R5, and R7 are H. refers to any of the methods mentioned OR; and R1, R2, R4, R5, and R6 are H. refers to any of the methods mentioned OR; and R1, R2, R3, R7, and R8 are H. refers to any of the methods mentioned OR; and R1, R2, R3, R6, and R8 are H. IVIA3ZUZZUU / ¿04 107 In certain embodiments, the invention relates to any of the aforementioned methods, wherein R4, R5, and R8 are OR; and R1, R2, R3, R6, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R4, R6, and R7 are OR; and R1, R2, R3, R5, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R4, R6, and R8 are OR; and R1, R2, R3, R5, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R4, R7, and R8 are OR; and R1, R2, R3, R5, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R5, R6, and R7 are OR; and R1, R2, R3, R4, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R5, R6, and R8 are OR; and R1, R2, R3, R4, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R5, R7, and R8 are OR; and R1, R2, R3, R4, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R6, R7, and R8 are OR; and R1, R2, R3, R4, and R5 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, and R4 are OR; and R5, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, and R5 are OR; and R4, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, and R6 are OR; and R4, R5, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, and R7 are OR; and R4, R5, R6, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, and R8 are OR; and R4, R5, R6, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, and R5 are OR; and R3, R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, and R6 are OR; and R3, R5, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, and R7 are OR; and R3, R5, R6, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R4, and R8 are OR; and R3, R5, R6, and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R5, and R6 are OR; and R3, R4, R7, and R8 are H. iviAazuzzuu / ¿04 In certain embodiments, the invention above, where R1, R2, R5, and R7 In certain embodiments, the invention above, where R1, R2, R5, and R8 In certain embodiments, the invention above, wherein R1, R2, R6, and R7 In certain embodiments, the invention above, wherein R1, R2, R6, and R8 In certain embodiments, the invention above, where R1, R2, R7, and R8 In certain embodiments, the invention above, where R1, R3, R4, and R5 In certain embodiments, the invention above, wherein R1, R3, R4, and R6 In certain embodiments, the invention above, wherein R1, R3, R4, and R7 In certain embodiments, the invention above, wherein R1, R3, R4, and R8 In certain embodiments, the invention above, where R1, R3, R5, and R6 In certain embodiments, the invention above, where R1, R3, R5, and R7 In certain embodiments, the invention above, wherein R1, R3, R5, and R8 In certain embodiments, the invention above, wherein R1, R3, R6, and R7 In certain embodiments, the invention above, wherein R1, R3, R6, and R8 In certain embodiments, the invention above, where R1, R3, R7, and R8 In certain embodiments, the invention above, where R1, R4, R5, and R6 In certain embodiments, the invention above, wherein R1, R4, R5, and R7 In certain embodiments, the invention above, wherein R1, R4, R5, and R8 108 refers to any of the methods mentioned are OR; and R3, R4, R6, and R8 are H. refers to any of the mentioned methods are OR; and R3, R4, R6, and R7 are H. refers to any of the mentioned methods are OR; and R3, R4, R5, and R8 are H. refers to any of the mentioned methods are OR; and R3, R4, R5, and R7 are H. refers to any of the mentioned methods are OR; and R3, R4, R5, and R6 are H. refers to any of the mentioned methods are OR; and R2, R6, R7, and R8 are H. refers to any of the mentioned methods are OR; and R2, R5, R7, and R8 are H. refers to any of the mentioned methods are OR; and R2, R5, R6, and R8 are H. refers to any of the mentioned methods are OR; and R2, R5, R6, and R7 are H. refers to any of the mentioned methods are OR; and R2, R4, R7, and R8 are H. refers to any of the mentioned methods are OR; and R2, R4, R6, and R8 are H. refers to any of the mentioned methods are OR; and R2, R4, R6, and R7 are H. refers to any of the mentioned methods are OR; and R2, R4, R5, and R8 are H. refers to any of the mentioned methods are OR; and R2, R4, R5, and R7 are H. refers to any of the mentioned methods are OR; and R2, R4, R5, and R6 are H. refers to any of the mentioned methods are OR; and R2, R3, R7, and R8 are H. refers to any of the mentioned methods are OR; and R2, R3, R6, and R8 are H. refers to any of the mentioned methods are OR; and R2, R3, R6, and R7 are H. IVIA / a / ¿U¿¿ / UU l ¿04 In certain embodiments, the invention above, wherein R1, R4, R6, and R7 In certain embodiments, the invention above, wherein R1, R4, R6, and R8 In certain embodiments, the invention above, wherein R1, R4, R7, and R8 In certain embodiments, the invention above, wherein R1, R5, R6, and R7 In certain embodiments, the invention above, where R1, R5, R6, and R8 In certain embodiments, the invention above, where R1, R5, R7, and R8 In certain embodiments, the invention above, wherein R1, R6, R7, and R8 In certain embodiments, the invention above, wherein R2, R3, R4, and R5 In certain embodiments, the invention above, wherein R2, R3, R4, and R6 In certain embodiments, the invention above, where R2, R3, R4, and R7 In certain embodiments, the invention above, where R2, R3, R4, and R8 In certain embodiments, the invention above, wherein R2, R3, R5, and R6 In certain embodiments, the invention above, wherein R2, R3, R5, and R7 In certain embodiments, the invention above, wherein R2, R3, R5, and R8 In certain embodiments, the invention above, where R2, R3, R6, and R7 In certain embodiments, the invention above, where R2, R3, R6, and R8 In certain embodiments, the invention above, wherein R2, R3, R7, and R8 In certain embodiments, the invention above, wherein R2, R4, R5, and R6 109 refers to any of the methods mentioned are OR; and R2, R3, R5, and R8 are H. refers to any of the mentioned methods are OR; and R2, R3, R5, and R7 are H. refers to any of the mentioned methods are OR; and R2, R3, R5, and R6 are H. refers to any of the mentioned methods are OR; and R2, R3, R4, and R8 are H. refers to any of the mentioned methods are OR; and R2, R3, R4, and R7 are H. refers to any of the mentioned methods are OR; and R2, R3, R4, and R6 are H. refers to any of the mentioned methods are OR; and R2, R3, R4, and R5 are H. refers to any of the mentioned methods are OR; and R1, R6, R7, and R8 are H. refers to any of the mentioned methods are OR; and R1, R5, R7, and R8 are H. refers to any of the mentioned methods are OR; and R1, R5, R6, and R8 are H. refers to any of the mentioned methods are OR; and R1, R5, R6, and R7 are H. refers to any of the mentioned methods are OR; and R1, R4, R7, and R8 are H. refers to any of the mentioned methods are OR; and R1, R4, R6, and R8 are H. refers to any of the mentioned methods are OR; and R1, R4, R6, and R7 are H. refers to any of the mentioned methods are OR; and R1, R4, R5, and R8 are H. refers to any of the mentioned methods are OR; and R1, R4, R5, and R7 are H. refers to any of the mentioned methods are OR; and R1, R4, R6, and R7 are H. refers to any of the mentioned methods are OR; and R1, R3, R7, and R8 are H. iviAazuzzuu / ¿04 In certain embodiments, the invention above, wherein R2, R4, R5, and R7 In certain embodiments, the invention above, wherein R2, R4, R5, and R8 In certain embodiments, the invention above, wherein R2, R4, R6, and R7 In certain embodiments, the invention above, wherein R2, R4, R6, and R8 In certain embodiments, the invention above, where R2, R4, R7, and R8 In certain embodiments, the invention above, where R2, R5, R6, and R7 In certain embodiments, the invention above, wherein R2, R5, R6, and R8 In certain embodiments, the invention above, wherein R2, R5, R7, and R8 In certain embodiments, the invention above, wherein R2, R6, R7, and R8 In certain embodiments, the invention above, where R3, R4, R5, and R6 In certain embodiments, the invention above, where R3, R4, R5, and R7 In certain embodiments, the invention above, wherein R3, R4, R5, and R8 In certain embodiments, the invention above, wherein R3, R4, R6, and R7 In certain embodiments, the invention above, wherein R3, R4, R6, and R8 In certain embodiments, the invention above, where R3, R4, R7, and R8 In certain embodiments, the invention above, where R3, R5, R6, and R7 In certain embodiments, the invention above, wherein R3, R5, R6, and R8 In certain embodiments, the invention above, wherein R3, R5, R7, and R8 110 refers to any of the methods mentioned are OR; and R1, R3, R6, and R8 are H. refers to any of the mentioned methods are OR; and R1, R3, R6, and R7 are H. refers to any of the mentioned methods are OR; and R1, R3, R5, and R8 are H. refers to any of the mentioned methods are OR; and R1, R3, R5, and R7 are H. refers to any of the mentioned methods are OR; and R1, R3, R5, and R6 are H. refers to any of the mentioned methods are OR; and R1, R3, R4, and R8 are H. refers to any of the mentioned methods are OR; and R1, R3, R4, and R7 are H. refers to any of the mentioned methods are OR; and R1, R3, R4, and R6 are H. refers to any of the mentioned methods are OR; and R1, R3, R4, and R5 are H. refers to any of the mentioned methods are OR; and R1, R2, R7, and R8 are H. refers to any of the mentioned methods are OR; and R1, R2, R6, and R8 are H. refers to any of the mentioned methods are OR; and R1, R2, R6, and R7 are H. refers to any of the mentioned methods are OR; and R1, R2, R5, and R8 are H. refers to any of the mentioned methods are OR; and R1, R2, R5, and R7 are H. refers to any of the mentioned methods are OR; and R1, R2, R5, and R6 are H. refers to any of the mentioned methods are OR; and R1, R2, R4, and R8 are H. refers to any of the mentioned methods are OR; and R1, R2, R4, and R7 are H. refers to any of the mentioned methods are OR; and R1, R2, R4, and R6 are H. MA / a / 2U22 / UU 1204 111 In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R3, R6, R7, and R8 are OR; and R1, R2, R4, and R5 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R4, R5, R6, and R7 are OR; and R1, R2, R3, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R4, R5, R6, and R8 are OR; and R1, R2, R3, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R4, R5, R7, and R8 are OR; and R1, R2, R3, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R4, R6, R7, and R8 are OR; and R1, R2, R3, and R5 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R5, R6, R7, and R8 are OR; and R1, R2, R3, and R4 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R4, and R5 are OR; and R6, R7, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R3, R4, and R6 are OR; and R5, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R4, and R7 are OR; and R5, R6, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R4, and R8 are OR; and R5, R6, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R5, and R6 are OR; and R4, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R5, and R7 are OR; and R4, R6, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R3, R5, and R8 are OR; and R4, R6, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R6, and R7 are OR; and R4, R5, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R3, R6, and R8 are OR; and R4, R5, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R7, and R8 are OR; and R4, R5, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, R5, and R6 are OR; and R3, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, R5, and R7 are OR; and R3, R6, and R8 are H. MA / a / 2U22 / UU 1204 112 In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R4, R5, and R8 are OR; and R3, R6, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, R6, and R7 are OR; and R3, R5, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, R6, and R8 are OR; and R3, R5, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, R7, and R8 are OR; and R3, R5, and R6 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R5, R6, and R7 are OR; and R3, R4, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R5, R6, and R8 are OR; and R3, R4, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R5, R7, and R8 are OR; and R3, R4, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R6, R7, and R8 are OR; and R3, R4, and R5 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R4, R5, and R6 are OR; and R2, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R4, R5, and R7 are OR; and R2, R6, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R4, R5, and R8 are OR; and R2, R6, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R4, R6, and R7 are OR; and R2, R5, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R4, R6, and R8 are OR; and R2, R5, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R4, R7, and R8 are OR; and R2, R5, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R5, R6, and R7 are OR; and R2, R4, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R3, R5, R6, and R8 are OR; and R2, R4, and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R3, R5, R7, and R8 are OR; and R2, R4, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R6, R7, and R8 are OR; and R2, R4, and R5 are H. iviAazuzzuu / ¿04 113 In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R4, R5, R6, and R7 are OR; and R2, R3, and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R4, R5, R6, and R8 are OR; and R2, R3, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R4, R5, R7, and R8 are OR; and R2, R3, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R4, R6, R7, and R8 are OR; and R2, R3, and R6 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R5, R6, R7, and R8 are OR; and R2, R3, and R4 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R4, R5, and R6 are OR; and R1, R7, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R4, R5, and R7 are OR; and R1, R6, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R4, R5, and R8 are OR; and R1, R6, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R4, R6, and R7 are OR; and R1, R5, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R4, R6, and R8 are OR; and R1, R5, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R4, R7, and R8 are OR; and R1, R5, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R5, R6, and R7 are OR; and R1, R4, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R5, R6, and R8 are OR; and R1, R4, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R5, R7, and R8 are OR; and R1, R4, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R6, R7, and R8 are OR; and R1, R4, and R5 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R4, R5, R6, and R7 are OR; and R1, R3, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R4, R5, R6, and R8 are OR; and R1, R3, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R4, R5, R7, and R8 are OR; and R1, R3, and R6 are H. MA / a / 2U22 / UU 1204 114 In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R4, R6, R7, and R8 are OR; and R1, R3, and R5 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R2, R5, R6, R7, and R8 are OR; and R1, R3, and R4 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R3, R4, R5, R6, and R7 are OR; and R1, R2, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R3, R4, R5, R6, and R8 are OR; and R1, R2, and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R3, R4, R5, R7, and R8 are OR; and R1, R2, and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R3, R4, R6, R7, and R8 are OR; and R1, R2, and R5 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R3, R5, R6, R7, and R8 are OR; and R1, R2, and R4 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R4, R5, R6, R7, and R8 are OR; and R1, R2, and R3 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R4, R5, and R6 are OR; and R7 and R8 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R3, R4, R5, and R7 are OR; and R6 and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R4, R5, and R8 are OR; and R6 and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R3, R4, R6, and R7 are OR; and R5 and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R4, R6, and R8 are OR; and R5 and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R3, R4, R7, and R8 are OR; and R5 and R6 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R3, R5, R6, and R7 are OR; and R4 and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R5, R6, and R8 are OR; and R4 and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R5, R7, and R8 are OR; and R4 and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R6, R7, and R8 are OR; and R4 and R5 are H. iviAazuzzuu / ¿04 115 In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, R5, R6, and R7 are OR; and R3 and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, R5, R6, and R8 are OR; and R3 and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, R5, R7, and R8 are OR; and R3 and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, R6, R7, and R8 are OR; and R3 and R5 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R5, R6, R7, and R8 are OR; and R3 and R4 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R4, R5, R6, and R7 are OR; and R2 and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R4, R5, R6, and R8 are OR; and R2 and R7 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R4, R5, R7, and R8 are OR; and R2 and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R4, R6, R7, and R8 are OR; and R2 and R5 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R5, R6, R7, and R8 are OR; and R2 and R4 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R4, R5, R6, R7, and R8 are OR; and R2 and R3 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R4, R5, R6, and R7 are OR; and R1, and R8 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R4, R5, R6, and R8 are OR; and R1 and R7 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R2, R3, R4, R5, R7, and R8 are OR; and R1 and R6 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R4, R6, R7, and R8 are OR; and R1 and R5 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R5, R6, R7, and R8 are OR; and R1 and R4 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R4, R5, R6, R7, and R8 are OR; and R1 and R3 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R3, R4, R5, R6, R7, and R8 are OR; and R1 and R2 are H. iviAazuzzuu / ¿04 116 In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R3, R4, R5, R6, and R7 are OR; and R8 is H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R3, R4, R5, R6, and R8 are OR; and R7 is H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R3, R4, R5, R7, and R8 are OR; and R6 is H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R3, R4, R6, R7, and R8 are OR; and R5 is H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R1, R2, R3, R5, R6, R7, and R8 are OR; and R4 is H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R2, R4, R5, R6, R7, and R8 are OR; and R3 is H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R1, R3, R4, R5, R6, R7, and R8 are OR; and R2 is H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R2, R3, R4, R5, R6, R7, and R8 are OR; and R1 is H. In certain embodiments, the invention relates to any of the methods mentioned above, where R is H. In certain embodiments, the invention relates to a method of increasing autophagy in a cell, comprising contacting the cell with an effective amount of a compound of Formula IV, thereby increasing autophagy in the cell; where the compound of Formula IV is iviAazuzzuu / ¿04 Formula IV where R9, R10, R11, R12, R13, and R14 are independently selected from the group consisting of H and OR; and R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide. In certain embodiments, the invention relates to any of the methods mentioned above, wherein autophagy is mitophagy. 117 In certain embodiments, the invention relates to any of the aforementioned methods, wherein the cell is selected from the group consisting of: embryonic stem cells, induced pluripotent stem cells, adult stem cells, differentiated cells, cells of the blood, hematopoietic cells, epithelial cells, exocrine cells, endocrine cells, connective tissue cells, adipose cells, bone cells, smooth muscle cells, striated muscle cells, nerve cells, sensory cells, cardiac cells, liver cells, cells gastric cells, intestinal cells, lung cells, kidney cells, and germ cells. In certain embodiments, the invention relates to a method of increasing longevity in an animal, comprising administering to an animal in need thereof an effective amount of a compound of Formula IV, thereby increasing the longevity of the animal, wherein the compound of Formula IV is Formula IV where R9, R10, R11, R12, R13, and R14 are independently selected from the group consisting of H and OR; and R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide. In certain embodiments, the invention relates to any of the aforementioned methods, wherein the animal is a mammal. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the mammal is a human. In certain embodiments, the invention relates to a method for increasing the longevity of eukaryotic cells in vitro, which comprises contacting the eukaryotic cells in vitro with an effective amount of a compound of Formula IV, thereby increasing the longevity of the cells. eukaryotic cells in vitro, where the compound of Formula IV is 118 MA / a / 2U22 / UU 1204 Formula IV where R9, R10, R11, R12, R13, and R14 are independently selected from the group consisting of H and OR; and R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide. In certain embodiments, the invention relates to any of the aforementioned methods, wherein the eukaryotic cells are eukaryotic cells in primary culture. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the eukaryotic cells are part of a cell line. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the eukaryotic cells are cells selected from the group consisting of: embryonic stem cells, induced pluripotent stem cells, adult stem cells, differentiated cells, blood, hematopoietic cells, epithelial cells, exocrine cells, endocrine cells, connective tissue cells, adipose cells, bone cells, smooth muscle cells, striated muscle cells, nerve cells, sensory cells, cardiac cells, liver cells , gastric cells, intestinal cells, lung cells, kidney cells, and germ cells. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the eukaryotic cells are cells selected from the group consisting of: embryonic stem cells, induced pluripotent stem cells, and adult stem cells. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R10, R11, R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein at least one of R9, R10, R11, R12, R13, and R14 is OR. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein at least two of R9, R10, R11, R12, R13, and R14 are OR. 119 In certain embodiments, the invention relates to any of the above-mentioned methods, wherein at least three of R9, R10, R11, R12, R13, and R14 are OR. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein at least four of R9, R10, R11, R12, R13, and R14 are OR. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein five of R9, R10, R11, R12, R13, and R14 are OR. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R9, R10, R11, R12, R13, and R14 are OR. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R9 is OR; and R10, R11, R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R10 is OR; and R9, R11, R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R11 is OR; and R9, R10, R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R9 and R10 are OR; and R11, R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R9 and R11 are OR; and R10, R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R9 and R12 are OR; and R10, R11, R13, and R14 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R9 and R13 are OR; and R10, R11, R12, and R14 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R9 and R14 are OR; and R10, R11, R12, and R13 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R10 and R11 are OR; and R9, R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R10 and R12 are OR; and R9, R11, R13, and R14 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R10 and R13 are OR; and R9, R11, R12, and R14 are H. In certain embodiments, the invention relates to any of the methods mentioned above, wherein R11 and R12 are OR; and R9, R10, R13, and R14 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R10, and R11 are OR; and R12, R13, and R14 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R10, and R12 are OR; and R11, R13, and R14 are H. iviAazuzzuu / ¿04 120 In certain embodiments, the Invention relates to any of the methods mentioned above, where R9, R10, and R13 are OR; and R11, R12, and R14 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R10, and R14 are OR; and R11, R12, and R13 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R11, and R12 are OR; and R10, R13, and R14 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R11, and R13 are OR; and R10, R12, and R14 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R11, and R14 are OR; and R10, R12, and R13 are H. In certain embodiments, the Invention relates to any of the aforementioned methods, where R9, R12, and R13 are OR; and R10, R11, and R14 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R10, R11, and R12 are OR; and R9, R13, and R14 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R10, R11, and R13 are OR; and R9, R12, and R14 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R10, R11, and R12 are OR; and R13 and R14 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R10, R11, and R13 are OR; and R12 and R14 are H. In certain embodiments, the invention relates to any of the above-mentioned methods, wherein R9, R10, R11, and R14 are OR; and R12 and R13 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R10, R12, and R13 are OR; and R11 and R14 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R10, R12, and R14 are OR; and R11 and R13 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R10, R13, and R14 are OR; and R11 and R12 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R11, R12, and R13 are OR; and R10 and R14 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R11, R12, and R14 are OR; and R10 and R13 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R10, R11, R12, and R13 are OR; and R9 and R14 are H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R10, R11, R12, and R13 are OR; and R14 is H. iviAazuzzuu / ¿04 121 In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R10, R11, R12, and R14 are OR; and R13 is H. In certain embodiments, the invention relates to any of the aforementioned methods, wherein R9, R10, R11, R13, and R14 are OR; and R12 is H. In certain embodiments, the invention relates to any of the methods mentioned above, where R is H. In certain embodiments, the invention relates to a method of treating or preventing metabolic stress, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing metabolic stress. In certain embodiments, the invention relates to a method of treating or preventing cardiovascular disease, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing cardiovascular disease. In certain embodiments, the invention relates to a method of treating or preventing cardiomyopathy, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing cardiomyopathy. In certain embodiments, the invention relates to a method of improving muscle function, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby improving muscle function. In certain embodiments, the invention relates to a method of treating or preventing sarcopenia, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing sarcopenia. IVIA / a / ZUZZ / UU / ¿04 122 In certain embodiments, the invention relates to a method of treating or preventing muscle degenerative disease, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III , a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing muscle degenerative disease. In certain embodiments, the invention relates to a method of treating or preventing Duchenne muscular dystrophy, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing Duchenne muscular dystrophy. In certain embodiments, the invention relates to a method of treating or preventing alcoholic liver disease, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III , a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing alcoholic liver disease. In certain embodiments, the invention relates to a method of treating or preventing nonalcoholic fatty liver disease, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing liver disease non-alcoholic fatty. In certain embodiments, the invention relates to a method of treating or preventing drug-induced liver injury, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing liver injury drug induced. In certain embodiments, the invention relates to a method for treating or preventing αΐ-antitrypsin deficiency, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of MA / a / 2U22 / UU 1204 123 Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing α1-antitrypsin deficiency. In certain embodiments, the invention relates to a method of treating or preventing ischemia-reperfusion injury, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing ischemia injury / reperfusion. In certain embodiments, the invention relates to a method of treating or preventing inflammation, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing inflammation. In certain embodiments, the invention relates to a method of treating or preventing inflammatory bowel disease, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing inflammatory bowel disease. In certain embodiments, the invention relates to a method of treating or preventing Crohn's disease, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III , a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing Crohn's disease. In certain embodiments, the invention relates to a method of treating or preventing obesity, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing obesity. In certain embodiments, the invention relates to a method of treating or preventing metabolic syndrome, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, 124 urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing metabolic syndrome. In certain embodiments, the invention relates to a method of treating or preventing type II diabetes mellitus, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing type II diabetes mellitus. In certain embodiments, the invention relates to a method of treating or preventing hyperlipidemia, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing hyperlipidemia. In certain embodiments, the invention relates to a method of treating or preventing osteoarthritis, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing osteoarthritis. In certain embodiments, the invention relates to a method of treating or preventing neurodegenerative disease, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing the neurodegenerative disease. In certain embodiments, the invention relates to a method of treating or preventing Alzheimer's disease, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III , a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing Alzheimer's disease. In certain embodiments, the invention relates to a method of treating or preventing Parkinson's disease, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III , a compound of Formula V, a compound of Formula VI, MA / a / ¿U¿¿ / UU l ¿04 125 urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing Parkinson's disease. In certain embodiments, the invention relates to a method of treating or preventing amyotrophic lateral sclerosis (ALS), comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing ALS. In certain embodiments, the invention relates to a method of treating or preventing cancer, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing cancer. In certain embodiments, the invention relates to a method of treating or preventing cognitive disorder, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing the cognitive disorder. In certain embodiments, the invention relates to a method of treating or preventing mood disorders, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III , a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing the mood disorder. In certain embodiments, the invention relates to a method of treating or preventing stress, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thereby treating or preventing stress. In certain embodiments, the invention relates to a method of improving activity during aging, comprising administering a therapeutically effective amount of a compound selected from the group consisting of: a compound of Formula II, a compound of Formula III, a compound of Formula V, a compound of Formula VI, MA / a / ¿U¿¿ / UU l ¿04 126 urolithin A, urolithin B, urolithin C, urolithin D, and ellagic acid, to a subject in need thereof, thus improving activity during aging. In certain embodiments, the invention relates to any of the aforementioned methods, wherein the compound is a compound of Formula II as defined herein. In certain embodiments, the invention relates to any of the aforementioned methods, wherein the compound is a compound of Formula III as defined herein. In certain embodiments, the invention relates to any of the aforementioned methods, wherein the compound is a compound of Formula V as defined herein. In certain embodiments, the invention relates to any of the aforementioned methods, wherein the compound is a compound of Formula VI as defined herein. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin A. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin B. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin C. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is urolithin D. In certain embodiments, the invention relates to any of the methods mentioned above, wherein the compound is ellagic acid. In certain embodiments, the invention relates to a method of treating or preventing metabolic stress, comprising administering a therapeutically effective amount of a compound of Formula I to a subject in need thereof, thereby treating or preventing metabolic stress, where the compound of Formula I is MA / a / ¿U¿¿ / UU l ¿04 formula where 127 R1, R2, R3, R4, R5, R6, R7, and R8 are independently selected from the group consisting of H and OR; and R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide. In certain embodiments, the invention relates to a method of treating or preventing cardiovascular disease, comprising administering a therapeutically effective amount of a compound of Formula I to a subject in need thereof, thereby treating or preventing cardiovascular disease, where the compound of Formula I is MA / a / 2U22 / UU 1204 formula where R1, R2, R3, R4, R5, R6, R7, and R8 are independently selected from the group consisting of H and OR; and R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide. In certain embodiments, the invention relates to a method of treating or preventing cardiomyopathy, comprising administering a therapeutically effective amount of a compound of Formula I to a subject in need thereof, thereby treating or preventing cardiomyopathy, wherein the compound of Formula I is Formula I where R1, R2, R3, R4, R5, R6, R7, and R8 are independently selected from the group consisting of H and OR; and R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide. 128 In certain embodiments, the invention relates to a method of improving muscle function, comprising administering a therapeutically effective amount of a compound of Formula I to a subject in need thereof, thereby improving muscle function, wherein the compound of Formula I is MA / a / 2U22 / UU 1204 Formula I where R1, R2, R3, R4, R5, R6, R7, and R8 are independently selected from the group consisting of H and OR; and R is H, substituted or unsubstituted alkyl, substituted or unsubstituted aryl, a substituted or unsubstituted monosaccharide; or a substituted or unsubstituted oligosaccharide. In certain embodiments, the invention relates to a method of treating or preventing sarcopenia, comprising administering a therapeutically effective amount of a compound of Formula I to a subject in need thereof, thereby tre...

Claims

1. A compound for use in extending the course of health in an animal, wherein the compound comprises an effective amount of a urolithin selected from the group consisting of urolithin A, urolithin B, urolithin C, and urolithin D, or a pharmaceutically acceptable salt thereof, wherein the course of health is extended by: improvement of stem cell function, improvement of the outcome of acute pancreatitis, improvement of cardiac output, improvement of left ventricular diastolic function, improvement of blood pressure, improvement of immune response to intracellular bacteria, improvement of podocyte resistance to injury, improvement of muscle function, improvement of balance and coordination, improvement of muscle strength, improvement of muscle endurance, improvement of muscle recovery after exercise, improvement of cellular endothelial dysfunction, improvement of angiogenesis,improvement of tissue mineral density, improvement of the outcome of infraocular inflammation or uveitis, improvement of pulmonary emphysema caused by anthrapsin-α1, improvement of clearance of aggressomas accumulating mutant cystic fibrosis transmembrane conductance regulator (CFTR) protein, improvement of the outcome of human idiopathic pulmonary fibrosis, improvement of the immune response to infection by pathogens or improvement of the outcome of chronic obstructive pulmonary disease; or increase in muscle mass and increase in bone strength; or reduction of muscle atrophy, reduction of age-related cataracts, reduction of photoreceptor injury from uveitis, reduction of glaucomatous neurodegeneration,Reduction of skin damage from excessive lipid oxidation commonly observed in aged and diseased skin or reduction of protein aggregates in cystic fibrosis; or prevention of age-related cardiac deterioration; or protection of cells during cardiac procedures such as angioplasty, bypass, or valve replacement; protection against glucose intolerance or leptin resistance, protection against muscle damage, protection of liver tissue, protection against endothelial cell injury, or protection against diabetic retinopathy; or maintenance of amino acid assemblies during starvation, or separation of intracellular microbes, separation of protein aggregates, or separation of protein aggregates in lung cells. MA / a / 2U22 / UU 1204 214, 2. The compound for use according to claim 1, wherein the compound is part of a nutraceutical composition, a pharmaceutical composition, a functional food, a medical food, or a food supplement.

3. The compound is to be used in accordance with the compound and is part of a nutraceutical composition.

4. The compound is to be used in accordance with the compound and is part of a pharmaceutical composition.

5. The compound is to be used in accordance with the compound as part of a functional food.

6. The compound is to be used in accordance with the compound and is part of a medical food.

7. The compound for use in accordance with claim 1, wherein the compound is part of a food supplement.

8. The compound for use according to claim 1, wherein urolithin is urolithin A or a pharmaceutically acceptable salt thereof.

9. The compound for use according to claim 1, wherein urolithin is urolithin B or a pharmaceutically acceptable salt thereof.

10. The compound to be used in accordance with claim 1, wherein the animal is a mammal.

11. The compound to be used in accordance with claim 1, wherein the mammal is a human.

12. The compound for use according to claim 1, wherein urolithin is urolithin A or a pharmaceutically acceptable salt thereof; wherein the animal is a mammal; and wherein the mammal is a human.