IRAK decomposers and their uses

Abstract

The present invention provides compounds, compositions thereof, and methods of using the same. The compounds provided by the present invention are also useful for studying the IRAK enzyme in biological and pathological phenomena; studying intracellular signaling pathways occurring in body tissues; and comparative evaluation of new IRAK inhibitors or IRAK degraders, or other regulators of kinase, signaling pathways, and cytokine levels in vitro or in vivo.

Description

[Technical Field]

[0001] Citation of Related Applications This application is a joint venture between U.S. Provisional Application No. 62 / 774,051 (filed November 30, 2018), U.S. Provisional Application No. 62 / 788,460 (filed January 4, 2019), U.S. Provisional Application No. 62 / 793,992 (filed January 18, 2019), U.S. Provisional Application No. 62 / 826,743 (filed March 29, 2019), U.S. Provisional Application No. 62 / 831,007 (filed April 8, 2019), and U.S. Provisional Application No. 62 / 831,007 (filed April 8, 2019). This application claims the benefit of U.S. Provisional Application No. 62 / 851,427 (filed May 22, 2019), U.S. Provisional Application No. 62 / 868,574 (filed June 28, 2019), U.S. Provisional Application No. 62 / 875,347 (filed July 17, 2019), and U.S. Provisional Application No. 62 / 879,117 (filed July 26, 2019), the contents of each of which are incorporated herein by reference.

[0002] FIELD OF THE INVENTION The present invention relates to compounds and methods useful for the modulation of one or more interleukin-1 receptor-associated kinases ("IRAKs") by ubiquitination and / or degradation by compounds according to the invention. The present invention also provides pharmaceutically acceptable compositions comprising the compounds of the invention, and methods of using said compositions in the treatment of various disorders. [Background technology]

[0003] Background of the Invention The ubiquitin-proteasome pathway (UPP) is a critical pathway that regulates key regulatory proteins and degrades misfolded or abnormal proteins. The UPP is central to numerous cellular processes, and when deficient or imbalanced, it leads to the pathogenesis of various diseases. Covalent attachment of ubiquitin to specific protein substrates is achieved through the action of E3 ubiquitin ligases.

[0004] There are over 600 E3 ubiquitin ligases that facilitate the ubiquitination of various proteins in vivo, which are divided into four families: HECT-domain E3s, U-box E3s, monomeric RING E3s, and multisubunit E3s. In general, Li et al. (PLOS One, 2008, 3, 1487) entitled "Genome-wide and functional annotation of human E3 ubiquitin ligases identifies MULAN, a mitochondrial E3 that regulates the organelle's dynamics and signaling."; Berndsen et al. (Nat. Struct. Mol. Biol., 2014, 21, 301-307) entitled "New insights into ubiquitin E3 ligase mechanism"; Deshaies et al. (Ann. Rev. Biochem., 2009, 78, 399-434) Title "RING domain E3 ubiquitin ligases."; Spratt et al. (Biochem. 2014, 458, 421-437) Title "RBR E3 ubiquitin ligases: new structures, new insights, new questions.”; and Wang et al. (Nat. Rev. Cancer., 2014, 14, 233-347) entitled “Roles of F-box proteins in cancer.”

[0005] The UPP plays a key role in the degradation of short-lived regulatory proteins important in a variety of fundamental cellular processes, including cell cycle regulation, cell surface receptor and ion channel regulation, and antigen presentation. The pathway is involved in the pathogenesis of several forms of malignancy, several genetic diseases (including cystic fibrosis, Angelman syndrome, and Liddle syndrome), immune surveillance / viral pathogenesis, and muscle wasting. Many diseases are associated with abnormal UPP and adversely affect the regulation of cell cycle and division, cellular responses to stress and extracellular modulators, neuronal network morphogenesis, cell surface receptors, ion channels, secondary pathways, DNA repair, and organelle biogenesis.

[0006] Abnormalities in this process have recently been implicated in the pathogenesis of several diseases, both congenital and acquired. These diseases fall into two major groups: (a) diseases resulting from loss of function leading to the stabilization of specific proteins, and (b) diseases resulting from gain of function (i.e., aberrant or accelerated degradation of protein targets).

[0007] UPP is used to induce selective protein degradation, including the use of fusion proteins to artificially ubiquitinate target proteins and synthetic small molecule probes to induce proteasome-dependent degradation. Bifunctional compounds consisting of a target protein-binding ligand and an E3 ubiquitin ligase ligand induced proteasome-mediated degradation of selected proteins through recruitment to these E3 ubiquitin ligases and subsequent ubiquitination. These drug-like molecules offer the possibility of temporally controlling protein expression. Such compounds can induce the inactivation of target proteins upon addition to cells or administration to animals or humans, and may be useful as biochemical reagents and provide a new paradigm for disease treatment by removing pathogenic or oncogenic proteins (Crews C, Chemistry & Biology, 2010, 17(6):551-555; Schnnekloth JS Jr., Chembiochem, 2005, 6(1):40-46). In the art, there is a continuing need for effective treatment of diseases, particularly hyperplasia and cancer, such as multiple myeloma.However, non-specific effects and the inability to target and regulate specific classes of proteins (e.g., transcription factors) together remain obstacles to the development of effective anti-cancer drugs.Therefore, small molecule therapeutic agents that affect E3 ligase-mediated protein degradation and target cancer-related proteins, such as interleukin-1 receptor-associated kinase ("IRAK"), hold promise as therapeutic agents.Therefore, there remains a need to find compounds that are IRAK decomposers useful as therapeutic agents. [Prior art documents] [Non-patent literature]

[0008] [Non-Patent Document 1] Li et al. (PLOS One, 2008, 3, 1487) Title: "Genome-wide and functional annotation of human E3 ubiquitin ligases identifies MULAN, a mitochondrial E3 that regulates the organelle's dynamics and signaling." [Non-patent document 2] Berndsen et al. (Nat. Struct. Mol. Biol., 2014, 21, 301-307) Title: "New insights into ubiquitin E3 ligase mechanism" [Non-patent document 3] Deshaies et al. (Ann. Rev. Biochem., 2009, 78, 399-434) Title: "RING domain E3 ubiquitin ligases." [Non-patent document 4] Spratt et al. (Biochem. 2014, 458, 421-437) Title: "RBR E3 ubiquitin ligases: new structures, new insights, new questions." [Non-Patent Document 5] Wang et al. (Nat. Rev. Cancer., 2014, 14, 233-347) Title: "Roles of F-box proteins in cancer." [Non-patent document 6] Crews C,Chemistry & Biology,2010,17(6):551-555;Schnnekloth JS Jr.,Chembiochem,2005,6(l):40-46 Summary of the Invention [Means for solving the problem]

[0009] Summary of the Invention The present application relates to novel bifunctional compounds that function to recruit IRAK kinase to E3 ubiquitin ligase for degradation, as well as methods for their preparation and use. In particular, the present disclosure provides bifunctional compounds that find utility as modulators of targeted ubiquitination of IRAK kinase, which are then degraded and / or otherwise inhibited by the bifunctional compounds described herein. Monovalent compounds that find utility as inducers of targeted ubiquitination of IRAK kinase, which are then degraded and / or otherwise inhibited by the monovalent compounds described herein, are also provided. An advantage of the compounds provided herein is that they are capable of a wide variety of pharmacological activities, consistent with the degradation / inhibition of IRAK kinase. Additionally, the present disclosure provides methods of using an effective amount of a compound described herein to treat or alleviate disease conditions, such as cancer, e.g., multiple myeloma.

[0010] The present application further relates to the targeted degradation of IRAK kinase through the use of bifunctional molecules, including bifunctional molecules that link a cereblon-binding moiety to a ligand that binds to the targeted IRAK kinase.

[0011] It has now been found that the compounds of the present invention, and pharmaceutically acceptable compositions thereof, are effective as degraders of IRAK kinase. Such compounds have the general formula I: [ka] or a pharmaceutically acceptable salt thereof, wherein each variable is as defined and described herein.

[0012] It has also now been found that the compounds of the present invention, and pharmaceutically acceptable compositions thereof, are effective as degraders of IRAK kinase. Such compounds have the general formula V: [ka] or a pharmaceutically acceptable salt thereof, wherein each variable is as defined and described herein.

[0013] The compounds of the present invention, and pharmaceutically acceptable compositions thereof, are useful for treating a variety of diseases, disorders, or conditions associated with modulation of signal transduction pathways involving IRAK kinase, including those described herein.

[0014] The compounds provided by the present invention are also useful for studying the IRAK enzyme in biological and pathological phenomena; studying intracellular signaling pathways occurring in body tissues; and comparative evaluation of new IRAK inhibitors or degraders, or other regulators of kinase, signaling pathways, and cytokine levels in vitro or in vivo. [Brief explanation of the drawings]

[0015] [Figure 1] FIG. 1 is an image showing a Western blot of degrader I-30 in OCI-LY10 at 24 hours.

[0016] [Figure 2] FIG. 2 is an image of the dose response curves of IKAK4 (% control) (y-axis) versus degrader I-30 concentration (μM) (x-axis) for OCI-LY10 and TMD8 cell lines, as well as the in vitro degradation results (DC90, μM).

[0017] [Figure 3] Figure 3 is an image of deep TMT proteomics scatter plots at 8 hours in OCI-LY10 showing Log2 FC 10 nM Degrader I-30 in DMSO (y-axis) and Log2 FC 10 nM Degrader in DMSO Rep1 (x-axis).

[0018] [Figure 4]Figure 4 includes a graphical image (A) showing the reduction of IRAK4 (with counts) (y-axis) versus IRAK (MFI) (x-axis) over 24 hours using several concentrations of the degrader I-30; a graphical image (B) showing the time-dependent induction of apoptosis with 50 nM of the degrader I-30, showing IRAK4 (% control) (left y-axis) and cleaved CASP3 (% control) (right y-axis) versus time (h) (x-axis); a graphical image (C) showing the inhibition of cell proliferation over 72 hours, showing counts (y-axis) versus Ki67 (MFI) (x-axis) at several concentrations of the degrader I-30; and a graphical image (D) showing the mechanism-specific induction of apoptosis, showing cleaved CASP3 (% control) (y-axis) and inactive (x-axis) for the degrader I-30 at several concentrations, respectively.

[0019] [Figure 5] FIG. 5 shows the results of a cell viability assay using the degrader I-30 together with OCI-LY10 and Daudi (CTG; IC50 in μM).

[0020] [Figure 6] Figure 6 includes graphical images showing xenograft results for control (SC, QD) and degrader I-30 (60 mg / kg SC, QD, N=5) showing tumor volume (mm) (y-axis) versus dosing interval (days after initiation of treatment) (x-axis) for OCI-LY10 (A and B) and TMD8 cells (C); data showing that final (8 h) degrader I-30 exposure correlates with IRAK4 reduction in OCI-LY10 tumor PK / PD using IRAK4 in tumor (% control) (y-axis) versus total degrader concentration (μM) in tumor (D); and data showing tumor volume (mm) (left y-axis) and IRAK4 I-30 degradation in tumor (% control) (right y-axis) versus dosing interval (days after initiation of treatment) (E).

[0021] [Figure 7]Figure 7 is a graphical image of xenograft results for vehicle (PO, BID) and disintegrant I-30 (PO, BID: 10 mg / kg; 30 mg / kg; and 100 mg / kg), showing tumor volume (mm3) (y-axis) versus dosing interval (days after start of treatment) (x-axis) for OCI-LY10 (MYD88 mutant) cells.

[0022] [Figure 8] Figure 8 is a graphical image showing the in vivo degradation of IRAK4 in BALB / c mouse spleens after three PO doses of the degrader I-30, shown as IRAK4 (% control) (y-axis) and PO dose (10 mg / kg; 30 mg / kg; and 100 mg / kg) (x-axis).

[0023] [Figure 9] FIG. 9 is a graphical image illustrating neutrophils in exudates collected from air pouches in mice after MSU crystal challenge, showing neutrophil count (% cells in extrudate) (y-axis) and (MSU; colchicine, 1 mg / kg SC; anakinra, 100 mg / kg SC; and PO I-30 doses: 10 mg / kg; 30 mg / kg; and 100 mg / kg) (x-axis).

[0024] [Figure 10] FIG. 10 is an image of the dose response curve for IKAK4 (% control) (y-axis) versus degrader I-30 concentration (uM) (x-axis) for the OCI-LY10 cell line, and in vitro degradation results (DC90, μM).

[0025] [Figure 11] Figure 11 is a graphical image showing oral degradant I-75 exposure in mice using plasma degradant concentration (ng / mL) (y-axis) versus time (hours) (x-axis) at doses of 30 mg / kg, 100 mg / kg, and 300 mg / kg (A), PK characteristics in CD1 mice (B), and oral bioavailability across species (C).

[0026] [Figure 12] FIG. 12 is a graphical image (A) showing apoptosis in OCI-LY10 at 72 hours as apoptotic cells (CC3+ / CPARP+, % control) (y-axis) in response to several concentrations (μM) of 2 nM ibrutinib, degrader I-30, and the combination of 2 nM ibrutinib and degrader I-30 (x-axis); and graphical results of a Cell Titer Glo assay showing synergistic effects (B).

[0027] [Figure 13] FIG. 13 is a graphical image of in vivo xenograft results for vehicle (PO, QD), degrader I-30 (PO, QD, 25 mg / kg), ibrutinib (PO, QD, 25 mg / kg), and degrader + ibrutinib (PO, QD:25 + 25 mg / kg), showing tumor volume (mm) (y-axis) versus dosing interval (days after start of treatment) (x-axis) for OCI-LY10 (MYD88 L265P, CD79 mutant) cells.

[0028] [Figure 14] FIG. 14 is a graphical image of in vivo xenograft results for vehicle (10% TPGS in water, PO, QD) and disintegrant I-75 (PO, QD: 25 mg / kg and 50 mg / kg), showing tumor volume (mm) (y-axis) versus dosing interval (days after start of treatment) (x-axis) for OCI-LY10 (MYD88 mutant) cells.

[0029] [Figure 15] FIG. 15 is a graphical image of an in vivo IL-1β study after MSU crystal challenge showing IL-1β (pg / mL) in plasma (y-axis) and (naive, vehicle PO; and degrader I-30 PO TID: 10 mg / kg; 30 mg / kg; and 100 mg / kg) (x-axis).

[0030] [Figure 16]FIG. 16 contains graphical images of comparative in vitro TLR-stimulated pro-inflammatory cytokine inhibition results using the degrader I-75 and the IRAK4 inhibitor PF-06550833 for LPS (TLR4)-induced IL-6 (A), LPS (TLR4)-induced TNFα (B), R848 (TLR7 / 8)-induced IL-8 (C), and LPS (TLR4)-induced IL-1β (D), showing DMSO control (%) (y-axis) versus concentration (log μM) (x-axis) in human whole blood.

[0031] [Figure 17] FIG. 17 includes graphical images of the anti-inflammatory and analgesic results of MSU-induced gouty arthritis, showing knee swelling (% control) (x-axis) and (vehicle PO; colchicine SC; anakinra IP; and resolving agent I-75 PO doses: 10 mg / kg; 30 mg / kg; and 100 mg / kg) (x-axis) (A); and pain sensitivity (% control) (x-axis) and (vehicle PO; colchicine SC; anakinra IP; and resolving agent PO doses: 10 mg / kg; 30 mg / kg; and 100 mg / kg) (x-axis) (B).

[0032] [Figure 18] FIG. 18 is a graphical image of IRAK4 degradation in OCI-LY10 tumor xenografts without regression for vehicle (PO, BID) and degrader I-257 (PO, BID, 150 mg / kg), showing tumor volume (mm) (y-axis) versus dosing interval (days after start of treatment) (x-axis).

[0033] [Figure 19] FIG. 19 is a graphical image of viability results using PF-06650833, pomalidomide, 1:1 PF-06650833:pomalidomide, and the degrader I-387, showing viability (% control) (y-axis) versus concentration (μM) (x-axis) for OCI-LY10 (MYD88 L265P, CD79 mutant) cells.

[0034] [Figure 20] FIG. 20 includes a transcriptome scatter plot of IFN signaling results showing the −log 10 p-values ​​(y-axis) for I-257, pomalidomide, and I-208 in DMSO.

[0035] [Figure 21] FIG. 21 is a graphical image of IRAK4 and Ikaros degradation in OCI-LY10 tumor xenografts with regression for vehicle (PO, QD) and the degrader I-208 (PO, QD; 24, 72, and 240 mg / kg), showing tumor volume (mm) (y-axis) versus dosing interval (days after initiation of treatment) (x-axis).

[0036] [Figure 22] FIG. 22 shows the pharmacokinetic results for I-75 and I-241.

[0037] [Figure 23] Figure 23 is a graphical image of xenograft results for vehicle (SC, QD) and disintegrators I-38 and I-73 (SC, QD: 60 mg / kg), showing tumor volume (mm3) (y-axis) versus dosing interval (days after start of treatment) (x-axis) for OCI-LY10 (MYD88 mutant) cells.

[0038] [Figure 24] FIG. 24 is a graphical image of xenograft results for vehicle (SC, 5 μL / g, QD) and the degraders I-3, I-11, I-62, I-110, I-113, and I-117 at various dosing regimens, showing tumor volume (mm) (y-axis) versus dosing interval (days after start of treatment) (x-axis) for OCI-LY10 (MYD88 mutant) cells.

[0039] [Figure 25]Figure 25 is a graphical image of xenograft results for vehicle (SC, 5 μL / g, QD) and the degraders I-41, I-61, I-114, I-123, I-125, I-127, and I-241 at various dosing regimens, showing tumor volume (mm3) (y-axis) versus dosing interval (days after start of treatment) (x-axis) for OCI-LY10 (MYD88 mutant) cells.

[0040] [Figure 26] FIG. 26 is a graphical image of xenograft results for vehicle (PO, BID) and the degraders I-125 and I-239 at various dosing regimens, showing tumor volume (mm) (y-axis) versus dosing interval (days after start of treatment) (x-axis) for OCI-LY10 (MYD88 mutant) cells.

[0041] [Figure 27] FIG. 27 is a graphical image of xenograft results for vehicle (PO, QD) and the degraders I-167 and I-259 at various dosing regimens, showing tumor volume (mm) (y-axis) versus dosing interval (days after start of treatment) (x-axis) for OCI-LY10 (MYD88 mutant) cells.

[0042] [Figure 28] Figure 28 is a graphical image of xenograft results for vehicle (PO, BID) and the degrading agent I-168 at various dosing regimens, showing tumor volume (mm3) (y-axis) versus dosing interval (days after start of treatment) (x-axis) for OCI-LY10 (MYD88 mutant) cells.

[0043] [Figure 29] Figure 29 is a graphical image of xenograft results for vehicle (PO, QD) and disintegrant I-221 (30 mg / kg, PO, QD), showing tumor volume (mm) (y-axis) versus dosing interval (days after start of treatment) (x-axis) for OCI-LY10 (MYD88 mutant) cells.

[0044] [Figure 30]Figure 30 is a graphical image of xenograft results for vehicle (SC, 5 μL / g, QD) and the degrader I-168 at various dosing regimens, showing tumor volume (mm3) (y-axis) versus dosing interval (days after start of treatment) (x-axis) for OCI-LY10 (MYD88 mutant) cells.

[0045] [Figure 31] FIG. 31 is a graphical image of xenograft results for vehicle (PO, BID) and the degraders I-168 and I-208 at various dosing regimens, showing tumor volume (mm) (y-axis) versus dosing interval (days after start of treatment) (x-axis) for SUDHL-2 cells.

[0046] [Figure 32] Figure 32 is a graphical image illustrating WBCs in exudates collected from air pouches in mice after MSU crystal challenge, showing counts (% cells in exudate) (y-axis) and (MSU; colchicine; 30, 100, and 300 mg / kg PO BID I-417; and 50 mg / kg PO BID I-257) (x-axis).

[0047] [Figure 33] Figure 33 is a graphical image illustrating neutrophils in exudates collected from air pouches in mice after MSU crystal challenge, showing counts (% cells in exudate) (y-axis) and (MSU; colchicine; 30, 100, and 300 mg / kg PO BID I-417; and 50 mg / kg PO BID I-257) (x-axis).

[0048] [Figure 34] Figure 34 is a graphical image illustrating IL-1b in exudates collected from air pouches in mice after MSU crystal challenge, showing counts (% cells in exudate) (y-axis) and (MSU; colchicine; 30, 100, and 300 mg / kg PO BID I-417; and 50 mg / kg PO BID I-257) (x-axis).

[0049] [Figure 35] FIG. 35 includes graph images illustrating the effect of pretreatment with I-417 on the TNFα content of exudates, showing mean TNFα (pg) (y-axis), and MSU, colchicine, and 30, 100, and 300 mg / kg PO I-417 (x-axis).

[0050] [Figure 36] FIG. 36 is a graphical image illustrating imiquimod (IMQ)-induced skin inflammation in mice, showing the change in ear thickness (μm) (y-axis) and vehicle, clobetasol, and I-417 (30, 100, and 300 mg / kg, PO, BID) (x-axis).

[0051] [Figure 37] FIG. 37 includes graph images illustrating the results of the mouse intraperitoneal MSU-induced peritonitis model, showing lavage fluid IL-1b levels (left) and plasma IL-6 levels (right) (pg / mL) (y-axis), and naive, vehicle (PO), and 10, 30, and 100 mg / kg I-30 (PO TID) (x-axis).

[0052] [Figure 38] FIG. 38 includes graph images illustrating the results of a PD study using I-417 in wild-type mice, showing IRAK4 levels (y-axis) versus time (hours) (x-axis) in the skin (left) and spleen (right). DETAILED DESCRIPTION OF THE INVENTION

[0053] Detailed Description of Specific Embodiments 1. General Description of Certain Embodiments of the Invention: The compounds of the present invention, and compositions thereof, are useful as degraders and / or inhibitors of one or more IRAK protein kinases. In some embodiments, provided compounds degrade and / or inhibit IRAK-1 / 2 / 3 / 4.

[0054] In certain embodiments, the present invention provides compounds of formula I: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I: IRAK is an IRAK-binding moiety capable of binding to one or more of IRAK-1, -2, -3, or -4; L is a bivalent moiety that binds IRAK to LBM; and LBM is the ligase binding moiety.

[0055] In certain embodiments, the present invention provides a compound of formula V: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula V: IRAK is an IRAK binding moiety capable of binding to one or more of IRAK-1, -2, -3, or -4; L is a bivalent moiety that binds IRAK to DIM; and DIM is a degradation-inducing moiety.

[0056] 2. Compounds and Definitions: The compounds of the present invention include those generally described above and are further exemplified by the classes, subclasses, and species disclosed herein. As used herein, unless otherwise specified, the following definitions shall apply. For the purposes of this invention, chemical elements are identified according to the Periodic Table of the Elements, CAS version, Handbook of Chemistry and Physics, 75th Edition. Furthermore, the general principles of organic chemistry are described in "Organic Chemistry", Thomas Sorrell, University Science Books, Sausalito: 1999, and "March's Advanced Organic Chemistry", 5th Edition, eds. Smith, M.B. and March, J., John Wiley & Sons, New York: 2001, the entire contents of which are incorporated herein by reference.

[0057] The term "aliphatic" or "aliphatic group," as used herein, means a straight-chain (i.e., unbranched) or branched, substituted or unsubstituted, hydrocarbon chain that is fully saturated or contains one or more unsaturated units, or a monocyclic or bicyclic hydrocarbon that is fully saturated or contains one or more unsaturated units, but is not aromatic (also referred to herein as "carbocycle," "alicyclic," or "cycloalkyl"), having one point of attachment to the remainder of the molecule. Unless otherwise specified, an aliphatic group contains 1-6 aliphatic carbon atoms. In some embodiments, an aliphatic group contains 1-5 aliphatic carbon atoms. In other embodiments, an aliphatic group contains 1-4 aliphatic carbon atoms. In still other embodiments, an aliphatic group contains 1-3 aliphatic carbon atoms, and in still other embodiments, an aliphatic group contains 1-2 aliphatic carbon atoms. In some embodiments, "alicyclic" (or "carbocycle" or "cycloalkyl") refers to a monocyclic C3-C6 hydrocarbon that is fully saturated or contains one or more units of unsaturation, but is not aromatic, and has one point of attachment to the rest of the molecule. Suitable aliphatic groups include, but are not limited to, straight-chain or branched, saturated or unsaturated, alkyl, alkenyl, alkynyl groups, and hybrids thereof (e.g., (cycloalkyl)alkyl, (cycloalkenyl)alkyl, or (cycloalkyl)alkenyl).

[0058] As used herein, the term "bridged bicyclic" refers to any bicyclic ring system (i.e., carbocyclic or heterocyclic) that is saturated or partially unsaturated and has at least one bridge. As defined by IUPAC, a "bridge" is an unbranched chain of atoms, or a single atom, or a valence bond connecting two bridgeheads, where a "bridgehead" is any skeletal atom of the ring system that is bonded to three or more skeletal atoms (other than hydrogen). In some embodiments, a bridged bicyclic group has 7 to 12 ring members and 0 to 4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. Such bridged bicyclic groups are well known in the art and include the groups described below, in which each group is attached to the remainder of the molecule at any suitable carbon or nitrogen atom. Unless otherwise specified, a bridged bicyclic group is optionally substituted with one or more substituents, such as those described for aliphatic groups. Additionally or alternatively, any substitutable nitrogen of a bridged bicyclic group is optionally substituted. Exemplary bridged bicyclic rings include: [ka] Examples include:

[0059] The term "lower alkyl" refers to C 1~4 " refers to a straight or branched chain alkyl group of the formula: Exemplary lower alkyl groups are methyl, ethyl, propyl, isopropyl, butyl, isobutyl, and tert-butyl.

[0060] The term "lower haloalkyl" refers to a C alkyl group substituted with one or more halogen atoms. 1~4 The term "alkyl" refers to a straight or branched chain alkyl group.

[0061] The term "heteroatom" refers to oxygen, sulfur, nitrogen, phosphorus, or silicon (any oxidized form of nitrogen, sulfur, phosphorus, or silicon; the quaternized form of any basic nitrogen; or a substitutable nitrogen of a heterocyclic ring (e.g., N (as in 3,4-dihydro-2H-pyrrolyl), NH (as in pyrrolidinyl), or NR +(as in N-substituted pyrrolidinyl)).

[0062] The term "unsaturated," as used herein, means a moiety having one or more units of unsaturation.

[0063] As used herein, the term "divalent C 1~8 (or C 1~6 ) saturated or unsaturated, straight or branched hydrocarbon chains" refers to straight or branched divalent alkylene, alkenylene, and alkynylene chains as defined herein.

[0064] The term "alkylene" refers to a divalent alkyl group. An "alkylene chain" is a polymethylene group, i.e., -(CH) n -, where n is a positive integer, preferably 1 to 6, 1 to 4, 1 to 3, 1 to 2, or 2 to 3. A substituted alkylene chain is a polymethylene group in which one or more methylene hydrogens are replaced with a substituent. Suitable substituents include those described below for substituted aliphatic groups.

[0065] The term "alkenylene" refers to a divalent alkenyl group. A substituted alkenylene chain is a polymethylene group containing at least one double bond in which one or more hydrogen atoms are replaced with substituents. Suitable substituents include those described below for substituted aliphatic groups.

[0066] As used herein, the term "cyclopropylenyl" refers to the following structure: [ka] The term "cyclopropyl" refers to a divalent cyclopropyl group of the formula:

[0067] The term "halogen" means F, Cl, Br, or I.

[0068] The term "aryl," used alone or as part of a larger moiety, as in "aralkyl," "aralkoxy," or "aryloxyalkyl," refers to a monocyclic or bicyclic ring system having a total of 5 to 14 ring members, in which at least one ring in the system is aromatic, and each ring in the system contains 3 to 7 ring members. The term "aryl" may be used interchangeably with the term "aryl ring." In certain embodiments of the invention, "aryl" refers to an aromatic ring system, including, but not limited to, phenyl, biphenyl, naphthyl, and anthracyl, which may bear one or more substituents. Included within the scope of the term "aryl," as used herein, are groups in which an aromatic ring is fused to one or more non-aromatic rings, such as, for example, indanyl, phthalimidyl, naphthimidyl, phenanthridinyl, or tetrahydronaphthyl.

[0069] The terms "heteroaryl" and "heteroara-," used alone or as part of a larger moiety (e.g., "heteroaralkyl" or "heteroaralkoxy"), refer to groups having 5 to 10 ring atoms, preferably 5, 6, or 9 ring atoms; having 6, 10, or 14 pi electrons shared in a cyclic arrangement; and having 1 to 5 heteroatoms in addition to carbon atoms. The term "heteroatom" refers to nitrogen, oxygen, or sulfur and includes any oxidized form of nitrogen or sulfur, and any quaternized form of a basic nitrogen. Heteroaryl groups include, but are not limited to, thienyl, furanyl, pyrrolyl, imidazolyl, pyrazolyl, triazolyl, tetrazolyl, oxazolyl, isoxazolyl, oxadiazolyl, thiazolyl, isothiazolyl, thiadiazolyl, pyridyl, pyridazinyl, pyrimidinyl, pyrazinyl, indolizinyl, purinyl, naphthyridinyl, and pteridinyl. The terms "heteroaryl" and "heteroara-," as used herein, also encompass groups in which a heteroaromatic ring is fused to one or more aryl, alicyclic, or heterocyclic rings, and the radical or point of attachment is on the heteroaromatic ring. Non-limiting examples include indolyl, isoindolyl, benzothienyl, benzofuranyl, dibenzofuranyl, indazolyl, benzimidazolyl, benzothiazolyl, quinolyl, isoquinolyl, cinnolinyl, phthalazinyl, quinazolinyl, quinoxalinyl, 4H-quinolizinyl, carbazolyl, acridinyl, phenazinyl, phenothiazinyl, phenoxazinyl, tetrahydroquinolinyl, tetrahydroisoquinolinyl, and pyrido[2,3-b]-1,4-oxazin-3(4H)-one. Heteroaryl groups may be monocyclic or bicyclic. The term "heteroaryl" may be used interchangeably with the terms "heteroaryl ring," "heteroaryl group," or "heteroaromatic," any of which terms include rings that are optionally substituted. The term "heteroaralkyl" refers to an alkyl group substituted by a heteroaryl, where the alkyl and heteroaryl portions independently are optionally substituted.

[0070] As used herein, the terms "heterocycle," "heterocyclyl," "heterocyclic radical," and "heterocyclic ring" are used interchangeably and refer to a stable 5- to 7-membered monocyclic or 7- to 10-membered bicyclic heterocyclic moiety that is either saturated or partially unsaturated and has, in addition to carbon atoms, one or more, preferably one to four, heteroatoms as defined above. When used in reference to a ring atom of a heterocycle, the term "nitrogen" includes substituted nitrogen. As an example, in a saturated or partially unsaturated ring having zero to three heteroatoms selected from oxygen, sulfur, or nitrogen, the nitrogen can be N (as in 3,4-dihydro-2H-pyrrolyl) or NH (as in pyrrolidinyl). + It may also be NR (as in N-substituted pyrrolidinyl).

[0071] A heterocyclic ring can be attached to its parent group at any heteroatom or carbon atom that results in a stable structure, and any of these ring atoms can be optionally substituted. Examples of such saturated or partially unsaturated heterocyclic radicals include, but are not limited to, tetrahydrofuranyl, tetrahydrothiophenyl, pyrrolidinyl, piperidinyl, pyrrolinyl, tetrahydroquinolinyl, tetrahydroisoquinolinyl, decahydroquinolinyl, oxazolidinyl, piperazinyl, dioxanyl, dioxolanyl, diazepinyl, oxazepinyl, thiazepinyl, morpholinyl, and quinuclidinyl. The terms "heterocycle," "heterocyclyl," "heterocyclyl ring," "heterocyclic group," "heterocyclic moiety," and "heterocyclic radical" are used interchangeably herein and also include groups in which a heterocyclyl ring is fused to one or more aryl, heteroaryl, or alicyclic rings (e.g., indolinyl, 3H-indolyl, chromanyl, phenanthridinyl, or tetrahydroquinolinyl). Heterocyclyl groups can be monocyclic or bicyclic. The term "heterocyclylalkyl" refers to an alkyl group substituted by a heterocyclyl, where the alkyl and heterocyclyl portions independently are optionally substituted.

[0072] As used herein, the term "partially unsaturated" refers to a ring moiety that contains at least one double or triple bond. The term "partially unsaturated" is intended to encompass rings with multiple sites of unsaturation, but is not intended to include aryl or heteroaryl moieties as defined herein.

[0073] As described herein, compounds of the invention may contain "optionally substituted" moieties. In general, the term "substituted," whether preceded by the term "optionally" or not, means that one or more hydrogens of the specified moiety have been replaced with a suitable substituent. Unless otherwise indicated, an "optionally substituted" group may have a suitable substituent at each substitutable position of the group, and when more than one position in any given structure may be substituted with more than one substituent selected from a specified group, the substituents may be either the same or different at each position. Combinations of substituents envisioned by the present invention are preferably those that result in the formation of stable or chemically feasible compounds. The term "stable," as used herein, refers to compounds that are substantially unchanged when subjected to conditions that permit their production, detection, and, in certain embodiments, their recovery, purification, and use for one or more of the purposes disclosed herein.

[0074] Suitable monovalent substituents on a substitutable carbon atom of an "optionally substituted" group are independently: halogen; -(CH) 0~4 R ○ ;-(CH2) 0~4 OR ○ ;-O(CH2) 0~4 R ○ , -O-(CH2) 0~4 C(O)OR ○ ;-(CH2) 0~4 CH(OR ○ )2;-(CH2) 0~4 SR ○ ;-(CH2) 0~4 Ph (which is R ○ -(CH2) 0~4 O(CH2) 0~1 Ph (which is R ○ -CH=CHPh (which may be substituted with R ○ -(CH2) 0~4 O(CH2) 0~1 -pyridyl (which is R ○which may be replaced by); -NO2; -CN; -N3; -(CH2) 0~4 N(R ○ )2; -(CH2) 0~4 N(R ○ )C(O)R ○ ; -N(R ○ )C(S)R ○ ; -(CH2) 0~4 N(R ○ )C(O)NR ○ 2; -N(R ○ )C(S)NR ○ 2; -(CH2) 0~4 N(R ○ )C(O)OR ○ ; -N(R ○ )N(R ○ )C(O)R ○ ; -N(R ○ )N(R ○ )C(O)NR ○ 2; -N(R ○ )N(R ○ )C(O)OR ○ ; -(CH2) 0~4 C(O)R ○ ; -C(S)R ○ ; -(CH2) 0~4 C(O)OR ○ ; -(CH2) 0~4 C(O)SR ○ ; -(CH2) 0~4 C(O)OSiR ○ 3; -(CH2) 0~4 OC(O)R ○ ; -OC(O)(CH2) 0~4 SR ○ ; -SC(S)SR ○ ; -(CH2) 0~4 SC(O)R ○ ; -(CH2) 0~4 C(O)NR ○ 2; -C(S)NR ○ 2; -C(S)SR ○ ; -(CH2) 0~4 OC(O)NR ○ 2; -C(O)N(OR ○ )R ○ ; -C(O)C(O)R ○ ; -C(O)CH2C(O)R ○;-C(NOR ○ )R ○ ;-(CH2) 0~4 SSR ○ ;-(CH2) 0~4 S(O)2R ○ ;-(CH2) 0~4 S(O)2OR ○ ;-(CH2) 0~4 OS(O)2R ○ ;-S(O)2NR ○ 2;-(CH2) 0~4 S(O)R ○ ;-N(R ○ )S(O)NR ○ 2;-N(R ○ )S(O)2R ○ ;-N(OR ○ )R ○ ;-C(NH)NR ○ 2;-P(O)2R ○ ;-P(O)R ○ 2;-OP(O)R ○ 2;-OP(O)(OR ○ )2;-SiR ○ 3;-(C 1~4 straight or branched chain alkylene)ON(R ○ )2; or -(C 1~4 straight or branched chain alkylene)C(O)ON(R ○ )2, where each R ○ may be substituted as defined below and independently represent hydrogen, C 1~6 Aliphatic, -CH2Ph, -O(CH2) 0~1 Ph, -CH2- (a 5- to 6-membered heteroaryl ring), or a 5- to 6-membered saturated, partially unsaturated, or aryl ring having 0 to 4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or, regardless of the above definitions, R ○ two independent occurrences of together with the atom(s) between them form a 3- to 12-membered saturated, partially unsaturated, or aryl monocyclic or bicyclic ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, which can be substituted as defined below.

[0075] R ○ (R ○ Suitable monovalent substituents on the ring formed by two independent occurrences of (a ring formed by two independent occurrences of together with the atom between them) are independently halogen, -(CH2) 0~2 R ● ,-(Halo R ● ), -(CH2) 0~2 OH, -(CH2) 0~2 OR ● , -(CH2) 0~2 CH(OR ● )2;-O(HaloR ● ), -CN, -N3, -(CH2) 0~2 C(O)R ● , -(CH2) 0~2 C(O)OH, -(CH2) 0~2 C(O)OR ● , -(CH2) 0~2 SR ● , -(CH2) 0~2 SH, -(CH2) 0~2 NH2, -(CH2) 0~2 NHR ● , -(CH2) 0~2 NR ● 2, -NO2, -SiR ● 3. -OSiR ● 3. -C(O)SR ● , -(C 1~4 straight or branched chain alkylene)C(O)OR ● , or -SSR ● where each R ● is unsubstituted or, if preceded by "halo", is substituted with only one or more halogens, and independently, C 1~4 Aliphatic, -CH2Ph, -O(CH2) 0~1 Ph, or a 5- to 6-membered saturated, partially unsaturated, or aryl ring having 0 to 4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. ○ Suitable divalent substituents on a saturated carbon atom of include ═O and ═S.

[0076] Suitable divalent substituents on a saturated carbon atom of an "optionally substituted" group include: ═O, ═S, ═NNR * 2, =NNHC(O)R * , =NNHC(O)OR * , =NNHS(O)2R * , =NR * , =NOR * , -O(C(R * 2)) 2~3 O-, or -S(C(R * 2)) 2~3 S-. Here R * Each independent occurrence of may be hydrogen, C, which may be substituted as defined below. 1~6 and an unsubstituted 5- to 6-membered saturated, partially unsaturated, or aryl ring having an aliphatic or 0-4 heteroatom independently selected from nitrogen, oxygen, or sulfur. Suitable divalent substituents attached to a vicinal substitutable carbon of an "optionally substituted" group include -O(CR * 2) 2~3 O-, where R * Each independent occurrence of may be hydrogen, C, which may be substituted as defined below. 1~6 It is selected from an aliphatic or unsubstituted 5- to 6-membered saturated, partially unsaturated, or aryl ring having 0 to 4 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0077] R * Suitable substituents on the aliphatic group include halogen, -R ● ,-(Halo R ● ), -OH, -OR ● , -O(HaloR ● ), -CN, -C(O)OH, -C(O)OR ● , -NH2, -NHR ● , -NR ● 2, or -NO2, where each R ● is unsubstituted or, if preceded by "halo", is substituted with only one or more halogens, and independently, C 1~4 Aliphatic, -CH2Ph, -O(CH2) 0~1Ph, or a 5- to 6-membered saturated, partially unsaturated, or aryl ring having 0 to 4 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0078] Suitable substituents on a substitutable nitrogen of an "optionally substituted" group include -R † , -NR † 2. -C(O)R † , -C(O)OR † , -C(O)C(O)R † , -C(O)CHC(O)R † , -S(O)2R † , -S(O)NR † 2. -C(S)NR † 2. -C(NH)NR † 2, or -N(R † )S(O)2R † where each R † are independently hydrogen, C which may be substituted as defined below 1~6 an aliphatic, unsubstituted -OPh, or an unsubstituted 5- to 6-membered saturated, partially unsaturated, or aryl ring having 0 to 4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or, regardless of the above definitions, R † two independent occurrences of together with the atom(s) between them form an unsubstituted 3- to 12-membered saturated, partially unsaturated, or aryl monocyclic or bicyclic ring having 0 to 4 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0079] R † Suitable substituents on the aliphatic group are independently halogen, -R ● ,-(Halo R ● ), -OH, -OR ● , -O(HaloR ● ), -CN, -C(O)OH, -C(O)OR ● , -NH2, -NHR ● , -NR ● 2, or -NO2, where each R ●is unsubstituted or, if preceded by "halo", is substituted with only one or more halogens, and independently, C 1~4 Aliphatic, -CH2Ph, -O(CH2) 0~1 Ph, or a 5- to 6-membered saturated, partially unsaturated, or aryl ring having 0 to 4 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0080] As used herein, the term "provided compounds" refers to any genus, subgenus, and / or species described herein.

[0081] As used herein, the term "pharmaceutically acceptable salt" refers to a salt that is, within the scope of sound medical judgment, suitable for use in contact with the tissues of humans and lower animals without undue toxicity, irritation, allergic response, etc., and commensurate with a reasonable benefit / risk ratio. Pharmaceutically acceptable salts are well known in the art. For example, S.M. Berge et al. describe pharmaceutically acceptable salts in detail in J. Pharmaceutical Sciences, 1977, 66, 1-19, which is incorporated herein by reference. Pharmaceutically acceptable salts of the compounds of the present invention include salts derived from suitable inorganic acids, inorganic bases, organic acids, and organic bases. Examples of pharmaceutically acceptable non-toxic acid addition salts are salts of amino groups formed with inorganic acids (e.g., hydrochloric acid, hydrobromic acid, phosphoric acid, sulfuric acid, and perchloric acid) or organic acids (e.g., acetic acid, oxalic acid, maleic acid, tartaric acid, citric acid, succinic acid, or malonic acid), or formed by using other methods used in the art, such as ion exchange. Other pharmaceutically acceptable salts include adipate, alginate, ascorbate, aspartate, benzenesulfonate, benzoate, bisulfate, borate, butyrate, camphorate, camphorsulfonate, citrate, cyclopentanepropionate, digluconate, dodecylsulfate, ethanesulfonate, formate, fumarate, glucoheptonate, glycerophosphate, gluconate, hemisulfate, heptanoate, hexanoate, hydroiodide, 2-hydroxy-ethanesulfonate, and the like. Examples of suitable salts include phosphate, lactobionate, lactate, laurate, lauryl sulfate, malate, maleate, malonate, methanesulfonate, 2-naphthalenesulfonate, nicotinate, nitrate, oleate, oxalate, palmitate, pamoate, pectinate, persulfate, 3-phenylpropionate, phosphate, pivalate, propionate, stearate, succinate, sulfate, tartrate, thiocyanate, p-toluenesulfonate, undecanoate, and valerate.

[0082] Salts derived from appropriate bases include alkali metal salts, alkaline earth metal salts, ammonium salts and N + (C 1~4 Representative alkali metal or alkaline earth metal salts include sodium, lithium, potassium, calcium, magnesium, and the like. Further pharmaceutically acceptable salts include non-toxic ammonium, quaternary ammonium, and amine cations, formed where appropriate using counterions such as halides, hydroxides, carbonates, sulfates, phosphates, nitrates, lower alkylsulfonates, and arylsulfonates.

[0083] Unless otherwise stated, structures depicted herein are also meant to include all isomeric (e.g., enantiomeric, diastereomeric, and geometric (or conformational)) forms of the structure, such as the R and S configurations for each asymmetric center, Z and E double bond isomers, and Z and E conformational isomers. Thus, single stereochemical isomers as well as enantiomeric, diastereomeric, and geometric (or conformational) mixtures of the compounds of the invention are within the scope of the invention. Unless otherwise stated, all tautomeric forms of the compounds of the invention are within the scope of the invention. Furthermore, unless otherwise stated, structures depicted herein are also meant to include compounds that differ only in the presence of one or more isotopically enriched atoms. For example, structures of the invention in which hydrogen is replaced by deuterium or tritium, or in which carbon is replaced by methyl ... 13 C or 14 Compounds having the invention in which C is replaced with an enriched carbon are within the scope of the invention. Such compounds are useful, for example, as analytical tools according to the invention, as probes in biological assays, or as therapeutic agents.

[0084] As used herein, the term "inhibitor" is defined as a compound that binds to and / or inhibits IRAK kinase with measurable affinity. In certain embodiments, an inhibitor has an IC of less than about 50M, less than about 1M, less than about 500nM, less than about 100nM, less than about 10nM, or less than about 1nM. 50 and / or have a binding constant.

[0085] As used herein, the term "degrading agent" is defined as a heterobifunctional compound that binds and / or inhibits both IRAK kinase and E3 ligase with measurable affinity, resulting in ubiquitination and subsequent degradation of the IRAK kinase. In certain embodiments, a degrading agent has a DC of less than about 50M, less than about 1M, less than about 500nM, less than about 100nM, less than about 10nM, or less than about 1nM. 50 As used herein, the term "monovalent" refers to a degrader compound that does not have an E3 ligase binding moiety attached.

[0086] The compounds of the present invention can be tethered to a detectable moiety. It is understood that such compounds are useful as imaging agents. Those skilled in the art will recognize that a detectable moiety can be attached to a provided compound via a suitable substituent. As used herein, the term "suitable substituent" refers to a moiety that can be covalently linked to a detectable moiety. Such moieties are well known to those skilled in the art and include, for example, groups containing carbonate, amino, thiol, or hydroxyl moieties, to name a few. It is understood that such moieties can be attached directly to a provided compound or via a tethering group such as a bivalent saturated or unsaturated hydrocarbon chain. In some embodiments, such moieties can be attached via click chemistry. In some embodiments, such moieties can be attached via 1,3-cycloaddition of an azide with an alkyne, optionally in the presence of a copper catalyst. Methods using click chemistry are known in the art and include those described by Rostovtsev et al., Angew. Chem. Int. Ed. 2002, 41, 2596-99 and Sun et al., Bioconjugate Chem., 2006, 17, 52-57.

[0087] As used herein, the term "detectable moiety" is used interchangeably with the term "label" and refers to any moiety that can be detected, such as primary and secondary labels. Radioisotopes (e.g., tritium, 32 P, 33 P, 35 S, or 14 C), primary labels, such as mass tags and fluorescent labels, are signal-generating reporter groups that can be detected without further modification. Detectable moieties also include luminescent and phosphorescent groups.

[0088] As used herein, the term "secondary label" refers to moieties such as biotin and various protein antigens that require the presence of a secondary intermediate to generate a detectable signal. For biotin, the secondary intermediate may include a streptavidin-enzyme conjugate. For antigen labels, the secondary intermediate may include an antibody-enzyme conjugate. Some fluorescent groups act as secondary labels because they transfer energy to another group in the process of non-radioactive fluorescence resonance energy transfer (FRET), and the second group generates the signal that is detected.

[0089] As used herein, the terms "fluorescent label," "fluorescent dye," and "fluorophore" refer to a moiety that absorbs light energy at a defined excitation wavelength and emits light energy at a different wavelength. Examples of fluorescent labels include Alexa Fluor dyes (Alexa Fluor 350, Alexa Fluor 488, Alexa Fluor 532, Alexa Fluor 546, Alexa Fluor 568, Alexa Fluor 594, Alexa Fluor 633, Alexa Fluor 660, and Alexa Fluor 680), AMCA, AMCA-S, BODIPY dyes (BODIPY FL, BODIPY R6G, BODIPY TMR, BODIPY TR, BODIPY530 / 550, BODIPY558 / 568, BODIPY564 / 570, BODIPY576 / 589, BODIPY581 / 591, BODIPY630 / 650, BODIPY650 / 665), carboxyrhodamine 6G, carboxy-X-rhodamine (ROX), Cascade Blue, Cascade Yellow, Coumarin 343, cyanine dyes (Cy3, Cy5, Cy3.5, Cy5.5), dansyl, dapoxyl, dialkylaminocoumarin, 4',5'-dichloro-2',7'-dimethoxy-fluorescein, DM-NERF, eosin, erythrosine, fluorescein, FAM, hydrochloride Examples of suitable dyes include, but are not limited to, roxycoumarin, IRDyes (IRD40, IRD700, IRD800), JOE, Lissamine rhodamine B, Marina Blue, methoxycoumarin, naphthofluorescein, Oregon Green 488, Oregon Green 500, Oregon Green 514, Pacific Blue, PyMPO, pyrene, rhodamine B, rhodamine 6G, rhodamine green, rhodamine red, rhodol green, 2',4',5',7'-tetra-bromosulfone-fluorescein, tetramethyl-rhodamine (TMR), carboxytetramethylrhodamine (TAMRA), Texas Red, and Texas Red-X.

[0090] As used herein, the term "mass tag" refers to any moiety that can be uniquely detected by its mass using mass spectrometry (MS) detection technology.Examples of mass tag include electrophoretic release tags such as N-[3-[4'-[(p-methoxytetrafluorobenzyl)oxy]phenyl]-3-methylglyceronyl]isonipeconic acid, 4'-[2,3,5,6-tetrafluoro-4-(pentafluorophenoxyl)]methylacetophenone and their derivatives.The synthesis and usefulness of these mass tags are described in U.S. Patent No. 4,650,750, U.S. Patent No. 4,709,016, U.S. Patent No. 5,360,8191, U.S. Patent No. 5,516,931, U.S. Patent No. 5,602,273, U.S. Patent No. 5,604,104, U.S. Patent No. 5,610,020 and U.S. Patent No. 5,650,270. Other examples of mass tags include, but are not limited to, nucleotides of various lengths and base compositions, dideoxynucleotides, oligonucleotides, oligopeptides, oligosaccharides, and other synthetic polymers of various lengths and monomer compositions. A wide variety of organic molecules (biomolecules or synthetic compounds), both neutral and charged, in the appropriate mass range (100-2000 daltons) may be used as mass tags.

[0091] The terms "measurable affinity" and "measurably inhibit," as used herein, refer to a measurable change in IRAK protein kinase activity between a sample containing a compound of the present invention or a composition thereof and IRAK protein kinase and an equivalent sample containing IRAK protein kinase without the compound or composition thereof present.

[0092] 3. Description of Exemplary Embodiments: As noted above, in certain embodiments, the present invention provides compounds of formula I: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I: IRAK is an IRAK binding moiety capable of binding to one or more of IRAK-1, -2, -3, or -4; L is a bivalent moiety that binds IRAK to LBM; and LBM is the ligase binding moiety.

[0093] In some embodiments, the present invention provides a compound of formula I: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I: IRAK is the IRAK-4 binding moiety; L is a bivalent moiety that binds IRAK to LBM; and LBM is the cereblon ligase binding moiety.

[0094] As noted above, in certain embodiments, the present invention provides compounds of formula V: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula V: IRAK is an IRAK binding moiety capable of binding to one or more of IRAK-1, -2, -3, or -4; L is a bivalent moiety that binds IRAK to DIM; and DIM is a degradation-inducing moiety.

[0095] In some embodiments, the present invention provides a compound of formula V: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula V: IRAK is the IRAK-4 binding moiety; L is a bivalent moiety that binds IRAK to DIM; and DIM is an LBM, a lysine mimetic, or a hydrogen atom. IRAK binding part (IRAK)

[0096] In certain embodiments, the present invention provides a compound according to the invention, wherein the IRAK is an IRAK-4 binding moiety, whereby the compound has formula II: [ka] or a pharmaceutically acceptable salt thereof, wherein in Formula II, L and LBM are as defined above and as described in embodiments herein, and Ring A is a 4- to 10-membered saturated mono- or bicyclic carbocyclic or heterocyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring B is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 9-membered monocyclic or bicyclic heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring C is phenyl or a 5- to 10-membered monocyclic or bicyclic heteroaryl ring having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 2 and L 3 each independently represents a covalent bond, or C 1~3 wherein one to three methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-; Each R 1 are independently hydrogen, deuterium, -R 5, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CFR2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, or -C(O)NR2; Each R is independently hydrogen, deuterium, or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same atom, optionally taken together with the atoms between them, form an optionally substituted 4- to 11-membered saturated or partially unsaturated carbocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, spiro, or heteroaryl ring having, in addition to the atom to which they are attached, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 2 are independently hydrogen, deuterium, -R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 4 teeth, [ka] , hydrogen, or an optionally substituted group, wherein the optionally substituted group is selected from C 1~6 selected from aliphatic or 4- to 11-membered saturated or partially unsaturated monocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, or spiro rings having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring D is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 3 are independently hydrogen, deuterium, -R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Each R 5 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 3- to 7-membered saturated or partially unsaturated carbocyclic or heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; each n is 0, 1, or 2; each m is 0, 1, 2, 3, or 4; and each p is 0, 1, 2, 3, or 4; wherein the compound of formula II is not compound I-99 or I-100 of Table 1A.

[0097] In certain embodiments, the present invention provides a compound of formula II': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II': Ring A is an optionally substituted 4- to 10-membered saturated mono- or bicyclic carbocyclic or heterocyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring B is phenyl, a 4- to 7-membered saturated or partially unsaturated carbocyclic or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring C is phenyl, a 4- to 7-membered saturated or partially unsaturated carbocyclic or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 6-membered heteroaryl ring having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 2 and L 3 each independently represents a covalent bond, or C 1~3 wherein one to three methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-; Each R 1 are independently hydrogen, deuterium, -R 5, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CFR2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, or -C(O)NR2, or two R on the same carbon 1 together to form =O or =S; Each R is independently hydrogen, deuterium, or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same atom, optionally taken together with the atoms between them, form an optionally substituted 4- to 11-membered saturated or partially unsaturated carbocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, spiro, or heteroaryl ring having, in addition to the atom to which they are attached, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 2 are independently hydrogen, deuterium, -R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R, or two R on the same carbon 2 together to form =O or =S; R 4 is hydrogen or [ka] Selected from; Ring D is a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic carbocyclic or heterocyclic ring having 1 to 3 heteroatoms independently selected from phenyl, nitrogen, oxygen, and sulfur, or a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 3 are independently hydrogen, deuterium, -R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R, or two R on the same carbon 3 together to form =O or =S; Each R 5 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 3- to 7-membered saturated or partially unsaturated carbocyclic or heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; each n is 0, 1, or 2; each m is 0, 1, 2, 3, or 4; each p is 0, 1, 2, 3, or 4;

[0098] In certain embodiments, the present invention provides a compound according to the invention, wherein the IRAK is an IRAK-4 binding moiety, whereby the compound is of formula Va: [ka] or a pharmaceutically acceptable salt thereof, wherein L and DIM are as defined above and as described in embodiments herein, and Ring A is a 4- to 10-membered saturated mono- or bicyclic carbocyclic or heterocyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring B is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 9-membered monocyclic or bicyclic heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring C is phenyl or a 5- to 10-membered monocyclic or bicyclic heteroaryl ring having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 2 and L 3 each independently represents a covalent bond, or C 1~3 wherein one to three methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-; Each R 1 are independently hydrogen, deuterium, -R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CFR2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, or -C(O)NR2; Each R is independently hydrogen, deuterium, or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same atom, optionally taken together with the atoms between them, form an optionally substituted 4- to 11-membered saturated or partially unsaturated carbocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, spiro, or heteroaryl ring having, in addition to the atom to which they are attached, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 2 are independently hydrogen, deuterium, -R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 4 teeth, [ka] , hydrogen, or an optionally substituted group, wherein the optionally substituted group is selected from C 1~6 selected from aliphatic or 4- to 11-membered saturated or partially unsaturated monocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, or spiro rings having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring D is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 3 are independently hydrogen, deuterium, -R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Each R 5 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, a 3- to 7-membered saturated or partially unsaturated carbocyclic or heterocyclic ring having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; each n is 0, 1, or 2; each m is 0, 1, 2, 3, or 4; and each p is 0, 1, 2, 3, or 4; wherein the compound of formula Va is not compound I-99 or I-100 of Table 1A.

[0099] The following embodiments, found in paragraphs

[0084] -

[0140] , are directed to compounds of formula II, II', and Va.

[0100] As generally defined above, Ring A is a 4- to 10-membered saturated mono- or bicyclic carbocyclic or heterocyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0101] In some embodiments, Ring A is cyclobutyl. In some embodiments, Ring A is cyclopentyl. In some embodiments, Ring A is cyclohexyl. In some embodiments, Ring A is cyclopentyl. In some embodiments, Ring A is [ka] In some embodiments, ring A is [ka] is.

[0102] In some embodiments, ring A is selected from those depicted in Table 1 below.

[0103] As generally defined above, Ring B is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 9-membered monocyclic or bicyclic heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0104] In some embodiments, ring B is phenyl. In some embodiments, ring B is a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic ring, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, ring B is a 5- to 9-membered monocyclic or bicyclic heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0105] In some embodiments, ring B is [ka] In some embodiments, ring B is [ka] In some embodiments, ring B is [ka] In some embodiments, ring B is [ka] In some embodiments, ring B is [ka] In some embodiments, ring B is [ka] is.

[0106] As generally defined above, Ring C is phenyl or a 5- to 10-membered monocyclic or bicyclic heteroaryl ring having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0107] In some embodiments, Ring C is phenyl. In some embodiments, Ring C is a 5- to 10-membered monocyclic or bicyclic heteroaryl ring having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0108] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] is.

[0109] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] is.

[0110] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] is.

[0111] In some embodiments, ring C is selected from those depicted in Table 1 below.

[0112] As generally defined above, L 2 is a covalent bond, or C 1~3 wherein one to three methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-.

[0113] In some embodiments, L 2 is a covalent bond. In some embodiments, L 2 is C 1~3 wherein 1 to 3 methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-. In some embodiments, L 2 is C 1~3 In some embodiments, L 2 is -CH-. In some embodiments, L 2 is -C(D)(H)-. In some embodiments, L 2 is -C(D)2-. In some embodiments, L 2is -CHCH-. In some embodiments, L 2 In some embodiments, L 2 is -CHNR-. In some embodiments, L 2 or -O-. In some embodiments, L 2 is —CH2O—. In some embodiments, L 2 is -S-. In some embodiments, L 2 is -OC(O)-. In some embodiments, L 2 is —C(O)O—. In some embodiments, L 2 is —C(O)—. In some embodiments, L 2 is —S(O)—. In some embodiments, L 2 is -S(O)-. In some embodiments, L 2 is -NRS(O)-. In some embodiments, L 2 is -S(O)NR-. In some embodiments, L 2 is -NRC(O)-. In some embodiments, L 2 is —C(O)NR—. In some embodiments, L 2 is —OC(O)NR—. In some embodiments, L 2 is -NRC(O)O-.

[0114] As generally defined above, L 3 is a covalent bond, or C 1~3 wherein one to three methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-.

[0115] In some embodiments, L 3 is C 1~3wherein 1 to 3 methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-. In some embodiments, L 3 is C 1~3 In some embodiments, L 3 is -CH-. In some embodiments, L 3 is -C(D)(H)-. In some embodiments, L 3 is -C(D)2-. In some embodiments, L 3 is -CHCH-. In some embodiments, L 3 In some embodiments, L 3 is -CHNR-. In some embodiments, L 3 or -O-. In some embodiments, L 3 is —CH2O—. In some embodiments, L 3 is -S-. In some embodiments, L 3 is -OC(O)-. In some embodiments, L 3 is —C(O)O—. In some embodiments, L 3 is —C(O)—. In some embodiments, L 3 is —S(O)—. In some embodiments, L 3 is -S(O)-. In some embodiments, L 3 is -NRS(O)-. In some embodiments, L 3 is -S(O)NR-. In some embodiments, L 3 is -NRC(O)-. In some embodiments, L 3 is —C(O)NR—. In some embodiments, L 3 is —OC(O)NR—. In some embodiments, L 3 is -NRC(O)O-.

[0116] In some embodiments, L 2 and L 3 is selected from those illustrated in Table 1 below.

[0117] As generally defined above, each R 1 are independently hydrogen, deuterium, -R 5 , Halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CFR2, -CF3, -CR2(OR) , -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, -N(R)S(O)2R, -N + (O - )R2, -OP(O)R2, -OP(O)(OR)2, -OP(O)(OR)NR2, -OP(O)(NR2)2, -P(O)R2, -SiR3, -Si(OR)R2, -SF5, or [ka] is.

[0118] In some embodiments, each R 1 are independently hydrogen. In some embodiments, R 1 is deuterium. In some embodiments, each R 1 are independent, -R 5 In some embodiments, each R 1 is independently halogen. In some embodiments, each R 1 is independently -CN. In some embodiments, each R 1 is independently -NO. In some embodiments, each R 1 is independently -OR. In some embodiments, each R 1is independently -SR. In some embodiments, each R 1 is independently -NR. In some embodiments, each R 1 is independently —S(O)R. In some embodiments, each R 1 is independently —S(O)NR. In some embodiments, each R 1 is independently —S(O)R. In some embodiments, each R 1 is independently —S(O)(NR)R. In some embodiments, each R 1 is independently -P(O)(OR). In some embodiments, each R 1 is independently —P(O)(NR). In some embodiments, each R 1 is independently -CF(R). In some embodiments, each R 1 is independently -CFR2. In some embodiments, each R 1 is independently -CF. In some embodiments, each R 1 is independently -CR(OR). In some embodiments, each R 1 is independently -CR(NR). In some embodiments, each R 1 is independently —C(O)R. In some embodiments, each R 1 is independently —C(O)OR. In some embodiments, each R 1 is independently —C(O)NR. In some embodiments, each R 1 is independently —C(O)N(R)OR. In some embodiments, each R 1 is independently —OC(O)R. In some embodiments, each R 1 is independently —OC(O)NR. In some embodiments, each R 1 is independently —N(R)C(O)OR. In some embodiments, each R 1 is independently —N(R)C(O)R. In some embodiments, each R 1is independently —N(R)C(O)NR. In some embodiments, each R 1 is independently —N(R)S(O)R. In some embodiments, each R 1 are independent, -N + (O - )R2. In some embodiments, each R 1 is independently -OP(O)R. In some embodiments, each R 1 is independently -OP(O)(OR). In some embodiments, each R 1 is independently -OP(O)(OR)NR. In some embodiments, each R 1 is independently -OP(O)(NR). In some embodiments, each R 1 is independently -P(O)R. In some embodiments, each R 1 is independently -SiR. In some embodiments, each R 1 is independently -Si(OR)R. In some embodiments, each R 1 is independently -SF. In some embodiments, each R 1 is independent, [ka] is.

[0119] In some embodiments, R 1 is -CHF2. In some embodiments, R 1 is —C(OH)(CH). In some embodiments, R 1 is —C(O)NH. In some embodiments, R 1 is —CF. In some embodiments, R 1 In some embodiments, R 1 is isoprene. In some embodiments, R 1 teeth [ka] In some embodiments, R 1 teeth [ka] is.

[0120] As generally defined above, R 2 and R 3 each independently represents hydrogen, deuterium, -R 5 , Halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CFR2, -CF3, -CR2(OR) , -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, -N(R)S(O)2R, -N + (O - )R2, -OP(O)R2, -OP(O)(OR)2, -OP(O)(OR)NR2, -OP(O)(NR2)2, -P(O)R2, -SiR3, -Si(OR)R2, -SF5, or [ka] is.

[0121] In some embodiments, R 2 and R 3 Each of R is independently hydrogen. 2 and R 3 Each of R is independently deuterium. 2 and R 3 each independently represents -R 5 In some embodiments, R 2 and R 3 Each of R is independently halogen. 2 and R 3Each of R is independently -CN. 2 and R 3 Each of R is independently -NO. 2 and R 3 Each of R is independently -OR. 2 and R 3 Each of R is independently -SR. 2 and R 3 Each of is independently -NR2. In some embodiments, R 2 and R 3 Each of is independently -S(O)R. In some embodiments, R 2 and R 3 Each of is independently -S(O)NR. In some embodiments, R 2 and R 3 Each of is independently -S(O)R. In some embodiments, R 2 and R 3 Each of is independently -S(O)(NR)R. In some embodiments, R 2 and R 3 Each of is independently -P(O)(OR). In some embodiments, R 2 and R 3 Each of is independently -P(O)(NR). In some embodiments, R 2 and R 3 Each of is independently -CF(R). In some embodiments, R 2 and R 3 Each of R is independently -CFR2. 2 and R 3 Each of is independently -CF. In some embodiments, R 2 and R 3 Each of R is independently -CR(OR). 2 and R 3 Each of is independently -CR2(NR2). In some embodiments, R2 and R 3 Each of is independently -C(O)R. In some embodiments, R 2 and R 3 Each of is independently -C(O)OR. In some embodiments, R 2 and R 3 Each of is independently —C(O)NR. In some embodiments, R 2 and R 3 Each of is independently -C(O)N(R)OR. In some embodiments, R 2 and R 3 Each of is independently -OC(O)R. In some embodiments, R 2 and R 3 Each of is independently -OC(O)NR. In some embodiments, R 2 and R 3 Each of is independently -N(R)C(O)OR. In some embodiments, R 2 and R 3 Each of is independently -N(R)C(O)R. In some embodiments, R 2 and R 3 Each of is independently —N(R)C(O)NR. In some embodiments, R 1 and R 2 Each of is independently -N(R)S(O)R. In some embodiments, R 2 and R 3 each independently represents -N + (O - )R2. In some embodiments, R 2 and R 3 Each of is independently -OP(O)R. In some embodiments, R 2 and R 3 Each of is independently -OP(O)(OR). In some embodiments, R 2 and R 3 Each of is independently -OP(O)(OR)NR. In some embodiments, R 2 and R 3Each of is independently -OP(O)(NR). In some embodiments, R 2 and R 3 Each of is independently -P(O)R. In some embodiments, R 2 and R 3 Each of is independently -SiR. In some embodiments, R 2 and R 3 Each of is independently -Si(OR)R. In some embodiments, R 2 and R 3 Each of R is independently -SF. 2 and R 3 Each of the [ka] is.

[0122] In some embodiments, R 2 is —CF. In some embodiments, R 2 teeth, [ka] In some embodiments, R 2 teeth, [ka] In some embodiments, R 2 teeth, [ka] In some embodiments, R 2 is —C(OH)(CH). In some embodiments, R 2 teeth, [ka] is.

[0123] In some embodiments, R3 is -NHCH3. In some embodiments, R 3 is -CH3. In some embodiments, R 3 teeth, [ka] In some embodiments, R 3 teeth, [ka] In some embodiments, R 3 is —C(OH)(CH). In some embodiments, R 3 teeth, [ka] is.

[0124] In some embodiments, R 1 , R 2 , and R 3 are each independently selected from those depicted in Table 1 below.

[0125] As generally defined above, R 4 teeth, [ka] , hydrogen, or an optionally substituted group, wherein the optionally substituted group is selected from C 1~6 aliphatic, or 4- to 11-membered saturated or partially unsaturated monocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, or spiro rings having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0126] In some embodiments, R 4 teeth [ka] In some embodiments, R4 is hydrogen. In some embodiments, R 4 is C 1~6 In some embodiments, R is an optionally substituted group selected from aliphatic. 4 is an optionally substituted 4- to 11-membered saturated or partially unsaturated monocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, or spiro ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0127] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] In some embodiments, R 4 teeth, [ka] is.

[0128] As generally defined above, Ring D is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0129] In some embodiments, ring D is phenyl. In some embodiments, ring D is a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic ring, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, ring D is a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0130] In some embodiments, ring D is [ka] In some embodiments, ring D is [ka] In some embodiments, ring D is [ka] In some embodiments, ring D is [ka] In some embodiments, ring D is [ka] In some embodiments, ring D is [ka] In some embodiments, ring D is [ka] In some embodiments, ring D is [ka] is.

[0131] In some embodiments, ring D is selected from those depicted in Table 1 below.

[0132] As generally defined above, each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or two R groups on the same atom optionally combined with atoms between them to form an optionally substituted 4- to 11-membered saturated or partially unsaturated carbocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, spiro, or heteroaryl ring having, in addition to the atom to which they are attached, 0 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0133] In some embodiments, each R is independently hydrogen. In some embodiments, each R is C 1~6In some embodiments, each R is an optionally substituted group selected from aliphatic. In some embodiments, each R is an optionally substituted phenyl. In some embodiments, each R is an optionally substituted 4- to 7-membered saturated or partially unsaturated heterocyclic ring having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, each R is an optionally substituted 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, two R groups on the same atom optionally combined with the atom between them form an optionally substituted 4- to 11-membered saturated or partially unsaturated carbocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, spiro, or heteroaryl ring having, in addition to the atom to which they are attached, 0 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0134] In some embodiments, each R is selected from those depicted in Table 1 below.

[0135] As generally defined above, each R 5 independently, C 1~6 An optionally substituted group selected from aliphatic, phenyl, 3- to 7-membered saturated or partially unsaturated carbocyclic or heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0136] In some embodiments, each R 5 independently, C 1~6 In some embodiments, each R is an optionally substituted group selected from aliphatic. 5 is independently optionally substituted phenyl. In some embodiments, each R 5are independently an optionally substituted 3- to 7-membered saturated or partially unsaturated carbocyclic or heterocyclic ring having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, each R 5 is independently an optionally substituted 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0137] In some embodiments, R 5 teeth [ka] In some embodiments, R 5 is replaced as necessary [ka] is.

[0138] In some embodiments, each R 5 is selected from those illustrated in Table 1 below.

[0139] As generally defined above, each n is independently 0, 1, or 2.

[0140] In some embodiments, each n is independently 0. In some embodiments, each n is independently 1. In some embodiments, each n is independently 2.

[0141] As generally defined above, each of m and p is independently 0, 1, 2, 3, or 4.

[0142] In some embodiments, each of m and p is independently 0. In some embodiments, each of m and p is independently 1. In some embodiments, each of m and p is independently 2. In some embodiments, each of m and p is independently 3. In some embodiments, each of m and p is independently 4.

[0143] In some embodiments, each of m and p is selected from those depicted in Table 1 below.

[0144] In some embodiments, the present invention provides a compound wherein ring A is cyclohexyl, ring B is pyrazolyl, and L 3 is a covalent bond, thereby forming a compound of formula II-a: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-a, LBM, L, R 1 , R 2 , R 3 , Ring C, Ring D, n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0145] In some embodiments, the present invention provides a compound wherein A is cyclohexyl, ring B is pyrazolyl, ring C is oxazolyl, and L 3 is a covalent bond, thereby forming a compound of formula II-b: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-b, LBM, L, R 1 , R 2 , R 3 , ring D, n, m, and p, both alone and in combination, are as defined above and as described in the embodiments herein.

[0146] In some embodiments, the present invention provides a compound wherein A is cyclohexyl, ring B is pyrazolyl, ring D is pyridyl, and L 3 is a covalent bond, thereby forming a compound of formula II-c: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-c, LBM, L, R 1 , R 2 , R 3 , rings C, n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0147] In some embodiments, the present invention provides compounds wherein A is cyclohexyl and ring B is pyrazolyl, thereby providing compounds of formula II-d: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-d, LBM, L, L 3 , R1, R 2 , R 4 , ring C, n, and m, both alone and in combination, are as defined above and as described in embodiments herein.

[0148] In certain embodiments, the present invention provides compounds of formula II-d: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-d, L and LBM are as defined above and as described in embodiments herein, and Ring C is phenyl or a 5- to 10-membered monocyclic or bicyclic heteroaryl ring having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 3is a covalent bond, or C 1~3 wherein one to three methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-; Each R 1 are independently hydrogen, deuterium, -R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CFR2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, or -C(O)NR2; Each R is independently hydrogen, deuterium, or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same atom, optionally taken together with the atoms between them, form an optionally substituted 4- to 11-membered saturated or partially unsaturated carbocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, spiro, or heteroaryl ring having, in addition to the atom to which they are attached, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 2 are independently hydrogen, deuterium, -R 5, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 4 teeth, [ka] , hydrogen, or an optionally substituted group, wherein the optionally substituted group is selected from C 1~6 aliphatic, or 4- to 11-membered saturated or partially unsaturated monocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, or spiro rings having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur. Ring D is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 3 are independently hydrogen, deuterium, -R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Each R 5 independently, C 1~6an optionally substituted group selected from aliphatic, phenyl, 3- to 7-membered saturated or partially unsaturated carbocyclic or heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; each n is 0, 1, or 2; each m is 0, 1, 2, 3, or 4; and Each p is 0, 1, 2, 3, or 4.

[0149] In some embodiments, the present invention provides compounds wherein A is cyclohexyl, ring B is pyrazolyl, and ring C is pyrazolo[1,5-a]pyrimidyl, thereby providing compounds of formula II-e: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-e, LBM, L, L 3 , R1, R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0150] In certain embodiments, the present invention provides compounds of formula II-e: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-e, L and LBM are as defined above and as described in embodiments herein, and L 3 is a covalent bond, or C 1~3wherein one to three methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-; Each R 1 are independently hydrogen, deuterium, -R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CFR2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, or -C(O)NR2; Each R is independently hydrogen, deuterium, or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same atom, optionally taken together with the atoms between them, form an optionally substituted 4- to 11-membered saturated or partially unsaturated carbocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, spiro, or heteroaryl ring having, in addition to the atom to which they are attached, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 2 are independently hydrogen, deuterium, -R 5, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 4 teeth, [ka] , hydrogen, or an optionally substituted group, wherein the optionally substituted group is selected from C 1~6 aliphatic, or 4- to 11-membered saturated or partially unsaturated monocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, or spiro rings having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur. Ring D is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 3 are independently hydrogen, deuterium, -R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Each R 5 independently, C 1~6an optionally substituted group selected from aliphatic, phenyl, 3- to 7-membered saturated or partially unsaturated carbocyclic or heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; each n is 0, 1, or 2; each m is 0, 1, 2, 3, or 4; and Each p is 0, 1, 2, 3, or 4.

[0151] In some embodiments, the present invention provides a compound wherein ring A is cyclohexyl, ring B is pyrazolyl, and L 3 is a covalent bond, which gives the formula Vb: [ka] and providing a compound of formula Va, wherein DIM, L, R 1 , R 2 , R 3 , Ring C, Ring D, n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0152] In some embodiments, the present invention provides a compound wherein ring A is cyclohexyl, ring B is pyrazolyl, ring C is oxazolyl, and L 3 is a covalent bond, which gives the formula Vc: [ka] or a pharmaceutically acceptable salt thereof, wherein the compound of formula Va is 1 , R 2 , R 3 , ring D, n, m, and p, both alone and in combination, are as defined above and as described in the embodiments herein.

[0153] In some embodiments, the present invention provides a compound wherein ring A is cyclohexyl, ring B is pyrazolyl, ring D is pyridyl, and L 3 is a covalent bond, which gives the formula Vd: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Vd, DIM, L, R 1 , R 2 , R 3 , rings C, n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0154] In some embodiments, the present invention provides a compound wherein ring A is cyclohexyl, ring B is pyrazolyl, and L 3 is a covalent bond, and R 4 is hydrogen, which gives the formula Ve: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Ve, DIM, L, L 3 , R 1 , R 2 , R 4 , ring C, n, and m, both alone and in combination, are as defined above and as described in embodiments herein.

[0155] In some embodiments, the present invention provides a compound wherein ring A is cyclohexyl, ring B is pyrazolyl, ring C is pyrazolo[1,5-a]pyrimidyl, and L 3 is a covalent bond, and R 4 is hydrogen, which gives the formula Vf: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Vf, DIM, L, L 3 , R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0156] In some embodiments, IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] is.

[0157] In certain embodiments, the present invention provides a compound according to the invention, wherein the IRAK is an IRAK-4 binding moiety, whereby the compound has formula III: [ka] or a pharmaceutically acceptable salt thereof, wherein in Formula III, L and LBM are as defined above and as described in embodiments herein, and: Ring A is a 4- to 7-membered saturated monocyclic ring having two ring nitrogen atoms; Ring B is a 4- to 10-membered saturated mono- or bicyclic carbocyclic or heterocyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring C is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic ring, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 10-membered monocyclic or bicyclic heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 2 is a covalent bond, or C 1~3 wherein one to three methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-; Each R 1 are independently hydrogen, deuterium, -R 4 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Each R is independently hydrogen, deuterium, or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same nitrogen optionally together with the atoms between them form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 4 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; and each n is 0, 1, 2, 3, or 4; wherein the compound of formula III is not compound I-101, I-102, I-103, I-104, or I-105 of Table 1A.

[0158] In certain embodiments, the present invention provides a compound according to the invention, wherein the IRAK is an IRAK-4 binding moiety, whereby the compound has the formula Vg: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Vg, L and DIM are as defined above and as described in embodiments herein, and: Ring A is a 4- to 7-membered saturated monocyclic ring having two ring nitrogen atoms; Ring B is a 4- to 10-membered saturated mono- or bicyclic carbocyclic or heterocyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring C is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic ring, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 10-membered monocyclic or bicyclic heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 2 is a covalent bond, or C 1~3 wherein one to three methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-; Each R 1 are independently hydrogen, deuterium, -R 4 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Each R is independently hydrogen, deuterium, or an optionally substituted group, and the optionally substituted group is C 1~6aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same nitrogen optionally together with the atoms between them form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 4 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; and each n is 0, 1, 2, 3, or 4; wherein the compound of formula Vg is not compound I-101, I-102, I-103, I-104, or I-105 of Table 1A.

[0159] The following embodiments, found in paragraphs

[0144] to

[0179] , are directed to compounds of formula III and Vg.

[0160] As generally defined above, ring A is a 4- to 7-membered saturated monocyclic ring having two ring nitrogen atoms.

[0161] In some embodiments, Ring A is piperazine. In some embodiments, Ring A is 1,4-diazepane.

[0162] In some embodiments, ring A is selected from those depicted in Table 1 below.

[0163] As generally defined above, Ring B is a 4- to 10-membered saturated mono- or bicyclic carbocyclic or heterocyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0164] In some embodiments, Ring B is cyclobutyl. In some embodiments, Ring B is cyclopentyl. In some embodiments, Ring B is cyclohexyl. In some embodiments, Ring B is cycloheptyl.

[0165] In some embodiments, ring B is selected from those depicted in Table 1 below.

[0166] As generally defined above, Ring C is a 9-membered bicyclic heteroaryl ring having 1 to 3 nitrogen atoms.

[0167] In some embodiments, Ring C is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic ring, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 10-membered monocyclic or bicyclic heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0168] In some embodiments, ring B is phenyl. In some embodiments, the ring is a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic ring, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, ring B is a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0169] In some embodiments, ring C is [ka] is.

[0170] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] is.

[0171] In some embodiments, ring C is [ka] In some embodiments, ring C is [ka] is.

[0172] In some embodiments, ring C is selected from those depicted in Table 1 below.

[0173] As generally defined above, L 2 is a covalent bond, or C 1~3wherein one to three methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-.

[0174] In some embodiments, L 2 is a covalent bond. In some embodiments, L 2 is C 1~3 wherein 1 to 3 methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-. In some embodiments, L 2 is C 1~3 In some embodiments, L 2 is -CH-. In some embodiments, L 2 is -C(D)(H)-. In some embodiments, L 2 is -C(D)2-. In some embodiments, L 2 is -CHCH-. In some embodiments, L 2 In some embodiments, L 2 is -CHNR-. In some embodiments, L 2 or -O-. In some embodiments, L 2 is —CH2O—. In some embodiments, L 2 is -S-. In some embodiments, L 2 is -OC(O)-. In some embodiments, L 2 is —C(O)O—. In some embodiments, L 2 is —C(O)—. In some embodiments, L 2 is —S(O)—. In some embodiments, L2 is -S(O)-. In some embodiments, L 2 is -NRS(O)-. In some embodiments, L 2 is -S(O)NR-. In some embodiments, L 2 is -NRC(O)-. In some embodiments, L 2 is —C(O)NR—. In some embodiments, L 2 is —OC(O)NR—. In some embodiments, L 2 is -NRC(O)O-.

[0175] In some embodiments, L 2 is selected from those illustrated in Table 1 below.

[0176] As generally defined above, each R 1 are independently hydrogen, -R 4 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -CF2(R), -CR2(CN), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R.

[0177] In some embodiments, each R 1 is independently hydrogen. In some embodiments, each R 1 are independent, -R 4 In some embodiments, each R 1 is independently halogen. In some embodiments, each R 1 is independently -CN. In some embodiments, each R 1 is independently -NO. In some embodiments, each R 1 is independently -OR. In some embodiments, each R 1is independently -SR. In some embodiments, each R 1 is independently -NR. In some embodiments, each R 1 is independently —S(O)R. In some embodiments, each R 1 is independently —S(O)NR. In some embodiments, each R 1 is independently —S(O)R. In some embodiments, each R 1 is independently -CF(R). In some embodiments, each R 1 is independently -CR(CN). In some embodiments, each R 1 is independently -CF. In some embodiments, each R 1 is independently -CR(OR). In some embodiments, each R 1 is independently -CR(NR). In some embodiments, each R 1 is independently —C(O)R. In some embodiments, each R 1 is independently —C(O)OR. In some embodiments, each R 1 is independently —C(O)NR. In some embodiments, each R 1 is independently —C(O)NR. In some embodiments, each R 1 is independently —C(O)N(R)OR. In some embodiments, each R 1 is independently —OC(O)R. In some embodiments, each R 1 is independently —OC(O)NR. In some embodiments, each R 1 is independently —N(R)C(O)OR. In some embodiments, each R 1 is independently —N(R)C(O)R. In some embodiments, each R 1 is independently —N(R)C(O)NR. In some embodiments, each R 1 are independently —N(R)S(O)R.

[0178] In some embodiments, R 1 teeth [ka] is.

[0179] In some embodiments, R 1 teeth [ka] In some embodiments, R 1 teeth [ka] In some embodiments, R 1 In some embodiments, R is methyl. 1 is —CH(CN). In some embodiments, R 1 is -CN.

[0180] In some embodiments, each R 1 are independently selected from those depicted in Table 1 below.

[0181] As generally defined above, each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 Selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or two R groups on the same nitrogen optionally taken together with the atoms between them form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0182] In some embodiments, each R is independently hydrogen. In some embodiments, each R is C1~6 In some embodiments, R is an optionally substituted group selected from aliphatic. In some embodiments, each R is phenyl. In some embodiments, each R is a 4- to 7-membered saturated or partially unsaturated heterocyclic ring having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, each R is a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0183] In some embodiments, each R is selected from those depicted in Table 1 below.

[0184] As generally defined above, each R 4 independently, C 1~6 An optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0185] In some embodiments, each R 4 independently, C 1~6 In some embodiments, each R is an optionally substituted group selected from aliphatic. 4 is independently optionally substituted phenyl. In some embodiments, each R 4 are independently an optionally substituted 4- to 7-membered saturated or partially unsaturated heterocyclic ring having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, each R 4is independently an optionally substituted 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0186] In some embodiments, each R 4 is selected from those illustrated in Table 1 below.

[0187] As generally defined above, each n is independently 0, 1, or 2.

[0188] In some embodiments, each n is independently 0. In some embodiments, each n is independently 1. In some embodiments, each n is independently 2.

[0189] In some embodiments, each n is selected from those depicted in Table 1 below.

[0190] In some embodiments, the present invention provides compounds wherein Ring B is cyclohexyl, thereby providing compounds of formula III-a: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula III-a, LBM, L, L 2 , ring A, R 1 , ring C, and n, both alone and in combination, are as defined above and as described in embodiments herein.

[0191] In some embodiments, the present invention provides a method for treating a cancer comprising administering to a subject a 2 is a covalent bond, ring B is cyclohexyl, and ring C is pyrrolo[2,1-f][1,2,4]triazinyl, 7H-pyrrolo[2,3-d]pyrimidinyl, or quinazolinyl, thereby forming compounds of formula III-b, III-c, or III-d, respectively: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula III-b, III-c, and III-d, LBM, L, ring A, R 1 and n, both alone and in combination, are as defined above and as described in embodiments herein.

[0192] In some embodiments, the present invention provides compounds wherein ring B is cyclohexyl, thereby providing compounds of formula Vh: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Vh, DIM, L, L 2 , ring A, R 1 , ring C, and n, both alone and in combination, are as defined above and as described in embodiments herein.

[0193] In some embodiments, the present invention provides a method for treating a cancer comprising administering to a subject a 2 is a covalent bond, ring B is cyclohexyl, and ring C is pyrrolo[2,1-f][1,2,4]triazinyl, 7H-pyrrolo[2,3-d]pyrimidinyl, or quinazolinyl, thereby forming compounds of formula Vi-1, Vi-2, or Vi-3, respectively: [ka] or a pharmaceutically acceptable salt thereof, wherein in formulas Vi-1, Vi-2, and Vi-3, DIM, L, ring A, R 1 and n, both alone and in combination, are as defined above and as described in embodiments herein.

[0194] In some embodiments, IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] is.

[0195] In some embodiments, the IRAK is selected from those in Table 1 below.

[0196] In some embodiments, the present invention relates to a method for treating IRAK-4 infection, wherein the IRAK is an IRAK-4 inhibitor. [ka] which gives the compound of formula IV: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula IV: [ka] is attached to a modifiable carbon, oxygen, or nitrogen, and L and LBM are as defined above and described in embodiments herein.

[0197] In some embodiments, IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is: [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] In some embodiments, the IRAK is [ka] is.

[0198] In some embodiments, the IRAK is selected from those in Table 1 below. Ligase binding moiety (LBM)

[0199] In some embodiments, the LBM is an E3 ligase ligand. Such E3 ligase ligands are well known to those skilled in the art and are described in M. Toure, C. M. Crews, Angew. Chem. Int. Ed. 2016, 55, 1966, T. Uehara et al. Nature Chemical Biology 2017, 13, 675, WO 2017 / 176708, US 2017 / 0281784, WO 2017 / 161119, WO 2017 / 176957, WO 2017 / 176958, WO 2015 / 160845, US 2015 / 0291562, WO 2016 / 197032, WO 2016 / 105518, US 2018 / 0009779, WO 2017 / 007612, 2018 / 0134684, WO 2013 / 106643, US 2014 / 0356322, WO 2002 / 020740, US 2002 / 0068063, WO 2012 / 078559, US 2014 / 0302523, WO 2012 / 003281, US 2013 / 0190340, US 2016 / 0022642, WO 2014 / 063061, US 2015 / 0274738, WO 2016 / 118666, US 2016 / 0214972, WO 2016 / 149668, US 2016 / 0272639, WO 2016 / 169989, US 2018 / 0118733, WO 2016 / 197114, US 2018 / 0147202, WO 2017 / 011371, US 2017 / 0008904, WO 2017 / 011590, US 2017 / 0037004, WO 2017 / 079267, US 2017 / 0121321, WO 2017 / 117473, WO 2017 / 117474, WO 2013 / 106646, WO 2014 / 108452, WO 2017 / 197036, US 2019 / 0076540, WO 2017 / 197046, US 2019 / 0076542, WO 2017 / 197051, US 2019 / 0076539, WO 2017 / 197055, US 2019 / 0076541, and WO 2017 / 197056, each of which is incorporated by reference in its entirety.

[0200] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which result in: [ka] or a pharmaceutically acceptable salt thereof, wherein in Formulas Ia-1, Ia-2, Ia-3, Ia-4, Ia-5, Ia-6, Ia-7, Ia-8, Ia-9, and Ia-10, L and IRAK are as defined above and as described in embodiments herein, and: [ka] teeth, [ka] and; Y is a bond, Y, O, NH, NR, C(O)O, OC(O), C(O)NR, NR'C(O), Y-O, Y-NH, Y-NR, Y-C(O), Y-C(O)O, Y-OC(O), Y-C(O)NR', ​​or Y-NR'C(O), where Y is C 1~6 Alkylene, C 2~6 alkenylene, or C2-C6 alkynylene; X is C(O) or C(R3)2; X1-X2 are C(R3)=N or C(R3)2-C(R3)2; Each R1 is independently halogen, nitro, NH2, OH, C(O)OH, C 1~6 Alkyl, or C 1~6 is alkoxy; R2 is C 1~6 Alkyl, C 2~6 Alkenyl, C 3~8 Cycloalkyl, 3- to 8-membered heterocycloalkyl, C(O)-C 1~6 Alkyl, C(O)-C2~6 Alkenyl, C(O)-C 3~8 cycloalkyl, or C(O)-3- to 8-membered heterocycloalkyl, and R2 is halogen, N(R a )2, NHC(O)R a , NHC(O)OR a , OR b , C 3~8 Cycloalkyl, 3- to 8-membered heterocycloalkyl, C 6~10 aryl, or 5- to 10-membered heteroaryl, wherein the C 3~8 Cycloalkyl, 3- to 8-membered heterocycloalkyl, C 6~10 Each of the aryl and 5- to 10-membered heteroaryl is selected from the group consisting of halogen, NH, CN, nitro, OH, C(O)OH, C 1~6 Alkyl, C 1~6 Haloalkyl, C 1~6 Alkoxy, or C 1~6 optionally further substituted with one or more of haloalkoxy; R2' is H, C 1~6 Alkyl, C 2~6 Alkenyl, C 3~8 cycloalkyl, or 3- to 8-membered heterocycloalkyl, and R2′, when not H, is halogen, N(R a )2, NHC(O)R a , NHC(O)OR a , OR b , C 3~8 Cycloalkyl, 3- to 8-membered heterocycloalkyl, C 6~10 aryl, or 5- to 10-membered heteroaryl, wherein the C 3~8 Cycloalkyl, 3- to 8-membered heterocycloalkyl, C 6~10 Each of the aryl and 5- to 10-membered heteroaryl is selected from the group consisting of halogen, NH, CN, nitro, OH, C(O)OH, C 1~6 Alkyl, C 1~6 Haloalkyl, C 1~6 Alkoxy, or C 1~6optionally further substituted with one or more of haloalkoxy; Each R3 is independently H or C 6~10 C optionally substituted with aryl or 5- to 10-membered heteroaryl 1~3 is alkyl; Each R3' is independently C 1~3 is alkyl; Each R4 is independently H or C 1~3 alkyl; or two R4 together with the carbon atoms to which they are attached are C(O), C 3~6 forming a carbocyclic or 4-, 5-, or 6-membered heterocyclic ring containing 1 or 2 heteroatoms selected from N and O; R5 is H, C 1~3 alkyl, F, or Cl; Each R a are independently H or C 1~6 is alkyl; R b is H or tosyl; t is 0 or 1; m is 0, 1, 2, or 3; and n is 0, 1 or 2; As defined and described in WO 2017 / 007612 and US 2018 / 0134684, each of which is incorporated by reference herein in its entirety.

[0201] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] whereby the compound of formula I-a'-1, I-a'-2, I-a'-3, I-a'-4, I-a'-5, I-a'-6, I-a'-7, I-a'-8, I-a'-9, or I-a'-10, respectively: [ka] or a pharmaceutically acceptable salt thereof, wherein in formulas I-a'-1, I-a'-2, I-a'-3, I-a'-4, I-a'-5, I-a'-6, I-a'-7, I-a'-8, I-a'-9, and I-a'-10, L and IRAK are as defined above and as described in embodiments herein, and the variables [ka] , X, X1, X2, Y, R1, R3, R3', R4, R5, t, m, and n are as defined and described in WO 2017 / 007612 and US 2018 / 0134684, each of which is incorporated by reference in its entirety.

[0202] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] whereby a compound of formula I-a''-1, I-a''-2, I-a''-3, I-a''-4, I-a''-5, I-a''-6, I-a''-7, I-a''-8, I-a''-9, or I-a'-10, respectively: [ka] [ka] or a pharmaceutically acceptable salt thereof, wherein in formulas I-a''-1, I-a''-2, I-a''-3, I-a''-4, I-a''-5, I-a''-6, I-a''-7, I-a''-8, I-a''-9, and I-a'-10, L and IRAK are as defined above and as described in embodiments herein, and the variables [ka] , X, X1, X2, Y, R1, R3, R3', R4, R5, t, m, and n are as defined and described in WO 2017 / 007612 and US 2018 / 0134684, each of which is incorporated by reference in its entirety.

[0203] In certain embodiments, the present invention provides a method for the preparation of a VHL E3 ubiquitin ligase-binding moiety comprising administering to a mammalian subject the invention, ... an LBM comprising administering to a mammalian subject the invention, a VHL E3 ubiquitin ligase-binding moiety comprising administering to a mammalian subject the invention [ka] [ka] which give the formula Ib-1, Ib-2, Ib-3, Ib-4, or Ib-5, respectively: [ka] or a pharmaceutically acceptable salt thereof, wherein in Formulas Ib-1, Ib-2, Ib-3, Ib-4, and Ib-5, L and IRAK are as defined above and as described in embodiments herein, and the variable R 1’ , R 2’ , R 3’ , X, and X′ are each as defined and described in WO 2013 / 106643 and US 2014 / 0356322, each of which is incorporated by reference in its entirety.

[0204] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the compound of formula Ic: [ka] or a pharmaceutically acceptable salt thereof, wherein in Formula Ic, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic; Each R 2 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring A is [ka] [ka] [ka] is a bicyclic or tricyclic ring selected from Ring B is a fused ring selected from a 6-membered aryl containing 0-2 nitrogen atoms, a 5- to 7-membered partially saturated carbocyclyl, a 5- to 7-membered partially saturated heterocyclyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3is selected from hydrogen, halogen, —OR, —N(R)2, or —SR; Each R 4 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, 2, 3, or 4; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0205] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the compound of formula I-c': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-c′, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Each R 2 are independently hydrogen, deuterium, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -Si(R)3, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring A is [ka] [ka] is a bicyclic or tricyclic ring selected from Ring B is a fused ring selected from a 6-membered aryl containing 0-2 nitrogen atoms, a 5- to 7-membered partially saturated carbocyclyl, a 5- to 7-membered partially saturated heterocyclyl having 1-2 heteroatoms independently selected from boron, nitrogen, oxygen, silicon, or sulfur, or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 is selected from hydrogen, halogen, —OR, —N(R)2, or —SR; Each R 4 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, 2, 3, or 4; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0206] In some embodiments, the compound of formula I-c' has the formula I-c'' or I-c': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-c'' and I-c''': IRAK, Ring A, L, R 1 , R 2 , X 1 , X 2 , X 3 , and m are each as defined above.

[0207] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the formula Ic-1: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Ic-1, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3is a divalent moiety selected from -CH2- or -Si(R2)-; R 1a is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Each R 2a are independently hydrogen, deuterium, -R 6a , halogen, -CN, -NO2, -OR, -SR, -NR2, -Si(R)3, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring A a teeth, [ka] [ka] [ka] is a bicyclic or tricyclic ring selected from Ring B a is a fused ring selected from a 6-membered aryl containing 0-2 nitrogen atoms, a 5- to 7-membered partially saturated carbocyclyl, a 5- to 7-membered partially saturated heterocyclyl having 1-2 heteroatoms independently selected from boron, nitrogen, oxygen, silicon, or sulfur, or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3a is selected from hydrogen, halogen, —OR, —N(R)2, or —SR; Each R 4a are independently hydrogen, -R 6a, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5a is hydrogen, C 1~4 aliphatic, or -CN; Each R 6a independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, 2, 3, or 4; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0208] In some embodiments, the compound of formula Ic-1 has formula Ic-1′ or formula Ic-1'': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Ic-1′ and formula Ic-1″: IRAK, Ring A a , L, R 1a , R 2a , X 1 , X 2 , X 3 , and m are each as defined above.

[0209] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the formula Id: [ka] or a pharmaceutically acceptable salt thereof, wherein in Formula Id, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic; Ring A is [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2 are independently hydrogen, -R 6, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 and R 4 each independently represents hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1, and when p is 0, the bond connecting ring A and ring B is [ka] is bound to; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0210] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the compound of formula I-d': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-d′, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Ring A is [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2 are independently hydrogen, deuterium, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -Si(R)3, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 and R 4 each independently represents hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1, and when p is 0, the bond connecting ring A and ring B is [ka] is bound to; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0211] In some embodiments, the compound of formula I-d' has formula I-d'' or formula I-d': [ka] or a pharmaceutically acceptable salt thereof, in formula I-d'' and formula I-d''': IRAK, Ring A, Ring B, L, R 1 , R 2 , R 3 , X 1 , X 2 , X 3 , m, and p are each as defined above.

[0212] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the formula Id-1: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Id-1, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1b is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Ring A b teeth, [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2b are independently hydrogen, deuterium, -R 6b , halogen, -CN, -NO2, -OR, -SR, -NR2, -Si(R)3, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B bis selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3b and R 4b each independently represents hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5b is hydrogen, C 1~4 aliphatic, or -CN; Each R 6b independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1, where when p is 0, ring A b and Ring B b The bond that joins [ka] is bound to; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0213] In some embodiments, the compound of formula Id-1 has formula Id-1′ or formula Id-1'': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Id-1′ and formula Id-1″: IRAK, Ring A b , ring B b , L, R 1b , R 2b , R 3b , X 1 , X 2 , X 3 , m, and p are each as defined above.

[0214] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the compound of formula Ie: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Ie, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: R 1is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic; Ring A is [ka] [ka] [ka] [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 and R 4 each independently represents hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0215] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the formula I-e': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-e′, L and IRAK are as defined above and as described in embodiments herein, and: X 1is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Ring A is [ka] [ka] [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2 are independently hydrogen, deuterium, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -Si(R)3, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 and R 4 each independently represents hydrogen, -R6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0216] In some embodiments, the compound of formula I-e' above has the formula I-e'' or I-e'): [ka] or a pharmaceutically acceptable salt thereof, in formula I-e″ and I-e′″: IRAK, Ring A, Ring B, L, R 1 , R 2 , R 3 , X 1 , X 2 , X 3 , p, and m are each as defined above.

[0217] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the formula Ie-1: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Ie-1, L and IRAK are as defined above and as described in embodiments herein, and: X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1c is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Ring A c teeth, [ka] [ka] [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2c are independently hydrogen, deuterium, -R 6c , halogen, -CN, -NO2, -OR, -SR, -NR2, -Si(R)3, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B c is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3c and R 4c each independently represents hydrogen, -R 6c , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5c is hydrogen, C 1~4 aliphatic, or -CN; Each R 6c independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0218] In some embodiments, the compound of formula Ie-1 has formula Ie-1′ or formula Ie-1'': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Ie-1′ and formula Ie-1″: IRAK, Ring A c , ring B c , L, R 1c , R 2c , R 3c , X 1 , X 2 , X 3 , p, and m are each as defined above.

[0219] In certain embodiments, the present invention provides a method for the preparation of a VHL E3 ubiquitin ligase-binding moiety comprising administering to a mammalian subject the invention, ... an LBM comprising administering to a mammalian subject the invention, a VHL E3 ubiquitin ligase-binding moiety comprising administering to a mammalian subject the invention [ka] which results in the equations If-1, If-2, If-3, If-4, If-5 or If-6, respectively: [ka] [ka] or a pharmaceutically acceptable salt thereof, wherein in formulas If-1, If-2, If-3, If-4, If-5, and If-6, L and IRAK are as defined above and as described in embodiments herein, and variable R 1’ , R 2’ , R 3’ , R5, R6, R7, R9, R 10 , R 11 , R 14 , R 15 , R 16 , R 17 , R 23 , R 25 , E, G, M, X, X', Y, Z1, Z2, Z3, Z4, and o are as defined and described in WO 2016 / 149668 and US 2016 / 0272639, each of which is incorporated by reference in its entirety.

[0220] In certain embodiments, the LBM comprises a VHL E3 ubiquitin ligase binding moiety. [ka] or a pharmaceutically acceptable salt thereof, wherein: R 1’ is replaced by C 1~6 Alkyl groups, optionally substituted -(CH2) n OH, optionally substituted -(CH2) n SH, optionally substituted (CH2) n -O-(C1-C6) alkyl group, epoxide moiety W C O C W (where each W is independently H or C 1~3 optionally substituted (CH2) n -WCOCW-(C 0~6) alkyl group, optionally substituted -(CH2) n COOH, optionally substituted -(CH2) n C(O)-(C 1~6 alkyl), optionally substituted -(CH2) n NHC(O)-R1, optionally substituted -(CH2) n C(O)-NR1R2, optionally substituted -(CH2) n OC(O)-NR1R2, -(CHO) n H, optionally substituted -(CH2) n OC(O)-(C 1~6 alkyl), optionally substituted -(CH2) n C(O)-O-(C 1~6 alkyl), optionally substituted -(CHO) n COOH, optionally substituted -(OCH2) n O-(C1-C6 alkyl), optionally substituted -(CHO) n C(O)-(C 1~6 alkyl), optionally substituted -(OCH2) n NHC(O)-R1, optionally substituted -(CHO) n C(O)-NR1R2, -(CH2CH2O) n H, optionally substituted -(CH2CH2O) n COOH, optionally substituted -(OCH2CH2) n O-(C 1~6 alkyl), optionally substituted -(CH2CH2O) n C(O)—(C1-C6 alkyl), optionally substituted —(OCH2CH2) n NHC(O)-R1, optionally substituted -(CH2CH2O) n C(O)-NR1R2, optionally substituted -SO2R S , optionally substituted S(O)R S , NO2, CN, or halogen; R1 and R2 are each independently H or C 1~6 This C is an alkyl group. 1~6The alkyl group may be optionally substituted with one or two hydroxyl groups or up to three halogen groups; R S is C 1~6 an alkyl group, an optionally substituted aryl group, a heteroaryl group, or a heterocyclic group, or -(CH2) m is an NR1R2 group; X and X' are each independently C=O, C=S, -S(O), S(O)2; R is an optionally substituted -(CH2) n -(C=O) u (NR1) v (SO2) w Alkyl groups, optionally substituted -(CH2) n -(C=O) u (NR1) v (SO2) w NR 1N R 2N group, optionally substituted -(CH2) n -(C=O) u (NR1) v (SO2) w -aryl, optionally substituted -(CH2) n -(C=O) u (NR1) v (SO2) w -heteroaryl, optionally substituted -(CH2) n -(C=O) v NR1(SO2) w -heterocycle, optionally substituted -NR 1 -(CH2) n -C(O) u (NR1) v (SO2) w -alkyl, optionally substituted -NR 1 -(CH2) n -C(O) u (NR1) v (SO2) w -NR 1N R 2N , optionally substituted -NR 1 -(CH2) n -C(O) u(NR1) v (SO2) w -NR1C(O)R 1N , optionally substituted -NR 1 -(CH2) n -(C=O) u (NR1) v (SO2) w -aryl, optionally substituted -NR 1 -(CH2) n -(C=O) u (NR1) v (SO2) w -heteroaryl or optionally substituted -NR 1 -(CH2) n -(C=O) v NR1(SO2) w -heterocycle, optionally substituted -X R2’ -alkyl group; optionally substituted -X R2’ -aryl group; optionally substituted -X R2’ -heteroaryl group; optionally substituted -X R2’ - a heterocyclic group; R 3’ is an optionally substituted alkyl, an optionally substituted -(CH2) n -(O) u (NR1) v (SO2) w -alkyl, optionally substituted -(CH2) n -C(O) u (NR1) v (SO2) w -NR 1N R 2N , optionally substituted -(CH2) n -C(O) u (NR1) v (SO2) w -NR1C(O)R 1N , optionally substituted -(CH2) n -C(O) u (NR1) v (SO2) w -C(O)NR1R2, optionally substituted -(CH2) n -C(O)u (NR1) v (SO2) w -aryl, optionally substituted -(CH2) n -C(O) u (NR1) v (SO2) w -heteroaryl, optionally substituted -(CH2) n -C(O) u (NR1) v (SO2) w -heterocycle, optionally substituted -NR 1 -(CH2) n -C(O) u (NR1) v (SO2) w -alkyl, optionally substituted -NR 1 -(CH2) n -C(O) u (NR1) v (SO2) w -NR 1N R 2N , optionally substituted -NR 1 -(CH2) n -C(O) u (NR1) v (SO2) w -NR1C(O)R 1N , optionally substituted -NR 1 -(CH2) n -C(O) u (NR1) v (SO2) w -aryl, optionally substituted -NR 1 -(CH2) n -C(O) u (NR1) v (SO2) w -heteroaryl, optionally substituted -NR 1 -(CH2) n -C(O) u (NR1) v (SO2) w -heterocycle, optionally substituted -O-(CH2)n-(C=O) u (NR1) v (SO2) w-alkyl, optionally substituted -O-(CH2)n-(C=O) u (NR1) v (SO2) w -NR 1N R 2N , optionally substituted -O-(CH2)n-(C=O) u (NR1) v (SO2) w -NR1C(O)R 1N , optionally substituted -O-(CH2)n-(C=O) u (NR1) v (SO2) w -aryl, optionally substituted -O-(CH2) n -(C=O) u (NR1) v (SO2) w -heteroaryl or optionally substituted -O-(CH) n -(C=O) u (NR1) v (SO2) w -heterocycle;-(CH2) n -(V) n’ -(CH2) n -(V) n’ -alkyl group, optionally substituted -(CH2) n -(V) n’ -(CH2) n -(V) n’ -aryl group, optionally substituted -(CH2) n -(V) n’ -(CH2) n -(V) n’ -heteroaryl group, optionally substituted -(CH2) n -(V) n’ -(CH2) n -(V) n’ -heterocyclic group, optionally substituted -(CH2) n -N(R 1’ )(C=O) m’ -(V) n’ -alkyl group, optionally substituted -(CH)-N(R 1’ )(C=O) m’ -(V) n’-aryl group, optionally substituted -(CH2) n -N(R 1’ )(C=O) m’ -(V) n’ -heteroaryl group, optionally substituted -(CH2) n -N(R 1’ )(C=O) m’ -(V) n’ -heterocyclic group, optionally substituted -X R3’ -alkyl group, optionally substituted -X R3’ -aryl group, optionally substituted -X R3’ -heteroaryl group, optionally substituted -X R3’ -heterocyclic group, where R 1N and R 2N are each independently a C optionally substituted with H, one or two hydroxyl groups, and up to three halogen groups. 1~6 alkyl, or optionally substituted -CH2) n -aryl, -(CH2) n -heteroaryl or -(CH2) n - a heterocyclic group; V is O, S or NR1; R1 is the same as above; R 1 and R 1’ are each independently H or a C1-C3 alkyl group; X R2’ and X R3’ each independently represents an optionally substituted —CH n -, -CH2) n -CH(X v )=CH(X v )-, -CH2) n -CH≡CH-, -(CHCHO) n - or a C3-C6 cycloalkyl group, where X v is H, halo, or an optionally substituted C1-C3 alkyl group; each m is independently 0, 1, 2, 3, 4, 5, or 6; each m' is independently 0 or 1; each n is independently 0, 1, 2, 3, 4, 5, or 6; each n' is independently 0 or 1; each u is independently 0 or 1; each v is independently 0 or 1; and Each w is independently 0 or 1.

[0221] As used herein, the illustration of brackets surrounding any LBM [ka] teeth, [ka] This means that the moiety is covalently attached to the LBM at any available modifiable carbon, nitrogen, oxygen, or sulfur atom. For clarity, by way of example, such available modifiable carbon, nitrogen, oxygen, or sulfur atoms in the following LBM compound structure are illustrated below, where each wavy bond represents the bond described above. [ka] Show the attachment points to: [ka] .

[0222] In certain embodiments, the present invention provides a method for the preparation of a VHL E3 ubiquitin ligase-binding moiety comprising administering to a mammalian subject the invention, ... an LBM comprising administering to a mammalian subject the invention, a VHL E3 ubiquitin ligase-binding moiety comprising administering to a mammalian subject the invention [ka] [ka] which give the formula Ig-1, Ig-2, or Ig-3, respectively: [ka] or a pharmaceutically acceptable salt thereof, wherein in Formulas Ig-1, Ig-2, and Ig-3, L and IRAK are as defined above and as described in embodiments herein, and the variable R p , R9, R 10 , R 11 , R 14a , R 14b , R 15 , R 16 , W 3 , W 4 , W 5 , X 1 , X 2 Each of , and o is as defined and described in WO 2017 / 030814, WO 2016 / 118666 and US 2016 / 0214972, each of which is incorporated by reference in its entirety.

[0223] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the formula Ih-1, Ih-2, Ih-3, Ih-4, Ih-5, or Ih-6, respectively: [ka] [ka] or a pharmaceutically acceptable salt thereof, wherein in Formulas Ih-1, Ih-2, Ih-3, Ih-4, Ih-5, and Ih-6, L and IRAK are as defined above and as described in embodiments herein, and each of the variables A, G, G', Q1, Q2, Q3, Q4, R, R', W, X, Z, and n are as defined and described in WO 2016 / 197114 and US 2018 / 0147202, each of which is incorporated by reference in its entirety.

[0224] In certain embodiments, the present invention provides a method for the preparation of a medicament ... [ka] [ka] [ka] [ka] whereby the formula Ii-1, Ii-2, Ii-3, Ii-4, Ii-5, Ii-6, Ii-7, Ii-8, Ii-9, Ii-10, Ii-11, Ii-12, Ii-13, Ii-14, Ii-15, Ii-16, Ii-17, or Ii-18, respectively: [ka] [ka] [ka] [ka] [ka] [ka] [ka] or a pharmaceutically acceptable salt thereof, wherein in formulas Ii-1, Ii-2, Ii-3, Ii-4, Ii-5, Ii-6, Ii-7, Ii-8, Ii-9, Ii-10, Ii-11, Ii-12, Ii-13, Ii-14, Ii-15, Ii-16, Ii-17, and Ii-18, L and IRAK are as defined above and as described in embodiments herein, and the variables R1, R2, R3, R4, R5, R6, R7, R8, R9, R 10 , R 11 , R 12 , R 13 , R 14 , R 15 , R 16 , R 17 , R 18 , R 19 , R 20 , R 21 , R 22 , R 23 , R 24 , R 25 , R 26 , R 27 , R 28 , R 1’ , R 2’ , R 3’ , R 4’ , R 5’ , R 6’ , R 7’ , R 8’ , R 9’ , R 10’ , R 11’ , R 12’ , R 1’’ , A, A', A'', X, Y, and Z are as defined and described in WO 2017 / 011371 and US 2017 / 0008904, each of which is incorporated by reference in its entirety.

[0225] In certain embodiments, the LBM comprises an MDM2 E3 ligase binding moiety. [ka] or a pharmaceutically acceptable salt thereof, wherein: R1 and R2 are independently selected from the group consisting of an aryl or heteroaryl group, a heteroaryl group having one or two heteroatoms independently selected from sulfur or nitrogen, wherein the aryl or heteroaryl group may be monocyclic or bicyclic, or may be unsubstituted, or may be selected from: halogen, -CN, C 1~6 Alkyl group, C 3~6 may be substituted with 1 to 3 substituents independently selected from the group consisting of cycloalkyl, -OH, alkoxy having 1 to 6 carbons, fluorine-substituted alkoxy having 1 to 6 carbons, sulfoxide having 1 to 6 carbons, sulfone having 1 to 6 carbons, ketone having 2 to 6 carbons, amide having 2 to 6 carbons, and dialkylamine having 2 to 6 carbons; R 11 is -C(O)-N(R h )(R i ), where R h and R i is selected from the group consisting of H, C1-C6 alkyl, alkoxy-substituted alkyl, sulfone-substituted alkyl, aryl, heteroaryl, mono-, bis- or tri-substituted aryl or heteroaryl, alkylcarboxylic acid, heteroarylcarboxylic acid, alkylcarboxylic acid, fluorine-substituted alkylcarboxylic acid, aryl-substituted cycloalkyl, heteroaryl-substituted cycloalkyl; h and R i are independently H, bonded to form a ring, 4-hydroxycyclohexane; mono- and dihydroxy-substituted alkyl (C 3~6 3-hydroxycyclobutane; phenyl-4-carboxylic acid, and substituted phenyl-4-carboxylic acids; R 14 is selected from the group consisting of alkyl, substituted alkyl, alkenyl, substituted alkenyl, aryl, substituted aryl, heteroaryl, substituted heteroaryl, heterocyclic, substituted heterocyclic, cycloalkyl, substituted cycloalkyl, cycloalkenyl, and substituted cycloalkenyl; R 15is CN; R 1″ is selected from the group consisting of alkyl, aryl-substituted alkyl, alkoxy-substituted alkyl, cycloalkyl, aryl-substituted cycloalkyl, and alkoxy-substituted cycloalkyl; As defined and described in WO 2017 / 011371 and US 2017 / 0008904, each of which is incorporated by reference herein in its entirety.

[0226] In certain embodiments, the present invention relates to a method for producing an LBM comprising: [ka] [ka] and a CRBN or VHL E3 ubiquitin ligase binding moiety selected from the group consisting of: [ka] [ka] or a pharmaceutically acceptable salt thereof, wherein in Formulas Ij-1, Ij-2, Ij-3, Ij-4, Ij-5, Ij-6, and Ij-7, L and IRAK are as defined above and as described in embodiments herein, and variable A 1 , A 2 , A 3 , R 5 , G, and Z are each as defined and described in WO 2017 / 176958, the entirety of each of which is incorporated herein by reference.

[0227] In certain embodiments, the present invention relates to a method for producing an LBM comprising: [ka] and a CRBN or VHL E3 ubiquitin ligase binding moiety selected from the group consisting of: [ka] [ka] [ka] or a pharmaceutically acceptable salt thereof, wherein in formulas I-j'-1, I-j''-1, I-j'-2, I-j''-2, I-j'-3, I-j''-3, I-j'-4, I-j''-4, I-j'-7 and I-j''-7, L and IRAK are as defined above and as described in embodiments herein, and variable A 1 , A 2 , A 3 , R 5 , G, and Z are each as defined and described in WO 2017 / 176958, the entirety of each of which is incorporated herein by reference.

[0228] In certain embodiments, the present invention provides a method for producing an IAP E3 ubiquitin ligase-binding moiety comprising administering to a mammalian subject the invention, wherein the LBM is an IAP E3 ubiquitin ligase-binding moiety. [ka] which results in the formula Ik-1, Ik-2, Ik-3, or Ik-4, respectively: [ka] [ka] or a pharmaceutically acceptable salt thereof, wherein in formulas Ik-1, Ik-2, Ik-3, and Ik-4, L and IRAK are as defined above and as described in embodiments herein, and R 1 is selected from hydrogen or alkyl; R 2 is selected from hydrogen or alkyl; R 3 is selected from hydrogen, alkyl, cycloalkyl, and heterocycloalkyl; R 5 and R 6 are independently selected from hydrogen, alkyl, cycloalkyl, heterocycloalkyl; R 5 and R 6 taken together form a pyrrolidine or piperidine ring, which is further optionally fused to one to two cycloalkyl, heterocycloalkyl, aryl, or heteroaryl rings, each of which may in turn be further fused to another cycloalkyl, heterocycloalkyl, aryl, or heteroaryl ring; or R 3 and R 5 are taken together to form a 5- to 8-membered ring, which is optionally further fused to 1 to 2 cycloalkyl, heterocycloalkyl, aryl, or heteroaryl rings; R 7 is selected from cycloalkyl, cycloalkylalkyl, heterocycloalkyl, heterocycloalkylalkyl, aryl, arylalkyl, heteroaryl, or heteroarylalkyl, each of which is further optionally substituted with 1 to 3 substituents selected from halogen, alkyl, haloalkyl, hydroxyl, alkoxy, cyano, (hetero)cycloalkyl, or (hetero)aryl; or R 7 is C(O)NHR 4 and R 4is selected from alkyl, cycloalkyl, heterocycloalkyl, cycloalkylalkyl, heterocycloalkylalkyl, aryl, arylalkyl, heteroaryl, heteroarylalkyl, optionally further substituted with 1 to 3 substituents selected from halogen, alkyl, haloalkyl, hydroxyl, alkoxy, cyano, (hetero)cycloalkyl, or (hetero)aryl; or R 7 is C(O)NHR 4 and As defined and described in WO 2017 / 011590 and US 2017 / 0037004, each of which is incorporated by reference herein in its entirety.

[0229] In certain embodiments, the present invention provides a method for producing an IAP E3 ubiquitin ligase-binding moiety comprising administering to a mammalian subject the invention, wherein the LBM is an IAP E3 ubiquitin ligase-binding moiety. [ka] which give the formula I-k'-1, I-k'-2, I-k'-3, or I-k'-4, respectively: [ka] [ka] or a pharmaceutically acceptable salt thereof, wherein in formulas I-k'-1, I-k'-2, I-k'-3, and I-k'-4, L and IRAK are as defined above and as described in embodiments herein, and variable R 1 , R 3 , R 4 , R 5 , R 6 , and R 7 each as defined and described in WO 2017 / 011590 and US 2017 / 0037004, each of which is incorporated by reference in its entirety.

[0230] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This results in formula II: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II, L and IRAK are as defined above and described herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic; Each R 2 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring A is [ka] [ka] [ka] is a bicyclic or tricyclic ring selected from Ring B is a fused ring selected from a 6-membered aryl containing 0-2 nitrogen atoms, a 5- to 7-membered partially saturated carbocyclyl, a 5- to 7-membered partially saturated heterocyclyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 is selected from hydrogen, halogen, —OR, —N(R)2, or —SR; Each R 4 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 1 is a covalent bond or a bivalent saturated or unsaturated straight or branched chain C 1~50 a hydrocarbon chain, wherein 0 to 6 methylene units of L are independently -Cy-, -O-, -NR-, -S-, -OC(O)-, -C(O)O-, -C(O)-, -S(O)-, -S(O)2-, -NRS(O)2-, -S(O)2NR-, -NRC(O)-, -C(O)NR-, -OC(O)NR-, -NRC(O)O-, [ka] [ka] has been replaced by, where: Each -Cy- is independently selected from phenylenyl, 8- to 10-membered bicyclic arylenyl, 4- to 7-membered saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated spirocarbocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, an optionally substituted bivalent ring selected from saturated or partially unsaturated spiroheterocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 5- to 6-membered heteroarylenyl having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 8- to 10-membered bicyclic heteroarylenyl having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; m is 0, 1, 2, 3 or 4; each n is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0231] -(R2 ) n When the attachment point of -(R 2 ) n It is contemplated, and one of ordinary skill in the art will appreciate, that the point of attachment of -R may be on ring A, and also may be at any available carbon or nitrogen atom on ring A to which ring B is fused. 2 But R 4 or R 5 If bonded to a nitrogen atom bonded to R 4 or R 5 does not exist, and -R 2 But this R 4 group or R 5 Occupies the -R group position. 2 But R 3 If attached to a carbon atom that is bonded to R 3 does not exist, and -R 2 But this R 3 Occupies the base position.

[0232] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This gives the compound of formula I-l': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-l′, L and IRAK are as defined above and described herein, and: X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3is a divalent moiety selected from -CH2- or -Si(R2)-; R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Each R 2 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring A is [ka] [ka] [ka] is a bicyclic or tricyclic ring selected from Ring B is a fused ring selected from a 6-membered aryl containing 0-2 nitrogen atoms, a 5- to 7-membered partially saturated carbocyclyl, a 5- to 7-membered partially saturated heterocyclyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 is selected from hydrogen, halogen, —OR, —N(R)2, or —SR; Each R 4 are independently hydrogen, -R 6, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 1 is a covalent bond or a bivalent saturated or unsaturated straight or branched chain C 1~50 a hydrocarbon chain, wherein 0 to 6 methylene units of L are independently -Cy-, -O-, -NR-, -S-, -OC(O)-, -C(O)O-, -C(O)-, -S(O)-, -S(O)2-, -NRS(O)2-, -S(O)2NR-, -NRC(O)-, -C(O)NR-, -OC(O)NR-, -NRC(O)O-, [ka] has been replaced by, where: Each -Cy- is independently selected from phenylenyl, 8- to 10-membered bicyclic arylenyl, 4- to 7-membered saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated spirocarbocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, an optionally substituted bivalent ring selected from saturated or partially unsaturated spiroheterocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 5- to 6-membered heteroarylenyl having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 8- to 10-membered bicyclic heteroarylenyl having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; m is 0, 1, 2, 3 or 4; each n is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0233] -(R 2 ) n When the attachment point of -(R 2 )n It is contemplated, and one of ordinary skill in the art will appreciate, that the point of attachment of -R may be on ring A, and also may be at any available carbon or nitrogen atom on ring A to which ring B is fused. 2 But R 4 or R 5 If bonded to a nitrogen atom bonded to R 4 or R 5 does not exist, and -R 2 But this R 4 group or R 5 Occupies the -R group position. 2 But R 3 If attached to a carbon atom that is bonded to R 3 does not exist, and -R 2 But this R 3 Occupies the base position.

[0234] In some embodiments, the compound of formula I-l' is represented by formula I-l'' or formula I-l': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-l'' and formula I-l''': IRAK, Ring A, L, L 1 , R 1 , R 2 , X 1 , X 2 , X 3 , and m are each as defined above.

[0235] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This gives the formula Il-1: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Il-1, L and IRAK are as defined above and described herein, and: X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1a is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Each R 2a are independently hydrogen, -R 6a , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring A a teeth, [ka] [ka] [ka] is a bicyclic or tricyclic ring selected from Ring B ais a fused ring selected from a 6-membered aryl containing 0-2 nitrogen atoms, a 5- to 7-membered partially saturated carbocyclyl, a 5- to 7-membered partially saturated heterocyclyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3a is selected from hydrogen, halogen, —OR, —N(R)2, or —SR; Each R 4a are independently hydrogen, -R 6a , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5a is hydrogen, C 1~4 aliphatic, or -CN; Each R 6a independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 1 is a covalent bond or a bivalent saturated or unsaturated straight or branched chain C 1~50 a hydrocarbon chain, wherein 0 to 6 methylene units of L are independently -Cy-, -O-, -NR-, -S-, -OC(O)-, -C(O)O-, -C(O)-, -S(O)-, -S(O)2-, -NRS(O)2-, -S(O)2NR-, -NRC(O)-, -C(O)NR-, -OC(O)NR-, -NRC(O)O-, [ka] [ka] has been replaced by, where: Each -Cy- is independently selected from phenylenyl, 8- to 10-membered bicyclic arylenyl, 4- to 7-membered saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated spirocarbocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, an optionally substituted bivalent ring selected from saturated or partially unsaturated spiroheterocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 5- to 6-membered heteroarylenyl having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 8- to 10-membered bicyclic heteroarylenyl having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; m is 0, 1, 2, 3 or 4; each n is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0236] -(R2a ) n When the attachment point of -(R 2a ) n It is contemplated, and one of ordinary skill in the art will appreciate, that the point of attachment of -R may be on ring A, and also may be at any available carbon or nitrogen atom on ring A to which ring B is fused. 2a But R 4a or R 5a If bonded to a nitrogen atom bonded to R 4a or R 5a does not exist, and -R 2a But this R 4a group or R 5a Occupies the -R group position. 2a But R 3a If attached to a carbon atom that is bonded to R 3a does not exist, and -R 2a But this R 3a Occupies the base position.

[0237] In some embodiments, the compound of formula Il-1 has formula Il-1′ or formula Il-1'': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Il-1′ and formula Il-1″: IRAK, Ring A a , L, L 1 , R 1a , R 2a , X 1 , X 2 , X 3 , and m are each as defined above.

[0238] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This gives the formula Im: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Im, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic; Ring A is [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 and R 4 each independently represents hydrogen, -R 6, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 1 is a covalent bond or a bivalent saturated or unsaturated straight or branched chain C 1~50 a hydrocarbon chain, wherein 0 to 6 methylene units of L are independently -Cy-, -O-, -NR-, -S-, -OC(O)-, -C(O)O-, -C(O)-, -S(O)-, -S(O)2-, -NRS(O)2-, -S(O)2NR-, -NRC(O)-, -C(O)NR-, -OC(O)NR-, -NRC(O)O-, [ka] [ka] has been replaced by, where: Each -Cy- is independently selected from phenylenyl, 8- to 10-membered bicyclic arylenyl, 4- to 7-membered saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated spirocarbocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, an optionally substituted bivalent ring selected from saturated or partially unsaturated spiroheterocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 5- to 6-membered heteroarylenyl having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 8- to 10-membered bicyclic heteroarylenyl having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1, and when p is 0, the bond connecting ring A and ring B is [ka] is bound to; each q is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0239] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This gives the formula I-m': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-m′, L and IRAK are as defined above and as described in embodiments herein, and: X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Ring A is [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 and R 4 each independently represents hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 1 is a covalent bond or a bivalent saturated or unsaturated straight or branched chain C 1~50 a hydrocarbon chain, wherein 0 to 6 methylene units of L are independently -Cy-, -O-, -NR-, -S-, -OC(O)-, -C(O)O-, -C(O)-, -S(O)-, -S(O)2-, -NRS(O)2-, -S(O)2NR-, -NRC(O)-, -C(O)NR-, -OC(O)NR-, -NRC(O)O-, [ka] has been replaced by, where: Each -Cy- is independently selected from phenylenyl, 8- to 10-membered bicyclic arylenyl, 4- to 7-membered saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated spirocarbocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, an optionally substituted bivalent ring selected from saturated or partially unsaturated spiroheterocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 5- to 6-membered heteroarylenyl having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 8- to 10-membered bicyclic heteroarylenyl having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1, and when p is 0, the bond connecting ring A and ring B is [ka] is bound to; each q is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0240] In some embodiments, the compound of formula I-m' has formula I-m'' or formula I-m': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-m″ and formula I-m′″: IRAK, Ring A, Ring B, L, L 1 , R 1 , R 2 , R 3 , X 1 , X 2 , X 3 , n, p, and m are each as defined above.

[0241] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This gives the formula Im-1: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Im-1, L and IRAK are as defined above and as described in embodiments herein, and X 1is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1b is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Ring A b teeth, [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2b are independently hydrogen, -R 6b , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B b is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3b and R 4b each independently represents hydrogen, -R 6b, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5b is hydrogen, C 1~4 aliphatic, or -CN; Each R 6b independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 1 is a covalent bond or a bivalent saturated or unsaturated straight or branched chain C 1~50 a hydrocarbon chain, wherein 0 to 6 methylene units of L are independently -Cy-, -O-, -NR-, -S-, -OC(O)-, -C(O)O-, -C(O)-, -S(O)-, -S(O)2-, -NRS(O)2-, -S(O)2NR-, -NRC(O)-, -C(O)NR-, -OC(O)NR-, -NRC(O)O-, [ka] has been replaced by, where: Each -Cy- is independently selected from phenylenyl, 8- to 10-membered bicyclic arylenyl, 4- to 7-membered saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated spirocarbocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, an optionally substituted bivalent ring selected from saturated or partially unsaturated spiroheterocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 5- to 6-membered heteroarylenyl having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 8- to 10-membered bicyclic heteroarylenyl having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1, and when p is 0, the bond connecting ring A and ring B is [ka] is bound to; each q is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0242] In some embodiments, the compound of formula I-m' has the formula I-m'' or I-m': [ka] or a pharmaceutically acceptable salt thereof, in formula I-m″ and I-m′″: IRAK, Ring A b , ring B b , L, L 1 , R 1b , R 2b , R 3b , X 1 , X 2 , X 3 , n, p, and m are each as defined above.

[0243] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This allows the expression In: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula ln, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: R1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic; Ring A is [ka] [ka] [ka] [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 and R 4 each independently represents hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 1 is a covalent bond or a bivalent saturated or unsaturated straight or branched chain C 1~50 a hydrocarbon chain, wherein 0 to 6 methylene units of L are independently -Cy-, -O-, -NR-, -S-, -OC(O)-, -C(O)O-, -C(O)-, -S(O)-, -S(O)2-, -NRS(O)2-, -S(O)2NR-, -NRC(O)-, -C(O)NR-, -OC(O)NR-, -NRC(O)O-, [ka] has been replaced by, where: Each -Cy- is independently selected from phenylenyl, 8- to 10-membered bicyclic arylenyl, 4- to 7-membered saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated spirocarbocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, an optionally substituted bivalent ring selected from saturated or partially unsaturated spiroheterocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 5- to 6-membered heteroarylenyl having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 8- to 10-membered bicyclic heteroarylenyl having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1; each q is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0244] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This gives the compound of formula I-n': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-n′, L and IRAK are as defined above and as described in embodiments herein, and: X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Ring A is [ka] [ka] [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2 are independently hydrogen, -R 6, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 and R 4 each independently represents hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 1 is a covalent bond or a bivalent saturated or unsaturated straight or branched chain C 1~50 a hydrocarbon chain, wherein 0 to 6 methylene units of L are independently -Cy-, -O-, -NR-, -S-, -OC(O)-, -C(O)O-, -C(O)-, -S(O)-, -S(O)2-, -NRS(O)2-, -S(O)2NR-, -NRC(O)-, -C(O)NR-, -OC(O)NR-, -NRC(O)O-, [ka] has been replaced by, where: Each -Cy- is independently selected from phenylenyl, 8- to 10-membered bicyclic arylenyl, 4- to 7-membered saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated spirocarbocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, an optionally substituted bivalent ring selected from saturated or partially unsaturated spiroheterocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 5- to 6-membered heteroarylenyl having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 8- to 10-membered bicyclic heteroarylenyl having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1; each q is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or

[0245] Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0246] In some embodiments, the compound of formula I-n' is of formula I-n'' or formula I-n''': [ka] or a pharmaceutically acceptable salt thereof, in formula I-n'' and formula I-n''': IRAK, Ring A, Ring B, L, L 1 , R 1 , R 2 , R 3 , X 1 , X 2 , X 3 , n, p, and m are each as defined above.

[0247] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This results in the formula In-1: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula In-1, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1c is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Ring A c teeth, [ka] [ka] [ka] [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2c are independently hydrogen, -R 6c , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B c is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3c and R 4c each independently represents hydrogen, -R 6c, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5c is hydrogen, C 1~4 aliphatic, or -CN; Each R 6c independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 1 is a covalent bond or a bivalent saturated or unsaturated straight or branched chain C 1~50 a hydrocarbon chain, wherein 0 to 6 methylene units of L are independently -Cy-, -O-, -NR-, -S-, -OC(O)-, -C(O)O-, -C(O)-, -S(O)-, -S(O)2-, -NRS(O)2-, -S(O)2NR-, -NRC(O)-, -C(O)NR-, -OC(O)NR-, -NRC(O)O-, [ka] has been replaced by, where: Each -Cy- is independently selected from phenylenyl, 8- to 10-membered bicyclic arylenyl, 4- to 7-membered saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated spirocarbocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, an optionally substituted bivalent ring selected from saturated or partially unsaturated spiroheterocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 5- to 6-membered heteroarylenyl having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 8- to 10-membered bicyclic heteroarylenyl having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1; each q is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0248] In some embodiments, the compound of formula In-1 has formula In-1′ or formula In-1'': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula In-1′ and formula In-1″: IRAK, Ring A c , ring B c , L, L 1 , R 1c , R 2c , R 3c , X 1 , X 2 , X 3 , n, p, and m are each as defined above.

[0249] In some embodiments, the LBM comprises: [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] is.

[0250] In some embodiments, the LBM comprises: [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] is.

[0251] In some embodiments, the LBM comprises: [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] is.

[0252] In some embodiments, the LBM comprises: [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] is.

[0253] In some embodiments, the LBM comprises: [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] is.

[0254] In some embodiments, the LBM comprises: [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] In some embodiments, the LBM is [ka] is.

[0255] In some embodiments, the LBM is selected from those depicted in Table 1 below.

[0256] In some embodiments, the present invention provides a compound of formula II having formula II-f: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-f, X of the LBM moiety 1 , X 2 , X 3 , R 1a , R 2a , ring A a , and m, L, and L of the IRAK part 2 , L 3 , ring A, ring B, ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0257] In certain embodiments, the present invention provides compounds of formula II-f: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-f: L is ring A a is a divalent moiety attached to ring A of X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1a is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Each R 2a are independently hydrogen, R 6a , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring A a teeth, [ka] [ka] [ka] is a bicyclic or tricyclic ring selected from Ring B a is a fused ring selected from a 6-membered aryl containing 0-2 nitrogen atoms, a 5- to 7-membered partially saturated carbocyclyl, a 5- to 7-membered partially saturated heterocyclyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3a is selected from hydrogen, halogen, —OR, —N(R)2, or —SR; Each R 4a are independently hydrogen, R 6a, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5a is hydrogen, C 1~4 aliphatic, or -CN; Each R 6a independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring A is a 4- to 10-membered saturated mono- or bicyclic carbocyclic or heterocyclic ring having 0-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring B is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 9-membered monocyclic or bicyclic heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring C is phenyl or a 5- to 10-membered monocyclic or bicyclic heteroaryl ring having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, and sulfur; L 2 and L 3 each independently represents a covalent bond, or C 1~3 wherein one to three methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-; Each R 1 are independently hydrogen, deuterium, R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CFR2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, or -C(O)NR2; Each R is independently hydrogen, deuterium, or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same atom, optionally taken together with the atoms between them, form an optionally substituted 4- to 11-membered saturated or partially unsaturated carbocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, spiro, or heteroaryl ring having, in addition to the atom to which they are attached, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 2 are independently hydrogen, deuterium, R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 4 teeth, [ka] , hydrogen, or an optionally substituted group, wherein the optionally substituted group is selected from C 1~6 selected from aliphatic or 4- to 11-membered saturated or partially unsaturated monocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, or spiro rings having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring D is phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic, or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 3 are independently hydrogen, deuterium, R 5 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -S(O)(NR)R, -P(O)(OR)2, -P(O)(NR2)2, -CF2(R), -CF3, -CR2(OR), -CR2(NR2), -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Each R 5 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 3- to 7-membered saturated or partially unsaturated carbocyclic or heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; n is 0, 1, or 2; each m is independently 0, 1, 2, 3, or 4; and p is 0, 1, 2, 3 or 4;

[0258] In some embodiments, the present invention provides a method for treating a cancer comprising administering to a subject a cancer-causing agent comprising: 2 is a carbon atom and X3 is —CH— and Ring B is pyrazolyl as shown, thereby providing formula II-f-1: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-f-1, X of the LBM moiety is 1 , R 1a , R 2a , ring A a , and m, L, and L of the IRAK part 2 , L 3 , ring A, ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0259] In some embodiments, the present invention provides a method for treating a cancer comprising administering to a subject a cancer-causing agent comprising: 2 is a carbon atom and X 3 is -CH2-, and ring A a but [ka] and Ring B is pyrazolyl as shown, thereby providing compounds of formula II-f-2: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-f-2, X of the LBM moiety is 1 , R 1a , R 2a , and m, L, and L of the IRAK part 2 , L 3 , ring A, ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0260] In some embodiments, the present invention provides a method for treating a cancer comprising administering to a subject a cancer-causing agent comprising: 2 is a carbon atom and X 3 is -CH2-, ring A is cyclohexyl, and L 2 is a covalent bond and Ring B is pyrazolyl as shown, thereby providing formula II-f-3: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-f-3, X of the LBM moiety is 1 , R 1a , R 2a , ring A a , and m, L, and L of the IRAK part 3 , ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0261] In some embodiments, the present invention provides a method for treating a cancer comprising administering to a subject a cancer-causing agent comprising: 2 is a carbon atom and X 3 is —CH—, Ring C is a pyrazolo[1,5-a]pyrimidine, and Ring B is a pyrazolyl as shown, thereby providing formula II-f-4: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-f-4, X of the LBM moiety is 1 , R 1a , R 2a , ring A a , and m, L, and L of the IRAK part 2 , L 3 , ring A, ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0262] In some embodiments, the present invention provides a method for treating a cancer comprising administering to a subject a cancer-causing agent comprising: 2 is a carbon atom and X 3 is -CH2- and L is [ka] and Ring B is pyrazolyl as shown, thereby providing compounds of formula II-f-5: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-f-5, X of the LBM moiety is 1 , R 1a , R 2a , ring A a , and m, and L of the IRAK part 2 , L 3 , ring A, ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0263] In some embodiments, the present invention provides a method for treating a cancer comprising administering to a subject a 2 is a covalent bond, ring A is cyclohexyl, ring B is pyrazolyl, ring C is oxazolyl, and ring D is pyridyl, thereby providing a compound of formula II-g: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-g, X of the LBM moiety is 1 , X 2 , X 3 , R 1a , R 2a , ring A a , and m, L, and R of the IRAK part 1 , R 2 , R 3, n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0264] In some embodiments, the present invention provides a method for treating a cancer cell comprising administering to a subject the method ... [ka] whereby formula II-h: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-h, L, L 2 , L 3 , ring A, ring B, ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0265] In some embodiments, the present invention provides a method for treating a cancer cell comprising administering to a subject the method ... [ka] and L 2 is a covalent bond, ring A is cyclohexyl, ring B is pyrazolyl, ring C is oxazolyl, and ring D is pyridyl, thereby providing a compound of formula II-i: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-i, L, R 1 , R 2 , R 3 , n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0266] In certain embodiments, the present invention provides a method for treating LBM [ka] and L 2 is a covalent bond, ring A is cyclohexyl, and ring B is pyrazolyl as shown, thereby providing formula II-d-1: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-d-1, L, L 3 , ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0267] In certain embodiments, the present invention provides a method for treating LBM [ka] and L 2 is a covalent bond, ring A is cyclohexyl, ring C is pyrazolo[1,5-a]pyrimidine, and ring B is pyrazolyl as shown, thereby providing a compound of formula II-e-1: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-e-1, L, R 1 , R 2 , R 3 , n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0268] In some embodiments, the present invention provides a method for treating a cancer cell comprising administering to a subject the method ... [ka] which gives the formula II-j: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-j, L, L 2 , L 3 , ring A, ring B, ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0269] In some embodiments, the present invention provides a method for treating a cancer cell comprising administering to a subject the method ... [ka] and L 2 is a covalent bond, ring A is cyclohexyl, ring B is pyrazolyl, ring C is oxazolyl, and ring D is pyridyl, thereby providing a compound of formula II-k: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-k, L, R 1 , R 2 , R 3 , n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0270] In certain embodiments, the present invention provides a method for treating LBM [ka] and L 2 is a covalent bond, ring A is cyclohexyl, and ring B is pyrazolyl as shown, thereby providing formula II-d-2: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-d-2, L, L 3 , ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0271] In certain embodiments, the present invention provides a method for treating LBM [ka] and L 2 is a covalent bond, ring A is cyclohexyl, ring C is pyrazolo[1,5-a]pyrimidine, and ring B is pyrazolyl as shown, thereby providing a compound of formula II-e-2: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-e-2, L, R 1 , R 2 , R 3 , n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0272] In some embodiments, the present invention provides a method for treating a cancer cell comprising administering to a subject the method ... [ka] and L 2 is a covalent bond, ring A is cyclohexyl, ring B is pyrazolyl, ring C is oxazolyl, and ring D is pyridyl, thereby providing a compound of formula II-l: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-l, L, R 1 , R2 , R 3 , n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0273] In certain embodiments, the present invention provides a method for treating LBM [ka] and L 2 is a covalent bond, ring A is cyclohexyl, and ring B is pyrazolyl as shown, thereby providing formula II-d-3: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-d-3, L, L 3 , ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0274] In certain embodiments, the present invention provides a method for treating LBM [ka] and L 2 is a covalent bond, ring A is cyclohexyl, ring C is pyrazolo[1,5-a]pyrimidine, and ring B is pyrazolyl as shown, thereby providing a compound of formula II-e-3: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-e-3, L, R 1 , R 2 , R 3 , n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0275] In some embodiments, the present invention provides a method for treating a cancer cell comprising administering to a subject the method ... [ka] wherein ring A is cyclohexyl, ring B is pyrazolyl, ring C is oxazolyl, and ring D is pyridyl, thereby providing a compound of formula II-m: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-m, L, R 1 , R 2 , R 3 , n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0276] In certain embodiments, the present invention provides a method for treating LBM [ka] which gives the compound of formula II-d-4: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-d-4, L, L 3 , ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0277] In certain embodiments, the present invention provides a method for treating LBM [ka] which gives the compound of formula II-e-4: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-e-4, L, R 1 , R 2 , R 3 , n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0278] In some embodiments, the present invention provides a method for treating a cancer cell comprising administering to a subject the method ... [ka] This gives the compound of formula II-n: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-n, L, L 2 , L 3 , ring A, ring B, ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0279] In some embodiments, the present invention provides a method for treating a cancer cell comprising administering to a subject the method ... [ka] wherein ring A is cyclohexyl, ring B is pyrazolyl, ring C is oxazolyl, and ring D is pyridyl, thereby providing a compound of formula II-o: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-o, L, R 1 , R 2 , R 3, n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0280] In certain embodiments, the present invention provides a method for treating LBM [ka] which gives the compound of formula II-d-5: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-d-5, L, L 3 , ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0281] In certain embodiments, the present invention provides a method for treating LBM [ka] which gives the compound of formula II-e-5: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-e-5, L, R 1 , R 2 , R 3 , n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0282] In some embodiments, the present invention provides a method for treating a cancer cell comprising administering to a subject the method ... [ka] which gives the formula II-p: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-p, L, L 2 , L 3 , ring A, ring B, ring C, R 1 , R 2 , R 4 Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0283] In some embodiments, the present invention provides a method for treating a cancer cell comprising administering to a subject the method ... [ka] wherein ring A is cyclohexyl, ring B is pyrazolyl, ring C is oxazolyl, and ring D is pyridyl, thereby providing a compound of formula II-q: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-q, L, R 1 , R 2 , R 3 , n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0284] In certain embodiments, the present invention provides a method for treating LBM [ka] This gives the compound of formula II-d-6: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-d-6, L, L 3 , ring C, R 1 , R 2 , R 4Each of n, n, and m, both alone and in combination, is as defined above and as described in embodiments herein.

[0285] In certain embodiments, the present invention provides a method for treating LBM [ka] which gives the compound of formula II-e-6: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula II-e-6, L, R 1 , R 2 , R 3 , n, m, and p, both alone and in combination, are as defined above and as described in embodiments herein.

[0286] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This gives the formula Io: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Io, L and IRAK are as defined above and as described in embodiments herein, and the variables Ar, R 1 , R 2 , R 3 , R 4 , R 5 , R 8 ,L,x,and bond [ka] each as described and defined in WO 2017 / 161119, the entirety of each of which is incorporated herein by reference.

[0287] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the formula Ip: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Ip, L and IRAK are as defined above and as described in embodiments herein, and the variables Ar, R 1 , R 2 , R 3 , R 4 , R 5 , R 6 , R 7 , R 8 ,A,x,and bond [ka] each as described and defined in WO 2017 / 161119, the entirety of each of which is incorporated herein by reference.

[0288] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This gives the formula Iq: [ka] or a pharmaceutically acceptable salt thereof, wherein in Formula Iq, L and IRAK are as defined above and as described in embodiments herein, and variable R 1 , R 2 , R 3 , R 4 , R 5 , R 6 , R 7 , R 8 ,A,x,and bond [ka] each as described and defined in WO 2017 / 161119, the entirety of each of which is incorporated herein by reference.

[0289] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This results in the compound of formula Ir: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Ir, L and IRAK are as defined above and as described in embodiments herein, and the variables Ar, R 1 , R 2 , R 3 , R 4 , R 5 , R 8 , L, x, y, and bond [ka] each as described and defined in WO 2017 / 161119, the entirety of each of which is incorporated herein by reference.

[0290] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This gives the formula Is: [ka] or a pharmaceutically acceptable salt thereof, wherein in Formula Is, L and IRAK are as defined above and as described in embodiments herein, and variables G, R 3 , R 4 , R 5 , R 6 , R 7 , R 8 , x, and bond [ka] each as described and defined in WO 2017 / 161119, the entirety of each of which is incorporated herein by reference.

[0291] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This allows the expression It: [ka] or a pharmaceutically acceptable salt thereof, wherein L and IRAK are as defined above and as described in embodiments herein, and variable R 3 , R 4 , R 5 , R 6 , R 7 , R 8 , x, and bond [ka] each as described and defined in WO 2017 / 161119, the entirety of each of which is incorporated herein by reference.

[0292] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This results in formula Iu: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula Iu, L and IRAK are as defined above and as described in embodiments herein, and variable R 3 , R 4 , R 5 , R 8 , L, and bond [ka] each as described and defined in WO 2017 / 161119, the entirety of each of which is incorporated herein by reference.

[0293] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This results in formula IV: [ka] or a pharmaceutically acceptable salt thereof, wherein in Formula IV, L and IRAK are as defined above and as described in embodiments herein, and variable R 1 , R 3 , R 4 , R 5 , L, y, and bond [ka] each as described and defined in WO 2017 / 161119, the entirety of each of which is incorporated herein by reference.

[0294] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] and; This gives the compound of formula Ix: [ka] or a pharmaceutically acceptable salt thereof, wherein in Formula IX, L and IRAK are as defined above and in embodiments herein, and each of the variables A, B, C, W, X, Y, and Z are as described and defined in U.S. Pat. No. 5,721,246, the entirety of each of which is incorporated herein by reference.

[0295] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] , DCAF15 E3 ubiquitin ligase binding moiety [ka] , or VHL E3 ubiquitin ligase binding moiety [ka] which results in the formula Iy-1, Iy-2, or Iy-3: [ka] [ka] or a pharmaceutically acceptable salt thereof, wherein in formulas Iy-1, Iy-2, and Iy-3, IRAK is as defined above and as described in embodiments herein, and: X 1 , X 2 , and X 3 each independently represents a covalent bond, —CH—, —C(O)—, —C(S)—, or [ka] is a divalent moiety selected from: X 4 and X 5 each independently is —CH—, —C(O)—, —C(S)—, or [ka] is a divalent moiety selected from: R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic; R 2 , R 3 , and R 4 each independently represents hydrogen, -R 6, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen or C 1~6 It is aliphatic; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring A is a fused ring selected from a 6-membered aryl containing 0-2 nitrogen atoms, a 5- to 7-membered partially saturated carbocyclyl, a 5- to 7-membered partially saturated heterocyclyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or an 8-10-membered bicyclic heteroaryl having 1-5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; Ring C is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; L is a covalent bond or a divalent saturated or unsaturated straight or branched chain C 1~50 a hydrocarbon chain, wherein 0 to 6 methylene units of L are independently -Cy-, -O-, -NR-, -S-, -OC(O)-, -C(O)O-, -C(O)-, -S(O)-, -S(O)2-, -NRS(O)2-, -S(O)2NR-, -NRC(O)-, -C(O)NR-, -OC(O)NR-, -NRC(O)O-, [ka] has been replaced by, where: Each -Cy- is independently selected from phenylenyl, 8- to 10-membered bicyclic arylenyl, 4- to 7-membered saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated spirocarbocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated carbocyclylenyl, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 4- to 7-membered saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, an optionally substituted bivalent ring selected from saturated or partially unsaturated spiroheterocyclylenyl, 8- to 10-membered bicyclic saturated or partially unsaturated heterocyclylenyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, 5- to 6-membered heteroarylenyl having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or 8- to 10-membered bicyclic heteroarylenyl having 1 to 5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; m is 0, 1, 2, 3 or 4; each n is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; p is 0, 1, 2, 3 or 4; q is 0, 1, 2, 3, or 4; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0296] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] whereby the formula I-y'-1 or I-y''-1: [ka] wherein in formula I-y'-1 and I-y''-1, IRAK, L, ring A, X 1 , X 2 , X 3 , R 1 , R 2 and m is as defined above.

[0297] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which results in the formula Iz-1, Iz-2, or Iz-3, respectively: [ka] or a pharmaceutically acceptable salt thereof, wherein in Formulas Iz-1, Iz-2, and Iz-3, L and IRAK are as defined above and described herein, and variable R 1 , R 2 , R 4 , R 5 , R 10 , R 11 , R 14 , R 17 , W1 , W 2 , X, and n are as defined in WO 2017 / 197051, the entirety of each of which is incorporated herein by reference; and [ka] is R 1 is bonded to R 1 and R 2 or R 12 R of the binding site of 17 is as defined in WO 2017 / 197051, so that [ka] But this R 12 Occupy the position of the substituent.

[0298] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] whereby compounds of formula I-aa: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-aa, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic; Each R2 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring A is Ring B is other than imidazo or benzo [ka] [ka] , ring B is other than benzo [ka] , ring B is other than benzo [ka] [ka] , ring B is other than benzo [ka] [ka] [ka] is a bicyclic or tricyclic ring selected from Ring B is a fused ring selected from a 6-membered aryl containing 0-2 nitrogen atoms, a 5- to 7-membered partially saturated carbocyclyl, a 5- to 7-membered partially saturated heterocyclyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3is selected from hydrogen, halogen, —OR, —N(R)2, or —SR; Each R 4 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, 2, 3, or 4; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0299] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] whereby the compound of formula I-aa': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-aa′, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Each R 2 are independently hydrogen, deuterium, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -Si(R)3, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring A is Ring B is other than imidazo or benzo [ka] [ka] , ring B is other than benzo [ka] , ring B is other than benzo [ka] [ka] [ka] , ring B is other than benzo [ka] [ka] [ka] is a bicyclic or tricyclic ring selected from Ring B is a fused ring selected from a 6-membered aryl containing 0-2 nitrogen atoms, a 5- to 7-membered partially saturated carbocyclyl, a 5- to 7-membered partially saturated heterocyclyl having 1-3 heteroatoms independently selected from boron, nitrogen, oxygen, silicon, or sulfur, or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 is selected from hydrogen, halogen, —OR, —N(R)2, or —SR; Each R 4 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, 2, 3, or 4; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0300] In some embodiments, the compound of formula I-aa' has formula I-aa'' or I-aa': [ka] or a pharmaceutically acceptable salt thereof, in formula I-aa″ and I-aa′″: IRAK, Ring A, L, R 1 , R 2 , X 1 , X 2 , X 3 , and m are each as defined above.

[0301] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the formula I-bb: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-bb, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic; Ring A is [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 and R 4 each independently represents hydrogen, -R 6, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1, and when p is 0, the bond connecting ring A and ring B is [ka] is bound to; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0302] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the formula I-bb': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-bb', L and IRAK are as defined above and as described in embodiments herein, and: X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Ring A is [ka] is a monocyclic or bicyclic ring selected from: Each R 2 are independently hydrogen, deuterium, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -Si(R)3, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 and R 4 each independently represents hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1, and when p is 0, the bond connecting ring A and ring B is [ka] is bound to; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0303] In some embodiments, the compound of formula I-bb' may be represented by formula I-bb'' or formula I-bb''': [ka] or a pharmaceutically acceptable salt thereof, in formula I-bb'' and formula I-bb''': IRAK, Ring A, Ring B, L, R 1 , R 2 , R 3 , X 1 , X 2 , X 3 , p, and m are each as defined above.

[0304] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the formula I-cc: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-cc, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: R 1is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic; Ring A is [ka] [ka] [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2 are independently hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 and R 4 each independently represents hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0305] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the formula I-cc': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-cc′, L and IRAK are as defined above and as described in embodiments herein, and X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Ring A is [ka] [ka] [ka] is a monocyclic or bicyclic ring selected from: Each R 2 are independently hydrogen, deuterium, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -Si(R)3, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; R 3 and R 4 each independently represents hydrogen, -R 6, halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen, C 1~4 aliphatic, or -CN; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; m is 0, 1, or 2; n is 0, 1, 2, 3, or 4; p is 0 or 1; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0306] In some embodiments, the compound of formula I-cc' above can be represented by formula I-cc'' or formula I-cc''': [ka] or a pharmaceutically acceptable salt thereof, in formula I-cc'' and formula I-cc''': IRAK, Ring A, Ring B, L, R 1 , R 2 , R 3 , X 1 , X 2 , X 3 , p, n, and m are as defined above.

[0307] As defined above and described herein, an LBM is a ligase binding moiety.

[0308] In some embodiments, the LBM comprises an E3 ubiquitin ligase (cereblon) binding moiety. [ka] , DCAF15 E3 ubiquitin ligase binding moiety [ka] , or VHL E3 ubiquitin ligase binding moiety [ka] where X 1 , X 2 , and X 3 each independently represents a covalent bond, —CH—, —C(O)—, —C(S)—, or [ka] is a divalent moiety selected from: X 4 and X 5 each independently is —CH—, —C(O)—, —C(S)—, or [ka] is a divalent moiety selected from: R 1is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic; R 2 , R 3 , and R 4 each independently represents hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R; R 5 is hydrogen or C 1~6 It is aliphatic; Each R 6 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring A is a fused ring selected from a 6-membered aryl containing 0-2 nitrogen atoms, a 5- to 7-membered partially saturated carbocyclyl, a 5- to 7-membered partially saturated heterocyclyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or an 8-10-membered bicyclic heteroaryl having 1-5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; Ring C is selected from a 6-membered aryl containing 0-2 nitrogen atoms or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; m is 0, 1, 2, 3 or 4; each n is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; p is 0, 1, 2, 3 or 4; q is 0, 1, 2, 3, or 4; and Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or Two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0309] In some embodiments, the LBM is selected from those depicted in Table 1 below.

[0310] X, as defined above and described herein 1 , X 2 , and X 3 each independently represents a covalent bond, —CH—, —C(O)—, —C(S)—, or [ka] is a divalent moiety selected from

[0311] In some embodiments, X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is.

[0312] In some embodiments, X 1is selected from those illustrated in Table 1 below.

[0313] In some embodiments, X 2 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is.

[0314] In some embodiments, X 2 is selected from those illustrated in Table 1 below.

[0315] In some embodiments, X 3 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is.

[0316] In some embodiments, X 3 is selected from those illustrated in Table 1 below.

[0317] X, as defined above and described herein 4 and X 5 each independently is —CH—, —C(O)—, —C(S)—, or [ka] is a divalent moiety selected from

[0318] In some embodiments, X 4 is -CH2-, -C(O)-, -C(S)-, or [ka] is.

[0319] In some embodiments, X 4is selected from those illustrated in Table 1 below.

[0320] In some embodiments, X 5 is -CH2-, -C(O)-, -C(S)-, or [ka] is.

[0321] In some embodiments, X 5 is selected from those illustrated in Table 1 below.

[0322] As defined above and described herein, R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic.

[0323] In some embodiments, R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, or an optionally substituted C 1~4 It is aliphatic.

[0324] In some embodiments, R 1 is selected from those illustrated in Table 1 below.

[0325] As defined above and described herein, R 2 , R 3 , and R 4 each independently represents hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R.

[0326] In some embodiments, R 2 is hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R.

[0327] In some embodiments, R 2 is selected from those illustrated in Table 1 below.

[0328] In some embodiments, R 3 is hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R.

[0329] In some embodiments, R 3 is methyl.

[0330] In some embodiments, R 3 is selected from those illustrated in Table 1 below.

[0331] In some embodiments, R 4 is hydrogen, -R 6 , halogen, -CN, -NO2, -OR, -SR, -NR2, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)NR2, -C(O)N(R)OR, -OC(O)R, -OC(O)NR2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, or -N(R)S(O)2R.

[0332] In some embodiments, R 4 is methyl.

[0333] In some embodiments, R 4 is selected from those illustrated in Table 1 below.

[0334] As defined above and described herein, R 5 is hydrogen or C 1~6 It is aliphatic.

[0335] In some embodiments, R 5 is t-butyl.

[0336] In some embodiments, R 5 is selected from those illustrated in Table 1 below.

[0337] As defined above and described herein, each R 6 independently, C 1~6 An optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0338] In some embodiments, R 6 is replaced by C 1~6 In some embodiments, R 6 is optionally substituted phenyl. In some embodiments, R 6 is an optionally substituted 4- to 7-membered saturated or partially unsaturated heterocyclic ring having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, R 6is an optionally substituted 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0339] In some embodiments, R 6 is selected from those illustrated in Table 1 below.

[0340] As defined above and described herein, ring A is a fused ring selected from a 6-membered aryl containing 0 to 2 nitrogen atoms, a 5- to 7-membered partially saturated carbocyclyl, a 5- to 7-membered partially saturated heterocyclyl having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or a 5-membered heteroaryl having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0341] In some embodiments, ring A is a fused 6-membered aryl containing 0-2 nitrogen atoms. In some embodiments, ring A is a fused 5- to 7-membered partially saturated carbocyclyl. In some embodiments, ring A is a fused 5- to 7-membered partially saturated heterocyclyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, or sulfur. In some embodiments, ring A is a fused 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0342] In some embodiments, ring A is a fused phenyl.

[0343] In some embodiments, ring A is selected from those depicted in Table 1 below.

[0344] As defined above and described herein, Ring B is selected from a 6-membered aryl containing 0-2 nitrogen atoms or an 8- to 10-membered bicyclic heteroaryl having 1-5 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0345] In some embodiments, Ring B is a 6-membered aryl containing 0-2 nitrogen atoms. In some embodiments, Ring B is an 8- to 10-membered bicyclic heteroaryl having 1-5 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0346] In some embodiments, ring B is [ka] is.

[0347] In some embodiments, ring B is selected from those depicted in Table 1 below.

[0348] As defined above and described herein, Ring C is selected from a 6-membered aryl containing 0 to 2 nitrogen atoms or a 5-membered heteroaryl having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0349] In some embodiments, Ring C is a 6-membered aryl containing 0-2 nitrogen atoms. In some embodiments, Ring C is a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0350] In some embodiments, ring C is [ka] is.

[0351] In some embodiments, ring C is selected from those depicted in Table 1 below.

[0352] As defined above and described herein, m is 0, 1, 2, 3, or 4.

[0353] In some embodiments, m is 0. In some embodiments, m is 1. In some embodiments, m is 2. In some embodiments, m is 3. In some embodiments, m is 4.

[0354] In some embodiments, m is selected from those depicted in Table 1 below.

[0355] As defined above and described herein, each occurrence of n is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10.

[0356] In some embodiments, n is 0. In some embodiments, n is 1. In some embodiments, n is 2. In some embodiments, n is 3. In some embodiments, n is 4. In some embodiments, n is 5. In some embodiments, n is 6. In some embodiments, n is 7. In some embodiments, n is 8. In some embodiments, n is 9. In some embodiments, n is 10.

[0357] In some embodiments, n is selected from those depicted in Table 1 below.

[0358] As defined above and described herein, p is 0, 1, 2, 3, or 4.

[0359] In some embodiments, p is 0. In some embodiments, p is 1. In some embodiments, p is 2. In some embodiments, p is 3. In some embodiments, p is 4.

[0360] In some embodiments, p is selected from those depicted in Table 1 below.

[0361] As defined above and described herein, q is 0, 1, 2, 3, or 4.

[0362] In some embodiments, q is 0. In some embodiments, q is 1. In some embodiments, q is 2. In some embodiments, q is 3. In some embodiments, q is 4.

[0363] In some embodiments, q is selected from those depicted in Table 1 below.

[0364] As defined above and described herein, each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or: two R groups on the same nitrogen optionally combine with the atoms between them to form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0365] In some embodiments, R is hydrogen. In some embodiments, R is phenyl. In some embodiments, R is a 4- to 7-membered saturated or partially unsaturated heterocyclic ring having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, R is a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, two R groups on the same nitrogen optionally, together with the atoms between them, form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0366] In some embodiments, R is selected from those depicted in Table 1 below.

[0367] In some embodiments, the LBM is an E3 ubiquitin ligase (cereblon) binding moiety as described in Varfolomeev, E. et al., IAP Antagonists Induce Autoubiquitination of c-IAPs, NF-κB activation, and TNFα-Dependent Apoptosis, Cell, 2007, 131(4):669-81, e.g., [ka] [ka] where [ka] is attached to a modifiable carbon, oxygen, nitrogen, or sulfur atom.

[0368] In some embodiments, R is selected from those depicted in Table 1 below.

[0369] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety, whereby the LBM is an E3 ubiquitin ligase (cereblon)-binding moiety, such as represented by formula I-dd: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-dd: X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same nitrogen, taken together with the atoms between them, form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 2 are independently hydrogen, -R 3, halogen, -CN, -NO2, -OR, -SR, -N(R)2, -Si(R)3, -S(O)2R, -S(O)2N(R)2, -S(O)R, -C(O)R, -C(O)OR, -C(O)N(R)2, -C(O)N(R)OR, -C(R )2N(R)C(O)R, -C(R)2N(R)C(O)N(R)2, -OC(O)R, -OC(O)N(R)2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)N(R)2, or -N(R)S(O)2R; Each R 3 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring A is [ka] a tricyclic ring selected from each of ring B, ring C, and ring D is independently a fused ring selected from a 6-membered aryl containing 0 to 3 nitrogen atoms, a 5- to 7-membered saturated or partially unsaturated carbocyclyl, a 5- to 7-membered saturated or partially unsaturated heterocyclyl ring having 1 to 3 heteroatoms independently selected from boron, nitrogen, oxygen, silicon, or sulfur, or a 5-membered heteroaryl having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; and m is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16; wherein L and IRAK are as described in the embodiments herein.

[0370] In some embodiments, the compound of formula I-dd has formula I-dd' or formula I-dd'': [ka] [ka] or a pharmaceutically acceptable salt thereof, in formula I-dd′ and formula I-dd″: IRAK, Ring A, L, R 1 , R 2 , X 1 , X 2 , X 3 , and m are each as defined above.

[0371] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety comprising administering to a mammalian subject the ubiquitin ligase (LBM) a ubiquitin ligase (cereblon)-binding moiety. [ka] which gives the formula I-dd-1: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-dd-1: X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: X 2 is a carbon atom or a silicon atom; X 3 is a divalent moiety selected from -CH2- or -Si(R2)-; R 1d is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same nitrogen, taken together with the atoms between them, form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 2d are independently hydrogen, -R 3d , halogen, -CN, -NO2, -OR, -SR, -N(R)2, -Si(R)3, -S(O)2R, -S(O)2N(R)2, -S(O)R, -C(O)R, -C(O)OR, -C(O)N(R)2, -C(O)N(R)OR, -C(R )2N(R)C(O)R, -C(R)2N(R)C(O)N(R)2, -OC(O)R, -OC(O)N(R)2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)N(R)2, or -N(R)S(O)2R; Each R 3d independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring A d teeth, [ka] a tricyclic ring selected from Ring B d , ring C d , and ring D dare each independently a fused ring selected from a 6-membered aryl containing 0 to 3 nitrogen atoms, a 5- to 7-membered saturated or partially unsaturated carbocyclyl, a 5- to 7-membered saturated or partially unsaturated heterocyclyl ring having 1 to 3 heteroatoms independently selected from boron, nitrogen, oxygen, silicon, or sulfur, or a 5-membered heteroaryl having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; and m is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16; wherein L and IRAK are as described in the embodiments herein.

[0372] In some embodiments, the compound of formula I-dd-1 has formula I-dd-1' or formula I-dd-1'': [ka] [ka] or a pharmaceutically acceptable salt thereof, in formula I-dd-1′ and formula I-dd-1″: IRAK, Ring A d , L, R 1d , R 2d , X 1 , X 2 , X 3 , and m are each as defined above.

[0373] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety, whereby the LBM is an E3 ubiquitin ligase (cereblon)-binding moiety, such as represented by formula I-dd-2 or I-dd-3: [ka] or a pharmaceutically acceptable salt thereof, wherein in formulas I-dd-2 and I-dd-3, L and SMARCA are as defined above and as described in embodiments herein, and Each R 2d are independently hydrogen, deuterium, -R 3d , halogen, -CN, -NO2, -OR, -SR, -NR2, -SiR3, -S(O)2R, -S(O)2NR2, -S(O)R, -C(O)R, -C(O)OR, -C(O)N R2, -C(O)N(R)OR, -C(R)2N(R)C(O)R, -C(R)2N(R)C(O)N(R)2, -OC(O)R, -OC(O)N(R)2, -OP(O)R2, - OP(O)(OR)2, -OP(O)(OR)NR2, -OP(O)(NR2)2-, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR2, -N(R)S (O)2R, -NP(O)R2, -N(R)P(O)(OR)2, -N(R)P(O)(OR)NR2, -N(R)P(O)(NR2)2, or -N(R)S(O)2R; Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same nitrogen, taken together with the atoms between them, form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 3d independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring B d , ring C d , and ring D deach is independently a fused ring selected from a 6-membered aryl, a 6-membered heteroaryl containing 1 to 4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, a 5-membered to 7-membered saturated or partially unsaturated carbocyclyl, a 5-membered to 7-membered saturated or partially unsaturated heterocyclyl having 1 to 3 heteroatoms independently selected from boron, nitrogen, oxygen, silicon, or sulfur, or a 5-membered heteroaryl having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, or sulfur; L 1 is a covalent bond, or C 1~3 wherein one to two methylene units of the chain are optionally replaced independently by -O-, -C(O)-, -C(S)-, -C(R)2-, -CH(R)-, -C(F)2-, -N(R)-, -S-, -S(O)2-, or -CR=CR-; m is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16; and R 4 , R 10 , R 11 , R 15 , W 1 , W 2 and X are as defined in WO 2019 / 099868, the entirety of each of which is incorporated herein by reference.

[0374] [ka] The attachment point of ring B d , ring C d , or ring D d If shown above, this [ka] B d or ring D d is ring C d Ring B, including the ring fused to d , ring C d , or ring D dIt is intended, and one of ordinary skill in the art will understand, that the carbon atom may be at any available carbon or nitrogen atom above.

[0375] -(R 2d ) m The attachment point of ring B d , ring C d , or ring D d In the case shown above, this -(R 2 ) m The connection point of B d or ring D d is ring C d Ring B, including the carbon atom fused to d , ring C d , or ring D d It is intended, and one of ordinary skill in the art will understand, that the carbon atom may be at any available carbon or nitrogen atom above.

[0376] [ka] The attachment point of ring B d , ring C d , or ring D d If shown above, this [ka] B d or ring D d is ring C d Ring B, including the carbon atom fused to d , ring C d , or ring D d It is intended, and one of ordinary skill in the art will understand, that the carbon atom may be at any available carbon or nitrogen atom above.

[0377] In certain embodiments, the present invention provides a method for treating a fibronectin-binding protein (FBG) comprising administering to a mammalian subject the present invention, wherein the FBG is an E3 ubiquitin ligase (cereblon) binding moiety, such that the FBG is of formula I-ee: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-ee: X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same nitrogen, taken together with the atoms between them, form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 2 are independently hydrogen, -R 3 , halogen, -CN, -NO2, -OR, -SR, -N(R)2, -Si(R)3, -S(O)2R, -S(O)2N(R)2, -S(O)R, -C(O)R, -C(O)OR, -C(O)N(R)2, -C(O)N(R)OR, -C(R )2N(R)C(O)R, -C(R)2N(R)C(O)N(R)2, -OC(O)R, -OC(O)N(R)2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)N(R)2, or -N(R)S(O)2R; Each R 3 independently, C 1~6an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring A is [ka] a tricyclic ring selected from each of ring B, ring C, and ring D is independently a fused ring selected from a 6-membered aryl containing 0 to 3 nitrogen atoms, a 5- to 7-membered saturated or partially unsaturated carbocyclyl, a 5- to 7-membered saturated or partially unsaturated heterocyclyl ring having 1 to 3 heteroatoms independently selected from boron, nitrogen, oxygen, silicon, or sulfur, or a 5-membered heteroaryl having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; and m is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16; wherein L and IRAK are as described in the embodiments herein.

[0378] In some embodiments, the compound of formula I-ee has formula I-ee' or formula I-ee'': [ka] or a pharmaceutically acceptable salt thereof, in formula I-ee' and formula I-ee'': IRAK, Ring A, L, R 1 , R 2 , X 1 , and m are each as defined above.

[0379] In certain embodiments, the present invention provides a method for the preparation of a ubiquitin ligase (cereblon)-binding moiety, whereby the LBM is an E3 ubiquitin ligase (cereblon)-binding moiety, such as represented by formula I-ff: [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-ff: X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same nitrogen, taken together with the atoms between them, form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 2 are independently hydrogen, -R 3 , halogen, -CN, -NO2, -OR, -SR, -N(R)2, -Si(R)3, -S(O)2R, -S(O)2N(R)2, -S(O)R, -C(O)R, -C(O)OR, -C(O)N(R)2, -C(O)N(R)OR, -C(R )2N(R)C(O)R, -C(R)2N(R)C(O)N(R)2, -OC(O)R, -OC(O)N(R)2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)N(R)2, or -N(R)S(O)2R; Each R 3 independently, C 1~6an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring A is [ka] a tricyclic ring selected from each of ring B and ring C is independently a fused ring selected from a 6-membered aryl containing 0 to 3 nitrogen atoms, a 5- to 7-membered saturated or partially unsaturated carbocyclyl, a 5- to 7-membered saturated or partially unsaturated heterocyclyl ring having 1 to 3 heteroatoms independently selected from boron, nitrogen, oxygen, or sulfur, or a 5-membered heteroaryl having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; Ring D is a fused ring selected from aryl having 0-3 nitrogen atoms, saturated or partially unsaturated carbocyclyl, saturated or partially unsaturated heterocyclyl having 1-2 heteroatoms independently selected from nitrogen, oxygen, silicon, or sulfur, or heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; [ka] is a single or double bond; m is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16; wherein L and IRAK are as described in the embodiments herein.

[0380] In some embodiments, the compound of formula I-ff can be represented by formula I-ff' or formula I-ff'': [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-ff′ and formula I-ff″: IRAK, Ring A, L, R 1 , R 2 , X 1 , and m are each as defined above.

[0381] In certain embodiments, the present invention provides a method for the treatment of HIV-1-associated ... [ka] or a pharmaceutically acceptable salt thereof, wherein in formula I-gg: X 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from: R 1 is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -N(R)2, -Si(R)3, or optionally substituted C 1~4 It is aliphatic; Each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or two R groups on the same nitrogen, taken together with the atoms between them, form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R 2 are independently hydrogen, -R 3, halogen, -CN, -NO2, -OR, -SR, -N(R)2, -Si(R)3, -S(O)2R, -S(O)2N(R)2, -S(O)R, -C(O)R, -C(O)OR, -C(O)N(R)2, -C(O)N(R)OR, -C(R )2N(R)C(O)R, -C(R)2N(R)C(O)N(R)2, -OC(O)R, -OC(O)N(R)2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)N(R)2, or -N(R)S(O)2R; Each R 3 independently, C 1~6 an optionally substituted group selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring A is [ka] [ka] a tricyclic ring selected from each of ring B and ring C is independently a fused ring selected from a 6-membered aryl containing 0-2 nitrogen atoms, a 5-membered to 7-membered saturated or partially unsaturated carbocyclyl, a 5-membered to 7-membered saturated or partially unsaturated heterocyclyl ring having 1-3 heteroatoms independently selected from boron, nitrogen, oxygen, silicon, or sulfur, or a 5-membered heteroaryl having 1-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur; [ka] is a single or double bond; m is 0, 1, 2, 3, 4, 5, 6, 7, or 8; wherein L and IRAK are as described in the embodiments herein.

[0382] In some embodiments, the compound of formula I-gg has formula I-gg' or formula I-gg'': [ka] or a pharmaceutically acceptable salt thereof, in formula I-gg′ and formula I-gg″: IRAK, Ring A, L, R 1 , R 2 , X 1 , and m are each as defined above.

[0383] X, as defined above and described herein 1 is a covalent bond, -CH2-, -C(O)-, -C(S)-, or [ka] is a divalent moiety selected from

[0384] In some embodiments, X 1 is a covalent bond. In some embodiments, X 1 is -CH2-. In some embodiments, X 1 is —C(O)—. In some embodiments, X 1 is -C(S)-. In some embodiments, X 1 teeth [ka] is.

[0385] In some embodiments, X 1 is selected from those illustrated in Table 1 below.

[0386] X, as defined above and described herein 2 is a carbon atom or a silicon atom.

[0387] In some embodiments, X 2is a carbon atom. In some embodiments, X 2 is a silicon atom.

[0388] In some embodiments, X 2 is selected from those illustrated in Table 1 below.

[0389] X, as defined above and described herein 3 is a divalent moiety selected from -CH2- or -Si(R2)-.

[0390] In some embodiments, X 3 is -CH2-. In some embodiments, X 2 is -Si(R2)-.

[0391] In some embodiments, X 3 is selected from those illustrated in Table 1 below.

[0392] As defined above and described herein, R 1 or R 1d is hydrogen, deuterium, halogen, -CN, -OR, -SR, -S(O)R, -S(O)2R, -NR2, -Si(R3), or optionally substituted C 1~4 It is aliphatic.

[0393] In some embodiments, R 1 or R 1d is hydrogen. In some embodiments, R 1 or R 1d is deuterium. In some embodiments, R 1 or R 1d is halogen. In some embodiments, R 1 or R 1d is -CN. In some embodiments, R 1 or R 1d In some embodiments, R 1 or R 1dIn some embodiments, R 1 or R 1d is -S(O)R. In some embodiments, R 1 or R 1d is —S(O)R. In some embodiments, R 1 or R 1d is -NR2. In some embodiments, R 1 or R 1d is —Si(R). In some embodiments, R 1 or R 1d is replaced by C 1~4 It is aliphatic.

[0394] In some embodiments, R 1 or R 1d is selected from those illustrated in Table 1 below.

[0395] As defined above and described herein, each R is independently hydrogen or an optionally substituted group, and the optionally substituted group is C 1~6 selected from aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1-2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1-4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; or: two R groups on the same nitrogen, taken together with the atoms between them, form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0396] In some embodiments, R is hydrogen. In some embodiments, R is optionally substituted C 1~6It is aliphatic. In some embodiments, R is an optionally substituted phenyl. In some embodiments, R is an optionally substituted 4- to 7-membered saturated or partially unsaturated heterocyclic ring having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, R is an optionally substituted 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur. In some embodiments, two R groups on the same nitrogen, together with the atom between them, form a 4- to 7-membered saturated, partially unsaturated, or heteroaryl ring having, in addition to the nitrogen, 0 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

[0397] In some embodiments, R is selected from those depicted in Table 1 below.

[0398] As defined above and described herein, R 2 or R 2d each independently represents hydrogen, -R 3 , -R 3d , halogen, -CN, -NO2, -OR, -SR, -N(R)2, -Si(R3), -S(O)2R, -S(O)2N(R)2, -S(O)R, -C(O)R, -C(O)OR, -C(O)N(R)2, -C(O)N(R)OR, -C(R )2N(R)C(O)R, -C(R)2N(R)C(O)N(R)2, -OC(O)R, -OC(O)N(R)2, -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)N(R)2, or -N(R)S(O)2R.

[0399] In some embodiments, R 2 or R 2d is hydrogen. In some embodiments, R 2 Ha-R 3 In some embodiments, R 2d Ha-R 3d In some embodiments, R 2 or R 2dis halogen. In some embodiments, R 2 or R 2d is -CN. In some embodiments, R 2 or R 2d is —NO. In some embodiments, R 2 or R 2d In some embodiments, R 2 or R 2d In some embodiments, R 2 is -NR2. In some embodiments, R 2 or R 2d is —Si(R). In some embodiments, R 2 or R 2d is —S(O)R. In some embodiments, R 2 or R 2d is —S(O)NR. In some embodiments, R 2 or R 2d is -S(O)R. In some embodiments, R 2 or R 2d is —C(O)R. In some embodiments, R 2 or R 2d is —C(O)OR. In some embodiments, R 2 or R 2d is —C(O)NR. In some embodiments, R 2 or R 2d is —C(O)N(R)OR. In some embodiments, R 2 or R 2d is —C(R)N(R)C(O)R. In some embodiments, R 2 or R 2d is —C(R)N(R)C(O)N(R). In some embodiments, R 2 or R 2d is -OC(O)R. In some embodiments, R 2 or R 2d is —OC(O)NR. In some embodiments, R 2or R 2d is —N(R)C(O)OR. In some embodiments, R 2 or R 2d is —N(R)C(O)R. In some embodiments, R 2 or R 2d is —N(R)C(O)NR. In some embodiments, R 2 or R 2d is -N(R)S(O)R.

[0400] In some embodiments, R ...

Claims

1. Formula II-f-5: 【Chemistry 3001】 or a pharma- ceutically acceptable salt thereof, in formula II-f-5: 【Chemistry 3008】 teeth, 【Chemistry 3009】 and Ring A is cyclohexyl; Ring C is 【Chemistry 3010】 and L ２ and L ３ is a covalent bond; R １ is -CF ２ (R); Each R is independently hydrogen or an optionally substituted group, the optionally substituted group being C １～６ or selected from: aliphatic, phenyl, 4- to 7-membered saturated or partially unsaturated heterocyclic rings having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and 5- to 6-membered heteroaryl rings having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; two R groups on the same atom optionally taken together with the atoms between them form an optionally substituted 4-11 membered saturated or partially unsaturated carbocyclic or heterocyclic monocyclic, bicyclic, bridged bicyclic, spiro, or heteroaryl ring having, in addition to the atom to which they are attached, 0-3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R ２ are independently hydrogen, -R ５ , halogen, -CN, -NO ２ , -OR, -SR, -NR ２ , -S(O) ２ R, -S(O) ２ N.R. ２ , -S(O)R, -S(O)(NR)R, -P(O)(OR) ２ , -P(O)(NR ２ ) ２ , -CF ２ (R), -CF ３ , -CR ２ (OR), -CR ２ (NR ２ ), -C(O)R, -C(O)OR, -C(O)NR ２ , -C(O)N(R)OR, -OC(O)R, -OC(O)NR ２ , -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR ２ , or -N(R)S(O) ２ R; R ４ teeth, 【Chemistry 3006】 , hydrogen, or an optionally substituted group, the optionally substituted group being selected from C １～６ selected from aliphatic, or 4- to 11-membered saturated or partially unsaturated monocyclic, bicyclic, bridged bicyclic, or spiro rings having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Ring D is a phenyl, a 4- to 10-membered saturated or partially unsaturated monocyclic or bicyclic, carbocyclic or heterocyclic ring having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur, or a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; Each R ３ are independently hydrogen, -R ５ , halogen, -CN, -NO ２ , -OR, -SR, -NR ２ , -S(O) ２ R, -S(O) ２ N.R. ２ , -S(O)R, -S(O)(NR)R, -P(O)(OR) ２ , -P(O)(NR ２ ) ２ , -CF ２ (R), -CF ３ , -CR ２ (OR), -CR ２ (NR ２ ), -C(O)R, -C(O)OR, -C(O)NR ２ , -C(O)N(R)OR, -OC(O)R, -OC(O)NR ２ , -N(R)C(O)OR, -N(R)C(O)R, -N(R)C(O)NR ２ , or -N(R)S(O) ２ R; Each R ５ is independent, C １～６ an optionally substituted group selected from aliphatic, phenyl, a 3- to 7-membered saturated or partially unsaturated carbocyclic or heterocyclic ring having 1 to 2 heteroatoms independently selected from nitrogen, oxygen, and sulfur, and a 5- to 6-membered heteroaryl ring having 1 to 4 heteroatoms independently selected from nitrogen, oxygen, and sulfur; n is 1; m is independently 0, 1, 2, 3 or 4; each p is 0, 1, 2, 3 or 4; A compound or a pharma- ceutically acceptable salt thereof.

2. n is 1, R １ Ga-CHF ２ 2. The compound of claim 1,

3. R ４ But, C １－６ 3. The compound of claim 1 or 2, which is an optionally substituted group selected from aliphatic, or 4- to 11-membered, saturated or partially unsaturated monocyclic, bicyclic, bridged bicyclic, or spiro rings having 1 to 3 heteroatoms independently selected from nitrogen, oxygen, and sulfur.

4. R ４ but, 【Chemistry 3011】 The compound according to any one of claims 1 to 3,

5. The compound is 【Chemistry 3012】 【Chemistry 3013】 【Chemistry 3014】 【Chemistry 3015】 or a pharma- ceutically acceptable salt thereof.

6. The compound is 【Chemistry 3016】 or a pharma- ceutically acceptable salt thereof.

7. A pharmaceutical composition comprising a compound according to any one of claims 1 to 6, and a pharma- ceutically acceptable carrier, adjuvant, or vehicle.

8. 10. A composition comprising a compound according to any one of claims 1 to 6 for treating an autoimmune disease, an inflammatory disorder, or an immune deficiency disorder in a patient, the composition being administered to the patient.

9. The disease or disorder is selected from the group consisting of systemic lupus erythematosus, polychondritis, scleroderma, Wegener's granulomatosis, dermatomyositis, chronic active hepatitis, myasthenia gravis, Stevens-Johnson syndrome, idiopathic sprue, ulcerative colitis, Crohn's disease, irritable bowel syndrome, celiac disease, periodontitis, pulmonary hyaline membrane disease, renal disease, glomerular disease, alcoholic liver disease, endocrine eye disorders, Graves' disease, sarcoidosis, alveolitis, chronic hypersensitivity pneumonitis, multiple sclerosis, primary biliary cirrhosis, uveitis (anterior and posterior), Sjogren's syndrome, vernal keratoconjunctivitis, interstitial pulmonary fibrosis, psoriatic arthritis, systemic juvenile idiopathic arthritis, nephritis, diverticulitis, interstitial cystitis, glomerulonephritis (with or without nephrotic syndrome including idiopathic nephrotic syndrome or minimal change nephropathy), chronic granulomatous disease, endometriosis, leptospirosis, kidney disease, glaucoma, retinal disease, headache, pain, complex regional pain syndrome, cardiac hypertrophy, catabolic disorders, obesity, fetal growth retardation, hypercholesterolemia, heart disease, chronic heart failure, mesothelioma, anhidrotic ectodermal dysplasia, Behcet's disease, incontinentia pigmenti, Paget's disease, pancreatitis, hereditary periodic fever syndromes, asthma (allergic, nonallergic, mild, moderate, Severe, bronchitis, or exercise-induced), acute lung injury, acute respiratory distress syndrome, eosinophilia, hypersensitivity, anaphylaxis, sinusitis, silica-induced disease, chronic obstructive pulmonary disease (COPD) (reduction of damage, airway inflammation, bronchial hyperactivity, remodeling or disease progression), lung disease, cystic fibrosis, acid-induced lung injury, pulmonary hypertension, polyneuropathy, cataracts, muscle inflammation associated with systemic sclerosis, inclusion body myositis, myasthenia gravis, thyroiditis, Addison's disease, lichen planus, type 1 diabetes, type 2 diabetes, appendicitis, atopic dermatitis, allergies, blepharitis, bronchiolitis , bronchitis, bursitis, cervicitis, cholangitis, cholecystitis, chronic graft rejection, colitis, conjunctivitis, cystitis, dacryoadenitis, dermatitis, dermatomyositis, encephalitis, endocarditis, endometritis, enteritis, small intestine colitis, epicondylitis, epididymitis, fasciitis, fibromyalgia, gastritis, gastroenteritis, Henoch-Schonlein purpura, hepatitis, sweat gland abscess, immunoglobulin A nephropathy, interstitial lung disease, laryngitis, mastitis, meningitis, myelitis, myocarditis, myositis, nephritis, oophoritis, orchitis, osteitis, otitis, pancreatitis, parotitis, pericarditis, peritonitis, pharyngitis, pleurisy, phlebitis, pneumonia, polymyositis, proctitis, prostatitis, pyelonephritis, rhinitis, salpingitis,9. The composition of claim 8, wherein the disease is sinusitis, stomatitis, synovitis, tendonitis, tonsillitis, vaginitis, vasculitis, vulvitis, alopecia areata, erythema multiforme, dermatitis herpetiformis, scleroderma, vitiligo, hypersensitivity vasculitis, urticaria, bullous pemphigoid, pemphigus vulgaris, pemphigus foliaceus, paraneoplastic pemphigus, epidermolysis bullosa acquisita, acute and chronic gout, chronic gouty arthritis, psoriasis, psoriatic arthritis, rheumatoid arthritis, juvenile rheumatoid arthritis, cryopyrin-associated periodic syndrome, adult-onset Still's disease, macrophage activation syndrome, primary and secondary hemophagocytic lymphohistiocytosis, familial Mediterranean fever, NLRP12 autoinflammatory syndrome, or osteoarthritis.

10. The disease or disorder is selected from the group consisting of ocular allergy, conjunctivitis, keratoconjunctivitis sicca, vernal conjunctivitis, allergic rhinitis or chronic rhinosinusitis with nasal polyposis (CRSwNP), hemolytic anemia, aplastic anemia, red cell anemia, idiopathic thrombocytopenia, eosinophilia, Löffler's syndrome, eosinophilic pneumonia, tropical eosinophilia, bronchopulmonary aspergillosis, polyarteritis nodosa, Churg-Strauss syndrome, eosinophilic granuloma, eosinophilic asthma, eosinophilic chronic obstructive pulmonary disease, psoriasis, generalized pustular psoriasis, psoriasis vulgaris, contact dermatitis, atopic dermatitis, alopecia areata, erythema multiforme, dermatitis herpetiformis, scleroderma, vitiligo, hypercalcaemia, erythema multiforme, erythema herpetiformis, scleroderma, vitiligo, hypercalcaemia, erythema multiforme, erythema herpetiformis, erythema multiforme ...

9. The composition of claim 8, wherein the treatment is selected from the group consisting of inflammatory bowel disease, urticaria, bullous pemphigoid, lupus, lupus erythematosus, systemic lupus erythematosus, pemphigus vulgaris, pemphigus foliaceus, paraneoplastic pemphigus, epidermolysis bullosa acquisita, acne vulgaris, hidradenitis suppurativa, Sweet's syndrome, pyoderma gangrenosum, allergic conditions of the skin, acute and chronic gout, chronic gouty arthritis, psoriatic arthritis, rheumatoid arthritis, juvenile rheumatoid arthritis, cryopyrin-associated periodic syndrome, adult-onset Still's disease, macrophage activation syndrome, primary and secondary hemophagocytic lymphohistiocytosis, familial Mediterranean fever, and NLRP12 autoinflammatory syndrome.

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