Parathyroid hormone polypeptide conjugates and methods of their use

Abstract

Disclosed are peptide-fatty acid conjugates, pharmaceutical compositions containing them, and methods of their medical use in the treatment of, e.g., a disease or condition associated with the PTHR1 signaling overactivity (e.g., hypercalcemia, hypophosphatemia, hyperparathyroidism, or Jansen's metaphyseal chondrodysplasia) or deficiency (e.g., hypoparathyroidism, hyperphosphatemia, osteoporosis, fracture repair, osteomalacia, arthritis, thrombocytopenia, or chronic kidney disease).

Description

[0001] PARATHYROID HORMONE POLYPEPTIDE CONJUGATES AND METHODS OF THEIR USE

[0002] STATEMENT AS TO FEDERALLY FUNDED RESEARCH

[0003] This invention was made with government support under 5R01 DK113039-04, 5P01 DK011794-50, and P30 AR075042 awarded by the NIH. The government has certain rights in the invention.

[0004] SEQUENCE LISTING

[0005] The instant application contains a Sequence Listing which has been submitted electronically in XML format and is hereby incorporated by reference in its entirety. Said XML copy, created on May 29, 2025, is named “51313-003WO2_Sequence_Listing_5_29_25” and is 144,830 bytes in size.

[0006] BACKGROUND OF THE INVENTION

[0007] Parathyroid hormone receptor 1 (PTHR1) functions as a receptor for parathyroid hormone (PTH) and parathyroid-hormone related protein (PTHrP). PTHR1 is expressed in high levels in bone and kidney and regulates calcium ion homeostasis. Regulation of extracellular calcium concentration is necessary for the normal function of the gastrointestinal, skeletal, neurologic, neuromuscular, and cardiovascular systems. PTH synthesis and release are controlled principally by the serum calcium level; a low level stimulates and a high level suppresses both hormone synthesis and release. PTH, in turn, maintains the serum calcium level by directly or indirectly promoting calcium entry into the blood at three sites of calcium exchange: gut, bone, and kidney. PTH contributes to net gastrointestinal absorption of calcium by favoring the renal synthesis of the active form of vitamin D. PTH promotes calcium resorption from bone indirectly by stimulating differentiation of the bone-resorbing cells, osteoclasts. It also mediates at least three main effects on the kidney: stimulation of tubular calcium reabsorption, enhancement of phosphate clearance, and promotion of an increase in the enzyme that completes synthesis of the active form of vitamin D.

[0008] Both increased and decreased signaling of PTHR1 are associated with disease. For example, decreased signaling of PTHR1 due to inadequate production of parathyroid hormone (PTH) by the parathyroid glands is associated with the life-long condition hypoparathyroidism. Because PTH is critical for regulation of calcium and phosphate levels, loss of PTH reduces calcium levels in blood and bones and increases phosphate levels (hypocalcemia and hyperphosphatemia). Hypocalcemia leads to symptoms such as neuromuscular irritability, including paresthesias, muscle twitching, laryngeal spasms (which can lead to inability to speak and to alert health providers to the underlying medical condition, which has led to delayed or incorrect treatment), and possibly tetany and seizures.

[0009] Excessive signaling activity of parathyroid hormone receptor 1 (PTHR1) is known to be associated with hypercalcemia, hypophosphatemia, hyperparathyroidism, and Jansen’s metaphyseal chondrodysplasia. These diseases can arise from overproduction of either of the two endogenous PTHR1 ligands - PTH, as in primary or secondary hyperparathyroidism (HPT), or PTH-related protein (PTHrP), as in humoral hypercalcemia of malignancy. These diseases are characterized by high levels of blood calcium, excessive urinary excretion of calcium and / or phosphate, and can further be associated with abnormal bones, due to alterations in bone formation / resorption activities mediated by PTHR1. Disruption of calcium homeostasis may produce many clinical conditions (e.g., severe bone disease, anemia, renal impairment, ulcers, myopathy, and neuropathy) and usually results from conditions that produce an alteration in the level of parathyroid hormone. Hypercalcemia is a condition that is characterized by an elevation in the serum calcium level. It is often associated with primary hyperparathyroidism in which an excess of PTH production occurs as a result of a parathyroid gland lesion (e.g., adenoma, hyperplasia, or carcinoma). Another type of hypercalcemia, humoral hypercalcemia of malignancy (HHM), is a common paraneoplastic syndrome. It appears to result in most instances from the production by tumors (e.g., squamous, renal, ovarian, or bladder carcinomas) of PTHrP, which appears to mimic certain of the renal and skeletal actions of PTH and is believed to interact with the PTH receptor in these tissues.

[0010] PTH(1-34) is a therapeutic in treatment of osteoporosis and conditions of PTH deficiency, namely hypoparathyroidism. PTH(1 -34) has been identified as a safe and effective alternative to calcitriol therapy for hypoparathyroidism and is able to maintain normal serum calcium levels without hypercalciuria (Winer et al., J. Clin. Endocrinol. Metab. 88:4214-4220, 2003). Nonetheless, the polypeptide requires injection at least twice daily, and the need in this disease for a long-acting PTH(1-34) analog has therefore been recognized (Winer et al., supra).

[0011] Thus, there exists a need for additional PTHR1 agonists, antagonists, and inverse agonists, particularly those that retain high affinity for PTHR1 and exhibit prolonged pharmacokinetic and pharmacodynamic properties.

[0012] SUMMARY OF THE INVENTION

[0013] In one aspect, the invention features a conjugate, or a pharmaceutically acceptable salt thereof, comprising a polypeptide and a fatty acid acyl, wherein the polypeptide comprises a sequence of formula (I): Xoi-Val-Xo3-Glu-Ile-Gln-Leu-Xo8-His-Xio-Xn-Xl2-Xl3-Xl4-Xl5-Xl6-Xl7-Xl8-Xl9-X2o-X21-X22-X23-X24-X25-X26- X27-X28-X29-X30-X31 -X32-X33-X34 (I) , wherein:

[0014] X01 is ACPC, Ala, or Aib;

[0015] X03 is Ser, Aib, or Ala;

[0016] X08 is Met or Nle;

[0017] X10 is Gin or Asn;

[0018] X11 is Lys, Arg, Leu, or hArg;

[0019] X12 is Lys, Ala, Gly, or absent;

[0020] X13 is Lys or absent;

[0021] X14 is Lys, His, Trp, or absent;

[0022] X15 is Tyr, Leu, or absent;

[0023] X16 is Ala, Asn, or absent;

[0024] X17 is Ser or absent;

[0025] Xis is Vai, Met, or absent;

[0026] X19 is Glu, Arg, or absent; X20 is Arg or absent;

[0027] X21 is Nle, Vai, or absent;

[0028] X22 is Gin, Glu, or absent;

[0029] X23 is Trp or absent;

[0030] X24 is Leu or absent;

[0031] X25 is Arg or absent;

[0032] X26 is Lys or absent;

[0033] X27 is Lys or absent;

[0034] X28 is Leu or absent;

[0035] X29 is Gin or absent;

[0036] X30 is Asp or absent;

[0037] X31 is Vai or absent;

[0038] X32 is His or absent;

[0039] X33 is Asn or absent; and

[0040] X34 is Tyr or absent, or a fragment thereof comprising 11 to 15 contiguous amino acid residues, wherein the fatty acid acyl is covalently linked to the side chain amine of a Lys residue at position X11 , X12, or X of the polypeptide by way of an amino acid spacer.

[0041] In some embodiments, the polypeptide is a fragment comprising amino acid residues 1-11 of formula (I). In some embodiments, the polypeptide comprises the sequence of ACPC-Val-Aib-Glu-lle-GIn- Leu-Nle-His-Gln-Lys-NH2(SEQ ID NO: 35).

[0042] In some embodiments, the polypeptide is a fragment comprising amino acid residues 1-12 of formula (I). In some embodiments, the polypeptide comprises the sequence of: ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys-NH2(SEQ ID NO: 36); or ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys-Lys-NH2(SEQ ID NO: 37).

[0043] In some embodiments, the polypeptide is a fragment comprising amino acid residues 1-13 of formula (I). In some embodiments, the polypeptide comprises the sequence of: ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys-NH2(SEQ ID NO: 38); or ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys-Ala-Lys-NH2(SEQ ID NO: 39).

[0044] In some embodiments, the polypeptide is a fragment comprising amino acid residues 1-14 of formula (I). In some embodiments, the polypeptide comprises the sequence of ACPC-Val-Aib-Glu-lle-GIn- Leu-Nle-His-Gln-hArg-Ala-Lys-Lys-NH2(SEQ ID NO: 40).

[0045] In some embodiments, the polypeptide is a fragment comprising amino acid residues 1-15 of formula (I). In some embodiments, the polypeptide comprises the sequence of: ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys-Trp-Tyr-NH2(SEQ ID NO: 41); or ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys-Ala-Lys-Trp-Tyr-NH2(SEQ ID NO: 42).

[0046] In some embodiments, the polypeptide is a fragment comprising amino acid residues 1-34 of formula (I). In some embodiments, the polypeptide comprises the sequence of: Ala-Val-Ser-Glu-lle-GIn-Leu-Nle-His-Asn-Lys-Gly-Lys-His-Leu-Ala-Ser-Val-Glu-Arg-Nle-GIn-Trp-Leu-Arg- Lys-Lys-Leu-Gln-Asp-Val-His-Asn-Tyr-NH2(SEQ ID NO: 43); or Ala-Val-Ser-Glu-lle-GIn-Leu-Nle-His-Asn-Leu-Gly-Lys-His-Leu-Ala-Ser-Val-Glu-Arg-Nle-GIn-Trp-Leu-Arg- Lys-Lys-Leu-Gln-Asp-Val-His-Asn-Tyr-NH2(SEQ ID NO: 44).

[0047] In some embodiments, the polypeptide is a PTHR1 agonist.

[0048] In another aspect, the invention features a conjugate, or a pharmaceutically acceptable salt thereof, comprising a polypeptide and a fatty acid acyl, wherein the polypeptide comprises a sequence of formula (II): Xo7-Xo8-Xo9-Xio-Xii-Xi2-Lys-Xi4-lle-Gln-Asp-Xi8-Arg-Arg-Arg-X22-Trp-Leu-His-X26-Leu-lle-Ala-Glu-lle-His- Thr-Ala-Glu-X36 (II), wherein

[0049] X07 is Leu or Lys;

[0050] Xos is Leu, Lys, or Nle;

[0051] X09 is His or Lys;

[0052] X10 is Asp, Lys, Asn, or Gin;

[0053] X11 is Lys or Leu;

[0054] X12 is Lys or dTrp;

[0055] X14 is Lys, Ser, or Trp;

[0056] Xis is Leu or Ala;

[0057] X22 is Phe or Ala;

[0058] X26 is His or Lys; and

[0059] X36 is Tyr or lie; wherein the fatty acid acyl is covalently linked to:

[0060] (a) the side chain amine of a Lys residue at position X7, Xs, X9, X10, Xu , X12, X13, or Xi4 of the polypeptide by way of an amino acid spacer; or

[0061] (b) the N-terminal amine of the polypeptide.

[0062] In some embodiments, the polypeptide comprises the sequence of: Leu-Leu-His-Asp-Leu-Lys-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu-lle- His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 45); Leu-Leu-His-Asp-Leu-dTrp-Lys-Lys-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 46); Leu-Leu-His-Asp-Lys-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 47); Leu-Leu-His-Lys-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 48); Leu-Leu-Lys-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 49); Leu-Lys-His-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 50); Lys-Leu-His-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 51); Leu-Leu-His-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 52); or

[0063] Leu-Nle-His-GIn-Leu-dTrp-Lys -Trp-lle-GIn-Asp-Ala-Arg-Arg-Arg-Ala-Trp-Leu-His-Lys-Leu-lle-Ala-Glu-lle- His-Thr-Ala-Glu-lle-NH2(SEQ ID NO: 53).

[0064] In some embodiments, the polypeptide is a PTHR1 antagonist or inverse agonist.

[0065] In some embodiments of any of the above aspects, the fatty acid acyl is covalently linked to the side chain amine of a Lys residue of the polypeptide by way of an amino acid spacer, wherein the amino acid spacer is Arg, dArg, Glu, or dGlu. In some embodiments, the fatty acid acyl is covalently linked to the side chain amine of a Lys residue of the polypeptide through a linker of formula (III): w i v . wherein X is the amino acid residue side chain of Arg, dArg, Glu, or dGlu, wherein I 1 represents the bond to the side chain amine of the Lys residue, and wherein represents the bond to the carbonyl carbon of the fatty acid acyl.

[0066] In some embodiments, the fatty acid acyl is a very long chain fatty acid or a long chain fatty acid acyl. In some embodiments, the fatty acid acyl is a long chain fatty acid acyl. In some embodiments, the long chain fatty acid acyl is palmitoyl. In some embodiments, the long chain fatty acid acyl is octadecanedioic acid.

[0067] In some embodiments, the polypeptide is covalently linked to an additional moiety.

[0068] In some embodiments, the additional moiety is a dye. In some embodiments, the dye is conjugated to a Lys residue of the polypeptide.

[0069] In some embodiments, the additional moiety is a second fatty acid acyl.

[0070] In some embodiments, the second fatty acid acyl is covalently linked to the side chain amine of a second Lys residue of the polypeptide by way of an amino acid spacer. In some embodiments, the amino acid spacer is Arg, dArg, Glu, or dGlu. In some embodiments, the second fatty acid acyl is covalently linked to the side chain amine of a second Lys residue of the polypeptide through a linker of formula (III): * / VW I - wherein X is the amino acid residue side chain of Arg, dArg, Glu, or dGlu, wherein I 1 represents the bond to the side chain amine of the second Lys residue , and wherein represents the bond to the carbonyl carbon of the second fatty acid acyl. In some embodiments, the second fatty acid acyl is covalently linked to the C-terminus of the polypeptide. In some embodiments, the second fatty acid acyl is covalently linked to the C-terminus of the polypeptide through a linker of formula (IV): wherein n is an integer from 0 to 10; each of m and q is an integer from 2 to 5; each AAi and each AA2 is independently a proteinogenic amino acid; and

[0071] R is a bond to the carbonyl carbon of the fatty acid acyl.

[0072] In some embodiments, -C(O)-(AAi)m-NH- in the linker structure is -C(O)-EYE-NH- or -C(O)-SYE- NH-. In some embodiments, -(AA2)q in the linker structure is -EYE or -ESE. In some embodiments, the C- terminus of -(AA2)q is carboxamide.

[0073] In some embodiments, the second fatty acid acyl is a very long chain fatty acid or a long chain fatty acid acyl. In some embodiments, the second fatty acid acyl is a long chain fatty acid. In some embodiments, the second fatty acid acyl is palmitoyl.

[0074] In some embodiments, the conjugate comprises a sequence of: ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Glu)palm-NH2(SEQ ID NO: 1); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(dGlu)palm-NH2(SEQ ID NO: 2); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-NH2(SEQ ID NO: 3); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(dArg)palm-NH2(SEQ ID NO: 4); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)dioic-NH2(SEQ ID NO: 5); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys(Glu)palm-NH2(SEQ ID NO: 6); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys(dGlu)palm-NH2(SEQ ID NO: 7); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys(Arg)palm-NH2(SEQ ID NO: 8); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys(dArg)palm-NH2(SEQ ID NO: 9); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-Lys(TMR)-NH2(SEQ ID NO: 10); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)dioic-Lys(TMR)-NH2(SEQ ID NO: 11); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Glu)palm-NH2(SEQ ID NO: 12); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(dGlu)palm-NH2(SEQ ID NO: 13); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)palm-NH2(SEQ ID NO: 14); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(dArg)palm-NH2(SEQ ID NO: 15); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-Ala-Lys(Arg)palm-NH2(SEQ ID NO: 16); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)dioic-NH2(SEQ ID NO: 17); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)palm-Lys(TMR)-NH2(SEQ ID NO: 18); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)dioic-Lys(TMR)-NH2(SEQ ID NO: 19); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)palm-Trp-Tyr-NH2(SEQ ID NO: 20);

[0075] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-Ala-Lys-Trp-Tyr-NH2(SEQ ID NO: 21);

[0076] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-Ala-Lys-Trp-Tyr(PEG2)EYEK(palm)EYE-NH2(SEQ ID NO: 22);

[0077] Ala-Val-Ser-Glu-lle-Gln-Leu-Nle-His-Asn-Lys(Arg)palm-Gly-Lys-His-Leu-Ala-Ser-Val-Glu-Arg-Nle-Gln- Trp-Leu-Arg-Lys-Lys-Leu-Gln-Asp-Val-His-Asn-Tyr-NH2(SEQ ID NO: 23); or Ala-Val-Ser-Glu-lle-Gln-Leu-Nle-His-Asn-Leu-Gly-Lys(Arg)palm-His-Leu-Ala-Ser-Val-Glu-Arg-Nle-Gln- Trp-Leu-Arg-Lys-Lys-Leu-Gln-Asp-Val-His-Asn-Tyr-NH2(SEQ ID NO: 24).

[0078] In some embodiments, the conjugate comprises a sequence of:

[0079] Leu-Leu-His-Asp-Leu-Lys(Arg)palm-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 25);

[0080] Leu-Leu-His-Asp-Leu-dTrp-Lys-Lys(Arg)palm-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 26);

[0081] Leu-Leu-His-Asp-Lys(Arg)palm-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 27);

[0082] Leu-Leu-His-Lys(Arg)palm-Leu-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 28);

[0083] Leu-Leu-Lys(Arg)palm-Asp-Leu-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 29);

[0084] Leu-Lys(Arg)palm-His-Asp-Leu-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 30);

[0085] Lys(Arg)palm-Leu-His-Asp-Leu-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 31); palm-Leu-Leu-His-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala- Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 32);

[0086] Leu-Nle-His-Gln-Leu-dTrp-Lys(Arg)palm-Trp-lle-Gln-Asp-Ala-Arg-Arg-Arg-Ala-Trp-Leu-His-Lys-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-lle-NH2(SEQ ID NO: 33); or Leu-Leu-His-Asp-Leu-dTrp-Lys(Arg)palm-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 34).

[0087] In another aspect, the invention features a method of modulating the activity of PTHR1 in a cell, the method comprising contacting the cell with a conjugate described herein or a pharmaceutical composition thereof.

[0088] In another aspect, the invention features a method of agonizing the activity of PTHR1 in a cell, the method comprising contacting the cell with a conjugate described herein or a pharmaceutical composition thereof.

[0089] In another aspect, the invention features a method of antagonizing or inversely agonizing the activity of PTHR1 in a cell, the method comprising contacting the cell with a conjugate described herein or a pharmaceutical composition thereof.

[0090] In some embodiments, the cell is a human cell. In another aspect, the invention features a method of treating a subject having a disease selected from the group consisting of hypoparathyroidism, hyperphosphatemia, osteoporosis, fracture repair, osteomalacia, arthritis, thrombocytopenia, and chronic kidney disease, the method comprising administering to the subject a conjugate described herein or a pharmaceutical composition thereof in an amount sufficient to treat said disease.

[0091] In another aspect, the invention features a method of treating a subject with a disease or condition associated with PTHR1 signaling overactivity, the method comprising administering to the subject an effective amount of a conjugate of described herein or a pharmaceutical composition thereof. In some embodiments, the disease or condition is hypercalcemia, hypophosphatemia, hyperparathyroidism, or Jansen’s metaphyseal chondrodysplasia. In some embodiments, the hyperparathyroidism is primary hyperparathyroidism or secondary hyperparathyroidism. In some embodiments, the conjugate or pharmaceutical composition is administered in an amount sufficient to reduce PTHR1 signaling.

[0092] In some embodiments, the administering comprises oral, subcutaneous, intravenous, intranasal, transpulmonary, transdermal, or transmucosal administration of the conjugate or pharmaceutical composition to the subject. In some embodiments, the administering comprises oral administration of the conjugate or pharmaceutical composition to the subject.

[0093] Advantageously, the invention provides conjugates with PTHR1 agonist, antagonist, and inverse agonist activity that have superior signaling and biological activity. The inventors have shown that conjugation of a fatty acid acyl to a PTHR1 agonist, antagonist, and inverse agonist polypeptide enhances association with serum albumin, which reduces the rate of renal clearance and prolongs the calcemic response induced upon a single injection of the conjugate. In addition, the inventors have shown that conjugation of a fatty acid acyl to a polypeptide anchors the polypeptide to the plasma membrane as the polypeptide is bound to the receptor, which prolongs the cAMP signaling response and augments the impact of the peptides on bone metabolism. Accordingly, the conjugates the invention can be used to treat diseases involving PTHR1 signaling overactivity (e.g., hypercalcemia, hypophosphatemia, hyperparathyroidism, or Jansen’s metaphyseal chondrodysplasia) or PTHR1 signaling deficiency (e.g., hypoparathyroidism, hyperphosphatemia, osteoporosis, fracture repair, osteomalacia, arthritis, thrombocytopenia, or chronic kidney disease).

[0094] Other features and advantages of the invention will be apparent from the following detailed description and figures, and from the claims.

[0095] Definitions

[0096] The term “dye” is used herein to mean an agent known in the art to be useful in the imaging of biological systems (e.g., a fluorescent dye (e.g., tetramethylrhodamine)).

[0097] The term “effective amount,” when used in reference to treating a condition or disease (e.g., a disease associated with the PTHR1 signaling overactivity (e.g., hypercalcemia, hypophosphatemia, hyperparathyroidism, or Jansen’s metaphyseal chondrodysplasia) or deficiency (e.g., hypoparathyroidism, hyperphosphatemia, osteoporosis, fracture repair, osteomalacia, arthritis, thrombocytopenia, or chronic kidney disease)), refers to an amount of a conjugate of the invention or a pharmaceutically acceptable salt thereof that treats the condition or disease in a subject.

[0098] The term “endogenous agonist” of a parathyroid hormone receptor 1 (PTHR1) is used herein to mean a compound produced by an organism, or a synthetic phenocopy of that compound, i.e., a compound having the same pharmacological activity as the endogenous agonist. For example, the native PTH peptide is (1-84), and PTHrP is ~(1 -140) amino acids; phenocopies of these ligands include PTH(1 - 34) and PTHrP(1-36), respectively. An endogenous agonist is involved in or modulates the normal physiological activation of the PTHR1. PTHR1 has multiple endogenous agonists (e.g., PTH and PTHrP).

[0099] The term “fatty acid,” as used herein, represents a linear, saturated, acyclic, aliphatic carboxylic acid having 4 to 28 carbon atoms. A “long chain fatty acid” is a fatty acid having 13 to 21 carbon atoms (e.g., 14 to 18 carbon atoms), and a “very long chain fatty acid” is a fatty acid having 22 to 28 carbon atoms. Non-limiting examples of long chain fatty acids include myristic acid, palmitic acid, stearic acid, and octadecanedioic acid.

[0100] The term “fatty acid acyl,” as used herein, represents a monovalent group that is a fatty acid having a carboxylic hydroxyl replaced with a valency.

[0101] As used herein, the terms “palm”, “palmitoyl”, and “palmitic acid” are used interchangeably and refer to a fatty acid having the structure of CH3-[CH2]i4-CO- (PubChem SID 26697177).

[0102] As used herein, the term “dioic” refers to octadecanedioic acid.

[0103] As used herein, the term “PEG2” refers to polyethylene glycol dimer.

[0104] As used herein, the term “TMR” refers to tetramethyl-rhodamine.

[0105] The term “fragment,” when used in reference to peptides, refers to a portion of the peptide. Thus, a 1-n polypeptide fragment refers to a polypeptide having a sequence that starts at the first N-terminal amino acid residue of the polypeptide and ends at the nthamino acid residue of the polypeptide. Similarly, a 3-n polypeptide fragment refers to a polypeptide having a sequence that starts at the third N- terminal amino acid residue of the polypeptide and ends at the nthamino acid residue of the polypeptide.

[0106] As used herein, the term “pharmaceutically acceptable salt” means those salts of the polypeptides or conjugates described that are suitable for use in contact with the tissues of humans and animals without undue toxicity, irritation, or allergic response. Pharmaceutically acceptable salts are well known in the art. For example, pharmaceutically acceptable salts are described in: Berge et al., J. Pharmaceutical Sciences 66:1-19, 1977 and in Handbook of Pharmaceutical Salts: Properties, Selection, and Use, (Eds. P.H. Stahl and C.G. Wermuth), Wiley-VCH, 2008. These salts may be acid addition salts involving inorganic or organic acids. The salts can be prepared in situ during the final isolation and purification of the polypeptides or conjugates described herein or separately by reacting to the free base group with a suitable acid. The terms “polypeptide” and “peptide” are used interchangeably herein to mean a compound that contains a sequence of amino acids bonded to each other through peptidic bonds.

[0107] The term “PTHR1” is used herein to mean a parathyroid hormone receptor 1 (e.g., a human parathyroid hormone receptor 1 (hPTHRI)). PTHR1 may be wild-type or may be a naturally-occurring mutant PTHR1 which has constitutive activity (e.g., PTHR1 expressed in cells of a subject having Jansen’s metaphyseal chondrodysplasia). For example, a naturally-occurring mutant PTHR1 which has constitutive activity can be PTHR1-H223R or PTHR1-T410P.

[0108] The term “PTHR1 agonist” is used herein to mean a conjugate or polypeptide capable of binding PTHR1 having a constitutive activity and, upon binding, increasing the activity of PTHR1. The activity of PTHR1 agonist may be assessed using methods known in the art for assessing agonist activity or using methods described herein.

[0109] The term “PTHR1 antagonist” is used herein to mean a conjugate or polypeptide capable of binding PTHR1 , thereby blocking or dampening endogenous agonist-mediated responses without agonizing the signaling activity of PTHR1 . The activity of PTHR1 antagonist may be assessed using methods known in the art for assessing antagonist activity or using methods described herein.

[0110] The term “PTHR1 inverse agonist” is used herein to mean a conjugate or polypeptide capable of binding PTHR1 having a constitutive activity and, upon binding, reducing the constitutive activity of PTHR1 . The activity of PTHR1 inverse agonist may be assessed using methods known in the art for assessing inverse agonist activity or using methods described herein.

[0111] The term “subject” is used herein to mean a mammal (e.g., a human) diagnosed by a medical practitioner as having a condition or disease, e.g., a disease associated with the PTHR1 signaling overactivity (e.g., hypercalcemia, hypophosphatemia, hyperparathyroidism, or Jansen’s metaphyseal chondrodysplasia) or deficiency (e.g., hypoparathyroidism, hyperphosphatemia, osteoporosis, fracture repair, osteomalacia, arthritis, thrombocytopenia, or chronic kidney disease). Diagnosis may be performed by techniques and methods known in the art. A subject to be treated according to the methods of the invention may have been subjected to standard tests (e.g., tests for serum calcium levels or serum phosphate levels) or may have been identified, without such tests, as one at high risk due to the presence of one or more risk factors (e.g., diseases associated with elevated serum calcium levels (e.g., cancer, tuberculosis, and sarcoidosis) and therapeutic regimens increasing the release of parathyroid hormone (e.g., lithium) or reducing serum phosphate levels (e.g., antacids)).

[0112] The terms “treating” or “treatment,” when used herein in reference to a subject, are used herein to mean ameliorating at least one symptom of a condition or disease in a subject having the condition or disease, e.g., a disease associated with the PTHR1 signaling overactivity (e.g., hypercalcemia, hypophosphatemia, hyperparathyroidism (e.g., primary hyperparathyroidism or secondary hyperparathyroidism), or Jansen’s metaphyseal chondrodysplasia) or deficiency (e.g., hypoparathyroidism, hyperphosphatemia, osteoporosis, fracture repair, osteomalacia, arthritis, thrombocytopenia, or chronic kidney disease), as compared with an equivalent untreated control. Such reduction in the symptom (e.g., a reduction in serum calcium levels or an increase in serum phosphate levels, or vice versa) is at least 5% (e.g., at least 10%, 20%, 40%, 50%, 60%, 80%, 90%, 95%, or 100%), as measured in accordance with methods recognized in the art as suitable for assessing the symptom (e.g., serum calcium or phosphate levels).

[0113] Throughout the description and claims the conventional one-letter and three-letter codes for natural (or “proteinogenic”) amino acids are used, as well as the one- and three- letter codes for other (non-natural or “non-proteinogenic”) amino acids provided in Table 1. Table 1. One-letter and three-letter codes for non-natural amino acids

[0114] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood to one of ordinary skill in the art to which this disclosure belongs. For any term present in the art which is identical to any term expressly defined in this disclosure, the term's definition presented in this disclosure will control in all respects. Although methods and materials similar or equivalent to those described herein can be used in the practice of the disclosed methods and compositions, the exemplary methods and materials are described herein.

[0115] BRIEF DESCRIPTION OF THE DRAWINGS

[0116] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application with color drawings will be provided by the Office upon request and payment of the necessary fee.

[0117] FIGS. 1A-1 F show design and characterization of Palm-PTH(1-34). FIG. 1A) Schematic of Palm-PTH(1 -34). PTH(1 -34) is C-terminally fused to a hepta-residue tag EYEK(palm)EYE optimized for albumin binding and containing a palmitoyl group (palm) linked to the central lysine side chain amine; a (PEG)2 (20 atom) spacer joins Phe34 of PTH to Glu1 of the tag. FIG. 1 B) cAMP responses in SGS-72 human osteoblast-derived cells expressing the giosensor cAMP reporter; data are calculated as the area- under-the-curve (AUC) of plots of luminescence vs. time (60’) normalized to the PTH(1 -34) maximum and are means±SEM of 10 independent experiments. FIGS. 1C-1 F) Pharmacodynamic and pharmacokinetic analyses of PTH(1 -34) and Palm-PTH(1-34) in 10-week-old female CD1 mice; peptides injected at a dose of 10 nmol / kg (FIGS. 1C-1 E) or 50 nmol / kg (FIG. 1 F). Blood concentrations of ionized calcium (Ca++, FIG. 1C) and inorganic phosphorus (Pi, FIG. 1 D) as a function of time after subcutaneously (SC) injection of peptide or vehicle; p<0.05 (2-way ANOVA, followed by LSD test): *, peptide vs. vehicle; +, PTH(1 -34) vs. Palm-PTH(1 -34). FIG. 1 E) Peptide concentrations in blood plasma as a function of time after SC injection. The inset shows the data plotted with the y-axis in log-io scale. Data for x = 1-24h were fit to a monophasic decay curve (dashed lines); the corresponding values of T1 / 2, AUC, Cmax (peak y), and Tmax (peak x) are shown. FIG. 1 F) Concentrations of tetramethylrhodamine (tmr)-labeled ligands in urine as a function time after SC injection of PTH(1 -34)tmror Palm-PTH(1 -34)tmr; tmr fluorescence (Aex = 531 ±25 nm, Aem = 595±60 nm) at each time point was corrected for background fluorescence (t=0) and net fluorescence was converted to peptide concentration using a standard curve formed with the corresponding tmr- peptide; p<0.05 (two-sided t-test): *, PTH(1-34) vs. Palm-PTH(1-34). The inset shows the data plotted with the x-axis extended to 8h; corresponding values of AUC (0-24h) and Tmax (peak x) are also shown. In FIGS. 1 C-1 F, t=0 represents pre-dose. Data are means±SEM of values from six (C, D), three (FIG. 1 E) or five (FIG. 1 F) mice per group. Corresponding changes in blood Ca++and plasma peptide concentrations after IV injection are shown in FIGS. 3A-3B.

[0118] FIGS. 2A-2F show effect of single injection of Palm-PTH(1-34) vs PTH(1-34) on concentrations of markers of mineral and bone metabolism in plasma and urine in mice. Nine- week-old female CD-1 mice were injected SC with either vehicle, PTH(1 -34) or Palm-PTH(1-34) each at a peptide dose of 50 nmol / kg (n=6 mice per group) and blood and spot urine were collected at 2, 7 and 24 hours post-injection; total Ca and Pi was measured in blood plasma and urine (FIGS. 2A-2D), and CTX1 and 1 ,25-dihydroxyvitamin D (7 and 24 hours only) was measured in plasma (FIG. 2E, FIG. 2F). p values (one-way ANOVA with Bonferroni’s multiple comparison test) are shown if < 0.05.

[0119] FIGS. 3A-3B show pharmacodynamic and pharmacokinetic properties of Palm-PTH(1-34) vs. PTH(1 -34) after sc. or iv. injection in 10-week-old female CD-1 mice. FIG. 3A) Blood Ca++ concentrations as a function of time (hours) after IV injection of PTH(1-34), Palm- PTH(1-34) or vehicle (t= 0 h is pre-dose). Data are means±SEM; n= 6 mice per group; p < 0.05 (2-way ANOVA followed by LSD test): *, peptide vs. vehicle; +, PTH(1 -34) vs. Palm-PTH(1-34). FIG. 3B) Peptide concentrations in blood plasma as a function of time after IV injection of peptides; means±SD; n=2 mice per group. Peptide concentrations were assessed using an ELISA for hPTH(1-34) calibrated with PTH(1-34) or Palm-PTH(1 - 34). The inset shows the data displayed with y axis in log 10 scale and the corresponding area-under-the- curve (AUC), Cmax (peak y) and Tmax (peak x) values. T1 / 2 values were derived by fitting the data (X= 0.03 to 7 hrs) to a monophasic decay curve (dashed line). Peptide injection doses were 10 nmol / kg-body weight. Blood Ca++ and plasma peptide concentrations after SC injection are shown in FIG. 1C and FIG. 1 E.

[0120] FIGS. 4A-4B show biolayer interferometry (BLI) analysis of peptide binding to bovine serum albumin (BSA). FIG. 4A) Sequences of peptides analyzed. FIG. 4B) BLI assessment of peptide binding to and dissociation from BSA. The detector's optical biosensor tips pre-absorbed with BSA were immersed in buffer containing various concentrations of test peptide (156-5,000 nM) for 300 secs (association phase) and then in buffer alone for 300 seconds (dissociation phase), during which times the optical signals were recorded. Plotted are the net shifts in wavelength (nm, background subtracted) as a function of time. Curves were fit to the data using the Association-Dissociation non-linear regression model in Graph Pad Prism, which for PTH(1 -34) and Palm-PTH(1 -34) yielded KD values of 1 .61 and 0.42 nM, respectively, and for M-PTH(1-14) and Palm-PTH(1-14) yielded KD values of 6.31 and 1 .47 nM, respectively; the corresponding BMax values were 0.080, 0.247, 0.082 and 0.34, respectively.

[0121] FIGS. 5A-5B show evaluation of Palm-PTH(1-34) in parathyroidectomized mice. GFP-guided parathyroidectomy or sham surgery was performed on two-month old PTH-Cre;Rosa-mT / mG mice four days prior to the day of the experiment. FIG. 5A) Baseline blood Ca++concentrations in the sham- operated and parathyroidectomized (PTX) mice assessed 0.5 to 1 hour prior to injection. Boxplot shows Median, 25thand 75thpercentile as well as minima and maxima of n=5 (Sham) or 30 (PTX) mice per group, p-value determined by two-sided t-test. FIG. 5B) Blood Ca++concentrations as a function of time after SC injection of PTH(1-34) at a peptide dose of 50 nmol / kg-body weight, or Palm-PTH(1-34) at a peptide dose of 2, 10 or 50 nmol / kg-body weight or vehicle. Data are means±SEM of n=6 mice per group; p<0.05 (2-way ANOVA followed by LSD test): *, peptide vs. vehicle; +, PTH(1-34) vs. Palm-PTH(1-34), #, PTX-vehicle vs. Sham-vehicle. Values at t=O represent those shown in FIG. 5A distributed by injection group. Concentrations of bone and mineral metabolism markers in blood plasma collected 24 hours postinjection are shown in FIG. 6.

[0122] FIG. 6 shows the effect of injected peptides on blood markers of bone and mineral and metabolism in parathyroidectomized (PTX) mice. Serum concentrations of endogenous mouse PTH(1-84), 1 ,25-dihydroxyvitamin D3 and CTX1 in sham-operated and PTX mice measured 24 hours after SC injection with either vehicle, PTH(1-34) at a dose of 50 nmol / kg, or Palm- PTH(1-34) at doses of 2, 10 or 50 nmol / kg (n=6 mice per group), p values (one-way ANOVA with Bonferroni’s multiple comparison test) are shown if < 0.05. Injections were performed in 2-month old PTH- Cre;Rosa-mT / mG mice 4 days after sham surgery or GFP-guided parathyroidectomy. Blood Ca++ levels are shown in FIGS. 5A-5B.

[0123] FIGS. 7A-7C show characterization of Palm-M-PTH(1-14) in vitro and in vivo. FIG. 7A) Amino acid sequences of M-PTH(1-14) and Palm-M-PTH(1-14) and cAMP signaling responses in SGS- 72 cells assessed in the presence of varying concentrations of ligand (left, Ligand on), and after rinsing the cells to remove unbound ligand (right, washout). Responses were assessed as the area under the curve (AUC) of the cAMP-dependent luminescence signal vs. time plots and are plotted as a function of ligand concentration. Curves were fit to the data using a non-linear regression equation. FIG. 7B). Curve fit parameters for the data shown in FIG. 7A. Data are means±SEM of 4 independent experiments, p- value determined by two-sided t-test. FIG. 7C) Blood Ca++concentrations as a function of time after IV injection of peptide (10 nmol / kg-body weight) or vehicle in 10-week-old intact female CD1 mice. Data are means ± SEM values from six mice per group; p < 0.05 (2-way ANOVA followed by LSD test): *, vs. M- PTH(1-14); #, Palm-M-PTH(1-14) vs. PTH(1-34). Values at t=0 represent samples collected 0.5 to 1 hr prior to injection.

[0124] FIGS. 8A-8E show design and characterization in vitro of N-terminal PTH fragment analogs with side chain lipid appendages. FIG. 8A) Schematics of N-terminal PTH peptides containing a C16 palmitoyl (palm) group appended to the side chain amine of a C-terminal lysine via an Arg (R) dArg(r), Glu(E) or dGlu(e) spacer; the structure of K11(R)palm-PTH(1-11), and peptide sequences. FIG. 8B) Models of the receptor TMD (gray, with helix H1 in turquoise) bound to a PTH fragment peptide (red) containing a hypothetical lipid chain (orange scribble line) appended to the side chain of a C-terminal Lys at position 11 , 12 or 13. Views are from the extracellular surface and side. Images were generated using Pymol and PDB.6nBF (LA-PTH-PTH1 R-Gs cryo-EM structure). Lipid chains at positions 13 and 11 were drawn manually to depict their postulated extension through the H5-H6 and H1-H2 clefts, respectively. The lipid chain at position 12 depicts a clash with the inner wall of the binding pocket. FIG. 8C) cAMP responses in GP-2.3 cells to M-PTH(1-14), K13(R)palm-PTH(1-13), K12(R)palm-PTH(1-12) and K11(R)palm-PTH(1-11); responses were calculated as the AUCs of the cAMP-dependent luminescence vs. time plots observed after ligand addition (Ligand-on, 20') and in the same cells after rinsing to remove unbound ligand (washout, 120'), normalized to the maximum response observed for M-PTH(1-14) and are plotted as a function of peptide concentration, p-values were determined by two-sided t-test. FIG. 8D) Schematic of N-terminal PTH peptides containing octadecanedioic acid (dioic) group appended to the side chain amine of a lysine via an Arg (R), spacer. FIG. 8E) cAMP responses in GP-2.3 cells induced by PTH(1-34) or a PTH(1 -11) or PTH(1-13) peptide containing either a palmitoyl or dioic group appended to a lysine side chain. Responses calculated as in FIG. 8C but normalized to the maximum response of PTH(1-34). Data are means±SEM of four independent experiments. Curves were fit to the data using a non-linear regression equation; corresponding potency (pECso) values are shown at the bottom. Data for related peptides are shown in FIGS. 9A-9B and Tables 6 and 8.

[0125] FIGS. 9A-9B show cAMP signaling potency of N-terminal M-PTH fragment analogs with side chain lipid appendages in GP-2.3 cells. FIG. 9A) Representative peptide structures. FIG. 9B) Giosensor cAMP responses in GP-2.3 cells. Cells were stimulated with M-PTH(1-14) control peptide, or a PTH(1-11), PTH(1 -12) or PTH(1 -13) analog containing a palmitoyl group appended to a C-terminal Lys via a dArg (r), Glu(E) or dGlu (e) spacer amino acid, and luminescence was measured for 20 minutes in the presence of ligand (Ligand-on) and then for 120 minutes after rinsing to remove unbound ligand (washout). Responses were calculated as the AUC of the cAMP-dependent luminescence vs. time plots observed at each peptide concentration during the Ligand-on and washout phases, normalized to the maximum response observed to M-PTH(1-14), and plotted as a function of peptide concentration. Data are means±SEM of four independent experiments. Curves were fit to the data using a non-linear regression equation. Curve fit parameters are shown in Table 6.

[0126] FIGS. 10A-10B show cAMP signaling potency of N-terminal PTH fragment peptides with side chain lipid appendages in GD-5y cells (PTH1 R-DelNT). FIG. 10A) Dose-response analysis of cAMP responses in GD-5y cells (HEK293 cells stably expressing giosensor and PTHR1 -delNtYFP, which lacks the ECD) to PTH(1 -11), PTH(1-12) and PTH(1 -13) peptides containing a palmitoyl (palm) group linked to the side chain amine of a C-terminal lysine via an Arg(R), dArg(r), Glu(E) or dGlu(e) spacer. The AUCs of cAMP-dependent luminescence vs. time plots observed over 20 minutes after ligand addition (Ligand-on) and in the same cells over 120 minutes after rinsing to remove unbound ligand (washout) are plotted as a function of peptide concentration. Curves were fit to the data using a non-linear regression equation. Curve fit parameters are shown in Table 7. FIG. 10B) Time courses of the cAMP-dependent luminescence responses induced by peptides at their near ECao concentration (1x109or 1x107M). Data are means±SEM of five independent experiments.

[0127] FIGS. 11A-11C show PTH1 R internalization and p-Arrestin2yfp-recruitment responses to lipid-modified PTH peptides. FIGS. 11A-11 B) Ligand-induced PTH1 R internalization in GPG-10 cells (HEK293 cells stably expressing pHL2-hPTH1 R containing a pH-sensitive GFP, pHLourin2, inserted in the ECD). Cells were pretreated for 30 minutes with either DMSO (0.1 %, top row) or with Dyngo4A (3x1 O’5M, bottom row) and then with PTH(1-34), Palm-M-PTH(1-14), K13(R)palm-PTH(1 -13) or L11,dW12,W23,Y36-PTHrP(7-36) at concentrations from 1x10-8to 1x10-5M, or with buffer alone (0) and fluorescence ratios (Aex 485±14 nm: Aex 405±8 nm; Aem 535±25 nm) were monitored as a function of time (70') after ligand addition. AUCs of the corresponding fluorescence ratio vs. time curves plotted as a function of ligand concentration are shown in the two right-most panels. P (Ttest) vs. buffer (-9.0 on x- axis): * < 0.05; ** < 0.01 ; *** < 0.001 ; K13(R)palm-PTH(1-13) vs. Palm-M-PTH(1-14), # < 0.05. Data are means±SEM of three independent experiments. FIG. 11C) Fluorescence microscopy analysis of ligand- induced PTH1 R internalization and p Arrestin2yfprecruitment in GBR24 cells (HEK293 cells stably expressing pArrestin2yfp). Cells were treated with K13(tmr),Nle821-rPTH(1-34) (100 nM), K13(tmr)-M-PTH(1- 14) (1 uM) or K13(R)palm,K14(tmr)- M-PTH(1-14) (1 uM) for 30 minutes, then rinsed, fixed, mounted in the presence of propidium iodide (PI) and imaged by fluorescence microscopy for tmr (red), yfp (green) and nuclei (blue). Merged panels show overlays of the red and green channel images.

[0128] FIGS. 12A-12H show effects of lipid-modified PTH peptides in humanized PTH1 R mice.

[0129] FIG. 12A) Changes in blood Ca++ after single injection of PTH(1 -34), K11(r)palm-PTH(1-11), or M-PTH(1- 11) in 5-month-old male humanized PTH1 R mice. Mice were injected subcutaneously with peptide, each at a dose of 50 nmol / kg, or with vehicle, and blood Ca++ was measured at times after injection. Blood Ca++ concentrations are plotted as a function of time relative to injection (t=0 represents within 30 minutes before injection). Data are means±SEM, n= 5 mice per group. Statistical differences vs. vehicle analyzed by 2-way ANOVA followed by LSD test: *, p < 0.05; **, p < 0.01 ; ***, p < 0.001 . FIG. 12B) Body weights at the start and end of the study. FIGS. 12C-12E) Quantitative pCT analysis of femurs isolated from 5-month-old male humanized PTH1 R mice after 3 weeks of daily SC injection with either vehicle, PTH(1-34), Palm-PTH(1 -34), K11(r)palm-PTH(1-11), each at a dose of 50 nmol / kg / day, or with K11(R)dioic-PTH(1-11) at 500 nmol / kg / day. Parameters at the metaphysis are trabecular separation (Tb.Sp) and trabecular thickness (Tb.Th); Parameters at the midshaft are bone area (B.Ar), bone area fraction (B.Ar / Tt.Ar), medullary area (Ma.Ar), bone mineral density (B.TMD), cortical bone thickness (Ct.Th), cortical porosity, and minimum moment of inertia (Imin); low-density woven bone was excluded in the analysis of cortical bone thickness and cortical porosity. Additional pCT data are shown in FIGS. 13A- 13C and Table 9. FIGS. 12F-12H) Mechanical strength properties of femurs determined by a three-point bending test. Parameters obtained were bending rigidity, apparent modulus of elasticity, ultimate moment, apparent ultimate stress, work to ultimate moment, apparent toughness to ultimate moment, and apparent toughness to fracture (N, Newton; App., apparent; GPa, gigapascal; MPa, megapascal; mJ, millijoule; mm, millimeter). Parameters were calculated based on the measured force and displacement data, and, for apparent material properties, the mid-shaft geometry (minimum moment of inertia, Imin.) determined by pCT. Equations used for calculating mechanical testing parameters (adapted from ANSI / ASAE Standard S459 for Shear and Three-Point Bending Test of Animal Bone) are also shown. Data in FIGS. 12B-12H are means±SD of measurements from five mice indicated by points with adjacent mouse identification numbers. Statistical differences vs. vehicle were analyzed by one-way ANOVA with Dunnett's multiple comparison test: *, p < 0.05; **, p < 0.01 ; p < 0.001 ; ****, p <0.0001 ; ns, not significant.

[0130] FIGS. 13A-13C show effects of Lipid-modified PTH peptides on bone mass and mechanical strength in humanized h PTH 1 R mice. Five-month-old male humanized PTH 1 R mice were injected daily for three weeks with either vehicle, PTH(1 -34) Palm-PTH(1-34), K11(r)palm-PTH(1-11), each at a dose of 50 nmol / kg / day, or with K11(r)dioic-PTH(1-1 1) at a dose of 500 nmol / kg / day and femurs were isolated at the end of the experiment for analysis. FIG. 13A) Representative pCT radiographs of the isolated femurs; views are in the sagittal plane at the distal metaphysis (top) and in the transverse plane at the midshaft (bottom). Mouse identification numbers are shown adjacent to each image. FIG. 13B) Quantitative pCT parameters of trabecular bone volume fraction (BV / TV), trabecular bone mineral density (BMD, as mg of hydroxyapatite per cm3) and trabecular number (TB.N) measured in the distal metaphysis. FIG. 13C) Mechanical strength, as work to fracture, determined by a three-point bending test of the femurs. Data are means±SD of measurements from five mice indicated by points with adjacent mouse identification numbers. Statistical differences vs. vehicle were analyzed by one-way ANOVA with Dunnetts multiple comparison test: *, p < 0.05; **, p < 0.01 ; p < 0.001 ; ****, p < 0.0001 ; ns, not significant. Additional data are shown for pCT in FIG. 12A and Table 9), and mechanical testing in FIG. 12B).

[0131] FIG. 14 shows histological effects of Lipid-modified PTH peptides on distal femurs of humanized PTH1 R mice. Representative histological sections (Goldner’s trichrome stain) of distal femurs from 5-month-old male humanized PTH1 R mice after 3-weeks of daily injection with either vehicle, PTH(1-34), Palm-PTH(1 -34), K11(r)palm-PTH(1-11) each peptide at a dose of 50 nmol / kg / day, or with K11(R)dioic-PTH(1-11) at a dose of 500 nmol / kg / day. Mouse identification numbers are shown adjacent to each image. 20X magnification; bottom row shows 2X-enlarged views.

[0132] FIG. 15 shows blood markers of bone and mineral metabolism in 5-monthold male humanized PTH1 R mice after 3-weeks of daily injection. Serum from 5-month-old male humanized hPTHI R mice after 3-weeks of daily SC injection with either vehicle, PTH(1-34), Palm-PTH(1-34), K11(r)palm-PTH(1 -11) each peptide at a dose of 50 nmol / kg / day, or with K11(R)dioic-PTH(1-11) at a dose of 500 nmol / kg / day, was analyzed for total calcium, inorganic phosphorus (Pi), collagen-1 C-terminal X- linked peptide (CTX1) and procollagen-1 N-terminal peptide (P1 NP). Data are means±SD of measurements from five mice indicated by points with adjacent mouse identification numbers. Statistical differences vs. vehicle were analyzed by one-way ANOVA with Dunnett's multiple comparison test: *, p< 0.05; **, P < 0.01 ; ***, P < 0.001 ; ****, P < 0.0001 , ns, not significant.

[0133] FIGS. 16A-16L show effects of K13(r)palm-PTH(1-13) and other PTH analogs in 5-month-old male humanized hPTHI R mice after 3-weeks daily injection. Mice were injected with either vehicle, or with an N-terminal peptide: K13(r)palm-PTH(1-13), Palm-MPTH(1-14) or M-PTH(1 -14), each at a dose of 500 nmol / kg / day, or with PTH(1 -34) at a dose of 50 nmol / kg / day for three weeks and 24 hours after the last injection end-point tissues were collected for analysis. FIG. 16A) Representative pCT images of the femoral diaphysis (top) and distal metaphysis (bottom). FIGS. 16B-16D) Quantitative pCT analysis of the femurs. Parameters at the metaphysis are trabecular bone volume fraction (BV / TV), trabecular bone mineral density (BMD, as mg of hydroxyapatite per cm3), trabecular number (TB.N), trabecular separation (Tb.Sp) and trabecular thickness (Tb.Th); parameters at the midshaft are bone area (B.Ar), bone area fraction (B.Ar / Tt.Ar), medullary area (Ma.Ar), bone mineral density (B.TMD), cortical bone thickness (Ct.Th), cortical porosity, and minimum moment of inertia (Imin); low-density woven bone was excluded in the analysis of cortical bone thickness and cortical porosity. FIG. 16E) Representative histological images of proximal tibial sections stained with hemolysin and eosin. FIG. 16F) Histomorphometric quantification of bone volume fraction (BV / TV), bone area relative to total area (B.Ar / T.Ar); and fibrotic area relative to total area (F.Ar / T.Ar) in the trabecular bone compartment of proximal tibiae. FIGS. 16G-16H) Serum measurements of total Ca, Pi, CTX1 , P1 NP and blood urea nitrogen. FIG. 161) Body weights on day 0 (pre-dose), week-1 , week-2 and week-3. FIGS. 16J-16L) Mechanical strength properties of femurs determined by a three-point bending test. Parameters obtained were bending rigidity, apparent modulus of elasticity, ultimate moment, apparent ultimate stress, work to ultimate moment, apparent toughness to ultimate moment, and apparent toughness to fracture (N, Newton; App., apparent; GPa, gigapascal; MPa, megapascal; mJ, millijoule; mm, millimeter). Parameters were calculated based on the measured force and displacement data, and, for apparent material properties, the mid-shaft geometry (minimum moment of inertia, Imin.) determined by pCT. Data are means±SEM of measurements from 4 or 5 mice indicated by points in column graphs. Mouse identification numbers are shown adjacent to corresponding images and data points. Statistical analyses (One-way ANOVA with Dunnett's multiple comparison test) in FIGS. 16B-16D, FIGS. 16G-16H and FIGS. 16J-16L indicate differences vs. vehicle: * p< 0.05; ** p< 0.01 ; *** p < 0.001 ; ****, p < 0.0001 , ns, not significant.

[0134] FIG. 17 shows oral delivery of parathyroid hormone polypeptide conjugates. Experiments were performed as described in Example 2.

[0135] FIGS. 18A-18B show the potency of lipidated and control peptides for cAMP generation in HEK293 / hPTH1 R / glosensor (GP-2.3) cells. FIG. 18A) Results of a representative experiment of selected peptides; cAMP was measured as glosensor-derived luminescence for 20 minutes in the presence of various concentrations of each peptide (Add phase) and for a subsequent 90 minutes after washout of unbound peptide (wash phase) and the area under the curve values of plots of the response at each peptide concentration was derived and plotted vs peptide concentration to obtain dose-response curves, which were fit to a non-linear equation (slope =1 .0). FIG. 18B) Fit parameters of bottom, top, and pEC50 as means ±SD of values from 5 separate experiments. Experiments were performed as described in Example 3.

[0136] FIGS. 19A-19B show inhibition of PTH(1-34)-stimulated cAMP formation in osteoblastic SaOS2 / glosensor (SGS-72) cells. FIG. 19A) Cells were pretreated with a lipidated PTHrP(7-36) antagonist peptide, a non-lipidated PTHrP(7-36) antagonist peptide, each at varying concentrations, or with vehicle for 15 minutes, and then were stimulated with PTH(1-34) agonist at a concentration of 0.3 nM and cAMP was measured as glosensor-derived luminescence for 60 minutes. The peak luminescence signal observed at each antagonist concentration was normalized to the signal observed in the absence of antagonist (indicated as -11 on the x axis) and is plotted as a function of antagonist concentration. Line curves were fit to the data using a non-linear regression equation. FIG. 19B) Corresponding plC50 parameters obtained for the fitted data. Data are means ±SE of values from 5 separate experiments.

[0137] DETAILED DESCRIPTION OF THE INVENTION

[0138] In general, the present invention provides conjugates including a PTHR1 agonist, antagonist, or inverse agonist polypeptide and a fatty acid acyl.

[0139] Advantageously, conjugates of the invention may exhibit superior pharmacokinetic properties (e.g., ti / 2, AUC, and Cmax). Without wishing to be bound by theory, it is believed that a conjugate of the invention may form a complex with serum albumin upon administration to a subject, thereby reducing the clearance of the PTHR1 agonist, antagonist, or inverse agonist polypeptide from the subject. Additionally or alternatively, a conjugate of the invention may anchor to the cell membrane by way of its fatty acid acyl as the conjugate is bound to the receptor and hence increase its dwell time on the receptor.

[0140] The superior pharmacokinetic properties of conjugates of the invention may advantageously reduce the need for frequent administration of unconjugated polypeptides (e.g., PTH(1-34)). For example, a dosing regimen of a conjugate including a fatty acid acyl and a PTHR1 agonist, antagonist, or inverse agonist polypeptide may be, e.g., once daily, instead of multiple administrations per day, as is typically needed for PTH(1 -34).

[0141] The enhanced pharmacokinetics of the conjugates of the invention may be achieved without the use of modifications including long polyethylene glycol (PEG) chains, thereby facilitating preparation, purification, and / or characterization, as the conjugates of the invention are typically mono-dispersed, whereas polypeptides linked to long PEG chains are difficult to produce and purify as mono-dispersed compositions because of the heterogeneity of the PEG compositions and the steric effects of the PEG chains on peptide coupling.

[0142] I. Polypeptides

[0143] The conjugates of the invention include a PTHR1 agonist, antagonist, or inverse agonist polypeptide. In some embodiments, the polypeptide may be amidated at the C-terminus.

[0144] The polypeptides are amenable to production by solution- or solid-phase peptide synthesis and by in-situ synthesis using combination chemistry. The solid phase peptide synthesis technique, in particular, has been successfully applied in the production of human PTH and can be used for the production of these compounds (for guidance, see, e.g., Fairwell et al., Biochem. 22:2691 , 1983). Success with producing human PTH on a relatively large scale has been reported in Goud et al., J. Bone Min. Res. 6:781 , 1991. The peptide chemical synthesis approach generally entails the use of automated synthesizers and appropriate resin as solid phase, to which the C-terminal amino acid of a desired polypeptide is attached. Extension of the peptide in the N-terminal direction is then achieved by successively coupling a suitably protected form of the next desired amino acid, typically using chemical protocols based on amino-protecting groups (e.g., Fmoc-or Boc-based), until synthesis is complete. Protecting groups are then cleaved from the peptide, usually with concomitant cleavage of the peptide from the resin, and the peptide is then isolated and purified using conventional techniques, such as by reversed phase HPLC using appropriate mobile phase (e.g., acetonitrile as solvent and tri-fluoroacetic acid as an ion-pairing agent). Such procedures are generally described in numerous publications and reference may be made, for example, to Stewart and Young, “Solid Phase Peptide Synthesis,” 2ndEdition, Pierce Chemical Company, Rockford, IL (1984).

[0145] Polypeptides of the invention can also be made recombinantly by any method known in the art. Prokaryotic (e.g., bacterial) and eukaryotic (e.g., yeast and mammalian) expression systems can also be used to produce polypeptides of the invention, particularly, where the polypeptide includes only proteinogenic amino acids.

[0146] In some embodiments, the polypeptide is a PTHR1 agonist. In some embodiments, the polypeptide may include a sequence of formula (I): X01-Val-X03-GIU-lle-Gln-LeU-X08-HiS-Xl0-Xl1-Xl2-Xl3-Xl4-Xl5-Xl6-Xl7-Xl8-Xl9-X20-X21-X22-X23-X24-X25-X26- X27-X28-X29-X30-X31 -X32-X33-X34 (I) , wherein:

[0147] X01 is ACPC, Ala, or Aib;

[0148] X03 is Ser, Aib, or Ala; Xo8 is Met or Nle;

[0149] X10 is Gin or Asn;

[0150] X11 is Lys, Arg, Leu, or hArg;

[0151] X12 is Lys, Ala, Gly, or absent;

[0152] X13 is Lys or absent;

[0153] X14 is Lys, His, Trp, or absent;

[0154] X15 is Tyr, Leu, or absent;

[0155] X16 is Ala, Asn, or absent;

[0156] X17 is Ser or absent;

[0157] Xis is Vai, Met, or absent;

[0158] X19 is Glu, Arg, or absent;

[0159] X20 is Arg or absent;

[0160] X21 is Nle, Vai, or absent;

[0161] X22 is Gin, Glu, or absent;

[0162] X23 is Trp or absent;

[0163] X24 is Leu or absent;

[0164] X25 is Arg or absent;

[0165] X26 is Lys or absent;

[0166] X27 is Lys or absent;

[0167] X28 is Leu or absent;

[0168] X29 is Gin or absent;

[0169] X30 is Asp or absent;

[0170] X31 is Vai or absent;

[0171] X32 is His or absent;

[0172] X33 is Asn or absent; and

[0173] X34 is Tyr or absent, or a fragment thereof comprising 11 to 15 contiguous amino acid residues (e.g., a fragment comprising 11 , 12, 13, 14, or 15 contiguous amino acid residues), wherein the fatty acid acyl is covalently linked to the side chain amine of a Lys residue at position X11, X12, or X of the polypeptide by way of an amino acid spacer.

[0174] In some embodiments, at least one of Xu, X12, or X13 of formula (I) is a Lys residue. In some embodiments, the fatty acid acyl is covalently linked to the side chain amine of a Lys residue at position Xu. In some embodiments, the fatty acid acyl is covalently linked to the side chain amine of a Lys residue at position X12. In some embodiments, the fatty acid acyl is covalently linked to the side chain amine of a Lys residue at position X13.

[0175] In some embodiments, the polypeptide is a fragment comprising amino acid residues 1-11 of formula (I). In some embodiments, the polypeptide is a fragment comprising amino acid residues 1 -12 of formula (I). In some embodiments, the polypeptide is a fragment comprising amino acid residues 1 -13 of formula (I). In some embodiments, the polypeptide is a fragment comprising amino acid residues 1 -14 of formula (I). In some embodiments, the polypeptide is a fragment comprising amino acid residues 1 -15 of formula (I). In some embodiments, the polypeptide comprises amino acid residues 1-34 of formula (I).

[0176] The conjugates including PTHR1 agonist polypeptides can be used in a method of treating a condition or a disease of the PTHR1 signaling deficiency (e.g., hypoparathyroidism, hyperphosphatemia, osteoporosis, fracture repair, osteomalacia, arthritis, thrombocytopenia, or chronic kidney disease).

[0177] Exemplary PTHR1 agonist polypeptides of the invention are listed in Table 2.

[0178] Table 2. Exemplary PTHR1 agonist polypeptides

[0179] -NH2 indicates that the C-terminus of the polypeptide is amidated.

[0180] In some embodiments, the polypeptide is a PTHR1 antagonist or inverse agonist. In some embodiments, the polypeptide comprises a sequence of formula (II): Xo7-Xo8-Xo9-Xio-Xii-Xi2-Lys-Xi4-lle-Gln-Asp-Xi8-Arg-Arg-Arg-X22-Trp-Leu-His-X26-Leu-lle-Ala-Glu-lle-His- Thr-Ala-Glu-X36 (II), wherein

[0181] X07 is Leu or Lys;

[0182] Xos is Leu, Lys, or Nle;

[0183] X09 is His or Lys;

[0184] X10 is Asp, Lys, Asn, or Gin;

[0185] X11 is Lys or Leu;

[0186] X12 is Lys or dTrp;

[0187] X14 is Lys, Ser, or Trp;

[0188] Xis is Leu or Ala;

[0189] X22 is Phe or Ala;

[0190] X26 is His or Lys; and

[0191] X36 is Tyr or lie; wherein the fatty acid acyl is covalently linked to:

[0192] (a) the side chain amine of a Lys residue at position X7, Xa, X9, X10, Xu , X12, X13, or Xi4 of the polypeptide by way of an amino acid spacer; or

[0193] (b) the N-terminal amine of the polypeptide.

[0194] The conjugates including PTHR1 antagonist or inverse agonist peptides can be used in a method of treating a condition or a disease of the PTHR1 signaling overactivity (e.g., hypercalcemia, hypophosphatemia, hyperparathyroidism (e.g., primary hyperparathyroidism or secondary hyperparathyroidism), Jansen’s metaphyseal chondrodysplasia, and chronic kidney disease). These diseases are typically associated with higher than normal serum levels of calcium, with lower than normal serum levels of phosphate, with higher than normal levels of endogenous PTHR1 agonist(s), or with constitutive activity of PTHR1 mutants.

[0195] Exemplary PTHR1 antagonist or inverse agonist polypeptides of the invention are listed in Table

[0196] Table 3. Exemplary PTHR1 antagonist or inverse agonist polypeptides

[0197] -NH2 indicates that the C-terminus of the polypeptide is amidated.

[0198] II. Conjugates

[0199] Conjugates of the invention include a PTHR1 agonist, antagonist, or inverse agonist polypeptide and at least one fatty acid acyl. In some embodiments, the fatty acid acyl is a very long chain fatty acid or a long chain fatty acid acyl. For example, the fatty acid acyl may be palmitoyl or octadecanedioic acid. In some embodiments, the fatty acid is palmitoyl.

[0200] In some embodiments, the fatty acid acyl is covalently linked to the side chain amine of a Lys residue of the polypeptide by way of an amino acid spacer (i.e., the fatty acid acyl is covalently linked to the nitrogen atom of the e-amino group of the Lys side chain by way of an amino acid spacer). Exemplary amino acid spacers include Arg, dArg, Glu, or dGlu. For example, the fatty acid acyl may be covalently linked to the side chain amine of a Lys residue of the polypeptide through a linker of formula (III): wherein X is the amino acid residue side chain of Arg, dArg, Glu, or dGlu, wherein JW i V- represents the bond to the side chain amine of the Lys residue, and wherein1represents the bond to the carbonyl carbon of the fatty acid acyl. As shown in formula (III), the Lys residue of the polypeptide may be conjugated to the fatty acid acyl via a spacer amino acid (Arg, dArg, Glu, or dGlu), wherein the spacer amino acid is linked via its alpha-carboxy to the Lys side chain amine and via its alpha-amino to the carbonyl carbon of the fatty acid acyl. In some embodiments, the spacer amino acid is Arg. In some embodiments, the spacer amino acid is dArg. In some embodiments, the spacer amino acid is Glu. In some embodiments, the spacer amino acid is dGlu.

[0201] An exemplary conjugate (SEQ ID NO: 3) having a polypeptide of SEQ ID NO: 35 conjugated to palmitoyl via a linker of formula (III), wherein X is the side chain of Arg, is shown in FIG. 8A. An exemplary conjugate (SEQ ID NO: 5) having a polypeptide of SEQ ID NO: 35 conjugated to octadecanedioic acid via a linker of formula (III), wherein X is the side chain of Arg, is shown in FIG. 8D. An exemplary conjugate (SEQ ID NO: 14) having a polypeptide of SEQ ID NO: 38 conjugated to palmitoyl via a linker of formula (III), wherein X is the side chain of Arg, is shown in FIG. 9A, top. An exemplary conjugate (SEQ ID NO: 8) having a polypeptide of SEQ ID NO: 36 conjugated to palmitoyl via a linker of formula (III), wherein X is the side chain of Arg, is shown in FIG. 9A, middle. An exemplary conjugate (SEQ ID NO: 2) having a polypeptide of SEQ ID NO: 35 conjugated to palmitoyl via a linker of formula (III), wherein X is the side chain of dGlu, is shown in FIG. 9A, bottom.

[0202] In some embodiments, the fatty acid acyl is covalently linked to the N-terminal amine of the polypeptide. For example, the carbonyl carbon of the fatty acid acyl may be covalently bound to the N- terminal amine of the polypeptide.

[0203] Conjugates of the invention may be prepared using techniques and reactions known in the art. For example, a fatty acid may be reacted with an unprotected -NH2 in the lysine side-chain or an alpha amino of an N-terminal amino acid using amide coupling agents known in the art (e.g., diisopropylcarbodiimide and HOBt). The groups present in amino acids (e.g., -OH, -SH, -COOH, -NH2, and the like) may be protected to avoid undesired reactions with the amide coupling agents and / or fatty acid. Commonly used protecting groups are known in the art, e.g., in Greene, “Protective Groups in Organic Synthesis,” 3rdEdition (John Wiley & Sons, New York, 1999).

[0204] In some embodiments, the conjugate is a PTHR1 agonist including a PTHR1 agonist polypeptide and a fatty acid acyl. Exemplary PTHR1 agonist conjugates of the invention are listed in Table 4.

[0205] Table 4. Exemplary PTHR1 agonist conjugates*

[0206] *AII peptides in Table 4 have C-terminal NH2.

[0207] Sequences in Table 4 are in standard 1 -letter amino acid code for conventional amino acids; non- conventional amino acids are as follows: O, norleucine; B, alpha-amino isobutyric acid, R* homoarginine; Z, 1-Aminocyclopentane-1 -carboxylic acid; r, d-Arginine; e, d-Glutamic acid; w, d-Tryptophan. Other terms include: Palm, palmitoyl (CH3-[CH2]14-CO-, PubChem SID 26697177); Dioc, octadecanedioic acid; PEG2, polyethylene glycol dimer; TMR, tetramethyl-rhodamine; palmitoyl groups and octadecanedioic acid groups are linked to the side chain amine of a lysine either directly (distal palm in SEQ ID NO: 22) or via a spacer amino acid (R, r, E, or e, as indicated in parentheses in front of "palm" or “dioic”) that is linked via its alpha-carboxy to lysine amine and via its alpha-amino to palmitoyl or octadecanedioic acid.

[0208] In some embodiments, the PTHR1 agonist conjugates of the invention have improved activity relative to PTH(1-34), which has an amino acid sequence of SVSEIQLMHNLGKHLNSMERVEWLRKKLQDVHNF (SEQ ID NO: 54). In some embodiments, the PTHR1 agonist conjugates of the invention have improved activity relative to M-PTH(1-14), which has an amino acid sequence of BVBEIQLMHQR*AKW (SEQ ID NO: 55). In some embodiments, the PTHR1 agonist conjugates of the invention have improved activity relative to M-PTH(1-11), which has an amino acid sequence of ZVBEIQLMHQR* (SEQ ID NO: 56).

[0209] In some embodiments, the conjugate is a PTHR1 antagonist or inverse agonist including a PTHR1 antagonist or inverse agonist polypeptide and at least one fatty acid acyl. Exemplary PTHR1 antagonist or inverse agonist conjugates of the invention are listed in Table 5.

[0210] Table 5. Exemplary PTHR1 antagonist / inverse agonist conjugates*

[0211] *AII peptides in Table 5 have C-terminal NH2.

[0212] Sequences in Table 5 are in standard 1 -letter amino acid code for conventional amino acids; non- conventional amino acids are as follows: O, norleucine; B, alpha-amino isobutyric acid, R* homoarginine; Z, 1-Aminocyclopentane-1 -carboxylic acid; r, d-Arginine; e, d-Glutamic acid; w, d-Tryptophan. Other terms include: Palm, palmitoyl (CH3-[CH2]14-CO-, PubChem SID 26697177); PEG2, polyethylene glycol dimer; TMR, tetramethyl-rhodamine; palmitoyl groups are linked either to the N-terminal amine directly (in SEQ ID NO: 32) or via a spacer amino acid (R, r, E, or e, as indicated in parentheses in front of "palm") that is linked via its alpha-carboxy to lysine amine and via its alpha-amino to palmitoyl. In some embodiments, the PTHR1 antagonist / inverse agonist conjugates of the invention have improved activity relative to L11 ,dW12,W23,Y36-PTHrP(7-36), which has an amino acid sequence of LLHDLwKSIQDLRRRFWLHHLIAEIHTAEY (SEQ ID NO: 57).

[0213] In some embodiments, the polypeptides of the invention may include an additional modification, such as a dye. An exemplary dye that may be conjugated to the polypeptide is tetramethylrhodamine (TMR). The dye may be conjugated to a Lys residue of the polypeptide, for example, by conjugating the dye to the side chain amine of the Lys residue. The inclusion of a dye can permit tracking the polypeptide of the invention in cells or in vivo through the use of fluorescence.

[0214] In some embodiments, the polypeptides may be conjugated covalently to a second fatty acid acyl. For example, the second fatty acid acyl may be covalently linked to the side chain amine of a second Lys residue of the polypeptide by way of an amino acid spacer (i.e., the second fatty acid acyl may be covalently linked to the nitrogen atom of the e-amino group of the second Lys side chain by way of an amino acid spacer). Exemplary amino acid spacers include Arg, dArg, Glu, or dGlu. For example, the second fatty acid acyl may be covalently linked to the side chain amine of a second Lys residue of the polypeptide through a linker of formula (III): wherein X is the amino acid residue side chain of Arg, dArg, Glu, or dGlu, wherein » / W i V^ represents the bond to the side chain amine of the second Lys residue, and wherein1represents the bond to the carbonyl carbon of the second fatty acid acyl. In some embodiments, the spacer amino acid is

[0215] Arg. In some embodiments, the spacer amino acid is dArg. In some embodiments, the spacer amino acid is Glu. In some embodiments, the spacer amino acid is dGlu.

[0216] In some embodiments, the second fatty acid acyl may be covalently linked to the C-terminus of the polypeptide. For example, the polypeptide may be amidated at the C-terminus and the second fatty acid acyl may be covalently linked to the C-terminal NH2 of the polypeptide through a linker of formula (IV): wherein n is an integer from 0 to 10; each of m and q is an integer from 2 to 5; each AA1 and each AA2 is independently a proteinogenic amino acid; and R is a bond to the carbonyl carbon of the fatty acid acyl.

[0217] In some embodiments, -C(O)-(AAi)m-NH- in the linker structure is -C(O)-EYE-NH- or -C(O)-SYE- NH-. In some embodiments, -(AA2)q in the linker structure is -EYE or -ESE. In some embodiments, the C- terminus of -(AA2)q is carboxamide.

[0218] In some embodiments, the second fatty acid acyl is a very long chain fatty acid or a long chain fatty acid acyl. For example, the second fatty acid acyl may be palmitoyl or octadecanedioic acid.

[0219] III. Pharmaceutical Compositions

[0220] The conjugates disclosed herein may be formulated in a pharmaceutical composition providing an effective amount of the conjugate to a subject upon administration. The pharmaceutical compositions of the conjugates disclosed herein can contain an appropriate amount of a suitable carrier or excipient. The pharmaceutical compositions may contain from 0.1% to 95% (w / v) or (w / w) of the conjugate. The compositions may be provided in a dosage form that is suitable for parenteral (e.g., subcutaneous, intravenous, intramuscular, intraperitoneal), intranasal, transpulmonary, transdermal, transmucosal, or oral administration. In some embodiments, the compositions may be provided in a dosage form that is suitable for oral administration. The composition may be in the form of, e.g., tablets, ampules, capsules, pills, powders, granulates, suspensions, emulsions, solutions, gels including hydrogels, pastes, ointments, creams, plasters, drenches, osmotic delivery devices, suppositories, enemas, injectables, implants, sprays, or aerosols. The pharmaceutical compositions may be formulated according to conventional pharmaceutical practice (see, e.g., Remington: The Science and Practice of Pharmacy, 21stedition, 2005, Ed. D.B. Troy, Lippincott Williams & Wilkins, Philadelphia, and Encyclopedia of Pharmaceutical Technology, eds. J. Swarbrick and J. C. Boylan, 1988-1999, Marcel Dekker, New York).

[0221] IV. Methods of Treatment

[0222] The conjugates (e.g., a conjugate of any one of SEQ ID NOs: 25-34) and the pharmaceutical compositions disclosed herein may be used to treat a condition or a disease associated with PTHR1 signaling overactivity (e.g., hypercalcemia, hypophosphatemia, hyperparathyroidism (e.g., primary hyperparathyroidism or secondary hyperparathyroidism), and Jansen’s metaphyseal chondrodysplasia). PTHR1 signaling overactivity may be caused by various factors, such as elevated blood levels of PTH (e.g., hyperparathyroidism) or PTHrP (e.g., humoral hypercalcemia of malignancy).

[0223] Some forms of hypercalcemia are related to the interaction of PTHR1 with PTH or PTHrP (e.g., humoral hypercalcemia of malignancy). Hypercalcemia is a condition in which there is an abnormal elevation in serum calcium levels; it is often associated with other diseases, including hyperparathyroidism, osteoporosis, and cancer (e.g., carcinomas of the breast, lung and prostate, epidermoid cancers of the head and neck and of the esophagus, multiple myeloma, and hypernephroma).

[0224] Jansen’s metaphyseal chondrodysplasia is a rare disease caused by PTHR1 activating mutations (e.g. H223R and T410P) which result in excessive hormone-independent (constitutive) signaling by the receptor itself. Ligands that bind to such constitutively active PTHR1 mutants and suppress their signaling are classified as PTHR1 inverse agonists. Some, but not all, ligands that function as PTHR1 antagonists also function as PTHR1 inverse agonists. In accordance with yet a further aspect of the invention, there is provided a method for treating a disease or condition that is caused by overactivity of PTHR1 in a subject. The method involves administering to the subject an effective amount of the conjugate of the invention (e.g., a conjugate of any one of SEQ ID NOs: 25-34) or a pharmaceutically acceptable salt thereof or a fragment thereof or a pharmaceutical composition disclosed herein. The effective amount will typically be sufficient to reduce activation of the PTHR1 of the subject to non-pathological levels, as assessed by the treatment of the subject (e.g., a reduction in disease symptoms, reduced serum calcium levels).

[0225] In one embodiment, a subject having a disease or condition that is caused by the constitutive signaling activity of PTHR1 (e.g., Jansen’s metaphyseal chondrodysplasia) can be treated using conjugates of the invention which are PTHR1 inverse agonists (e.g., a conjugate of any one of SEQ ID NOs: 25-34). In this embodiment, the PTHR1 inverse agonist conjugate of the invention may be present as a pharmaceutically acceptable salt thereof or a fragment thereof or in a pharmaceutical composition disclosed herein.

[0226] In another embodiment, a subject having a disease or condition that is caused by the non- constitutive signaling overactivity of PTHR1 can be treated using conjugates of the invention which are PTHR1 antagonists (e.g., a conjugate of any one of SEQ ID NOs: 25-34). In this embodiment, the PTHR1 antagonist conjugate of the invention may be present as a pharmaceutically acceptable salt thereof or a fragment thereof or in a pharmaceutical composition disclosed herein.

[0227] The conjugates (e.g., a conjugate of any one of SEQ ID NOs: 1-24) and the pharmaceutical compositions disclosed herein may be used to treat a condition or a disease associated with PTHR1 signaling underactivity (e.g., hypoparathyroidism, hypocalcemia, hyperphosphatemia, osteoporosis, fracture repair, osteomalacia, arthritis (e.g., rheumatoid arthritis), thrombocytopenia, or chronic kidney disease) or to increase stem cell mobilization in a subject. The conjugates and the pharmaceutical compositions disclosed herein may also be used to increase bone formation and activate bone remodeling, which may lead to an increase in bone mineral density. PTHR1 signaling underactivity may be caused by reduced production of PTH from the parathyroid glands (e.g., hypoparathyroidism).

[0228] In accordance with yet a further aspect of the invention, there is provided a method for treating a disease or condition that is caused by underactivity of PTHR1 in a subject. The method involves administering to the subject an effective amount of the conjugate of the invention (e.g., a conjugate of any one of SEQ ID NOs: 1-24) or a pharmaceutically acceptable salt thereof or a fragment thereof or a pharmaceutical composition disclosed herein. The effective amount will typically be sufficient to increase activation of the PTHR1 of the subject to non-pathological levels, as assessed by the treatment of the subject (e.g., a reduction in disease symptoms (paresthesia, muscle aches or cramps, muscle spasms, fatigue or weakness), increased bone formation or bone mineral density, increased calcium levels, reduced phosphate levels).

[0229] In one embodiment, a subject having a disease or condition that is caused by the reduced signaling activity of PTHR1 (e.g., hypoparathyroidism) can be treated using conjugates of the invention which are PTHR1 agonists (e.g., a conjugate of any one of SEQ ID NOs: 1-24). In this embodiment, the PTHR1 agonist conjugate of the invention may be present as a pharmaceutically acceptable salt thereof or a fragment thereof or in a pharmaceutical composition disclosed herein. To administer the conjugate of the invention, the conjugate of the invention or a pharmaceutically acceptable salt thereof can be used in the manufacture of a medicament, generally by being formulated in an appropriate carrier or excipient such as, e.g., physiological saline, and administered through an appropriate route of administration (e.g., parenteral (e.g., subcutaneous, intravenous, intramuscular, intraperitoneal), intranasal, transpulmonary, transdermal, transmucosal, or oral administration). In some embodiments, the conjugate of the invention or a pharmaceutically acceptable salt thereof may be administered orally. An effective amount of the conjugate of the invention is typically present in the medicament. For example, typical dosage would be 1 ng to 10 mg of the conjugate, e.g., per kg body weight, e.g., per day. In some embodiments, a subject may be administered a conjugate of the invention once daily or once every other day.

[0230] V. Methods of Modulating PTHR1 Activity

[0231] The conjugates disclosed herein may be used to modulate the activity of PTHR1 in a cell. Thus, the present invention features a method of inversely agonizing the activity of PTHR1 in a cell, a method of antagonizing the activity of PTHR1 in a cell, and a method of agonizing the activity of PTHR1 in a cell. The method may involve contacting the cell with a conjugate having a desirable activity (e.g., PTHR1 antagonist activity, PTHR1 inverse agonist activity, or PTHR1 agonist activity). The cell may be in a mammal (e.g., in a subject).

[0232] The conjugate that is a PTHR1 antagonist (e.g., a conjugate of any one of SEQ ID NOs: 25-34) may be used in this method to antagonize the signaling activity of PTHR1 in a cell (e.g., by reducing the binding of endogenous agonists to PTHR1). The conjugate that is a PTHR1 inverse agonist (e.g., a conjugate of any one of SEQ ID NOs: 25-34) may be used in this method to inversely agonize the constitutive signaling activity of a naturally occurring PTHR1 mutant having constitutive signaling activity (e.g., PTHR1-H223R or PTHR1-T410P). A conjugate that is a PTHR1 antagonist or inverse agonist (e.g., a conjugate of any one of SEQ ID NOs: 25-34) (e.g., in the case of PTHR1 mutants having constitutive signaling activity) may reduce receptor activity by 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 95%, 98% or more. The cell may be in a mammal (e.g., in a subject).

[0233] The conjugate that is a PTHR1 agonist (e.g., a conjugate of any one of SEQ ID NOs: 1 -24) may be used in this method to agonize PTHR1 in a cell (e.g., by binding to PTHR1 and inducing or increasing PTHR1 signaling). A conjugate that is a PTHR1 agonist (e.g., a conjugate of any one of SEQ ID NOs: 1 - 24) may increase PTHR1 activity by 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 95%, 98% or more. The cell may be in a mammal (e.g., in a subject). EXAMPLES

[0234] The following examples are provided as a description of how the compositions and methods described herein may be used and evaluated and are intended to be purely exemplary of the invention and is not intended to limit the scope of what the inventors regard as their invention.

[0235] Table of Contents

[0236] Example 1. Prolonging Parathyroid Hormone Analog Action in vitro and in vivo through Peptide Lipidation

[0237] Parathyroid hormone (PTH) analogs with improved actions in vivo could lead to optimized treatments for bone and mineral ion diseases. Rapid clearance from the circulation and short dwell times on the PTH receptor limit the efficacies of conventional PTH peptides currently in medical use. This Example describes peptides with enhanced PTH efficacy using two distinct peptide lipidation strategies. First, we append a lipid chain to the peptide's C-terminus in a fashion to promote binding to serum albumin and hence prolong the peptide's circulation half-life in vivo. Second, we append a lipid chain to a lysine side chain in a fashion designed to anchor the peptide to the cell membrane as the ligand is bound to the receptor and hence increase its dwell time on the receptor. We find that both strategies of lipidation can profoundly enhance the efficacy of PTH peptides in vitro and in mice. Our results could lead to the development of modified PTH analogs with optimized therapeutic utility.

[0238] Introduction

[0239] The parathyroid hormone (PTH) receptor (PTH1 R) plays essential roles in calcium and phosphate homeostasis via interaction with PTH, as well as in the development of bone and other tissues via interaction with PTH-related peptide (PTHrP) (Cheloha et al., Nat Rev Endocrinol. 2015 Dec; 11 (12) 712-24). Recombinant PTH(1-34) and a PTHrP(1-34) analog (abaloparatide) are FDA- approved for the treatment of osteoporosis (Kostenuik et al., Curr Osteoporos Rep. 2023 Aug;21 (4):386- 400), and other longer-acting peptides, including a PTH(1-14) / PTHrP(15-36) hybrid peptide, called LA- PTH (eneboparatide) (Shimizu et al., J Bone Miner Res. 2016 Jul;31 (7):1405-12), and a self-cleaving PTH(1-34)-based pegylated compound called TransCon PTH(1-34)(palopegteriparatide) (Khan et al., J Bone Miner Res. 2023 Jan;38(1):14-25), are approved or in clinical trials for the treatment of hypoparathyroidism (Bilezikian et al., J Clin Endocrinol Metab. 2020 Jun 1 ;105(6): 1722-1736). For most PTH peptide-based therapies developed so far, efficacy in vivo is limited by a relatively short half-life in the body, which is typically on the order of minutes to an hour (Satterwhite et al., Calcif Tissue I nt. 2010 Dec;87(6):485-92), resulting in a need for frequent delivery, i.e. at least once-daily injection for hypoparathyroidism (Winer et al., Bone. 2019 Mar:120:535-541). A further potentially limiting factor affecting efficacy is the duration of the desired biological effect achieved by a ligand on its target receptor, which in turn is determined at least in part by how long the ligand remains bound to the receptor. Receptor internalization and desensitization responses activated in target cells of bone and kidney also likely limit the efficacy that an injected PTH ligand achieves in vivo (White et al., Sci Signal. 2021 Oct 5;14(703):eabc5944; White et al., Sci Signal. 2021 Oct 5;14(703):eabc5944).

[0240] In the current study, we explored the effects of lipid modifications on the actions in vitro and in vivo of a variety of PTH ligand analogs. We thus synthesized analogs of PTH(1-34), a commonly used and fully active PTH peptide, as well as minimized M-PTH(1-14)-derived peptides containing the previously reported C-terminal tag motif optimized for albumin-binding (Zorzi et al., Nat Commun. 2017 Jul 17:8:16092), as well as other M-PTH(1 -14) and M-PTH(1-11) peptides containing a lipid chain appended more directly to the side chain of a lysine at position 11 or 13 in a configuration designed for anchoring the ligand to the plasma membrane while the ligand is bound to the receptor's orthosteric pocket. Our results demonstrate that such lipid appendages can indeed have profound impacts on the pharmacological actions that a PTH ligand exhibits in cells and in mice and can thus lead to robust changes in bone and calcium metabolism, even for peptides as small as the PTH(1 -11) fragment that would otherwise be inactive in vivo.

[0241] Results

[0242] Palm-PTH(1-34): effects of the C-terminal albumin-binding motif on actions in cells and in vivo.

[0243] We first assessed the effects of linking the palmitoylated (C16) heptapeptide tag sequence [EYEK(palm)EYE] reported by Zorzi et al. to be optimized for serum albumin binding (Zorzi et al., Nat Commun. 2017 Jul 17:8:16092) to the C-terminus of PTH(1-34). A polyethylene glycol (PEG)2-like (20 atom) spacer was placed between the N-terminal Glu of the hexapeptide tag and Phe34 of PTH. The palmitoyl group was added post-synthetically to the central lysine of the tag. The resulting Palm-PTH(1- 34) (FIG. 1A) was assessed for cAMP signaling potency in SGS-72 cells, which are human osteoblastic cells that endogenously express the PTH1 R and stably express the giosensor cyclic adenosine monophosphate (cAMP) reporter. Palm-PTH(1-34) stimulated cAMP formation in these cells with a potency that was not significantly different from that of unmodified PTH(1-34) (pECsos ~ 9.65±0.1 and 9.60±0.01 , respectively, p (t-test) = 0.7, n=10) and with a comparable maximum efficacy (FIG. 1B).

[0244] Injection of PTH(1-34) into animals and humans results in an acute rise in blood ionized calcium (Ca++) levels and a concomitant decrease in blood inorganic phosphate (Pi). PTH increases directly or indirectly blood calcium by acting on target cells in bone and kidney while it decreases blood phosphate by reducing urinary Pi reabsorption. We hence assessed the pharmacodynamic (PD) actions of Palm- PTH(1-34) in vivo by subcutaneously (SC) injecting 10-week-old mice (strain CD-1) with either Palm- PTH(1-34) or PTH(1-34), each at a dose of 10 nmol / kg-body weight, or with vehicle and measuring effects on blood Ca++and plasma Pi at times after injection. Both injected PTH peptides caused blood Ca++levels to rise significantly above the pre-injection level by one hour after injection, but while the response to PTH(1-34) was transient, that to Palm-PTH(1-34) was markedly more robust and prolonged. The response to PTH(1-34) thus peaked at two hours and returned to baseline by six hours after injection, while that to Palm-PTH(1-34) attained a peak at six hours that was significantly higher than that of PTH(1-34) and remained slightly higher than vehicle control levels even at the 24-hour time point (FIG. 1C). Similarly, Palm-PTH(1-34) induced a more pronounced decrease in plasma Pi levels than did PTH(1-34) and the effect persisted for at least six hours after injection (FIG. 1 D).

[0245] A separate experiment was performed in intact mice to further assess the effects of a single injection of Palm-PTH(1-34) vs PTH(1-34) or vehicle, on markers of mineral ion homeostasis and bone metabolism. The peptides were injected SC, at a dose of 50 nmol / kg and at 2, 7 and 24 hours after injection blood plasma as well as urine was collected for analysis. Consistent with the changes in blood ionized calcium and Pi observed in the experiment of FIGS. 1C-1 D, injection of Palm-PTH(1-34) resulted in significantly greater increases in plasma total calcium and significantly greater decreases in plasma Pi levels than did injection of PTH(1-34), as measured at 7 hours post-injection (FIGS. 2A-2B). At two hours post injection, plasma total calcium tended to be increased to similar levels with the two peptides, as compared to the levels in mice injected with vehicle, but the differences were not significant, and variations between replicate measurements were wide, as compared to those in the measurements of ionized calcium in whole blood shown in FIG. 1C, which presumably reflects technical differences in the assay formats for whole blood ionized calcium vs. plasma total calcium (see Methods). Plasma Pi levels were similarly and significantly reduced at 2 hours post injection for both peptides, and no change in either plasma Pi or total calcium was detected at 24 hours-post injection (FIGS. 2A-2B).

[0246] Injection of Palm-PTH(1-34) also resulted in a significant increase in urine calcium levels at 24 hours-post injection and relative to the levels in the vehicle-injected mice, while PTH(1-34) injection tended to increase urine calcium only at 7 hours and the change was not significant; urine Pi was elevated in both peptide-injected groups at 2 hours post-injection but the change was significant only for PTH(1-34) (FIGS. 2C-2D). Neither ligand resulted in a change in CTX1 , but injection of Palm-PTH(1-34) caused blood levels of 1 ,25-dihydroxyvitamin D to increase to approximately twice the levels observed in mice injected with PTH(1-34) at 7-hours post-injection, and the levels remained elevated relative to those in the vehicle-injected mice at 24-hour post-injection (P < 0.001), by which time the levels in mice injected with PTH(1-34) had returned to base-line (FIGS. 2E-2F). These results on serum 1 ,25-dihydroxyvitamin D, together with the sustained effects on blood phosphorus levels establish that Palm-PTH(1-34) induces responses in kidney that are more sustained than those induced by conventional PTH(1-34).

[0247] To evaluate the pharmacokinetic (PK) properties of Palm-PTH(1-34), we measured the concentrations of the peptide, or that of PTH(1-34), in blood at times after SC injection. The levels of the two peptides were determined using a commercial ELISA developed for human PTH(1-34) and calibrating the assay with standard curves generated with either Palm-PTH(1-34) or PTH(1-34). By this approach, we found that while both peptides could be detected in the blood soon after injection, Palm-PTH(1-34) attained a maximum concentration (Cmax) that was at least 30-times that of PTH(1-34) (Cmax = 28.1 nm vs. 0.65 nM), and the time to attain the maximum was about 6-times slower for the lipidated analog than for the non-lipidated peptide (Tmax = 60 mins. vs. 10 mins, FIG. 1E). In addition, Palm-PTH(1-34) could be detected at the last 24-hour post-injection time point, whereas PTH(1-34) was not detected past six hours post-injection (FIG. 1 E). Fitting the data obtained at the 1- to 24-hour time points - i.e, from the peak onwards and thus excluding the initial absorption phase - to a monophasic decay function yielded an estimated half-life (T1 / 2) of 1 .9 hours for the lipidated peptide vs. 0.3 hours for PTH(1 -34). Similarly marked differences in the pharmacokinetic, as well as pharmacodynamic (blood Ca++) properties of the two peptides were obtained following intravenous (IV) injection of the peptides in mice (FIGS. 3A-3B).

[0248] We also evaluated the renal filtration properties of PTH(1-34) and Palm-PTH(1-34) by injecting fluorescent tmr-labeled versions of the peptides into mice and monitoring the appearance of tmr fluorescence in urine at times after injection. Each analog contained the tmr moiety appended to the side chain of Lys13, a modification known to have little if any impact on the functional properties of PTH ligands (Guo et al., J Bone Miner Res. 2017 Jan;32(1):86-98). Spot urine was collected at times after injection and measured for tmr fluorescence in a plate reader, which was converted to peptide concentration by extrapolating from standard curves generated with each control peptide. Following injection of PTH(1-34)tmr, tmr fluorescence was observed as a robust peak at the 1-hour time point and then then diminished to near base-line levels by 24 hours. In contrast, after injection of Palm-PTH(1- 34)tmr, the tmr fluorescence reached a much lower peak that occurred at 2 hours post-injection before diminishing to near base-line levels by 24 hours, such that the area-under-the-curve (AUC) values obtained for the data with Palrn-PTH(1-34)tmrwas approximately 1 / 2 that obtained with PTH(1-34)tmr(FIG. 1F). These data are consistent with a slower rate of excretion of Palrn-PTH(1-34)tmrinto the urine, relative to PTH(1-34)tmr, and thus a more prolonged persistence of the lipidated peptide in the circulation. Although we did not evaluate the possibility that a fraction of the tmr fluorescence measured in these experiments derives from excreted free tmr that became detached from the peptide by some unknown mechanism operating in vivo after injection, we note that such a scenario would likely impact the two peptides similarly, given that the tmr is similarly linked to a lysine at position-13 in each ligand, and hence would not be expected to contribute to the differences in the quantities in urine observed for the two peptides.

[0249] The pharmacokinetic data together indicate that the lipid modification in Palm-PTH(1-34) prolongs the peptide's bioavailability in the circulation and reduces its rate of renal elimination into the urine and are thus consistent with the hypothesis that the lipidated C-terminal tag promotes binding to serum albumin. The data do not exclude, however, the possible involvement of other contributing mechanisms, such as a reduction in the rate of absorption from the subcutaneous injection site compartment, an increase in distribution of the peptide to and subsequent release from soft tissues, and enhanced resistance to proteases.

[0250] To directly evaluate peptide binding to albumin, we conducted in vitro biolayer interferometry (BLI) experiments in which we analyzed the binding of Palm-PTH(1-34) as well as Palm-M-PTH(1-14) to bovine serum albumin that had been pre-adsorbed to the optical probes of the detector. We found that each lipidated peptide exhibited a dose-dependent increase in binding to albumin that was characterized by a Bmax value at least three-fold higher, and an estimated KD value at least three-fold lower than that obtained for the corresponding non-lipid counterpart peptide (FIGS. 4A-4B). These data thus support the notion that the C-terminal EYEK(palm)EYE tag attached to each of these two lipidated PTH peptides indeed promotes direct binding to serum albumin. Palm-PTH(1 -34) normalizes blood Ca++in parathyroidectomized mice.

[0251] We then assessed the translational potential of Palm-PTH(1-34) by using parathyroidectomized (PTX) mice as a model of surgical hypoparathyroidism (Bi et al., J Bone Miner Res. 2016 May;31 (5):975- 84). The parathyroid glands were surgically removed and four days later the mice were used for the experiment, by which time the mice had developed frank hypocalcemia (FIG. 5A), which characterizes hypoparathyroidism. Upon SC injection of PTH(1 -34) control peptide at a dose of 50 nmol / kg, blood Ca++levels in the PTX mice rose briefly but did not attain the Ca++levels of sham-surgery control mice, and the levels returned to baseline by six hours post-injection. In contrast, upon injection of Palm-PTH(1 -34), at a dose of 50 or 10 nmol / kg, blood Ca++levels rose to near or within the normal range and persisted at those levels for at least 24 hours (FIG. 5B). Even at a dose of 2.0 nmol / kg, Palm-PTH(1-34) increased blood Ca++to levels similar to those attained with PTH(1 -34) injected at a 25-fold higher dose.

[0252] In parallel to the robust increases in blood Ca++, serum levels of 1 ,25-dihydroxyvitamin D3 at 24- hours post-injection were elevated approximately 4-fold in the PTX mice injected with the 50 nmol / kg dose of Palm-PTH(1-34), as compared to the levels in PTX mice injected with vehicle (P<0.0001), but were unchanged in the PTX mice injected with PTH(1 -34) at the same dose as compared to the vehicle controls (FIG. 6).

[0253] The C-terminal albumin-binding motif prolongs the actions of M-PTH(1-14) in cells and in mice.

[0254] The pronounced improvements in PK / PD properties that the EYEK(palm)EYE tag conferred to PTH(1-34) led us to ask if the same tag could provide similar improvements to shorter length agonist PTH peptides, such as M-PTH(1-14). M-PTH(1-14) is modified (as indicated by "M") with six amino acid replacements that cumulatively improve agonist potency by at least 1 ,000-fold, relative to the nearly inert native PTH(1 -14), as assessed in cell-based signaling assays (Shimizu et al., J Biol Chem. 2001 Dec 28;276(52):49003-12). Despite the improvements in vitro, M-PTH(1-14) has been found to be inactive when tested in vivo (Murrills et al., Bone. 2004 Dec;35(6):1263-72), which likely is due to the peptide's small size (~1 ,700 Daltons) leading to a rapid rate of renal clearance as well as a rapid rate of dissociation from the receptor (Dean et al., Mol Endocrinol. 2006 Apr;20(4):931-43). We thus synthesized Palm-M-PTH(1 -14) containing the EYEK(palm)EYE tag linked to the peptide's C-terminus via a PEG2-like (20 atom) spacer. The resulting Palm-M-PTH(1-14) analog exhibited a potency for stimulating cAMP formation in SGS-72 cells that was greater than that of non-lipidated M-PTH(1-14), as assessed both during the Ligand-on phase and after washout of the unbound ligand (FIGS. 7A-7B). Interestingly, the improvements in signaling potency of up to 10-fold observed for Palm-M-PTH(1-14) vs. M-PTH(1-14) in SGS-72 cells were not observed in the studies with Palm-PTH(1-34) vs. PTH(1 -34) (FIG. 1 B), suggesting that the lipid moiety as attached to the C-terminus of the PTH(1 -14) scaffold, but not as attached to the C- terminus of the longer PTH(1-34), might provide favorable interactions with the cellular plasma membrane, a mechanism explored in the section below on membrane anchoring.

[0255] The favorable cAMP responses observed in vitro for Palm-M-PTH(1-14) prompted us to assess the effects of the peptide in vivo. We thus compared Palm-M-PTH(1-14) vs control peptides for effects on blood Ca++levels in intact adult CD-1 mice after a single-dose intravenous (IV) injection. Palm-M-PTH(1 - 14) (10 nmol / kg) caused blood Ca++levels to increase for at least 7 hours after injection, whereas an equal molar dose of PTH(1-34) caused blood Ca++to increase for no longer than 5 hours, and, as expected, injection of non-lipidated M-PTH(1-14) resulted in no change in blood Ca++(FIG. 7C).

[0256] Lipid-mediated membrane anchoring promotes actions in cells and in vivo by M-PTH(1-14) and M- PTH(1-11)

[0257] We then explored other modes of lipid attachment to specifically assess the possibility that a lipid chain appended to the M-PTH(1-14) scaffold in an appropriate manner might act to promote signaling by anchoring the ligand to the plasma membrane as the ligand is situated in the receptor's orthosteric pocket. We were inspired to pursue such a mechanism based in part on the recent X-ray crystal and Cryo-EM structures obtained for the PTH1 R in complex with various PTH ligands (Ehrenmann et al., Nat Struct Mol Biol. 2018 Dec;25(12):1086-1092; Zhao et al., Science. 2019 Apr 12;364(6436):148-153; Kobayashi et al., Mol Cell. 2022 Sep 15;82(18):3468-3483.e5; Cary et al., Structure. 2023 Jun 1 ;31 (6):668-676.e5). These structures thus reveal that the 1 -14 portion of the ligand is situated in the receptor's orthosteric pocket as an a-helix with the N-terminus positioned deep within the pocket and the 11-14 region located closer to the extracellular surface, such that the side chain at position 11 in the ligand projects towards a crevice that occurs between the extracellular ends of TM helices 1 and 2 while the side chain of residue 13 projects towards a crevice at the opposite end of the pocket between the extracellular ends TM helices 5 and 6. We further noted that certain designed peptide analogs of glucagon and / or GLP-1 contained a lipid moiety appended to the side chain of position 10 (Ward et al., Mol Metab. 2013 Sep 5;2(4):468-79; Finan et al., Nat Med. 2015 Jan;21 (1):27-36), which, upon amino acid sequence comparison (Wang et al., Proc Natl Acad Sci U S A. 2021 Aug 10; 118(32):e2101279118), aligns with residue 11 of PTH (Wang et al., Proc Natl Acad Sci U S A. 2021 Aug 10; 118(32):e2101279118). We thus hypothesized that a lipid chain appended via an appropriate spacer to the side chain of either residue 11 or 13 in the peptide would project through the respective crevice and insert into the lipid bilayer of the surrounding plasma membrane to thereby anchor the ligand in place as it is bound to the receptor (FIGS. 8A-8B). This model further predicts that a lipid appended at position 12 in the peptide, rotated by ~ 90° relative to residue 11 or 13, would project into the inner wall of the binding pocket, and thus not provide such an anchoring effect on the ligand-receptor complex (FIGS. 8A-8B).

[0258] To test the above hypothesis, we synthesized N-terminal PTH fragment peptides containing a C16 palmitoyl (palm) chain appended to the side chain amine of a C-terminal lysine located at either position 11 , 12 or 13, via a spacer amino acid that was either L-Glu(E), dGlu (e), L-Arg (R), or dArg (r) (FIGS. 8A-8B). The cAMP signaling responses induced by the peptides were assessed in GP-2.3 cells both in the presence of the ligand (Ligand-on phase) and after rinsing the cells to remove unbound ligand (washout phase). FIG. 8C shows dose-response potency curves generated from the AUCs of the time vs. cAMP-dependent luminescence responses obtained in these assays for the three peptides containing an L-Arg spacer. Both K13(R)palm-PTH(1-13) and K11(R)palm-PTH(1-11) exhibited a potency in the Ligand- on phase that was comparable to that of M-PTH(1 -14) and the potency of each ligand was largely maintained during the washout phase, whereas the potency of M-PTH(1-14) was diminished by ~ 90-fold following washout. K12(R)palm-PTH(1 -12) exhibited a potency that was ~14-fold weaker than that of M- PTH(1-14) in the Ligand-on phase, and its potency decreased ~2-fold further after the washout. These results are consistent with the hypothesis that the lipid chains extending from positions 11 or 13 in the ligand provide a stabilizing effect on the ligand-receptor complex to thereby enable prolonged signaling, whereas the lipid chain extending from position 12 provides less of a stabilizing effect and hence leads to a diminished and more transient signaling response, as compared to the responses seen with the peptides lipidated at position 11 or 13.

[0259] Similar findings were obtained with the three peptides in this series containing a d-Arg spacer amino acid, whereas the peptides having L-Glu or d-Glu as the spacer exhibited potencies during both the Ligand-on and washout phases that were weaker than those of the corresponding L-Arg and dArg counterpart peptides, as especially apparent for the PTH(1 -11) analogs (FIGS. 9A-99B and Table 6). These data suggest that the presence of a spacer between the peptide backbone and the lipid appendage is important for determining peptide bioactivity. Moreover, the superior performance of the Arg / dArg spacer relative to the Glu / dGlu spacers suggests a beneficial interaction between the positively charged guanidinium group of Arg and dArg in the spacer and the negatively charged headgroups of lipids in the cell membrane (Bouchet et al., Biochim Biophys Acta. 2010 Mar;1798(3):616-23).

[0260] Table 6. cAMP dose-response data for N-terminal PTH fragment peptides with sidechain palmitoyl appendages in GP-2.3 cells

[0261] EMax and pEC50 values for ligand-induced cAMP responses in GP-2.3 cells assessed for 20 minutes after ligand addition (Ligand-On phase) and for an additional 120 minutes after ligand washout (wash out). Data were normalized to the maximum AUC attained by M-PTH(1-14) and are means± SEM of four independent experiments, p, (two-sided t-test) peptide vs. M-PTH(1-14)

[0262] We ruled out the possibility that the effects of the lipid appendages on the cAMP signaling actions of the N-terminal PTH peptides involved interactions with the receptor's N-terminal extracellular domain (ECD) as we found that the lipids provided nearly the same enhancing effects on cAMP signaling in GD- 5y cells, which stably express a PTH1 R construct, PTHI R-delNT^P, that lacks the receptor's ECD, as those observed in GP-2.3 cells expressing the intact PTH1 R (FIGS. 10A-10B, Table 7). Indeed, the side chain lipids at positions 11 and 13 improved the signaling potency of the N-terminal fragment peptides after washout in GD-5y cells by as much as 200-fold, relative to the potency of the non-lipidated M- PTH(1-14) peptide. Table 7. cAMP dose-response data for N-terminal PTH fragment peptides with sidechain palmitoly appendages in GD-5y cells (PTHI pEC50 and EMax values for ligand-induced cAMP responses in GD-5y cells were obtained by plotting the cAMP response, assessed at each ligand concentration for 20 minutes after ligand addition (Ligand-On phase) and for an additional 120 minutes after ligand washout (wash out phase) as the AUC of time vs luminescence plots, as a function of ligand concentration and fitting the plots to a non-linear regression equation. nM values are derived from the corresponding pEC50 value. Data are means± SEM of five independent experiments, p = two-sided t-test vs M-PTH(1-14). As a further test of the hypothesis that the lipid chain extensions at position 11 or 13 promote signaling by inserting into the lipid compartment of the plasma membrane, we synthesized peptides incorporating a C18 diacid chain (dioic) at those positions to thereby introduce a polar carboxyl group at the distal end of the fatty acid chain (FIG. 8D). The rationale was that this distal polar carboxylate would be less effective at inserting into the hydrophobic component of the lipid bilayer of the plasma membrane, as compared to the fully apolar C16 chain of the palmitoyl group, and thus not provide the same stabilizing effect on the complex as achieved with the palmitoyl group. Consistent with this model, K13(R)dioic-PTH(1-13) and K11(R)dioic-PTH(1-11) each showed a potency for cAMP generation in GP-2.3 cells that while comparable to that of the corresponding palmitoyl peptide during the Ligand-on phase, was markedly weaker than that of the palmitoyl peptide as measured during the washout phase (FIG. 8E; Table 8). The results thus support a model by which the apolar palmitoyl chains of K13(R)palm-PTH(1-13) and K11(R)palm-PTH(1-11) promote complex stability and hence signaling via a mechanism involving in situ anchoring of the receptor-bound ligand to the surrounding cellular plasma membrane.

[0263] Table 8. cAMP dose-response data for N-terminal PTH fragment peptides with side chain palmitoly or dioic acid appendages in GP-2.3 cells

[0264] EMax and pEC50 values for ligand-induced cAMP responses in GP-2.3 cells were obtained by plotting the cAMP response, assessed at each ligand concentration for 20 minutes after ligand addition (Ligand- On phase) and for an additional 120 minutes after rinsing to remove unbound ligand washout (wash out) as the AUC of time vs luminescence plots, normalized to the maximum AUC attained by M-PTH(1-14), as a function of ligand concentration and fitting the plots using a non-linear regression equation. Data are means± SEM of four independent experiments, p values indicate statistical differences (two-sided t-test) between dioic and corresponding palm-PTH(1-13) or palm-PTH(1-11) peptide.

[0265] Lipidation at the C-terminus of Exendin4 has been shown to slow the rate at which this GLP-1 R peptide agonist induces GLP1 R internalization and to impair recruitment of barrestin2 (Lucey et al., Mol Pharmacol. 2021 Oct;100(4) :319-334). We assessed our lipidated PTH analogs for inducing receptor internalization using HEK293 cells stably expressing a PTH1 R derivative, PHL2-PTH1 R, containing a pH- sensitive GFP inserted into the ECD (GPG-10 cells), which permit the monitoring of ligand-induced PTH1 R trafficking into acidic endosomes as a time-dependent increase in GFP fluorescence (Sato et al., JBMR Plus. 2021 May 6;5(5):e10441). Both K13(R)palm-PTH(1-13) and Palm-M-PTH(1-14) dose- dependently induced internalization of the PHL2-PTH1 R into such acidic compartments, and these responses were inhibited by the dynamin GTPase inhibitor, Dyngo4A, consistent with a dynamin / clathrin- coated pit-mediated process of receptor internalization (FIGS. 11A-11 B). As expected, a PTHrP(7-36) antagonist peptide did not induce internalization. The internalization responses induced by K13(R)palm- PTH(1-13) at sub-micromolar concentrations were significantly weaker than those induced by Palm-M- PTH(1-14), suggesting a possible inhibitory effect of the lipid at position 13 on the internalization process.

[0266] Fluorescent microscopy imaging analysis performed in HEK293 cells stably expressing barrestin2yfpand transiently transfected with the PTH1 R revealed that by 30 minutes after addition, K13(R)palrn-PTH(1-14)tmr, formed clusters that colocalized with barrestin2yfpand were presumably located in endosomes with the PTH1 R, as also seen with non-lipidated PTH(1-34)tmrand M-PTH(1-14)tmr(FIG. 11C). The lipidated PTH(1-14) analog thus retains the capacity to recruit barrestin2 to the receptor.

[0267] Effects of lipidated PTH peptides on bone metabolism in humanized PTH1 R mice.

[0268] The positive results obtained with the lipidated N-terminal PTH peptides in cells encouraged us to evaluate these peptides for effects on calcium and bone physiology in vivo. We first assessed the capacity of K11(r)palm-PTH(1-11) to increase blood ionized calcium levels after a single acute injection in five-month-old male humanized PTH 1 R mice (Daley et al., Endocrinology. 2022 Jul 1 ;163(7):bqac054). The results shown in FIG. 12A demonstrate that whereas injection of non-lipidated M-PTH(1-11) had no effect on blood calcium, injection of K11(r)palm-PTH(1-11) resulted in an increase in serum calcium that was at least as robust and prolonged as that induced by PTH(1 -34) injected at the same peptide dose of 50 nmol / kg.

[0269] We then assessed the lipidated PTH peptides for longer-term effects in vivo by performing repeated daily injection studies. Repeated daily injections of PTH(1 -34) in humans and animals is well known to result in pronounced changes in bone metabolism and bone structure through direct effects on osteoblasts coupled with indirect effects on osteoclasts (Martin et al., Endocr Rev. 2021 Jul 16;42(4):383- 406), but shorter-length N-terminal peptides have so far been found to be inactive in vivo33. For the current studies, we injected five-month-old male humanized PTH1 R mice (Daley et al., Endocrinology. 2022 Jul 1 ;163(7):bqac054) with three lipidated PTH peptides that are predicted to function via three distinct modes of action: 1) K11(r)palm-PTH(1-11) as a lipidated N-terminal peptide that mediates potent and prolonged signaling actions via in-situ membrane anchoring; 2) K11(R)dioic-PTH(1-11) as a peptide of similar structure and acute cAMP signaling potency, but deficient in prolonged signaling due to a polar lipid substituent, and 3) Palm-PTH(1-34) as a full-length peptide with prolonged actions in vivo due to extended pharmacokinetics via albumin binding. Control mice were injected with unmodified PTH(1 -34) and vehicle. Peptides were injected at a dose of 50 nmol / kg / day, or, for K11(R)dioic-PTH(1-11), at a dose of 500 nmol / kg / day. We note that in a prior pilot experiment, we injected mice with K11(r)palm-PTH(1 -11) at dose of 500 nmol / kg / day and observed excessive hypercalcemia after 3-4 days of injection, and so a 50 nmol / kg / day dose was selected for that peptide in the current experiment, as also guided by the positive calcemic response induced by the peptide at a dose of 50 nmol / kg in the single injection experiment presented in FIG. 12A. We also note that the polar end group of the diacid C18 chain in K11(R)dioic-PTH(1-11) is not expected to result in a substantial difference in peptide pharmacokinetics as compared to that of K11(r)palm-PTH(1-11) containing the fully apolar palmitoyl C16 chain, given the similar sizes of the two acyl chains and their likely similar affinities for binding albumin (Knudsen et al., Front Endocrinol. 2019 Apr 12:10:155; Knudsen et al., J Med Chem. 2000 May 4;43(9):1664-9). The mice were injected daily for three weeks and 24 hours after the last injection were humanely euthanized, and bone and blood samples were collected for analysis. Compared to vehicle-injection controls, body weights remained unchanged after peptide analog injection (FIG. 12B). Microcomputed tomography (mCT) analysis of the isolated femurs revealed that injection of either

[0270] K11(r)palm-PTH(1-11) or Palm-PTH(1-34) resulted in profound increases in trabecular bone mass in the distal metaphyses, indicated by quantitatively significant increases in trabecular bone volume fraction (Tb.BV / TV), bone mineral density (Tb.BMD), and the number of bone trabeculae (Tb.N.) that were at least as substantial as those observed with PTH(1-34), whereas injection of K11(R)dioic-PTH(1-11) resulted in no significant increase in these parameters despite being injected at a dose 10-fold higher than that used for the other peptides (FIGS. 13A-13B, FIGS. 12C-12E, Table 9).

[0271] Table 9. uCT analysis of mouse femurs after 3-weeks of daily injection

[0272] uCT in the distal trabecular and midshaft areas of femurs from 5-month old male humanized PTH1 R mice after 3-weeks daily injection with vehicle or peptide doses of 50 nmol / kg / day or 500 nmol / kg / day (K(R)dioic-PTH(1-11). Mean±SD; n=5; Pavs vehicle, Pbvs PTH(1-34) One-Way ANOVA with Dunnett's comparison test. Low-density woven bone was excluded in the analysis of cortical bone thickness and porosity.

[0273] Histological sections of the distal femur stained with trichrome to show mineralized tissue (bluegreen) revealed marked increase in trabecular bone in the bones of mice injected with Palm-PTH(1 -34) or K11(r)palm-PTH(1 -11), as compared to those injected with vehicle, PTH(1 -34) or K11(R)dioic-PTH(1 -11) (FIG. 14).

[0274] In the area of the femur mid-shaft, which is normally comprised mostly of high-density cortical bone, the mCT radiographs revealed that injections of either K11(r)palm-PTH(1-11) or Palm-PTH(1 -34) resulted in marked accumulations of what appeared to be low-density woven bone on the inner as well as our surfaces of the mid-shaft wall (FIG. 13A). The markedly irregular contours of the mineralized bone in this region led us to limit our quantitative analyses at the mid-shaft to only the higher-density cortical bone areas. These analyses indicated significant increases in cortical bone porosity with injection of PTH(1 -34), K11(r)palm-PTH(1 -11) or especially Palm-PTH(1-34), relative to vehicle-injected controls, and no change with K11(R)dioic-PTH(1-11), as well as moderate decreases in cortical thickness with injection of Palm- PTH(1-34) or K11(r)palm-PTH(1-11) although the effect on thickness was significant with only the latter peptide (FIGS. 12C-12E, Table 9).

[0275] Despite the apparent irregularities in certain bone structural properties, injection of Palm-PTH(1 - 34) or K11(r)palm-PTH(1-1 1) resulted in significant increases in the mechanical strength of the femurs, as assessed by the work-to-fracture as well as the toughness-to-fracture under a three-point bending load (FIG. 13C, FIGS. 12F-12H). These increases in the bone-strength parameters observed for Palm-PTH(1- 34) and K11(r)palm-PTH(1 -11) were comparable to those observed for PTH(1-34) (P >0.05), although only PTH(1-34) significantly increased bending rigidity (FIGS. 12F-12H). Injection of K11(R)dioic-PTH(1 -11) had little or no effect on any bone structural parameter. The effects of Palm-PTH(1-34) and K11(r)palm- PTH(1-11) on bone toughness and resistance to fracture seem to parallel the increases in the trabecular bone structural parameters at the distal femur as assessed by mCT (FIGS. 13A-13B, FIGS. 12C-12H) and by histology (FIG. 14). The difference in the effects of Palm-PTH(1-34) and K11(r)palm-PTH(1-11) vs. PTH(1-34) on mechanical bending rigidity, on the other hand, might be related to the differences in the effects of the peptides on cortical bone structural properties at the mid-shaft, as the quantitative mCT data indicated that the two lipidated peptides induced significantly greater increases in cortical porosity at this site as compared to PTH(1-34) (FIGS. 12C-12E and Table 9).

[0276] Measurements of serum collected 24 hours after the last injection showed that relative to the levels in vehicle-injected mice, total serum calcium was modestly yet significantly increased with injection of Palm-PTH(1-34) but not with the other peptides, while serum phosphorus levels were not changed in any peptide-injected group (FIG. 15). In parallel with the marked changes in bone structure, serum levels of CTX1 and the bone formation marker, P1 NP, were significantly elevated in mice injected with either K11(r)palm-PTH(1-11) or Palm-PTH(1-34), while PTH(1-34) injection significantly increased P1 NP but not CTX1 , and no change in these markers occurred in mice injected with K11(R)dioic-PTH(1-11) (FIG. 15).

[0277] We performed a similar 3-week injection experiment in five-month-old male humanized PTH1 R mice to assess K13(r)palm-PTH(1-13) and Palm-M-PTH(1-14) along with M-PTH(1-14), PTH(1-34) and vehicle injection as controls. In this experiment, Palm-M-PTH(1-14) and K13(r)palm-PTH(1-13) were each injected at a dose of 500 nmol / kg / day, while PTH(1-34) was injected at a dose of 50 nmol / kg / day. Bone and blood samples were analyzed at the study end point, as described in the experiment above. MicroCT analysis of the isolated femurs revealed that injection of K13(r)palm-PTH(1-13) or Palm-M-PTH(1-14) resulted in marked increases in trabecular bone mass in the distal metaphyses, as well as dramatic accumulations of low-density woven bone on the endocortical surfaces at the mid-shaft while M-PTH(1- 14) resulted in little or no change in these parameters (FIGS. 16A-16D). Palm-M-PTH(1-14) also induced marked accumulations of woven bone mass on the periosteal bone surfaces.

[0278] Histological analysis of the proximal tibiae confirmed that injection of either K13(r)palm-PTH(1-13) or Palm-M-PTH(1-14) led to dramatic increases in bone mass as well as in fibrotic tissue surrounding the bone that together ultimately filled much of the marrow cavity area under the growth plates (FIGS. 16E- 16F). These changes in bone structure seen in the mice injected with K13(r)palm-PTH(1-13) and Palm-M- PTH(1-14) were paralleled by significant increases in serum levels of P1 NP, which were unchanged in mice injected with non-lipidated M-PTH(1-14) (FIGS. 16G-16H). Mechanical testing analysis revealed a moderate increase in the work to ultimate moment parameter with injection of K13(r)palm-PTH(1-13). These also revealed a decrease in bending rigidity and an increase in the toughness with injection of Palm-M-PTH(1-14), which paralleled the decrease in cortical bone thickness, the increase in cortical bone porosity, and the increase in woven bone that were apparent in the mCT data and images obtained for the bones of mice treated with this Palm-M-PTH(1-14) analog.

[0279] Discussion

[0280] Our data demonstrate that lipidation can be an effective means to alter the actions of PTH peptide ligands in vivo.

[0281] Our current results indicate that lipidation is also an effective strategy for prolonging and enhancing the actions of short N-terminal PTH(1-14) or even PTH(1-11) analogs in vivo and provide evidence support that the enhancing effects might occur through two distinct mechanisms - effects on PK via binding to serum albumin and effects on receptor engagement via lipid interactions with the plasma membrane - depending on the nature and position of the lipid appendage employed.

[0282] To specifically extend the PK properties of PTH analogs we employed the C-terminal lipidated hepta-residue tag motif, EYEK(palm)EYE. We established that this C-terminal addition on PTH(1-34) largely preserves signaling potency in cells and sustains the calcemic and hypophosphatemic responses in normal mice as well as provides for sustained normalization of blood calcium in a parathyroidectomized mouse model of surgical hypoparathyroidism. In support of an effect on pharmacokinetics, we showed that the lipidated Palm-PTH(1-34) analog persists in the blood after SC injection with a half-life at least six-times longer than that of PTH(1-34). We also showed that fluorescent Palrn-PTH(1-34)tmranalog appeared in the urine at a much slower rate and in lower total abundance after SC injection than did PTH(1-34)tmr, confirming a delayed rate of renal clearance for the lipid-modified peptide.

[0283] We further confirmed using BLI spectroscopy that the EYEK(palm)EYE motif in Palm-PTH(1-34) as well as in Palm-M-PTH(1-14) promoted binding to serum albumin, as compared to the corresponding non-lipidated peptide which exhibited only weak if any binding. Together, our in vitro and in vivo data strengthen the notion that C-terminal lipidation of PTH(1 -34) and C-terminally shortened peptide analogs can be an effective strategy for prolonging PTH1 R agonist peptide action in vivo and potentially for developing new ligands as therapeutics for hypoparathyroidism.

[0284] We found our observations apply to the shorter-length N-terminal PTH fragment peptides, M- PTH(1-14) and M-PTH(1 -11), which represent minimized agonist probes that bind only to the receptor's TMD region, unlike PTH(1-34) which binds to both the ECD and TMD regions, as typical for each endogenous peptide hormone that binds to a class B GPCR. M-PTH(1-14) and M-PTH(1-11) analogs contain up to six affinity- and / or cAMP signaling-enhancing amino acid substitutions that cumulatively result in cAMP-signaling potencies in cells comparable to that of PTH(1 -34). We showed that linking the EYEK(palm)EYE motif to the C-terminus of M-PTH(1-14) can confer activity in vivo, as Palm-M-PTH(1 - 14) upon IV injection in mice induced elevations in serum calcium that were even more robust and more prolonged than those induced by an equivalent dose of PTH(1 -34), whereas M-PTH(1-14) was, as predicted, without effect.

[0285] We also showed that this C-terminal modification did not interfere with the cAMP signaling potency of M-PTH(1-14) as assessed in the Ligand-on format. I ntriguingly , however, we observed that the signaling response was considerably prolonged after ligand washout, as compared to that of M-PTH(1- 14), which suggested the possibility that the lipid appendage on Palm-M-PTH(1-14) could act to anchor the ligand to the cell membrane and thereby prevent its removal during rinsing and facilitate its diffusion to the receptor.

[0286] We then considered the possibility that a lipid moiety appended to a PTH(1 -14) peptide at a certain position might provide a membrane-anchoring effect to stabilize the ligand-receptor complex in a productive geometry that leads to prolonged signaling.

[0287] We tested our membrane-anchoring hypothesis by synthesizing a series of N-terminal PTH peptides containing a lipid moiety appended to a C-terminal lysine located at position 11 , 12 or 13 at the end of the peptide chain. By having the lipid attached to a sidechain at one of these three positions we sought to probe different projection angles for the lipid according to a 100° rotation per residue along the alpha-helix axis such that the lipids at position 11 and 13 would project towards gaps located at opposing ends of the upper portion of the receptor's TMD pocket, whereas the lipid at position 12 would clash with the inner wall of the pocket (FIGS. 8A-8B). The functional data we obtained with these peptides in cells are fully consistent with these predictions. Thus, K11(R)palm-PTH(1-11) and K13(R)palm-PTH(1-13) each exhibited a potency for stimulating cAMP formation in SGS-72 cells that was about 10-fold greater than that of K12(R)palm-PTH(1 -12), as measured during the Ligand-on phase, and the difference was about 20-fold when measured during the washout phase. The signaling potencies of K11(R)palm-PTH(1-11) and K13(R)palm-PTH(1 -13) were thus largely maintained after the washout step, whereas that of the non- lipidated M-PTH(1 -14) parent peptide was reduced by ~200-fold as compared to the potencies measured in the Ligand-on phase.

[0288] We further showed that K11(R)dioic-PTH(1-11) and K13(R)dioic-PTH(1-13) containing a lipid chain with a terminal polar group were at least 20-fold less effective at maintaining signaling after washout than their respective counterpart peptides containing a fully apolar palmitoyl lipid chain. The overall results thus support our hypothesis that a lipid appended to the side chain at position 11 or 13 in an N-terminal PTH peptide can prolong signaling e.g. by anchoring the peptide to the plasma membrane as it is bound to the receptor's orthosteric pocket. Moreover, the potency of each of these peptides for stimulating cAMP signaling in cells expressing the GLP1 R or GCGR was at least 1 ,000-fold greater than that of the corresponding non-lipidated peptide, supporting the model by which the lipids help stabilize a productive interaction with the target receptor.

[0289] For our PTH peptides, we showed that an Arg or dArg is more compatible with function than is a Glu or dGlu as a spacer for linking the fatty acid to the peptide via the side chain amine of a lysine at position 11 or 13.

[0290] We note that animal body weights were maintained over the course of 3-weeks of daily injection, except with Palm-M-PTH(1-14) at dose of 500 nmol / kg), for which weights decreased by week 3 (FIG. 161). This reduction in body weight could be due to transient hypercalcemia that occurs from excess PTH1 R signaling in bone and or kidney cells after each injection, although blood total calcium levels in this group were normal by 24 hours after the last injection (FIG. 16G).

[0291] Our study demonstrates that lipidation can be an effective strategy for enhancing the efficacy in vivo of even minimized PTH agonist peptides.

[0292] In summary, we showed that signaling and biological actions of PTH(1 -34) and shorter-length peptides, including M-PTH(1-11) in cells and in mice can be profoundly enhanced by peptide side chain lipidation. While an appended lipid modification could impact peptide hormone function by several different routes, we presented evidence in support of two distinct modes of action, as determined by the configuration of the lipid appendage. We thus showed that attachment of a previously reported EYEK(palm)EYE motif to the C-terminus of PTH(1 -34) as well as to that M-PTH(1 -14) prolongs the calcemic response induced upon single injection of the ligand into mice, likely via a mechanism involving a reduced rate of renal clearance due to enhanced association with serum albumin. We also showed that lipid modification at position 11 or 13 in M-PTH(1-14) and even a PTH(1-11) peptide, prolongs the cAMP signaling responses induced by those ligands in cells, and greatly augments the impact that the peptides have on bone metabolism upon repeated daily injection into mice, via a mechanism proposed to involve in situ anchoring of the peptide to the plasma membrane as the ligand is bound to the receptor. While additional work is needed to determine, for example, the high-resolution molecular structure of a lipidated PTH ligand-PTH1 R complex and to thus help evaluate the proposed modes of action on the receptor, as well to help further define the effects that these ligands have on bone and calcium metabolism in vivo and hence their potential therapeutic utility towards diseases such as hypoparathyroidism and osteoporosis, our current studies should help prompt such further efforts aimed in these new directions.

[0293] The above results were obtained using the following materials and methods. Methods

[0294] Peptides and reagents

[0295] Peptides were synthesized at the Massachusetts General Hospital Biopolymer Core facility. Solid-phase peptide synthesis was performed in a microwave synthesizer or manually using Fmoc / tBu chemistry with H-Rink amide ChemMatrix resin and Oxyma / DIC-mediated coupling. Site-specific addition of either a palmitoyl (palm, C16H31O) or octadecanedioic acid (dioic, C18H33O3) group to the free amine of either a lysine side chain or the alpha amino of an N-terminal amino acid was performed on the peptide resin after removal of the orthogonal protection group. Fluorescent ligand analogs were derived by covalently linking tetramethyl rhodamine (tmr) to the free amine of a lysine side chain. Peptide sequences are shown in the corresponding figures.

[0296] Plasmids and cell lines

[0297] Functional assays were performed in stably transfected cell lines derived from HEK-293 cells (ATCC Cat. # CRL-1573) and expressing the giosensor cAMP reporter (plasmid p22f, Promega) along with either the human PTHR1 (GP-2.3 cells), pHL2-hPTHR1 , in which pHluorin2, a pH-sensitive GFP variant, is inserted into the E2 region of the hPTHI R's ECD (GPG-10 cells), PTHRI -delNt^P, in which the receptor's N-terminal extracellular domain (ECD) is replaced by yellow fluorescent protein (GD-5y cells), or p-Arrestin2yfp(GBR-24 cells). Assays were also performed in SGS-72 cells, which are derived from the human osteoblastic cell line Saos-2 (ATCC Cat. # HTB-85) and stably express giosensor.

[0298] Giosensor cAMP assays cAMP assays were performed in cell lines stably expressing the giosensor cAMP reporter (Portales-Castillo et al., Commun Biol. 2023 Jun 2;6(1):599). Confluent cell monolayers in 96-well white plates were rinsed with CO2-independent medium (ThermoFisher Cat # 18045088) containing BSA (sigma A8412) at 0.1 % w / v (CIDB), and then loaded with luciferin (Biotium) at 0.5 mM in CIDB (CIDB- Luc) for 30 minutes then treated with test ligands in CIDB and luminescence signals were recorded in an Envision plate reader (PerkinElmer, Waltham, MA, USA) at 60-second repeat cycles for 30 minutes (Ligand-on phase), then rinsed twice with CIDB, and after adding fresh CIDB-Luc, luminescence was again recorded for 90 minutes (washout phase). Peak luminescence signals, which typically occurred at 10-15 minutes after ligand addition, or the AUCs of time vs. luminescence plots were plotted vs. ligand concentration to derive potency curves.

[0299] Receptor internalization in GPG-10 cells

[0300] Ligand-induced PTH1 R internalization responses were assessed in GPG-10 cells (HEK293 cells stably expressing pHL2-PTH1 R containing a pH-sensitive GFP in the ECD) (Sato et al., JBMR Plus. 2021 May 6;5(5):e10441). These cells permit detection of receptor internalization to acidic endosomes as an increase in GFP fluorescence at 535 nm upon excitation at 485 nm relative to 535 nm fluorescence upon excitation at 405 nm. Confluent cell monolayers in black 96-well plates were rinsed with HANKS balanced salts solution containing bovine serum albumin (0.1 % w / v) and 10 mM HEPES buffer at pH 7.4 (HBSS), then incubated in HBSS for 10 minutes during which fluorescence at 535 nm with alternating excitation at 485 and 405 nm was recorded in the Envision plate reader at 1 minute repeat cycles to establish base line; test peptides were then added and fluorescence was again monitored for 90 minutes. Data were analyzed as a ratio of fluorescence intensities upon excitation at 485 / 405 nm over the course of 90 minutes. AUCs were calculated for the corresponding fluorescence ratio vs. time plots obtained at each ligand concentration. The role of dynamin in the PTH1 R internalization response was assessed by .5 pre-treating the cells with Dyngo4A (SelleckChem Cat# S716) at a concentration of (3x10 M) or with DMSO (0.1 %) as control in HBSS for 30 minutes prior to adding ligand (Portales-Castillo et al., Commun Biol. 2023 Jun 2;6(1):599).

[0301] Fluorescence microscopy analysis of PTHtmranalog internalization and p-arrestin2yfprecruitment

[0302] Ligand-induced recruitment of p-arrestin2vfpwas assessed in GBR-24 cells, which stably express p-arrestin2yfp(Portales-Castillo et al., Commun Biol. 2023 Jun 2;6(1):599). The cells in six-well plates were transiently transfected with plasmid DNA encoding PTH1 R-WT and 24 hours later seeded onto glass coverslips in 6-well plates. At 48 hours post-transfection, the cells were rinsed with HBSS and treated with K13(tmr),Nle821-rPTH(1-34) or K13(R)palm,K14(tmr)-M-PTH(1-14), each at 100 nM, for 30 minutes, then rinsed, fixed with 3.7% paraformaldehyde (Boston BioProducts Cat. No. BM-158) and mounted on a glass microscope slide with EverBrite mounting media (Biotium Cat. No 23002) containing 4',6-diamidino-2-phenylindole (DAPI). Slides were imaged by fluorescence microscopy using a Nikon Eclipse fluorescence microscope equipped with a CCD camera configured with SPOT imaging software. Regions of interest were digitally expanded 3-fold to improve views.

[0303] Biolayer Interferometry (BLI) Analysis of binding to bovine serum albumin (BSA).

[0304] Binding to and dissociation from BSA was assessed for PTH(1 -34), Palm-PTH(1-34), M-PTH(1- 14) and Palm-M-PTH(1-14) by Biolayer Interferometry using a Gator plus 8-channel analyzer (Gator Bio Inc.). The optical biosensor tips (Gator Probe Streptavidin; item No. 160002) were applied and hydrated by immersion for 30 minutes in PBS / 0.05% tween20 (PBST); the tips were then immersed in biotinylated BSA (Pierce ThermoFisher-Cat# 29130) at a concentration of 10 ug / cc (0.14 uM) for 200 s, rinsed in PBST for 30 s, followed by immersion in PBST containing various concentrations (156-5,000 nM) of test peptide for 300 secs (association phase) followed by immersion in PBST for 300 seconds (dissociation phase), during which times the optical signals were recorded and analyzed by the integrated analysis software. The net shifts in wavelength (nm, subtracted for background defined as the endpoint measurement) were plotted as a function of time using Graph Pad Prism. Curves were fit to the data using the Association-Dissociation non-linear regression model in Graph Pad Prism with the following constraints: HotnM = 5,000, Kon and Koff = shared, and TimeO = 300.

[0305] Pharmacology studies in mice.

[0306] All mice were housed in a specific pathogen-free (SPF) facility under controlled environmental conditions (temperature: 20-24°C, humidity: 40-60%) with a 12-hour light / dark cycle. Animals were provided with ad libitum access to autoclaved standard rodent chow and water. Mice were housed in groups of 3-5 five animals in individually ventilated cages (IVCs) containing autoclaved bedding and nesting material. Environmental enrichment, such as nesting material and shelters, was provided in all cages. Mice were treated in accordance with the ethical guidelines adopted by Massachusetts General Hospital, following a protocol approved by the Institutional Animal Care and Use Committee (IACUC) at MGH. Animals were housed in a temperature- and humidity-controlled vivarium with 12 hour day-night light cycles. Intact CD-1 (Charles River Laboratories), PTH-Cre;Rosa-mT / mG mice (Bi et al., J Bone Miner Res. 2016 May;31 (5):975-84) or humanized PTH1 R mice (CD-1 / C57BL / 6) (Daley et al., Endocrinology. 2022 Jul 1 ;163(7):bqac054) were used for PTH analog injection studies. Mice were injected either subcutaneously in the interscapular region or intravenously in the tail, with either vehicle (10 mM citric acid / 150 mM NaCI / 0.05%Tween-80, pH 5.0) or vehicle containing a test PTH peptide formulated to provide a peptide dose ranging from 2 to 500 nmol / kg-body weight; doses are indicated in the figure legends, and were selected based on results of in vitro cAMP signaling assays presented in the figures and tables, as well as the Results of pilot and prior published studies (Noda et al., JBMR Plus. 2020 May 30;4(7):e10367; Bi et al., J Bone Miner Res. 2016 May;31 (5):975-84; Daley et al., Endocrinology. 2022 Jul 1 ;163(7):bqac054).

[0307] Acute calcemic responses in intact CD-1 mice.

[0308] For short-term responses to a single injection, tail vein blood (40-100 ul) was collected 0.5 to 1 hour prior to injection (t=0) and at times from 0.5 to 24 hours after injection into heparinized capillary tubes (MultiCap-S, Siemens Medical Solutions, USA) and ionic calcium was measured directly in whole blood upon collection using a RAPIDLabs model 348 Ca++ / pH analyzer (Siemens Medical Solutions, USA).

[0309] Calcemic responses in Parathyroidectomized (PTX) mice.

[0310] GFP-guided parathyroidectomy or sham surgery was performed on two-month-old PTH- Cre;Rosa-mT / mG mice (Bi et al., J Bone Miner Res. 2016 May;31 (5):975-84). Mice were used for PTH injection studies four days after surgery, by which time the mice exhibited significant hypocalcemia. Blood Ca++concentrations were assessed as described above for intact mice. Mice were euthanized at 24h after the last injection under isoflurane anesthesia, during which blood was collected from the abdominal aorta, transferred to a MiniCollect Blood Collection Tube (Gold Cap 0.8 mL, Greiner Bio-One, Cat# 450472), centrifuged at 8,000xg for 15 minutes at 4°C and the serum supernatant was collected for analysis. Spot urine was collected into microfuge tubes, centrifuged at 8,000xg for 15 minutes at 4°C, and the supernatant was collected.

[0311] Pharmacokinetic studies -

[0312] Blood PTH analog concentrations.

[0313] 10-week old female CD-1 mice were injected SC or IV with PTH(1-34) or Palm-PTH(1-34), each at a dose of 10 nmol / kg-body weight, and at serial time points ranging from 2 minutes to 24 hours postinjection, blood (~15 ul) was collected from the tail vein into glass capillary tubes, transferred to a tube containing protease inhibitor cocktail (Sigma, Cat. No. P8340), centrifuged at 1 ,000xg for 15 minutes at 4°C, and the serum supernatant was analyzed using an ELISA kit specific for human PTH(1 -34) (QuidelOrtho Corp. San Diego, CA USA, Catalog No. 60-3900) calibrated with standard curves generated with dilutions of each corresponding test peptide, PTH(1-34) or Palm-PTH(1-34). Serum peptide concentrations were analyzed graphically as a function of time to derive values of AUC, Cmax (peak y) and Tmax (peak x) and fit to a monophasic decay equation to derive T1 / 2 values.

[0314] Urinary clearance of PTH analogs.

[0315] 10-week-old female CD-1 mice were injected SC injected tetramethylrhodamine (tmr)-labeled PTH(1-34)tmrand Palrn-PTH(1-34)tmrwas assessed by collecting spot urine at serial time points (2 hours to 24 hours) after SC injection of each peptide at a dose of 50 nmol / kg / bodyweight, diluting the urine 1 :7 in HB, and measuring 100 ul of each sample in a black 96-well plate in an Envision plate reader for tmr fluorescence (lex = 531 ±25 nm, lem = 595±60 nm). The fluorescence in urine collected from the mice 0.5 to one hour prior to injection (t=0) was subtracted and the resulting net fluorescence was converted to tmr-peptide concentration using a standard curve formed with the corresponding tmr-labeled peptide.

[0316] Peptide-injection studies in humanized hPTHI R mice.

[0317] Peptide were assessed in five-month-old male humanized PTH 1 R mice (Daley et al., Endocrinology. 2022 Jul 1 ;163(7):bqac054) after a single or repeated daily injection of test peptides. Our previous study in which we generate and characterize these humanized PTH1 R mice shows the basal skeletal phenotype and mineral ion physiology of these mice is not different from that of control wild-type mice (Daley et al., Endocrinology. 2022 Jul 1 ;163(7):bqac054). For short-term responses to a single injection, mice were injected subcutaneously with vehicle or vehicle containing either PTH(1 -34), K11(r)palm-PTH(1 -11) or M-PTH(1-11), each at a peptide dose of 50 nmol / kg body weight and tail vein blood (40-100 ul) was collected 0.5 to 1 hour prior to injection (t=0) and at 1 , 2, 4 and 6 hours after injection into heparinized capillary tubes (MultiCap-S, Siemens Medical Solutions, USA) and ionic calcium was measured directly in whole blood upon collection using a RAPIDLabs model 348 Ca++ / pH analyzer (Siemens Medical Solutions, USA). For repeat injection studies, humanized PTH1 R mice were subcutaneously injected daily with vehicle or vehicle containing either PTH(1 -34), Palm-PTH(1 -34) or K11(r)palm-PTH(1 -11), each at a peptide dose of 50 nmol / kg / injection, or containing K11(R)dioic-PTH(1- 11) at a dose of 500 nmol / kg / injection, for three weeks. At 24h after the last injection, mice were euthanized under isofluorane anesthesia, during which bladder urine and cardiac blood was collected. The blood was collected using a 21 G BD Vacutainer (Becton, Dickinson and Co., Cat No. 368652) into serum blood collection tubes (BD Vacutainer SST, Becton, Dickinson and Co., Cat No. 367986, centrifuged at 8,000xg for 12 minutes at 4°C and the serum supernatant was collected for analysis. Femurs were dissected at necroscopy.

[0318] Assays of biochemical markers in blood and urine

[0319] Plasma, serum and urine samples were measured for total calcium using a Calcium (CPC) LiquiColor Test kit (Stanbio Laboratory, Catalog No. 0150-250) and for inorganic phosphorus (Pi) using a Colorimetric Phosphate Assay Kit (Abeam Waltham, MA 02453, USA; Catalog No. ab65622). Serum or plasma levels of C-terminal telopeptide type I collagen (CTX-1), N-terminal propeptide of type I procollagen (P1 NP) and 1 ,25-dihydroxyvitamin Dj- were measured using EIA kits (Immunodiagnostic Systems Inc., Fountain Hills, AZ, USA; Catalog Nos. AC-06F1 , AC-33F1 and AC-62F1 , respectively). Endogenous PTH in serum was measured using an ELISA kit specific for mouse PTH(1 -84) (QuidelOrtho Corp. San Diego, CA USA, Catalog No. No. 60-2305). Cross-reactivity of the ELISA towards human PTH(1-34) and Palm-PTH(1-34) was <1 / 100,000 the reactivity towards mPTH(1 -84).

[0320] Microcomputed tomography (mCt) and mechanical testing of femurs

[0321] Right femurs were isolated from 5-month-old male humanized PTH1 R mice after 3-weeks of daily injection and stored wrapped in PBS-saturated gauze at -20°C until analysis. Bones were analyzed using a benchtop micro-tomographic imaging system (pCT 40, Scanco Medical AG, Bruttisellen, Switzerland). Samples were scanned with a 10-pm isotropic voxel size, 70 kV peak potential (kVp), 114pA X-ray tube intensity, and 300 ms integration time. Intramedullary trabecular bone and total volume were assessed in the distal femoral metaphysis in a region beginning at the peak of the growth plate and extending proximally 1 .0 mm (100 transverse slices). Parameters at the femoral mid-shaft were assessed in a region spanning 0.5 mm (50 transverse slices) and are reported as the means of the measurements across all slices in the region. Low-density woven bone present at the mid-shaft, which was present in femurs isolated from mice treated with lipidated PTH analogs, was excluded in the analyses of cortical bone thickness and cortical bone thickness.

[0322] After analysis by mCT, the femurs were tested in three-point bending to assess their mechanical properties. Testing was performed using an electrical force materials testing machine (Electroforce 3230, Bose Corporation, Eden Prairie, MN). The bending fixture had a bottom span length of 8 mm. The test was performed with the load point in displacement control moving at a rate of 0.1 mm / sec with force and displacement data collected at 50 Hz. All bones were positioned in the same orientation during testing with the cranial surface resting on the supports and being loaded in tension. Bending rigidity (El, N-mm2), apparent modulus of elasticity (Eapp, GPa), ultimate moment (Muit, N-mm), apparent ultimate stress (oapp, MPa) work to fracture (Wfrac, mJ), and apparent toughness to fracture (Uapp, mJ / mm3) were calculated based on the force and displacement data from the tests and, for apparent material properties, the midshaft geometry, as defined by the minimum moment of inertia (I min) determined by pCT (see equations in FIGS. 12F-12H). Work to fracture, the energy required to cause the femur to fracture, was calculated by finding the area under the force-displacement curve using the Riemann Sum method. Bending rigidity was calculated using the linear portion of the force-displacement curve.

[0323] Statistical analyses

[0324] Statistical analysis was performed by using GraphPad Prism version 8.4.3 for Mac (GraphPad Software, San Diego, CA, USA). Data are presented as the means ± standard error (SE) or standard deviation (SD) of the mean, as indicated in the figure legends. For comparison of two groups, data were analyzed by students two-sided t-test. For comparison of more than two groups, data were analyzed by one-way ANOVA followed by Dunnett’s or Bonferroni’s multiple comparison test, or by two-way ANOVA followed by Fisher's LSD test, as indicated in the figure legends. P values <0.05 were considered statistically significant. Box and whisker plots show individual mouse measurements as points, with whiskers indicating the range, boxes the 25th to 75th percentile, a line indicating the median and a plus indicating the mean.

[0325] Example 2. Oral delivery of parathyroid hormone polypeptide conjugates

[0326] Oral gavage was performed to administer test peptides dissolved in SNAC (Fisher Cat No.

[0327] NC1545578) to 5-month old male humanized PTH1 R mice. Test substances were (1) vehicle (SNAC / H2O) (n=7 mice); (2) PTH(1-34) / SNAC / H2O administered at a dose of 1000 nmol / kg (n=7 mice); and (3) K11(r)palm-PTH(1-11) / SNAC / H2O administered at a dose of 1000 nmol / kg (n=7 mice). Mice were briefly restrained manually and administered the test substance using a sterile, flexible oral gavage needle (20G, 38 mm length, curved, Instech Laboratories) attached to a 1 mL syringe. The dosage volume was calculated based on each animal's body weight and did not exceed 10 mL / kg to avoid gastric distress. Just prior to oral gavage, and at 2, 4, 6 , 8 and 10 hours after oral gavage tail vein blood (~40 ul) was drawn into a heparanized glass capillary tube and measured directly in a Siemens Rapid Lab model 348ex blood analyzer for Ca2+and pH. Animals were monitored closely for signs of distress or adverse effects post-administration. All procedures were performed in accordance with the guidelines of the Institutional Animal Care and Use Committee (IACUC).

[0328] Dose / formulation was based on Leone-Bay et al. Oral Delivery of Biologically Active Parathyroid Hormone Pharmaceutical Research, Vol. 18, No. 7, 2001 , which showed efficacy on bone after 2-month of daily oral gavage of PTH(1-34) at 1 / mg / kg + 4-MOAC (similar to SNAC) at 300 mg / kg in water.

[0329] The peptide dose was 20X 50 nmol / kg based on positive effects of 50 nmol / kg injected subcutaneously in the same hP1 R mice for bone and Ca++ and an expected bioavailability of about 5% for oral delivery.

[0330] Results are shown in FIG. 17. Oral administration of PTH(1-34) resulted in only small increases in blood Ca++ levels over the course of the experiment (0-10 hours), but the levels were not significantly different from the levels in vehicle-control mice (FIG. 17 square vs circle data points). Oral administration of K11(r)palm-PTH(1-11) resulted in noticeably larger increases in blood Ca++ levels, which at the four- hour time point were significantly different from the levels in vehicle-control mice (FIG. 17, triangle vs circle data points). These results thus show that side chain lipidation can be a means to improve the oral bioavailability and hence potency in vivo of even short N-terminal PTH(1-11) peptide analogs that without such a lipid modification would be inactive in vivo.

[0331] Example 3. Potency of lipidated and control peptides for cAMP generation in HEK293 / hPTH1 R / glosensor (GP-2.3) cells.

[0332] This Example describes the potency of lipidated and control peptides for cAMP generation in HEK293 / hPTH1 R / glosensor (GP-2.3) cells.

[0333] FIG. 18A shows results of a representative experiment of selected peptides; cAMP was measured as glosensor-derived luminescence for 20 minutes in the presence of various concentrations of each peptide (Add phase) and for a subsequent 90 minutes after washout of unbound peptide (wash phase) and the area under the curve values of plots of the response at each peptide concentration was derived and plotted vs peptide concentration to obtain dose-response curves, which were fit to a nonlinear equation (slope =1.0). FIG. 18B shows the fit parameters of bottom, top, and pEC50 as means ±SD of values from 5 separate experiments.

[0334] Example 4. Inhibition of PTH(1-34)-stimulated cAMP formation in osteoblastic SaOS2 / glosensor (SGS-72) cells.

[0335] This Example describes inhibition of PTH(1-34)-stimulated cAMP formation in osteoblastic SaOS2 / glosensor (SGS-72) cells.

[0336] Cells were pretreated with a lipidated PTHrP(7-36) antagonist peptide, a non-lipidated PTHrP(7- 36) antagonist peptide, each at varying concentrations, or with vehicle for 15 minutes and then were stimulated with PTH(1-34) agonist at a concentration of 0.3 nM and cAMP was measured as giosensor- derived luminescence for 60 minutes. Results are shown in FIG. 19A. The peak luminescence signal observed at each antagonist concentration was normalized to the signal observed in the absence of antagonist (indicated as -11 on the x axis) and is plotted as a function of antagonist concentration. Line curves were fit to the data using a non-linear regression equation. FIG. 19B shows the corresponding plC50 parameters obtained for the fitted data. Data are means ±SE of values from 5 separate experiments.

[0337] OTHER EMBODIMENTS

[0338] While the invention has been described in connection with specific embodiments thereof, it will be understood that it is capable of further modifications and this application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure come within known or customary practice within the art to which the invention pertains and may be applied to the essential features hereinbefore set forth.

[0339] All publications, patents, and patent applications are herein incorporated by reference in their entirety to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference in its entirety.

[0340] Some embodiments of the technology described herein can be defined according to any of the following numbered embodiments:

[0341] E1 . A conjugate, or a pharmaceutically acceptable salt thereof, comprising a polypeptide and a fatty acid acyl, wherein the polypeptide comprises a sequence of formula (I):

[0342] X01-Val-X03-GIU-lle-Gln-LeU-X08-HiS-Xl0-Xl1-Xl2-Xl3-Xl4-Xl5-Xl6-Xl7-Xl8-Xl9-X20-X21-X22-X23-X24-X25-X26- X27-X28-X29-X30-X31 -X32-X33-X34 (I) , wherein:

[0343] X01 is ACPC, Ala, or Aib;

[0344] X03 is Ser, Aib, or Ala;

[0345] X08 is Met or Nle;

[0346] X10 is Gin or Asn;

[0347] X11 is Lys, Arg, Leu, or hArg;

[0348] X12 is Lys, Ala, Gly, or absent;

[0349] X13 is Lys or absent; X14 is Lys, His, Trp, or absent;

[0350] X15 is Tyr, Leu, or absent;

[0351] X16 is Ala, Asn, or absent;

[0352] X17 is Ser or absent;

[0353] Xis is Vai, Met, or absent;

[0354] X19 is Glu, Arg, or absent;

[0355] X20 is Arg or absent;

[0356] X21 is Nle, Vai, or absent;

[0357] X22 is Gin, Glu, or absent;

[0358] X23 is Trp or absent;

[0359] X24 is Leu or absent;

[0360] X25 is Arg or absent;

[0361] X26 is Lys or absent;

[0362] X27 is Lys or absent;

[0363] X28 is Leu or absent;

[0364] X29 is Gin or absent;

[0365] X30 is Asp or absent;

[0366] X31 is Vai or absent;

[0367] X32 is His or absent;

[0368] X33 is Asn or absent; and

[0369] X34 is Tyr or absent, or a fragment thereof comprising 11 to 15 contiguous amino acid residues, wherein the fatty acid acyl is covalently linked to the side chain amine of a Lys residue at position X11 , X12, or X of the polypeptide by way of an amino acid spacer.

[0370] E2. The conjugate of E1 , wherein the polypeptide is a fragment comprising amino acid residues 1 -11 of formula (I).

[0371] E3. The conjugate of E1 or E2, wherein the polypeptide comprises the sequence of ACPC-Val-Aib- Glu-lle-Gln-Leu-Nle-His-Gln-Lys-NH2(SEQ ID NO: 35).

[0372] E4. The conjugate of E1 , wherein the polypeptide is a fragment comprising amino acid residues 1 -12 of formula (I).

[0373] E5. The conjugate of E1 or E4, wherein the polypeptide comprises the sequence of: ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys-NH2(SEQ ID NO: 36); or ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys-Lys-NH2(SEQ ID NO: 37).

[0374] E6. The conjugate of E1 , wherein the polypeptide is a fragment comprising amino acid residues 1 -13 of formula (I).

[0375] E7. The conjugate of E1 or E6, wherein the polypeptide comprises the sequence of: ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys-NH2(SEQ ID NO: 38); or ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys-Ala-Lys-NH2(SEQ ID NO: 39).

[0376] E8. The conjugate of E1 , wherein the polypeptide is a fragment comprising amino acid residues 1 -14 of formula (I). E9. The conjugate of E1 or E8, wherein the polypeptide comprises the sequence of ACPC-Val-Aib- Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys-Lys-NH2(SEQ ID NO: 40).

[0377] E10. The conjugate of E1 , wherein the polypeptide is a fragment comprising amino acid residues 1 -15 of formula (I).

[0378] E11 . The conjugate of E1 or E10, wherein the polypeptide comprises the sequence of: ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys-Trp-Tyr-NH2(SEQ ID NO: 41); or ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys-Ala-Lys-Trp-Tyr-NH2(SEQ ID NO: 42).

[0379] E12. The conjugate of E1 , wherein the polypeptide is a fragment comprising amino acid residues 1 -34 of formula (I).

[0380] E13. The conjugate of E1 or E12, wherein the polypeptide comprises the sequence of: Ala-Val-Ser-Glu-lle-GIn-Leu-Nle-His-Asn-Lys-Gly-Lys-His-Leu-Ala-Ser-Val-Glu-Arg-Nle-GIn-Trp- Leu-Arg-Lys-Lys-Leu-Gln-Asp-Val-His-Asn-Tyr-NH2(SEQ ID NO: 43); or Ala-Val-Ser-Glu-lle-GIn-Leu-Nle-His-Asn-Leu-Gly-Lys-His-Leu-Ala-Ser-Val-Glu-Arg-Nle-GIn-Trp- Leu-Arg-Lys-Lys-Leu-Gln-Asp-Val-His-Asn-Tyr-NH2(SEQ ID NO: 44).

[0381] E14. The conjugate of any one of E1-E13, wherein the polypeptide is a PTHR1 agonist.

[0382] E15. A conjugate, or a pharmaceutically acceptable salt thereof, comprising a polypeptide and a fatty acid acyl, wherein the polypeptide comprises a sequence of formula (II): Xo7-Xo8-Xo9-Xio-Xii-Xi2-Lys-Xi4-lle-Gln-Asp-Xi8-Arg-Arg-Arg-X22-Trp-Leu-His-X26-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-X36(II), wherein

[0383] X07 is Leu or Lys;

[0384] Xos is Leu, Lys, or Nle;

[0385] X09 is His or Lys;

[0386] X10 is Asp, Lys, Asn, or Gin;

[0387] Xu is Lys or Leu;

[0388] Xi2is Lys or dTrp;

[0389] X14 is Lys, Ser, or Trp;

[0390] Xis is Leu or Ala;

[0391] X22is Phe or Ala;

[0392] X26 is His or Lys; and

[0393] X36 is Tyr or lie; wherein the fatty acid acyl is covalently linked to:

[0394] (a) the side chain amine of a Lys residue at position X7, Xs, X9, X10, Xu , Xi2, Xi3, or Xi4 of the polypeptide by way of an amino acid spacer; or

[0395] (b) the N-terminal amine of the polypeptide.

[0396] E16. The conjugate of E15, wherein the polypeptide comprises the sequence of: Leu-Leu-His-Asp-Leu-Lys-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala- Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 45); Leu-Leu-His-Asp-Leu-dTrp-Lys-Lys-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 46); Leu-Leu-His-Asp-Lys-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 47);

[0397] Leu-Leu-His-Lys-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 48);

[0398] Leu-Leu-Lys-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 49);

[0399] Leu-Lys-His-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 50);

[0400] Lys-Leu-His-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 51);

[0401] Leu-Leu-His-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 52); or

[0402] Leu-Nle-His-GIn-Leu-dTrp-Lys -Trp-lle-GIn-Asp-Ala-Arg-Arg-Arg-Ala-Trp-Leu-His-Lys-Leu-lle-Ala- Glu-lle-His-Thr-Ala-Glu-lle-NH2(SEQ ID NO: 53).

[0403] E17. The conjugate of E15 or E16, wherein the polypeptide is a PTHR1 antagonist or inverse agonist.

[0404] E18. The conjugate of any one of E1-E17, wherein the fatty acid acyl is covalently linked to the side chain amine of a Lys residue of the polypeptide by way of an amino acid spacer, wherein the amino acid spacer is Arg, dArg, Glu, or dGlu.

[0405] E19. The conjugate of any one of E1-E18, wherein the fatty acid acyl is covalently linked to the side chain amine of a Lys residue of the polypeptide through a linker of formula (III):

[0406] »A / W I . wherein X is the amino acid residue side chain of Arg, dArg, Glu, or dGlu, wherein I 1 represents the bond to the side chain amine of the Lys residue, and wherein represents the bond to the carbonyl carbon of the fatty acid acyl.

[0407] E20. The conjugate of any one of E1-E19, wherein the fatty acid acyl is a very long chain fatty acid or a long chain fatty acid acyl.

[0408] E21. The conjugate of any one of E1-E20, wherein the fatty acid acyl is a long chain fatty acid acyl.

[0409] E22. The conjugate of E21 , wherein the long chain fatty acid acyl is palmitoyl.

[0410] E23. The conjugate of E21 , wherein the long chain fatty acid acyl is octadecanedioic acid.

[0411] E24. The conjugate of any one of E1-E23, wherein the polypeptide is covalently linked to an additional moiety.

[0412] E25. The conjugate of E24, wherein the additional moiety is a dye.

[0413] E26. The conjugate of E25, wherein the dye is conjugated to a Lys residue of the polypeptide.

[0414] E27. The conjugate of E24, wherein the additional moiety is a second fatty acid acyl. E28. The conjugate of E27, wherein the second fatty acid acyl is covalently linked to the side chain amine of a second Lys residue of the polypeptide by way of an amino acid spacer.

[0415] E29. The conjugate of E28, wherein the amino acid spacer is Arg, dArg, Glu, or dGlu.

[0416] E30. The conjugate of E28 or E29, wherein the second fatty acid acyl is covalently linked to the side chain amine of a second Lys residue of the polypeptide through a linker of formula (III): wherein X is the amino acid residue side chain of Arg, dArg, Glu, or dGlu, wherein represents the bond to the side chain amine of the second Lys residue , and wherein represents the bond to the carbonyl carbon of the second fatty acid acyl.

[0417] E31 . The conjugate of E27, wherein the second fatty acid acyl is covalently linked to the C-terminus of the polypeptide.

[0418] E32. The conjugate of E31 , wherein the second fatty acid acyl is covalently linked to the C-terminus of the polypeptide through a linker of formula (IV): wherein n is an integer from 0 to 10; each of m and q is an integer from 2 to 5; each AAi and each AA2 is independently a proteinogenic amino acid; and R is a bond to the carbonyl carbon of the fatty acid acyl.

[0419] E33. The conjugate of E32, wherein -C(O)-(AAi)m-NH- in the linker structure is -C(O)-EYE-NH- or -C(O)-SYE-NH-.

[0420] E34. The conjugate of E32 or E33, wherein -(AA2)q in the linker structure is -EYE or -ESE.

[0421] E35. The conjugate of any one of E32-E34, wherein the C-terminus of -(AA2)q is carboxamide.

[0422] E36. The conjugate of any one of E27-E35, wherein the second fatty acid acyl is a very long chain fatty acid or a long chain fatty acid acyl.

[0423] E37. The conjugate of E36, wherein the second fatty acid acyl is a long chain fatty acid.

[0424] E38. The conjugate of E37, wherein the second fatty acid acyl is palmitoyl.

[0425] E39. The conjugate of any one of E1-E14 and E18-E38, wherein the conjugate comprises a sequence of:

[0426] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Glu)palm-NH2(SEQ ID NO: 1); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(dGlu)palm-NH2(SEQ ID NO: 2);

[0427] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-NH2(SEQ ID NO: 3);

[0428] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(dArg)palm-NH2(SEQ ID NO: 4);

[0429] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)dioic-NH2(SEQ ID NO: 5);

[0430] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys(Glu)palm-NH2(SEQ ID NO: 6);

[0431] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys(dGlu)palm-NH2(SEQ ID NO: 7);

[0432] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys(Arg)palm-NH2(SEQ ID NO: 8);

[0433] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys(dArg)palm-NH2(SEQ ID NO: 9);

[0434] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-Lys(TMR)-NH2(SEQ ID NO: 10);

[0435] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)dioic-Lys(TMR)-NH2(SEQ ID NO: 11);

[0436] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Glu)palm-NH2(SEQ ID NO: 12);

[0437] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(dGlu)palm-NH2(SEQ ID NO: 13);

[0438] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)palm-NH2(SEQ ID NO: 14);

[0439] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(dArg)palm-NH2(SEQ ID NO: 15);

[0440] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-Ala-Lys(Arg)palm-NH2(SEQ ID NO: 16);

[0441] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)dioic-NH2(SEQ ID NO: 17);

[0442] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)palm-Lys(TMR)-NH2(SEQ ID NO:

[0443] 18);

[0444] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)dioic-Lys(TMR)-NH2(SEQ ID NO:

[0445] 19);

[0446] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)palm-Trp-Tyr-NH2(SEQ ID NO:

[0447] 20);

[0448] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-Ala-Lys-Trp-Tyr-NH2(SEQ ID NO: 21);

[0449] ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-Ala-Lys-Trp- Tyr(PEG2)EYEK(palm)EYE-NH2(SEQ ID NO: 22);

[0450] Ala-Val-Ser-Glu-lle-Gln-Leu-Nle-His-Asn-Lys(Arg)palm-Gly-Lys-His-Leu-Ala-Ser-Val-Glu-Arg-Nle- Gln-Trp-Leu-Arg-Lys-Lys-Leu-Gln-Asp-Val-His-Asn-Tyr-NH2(SEQ ID NO: 23); or Ala-Val-Ser-Glu-lle-Gln-Leu-Nle-His-Asn-Leu-Gly-Lys(Arg)palm-His-Leu-Ala-Ser-Val-Glu-Arg- Nle-Gln-Trp-Leu-Arg-Lys-Lys-Leu-Gln-Asp-Val-His-Asn-Tyr-NH2(SEQ ID NO: 24).

[0451] E40. The conjugate of any one of E15-E38, wherein the conjugate comprises a sequence of:

[0452] Leu-Leu-His-Asp-Leu-Lys(Arg)palm-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His- Leu-lle-Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 25);

[0453] Leu-Leu-His-Asp-Leu-dTrp-Lys-Lys(Arg)palm-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His- Leu-lle-Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 26);

[0454] Leu-Leu-His-Asp-Lys(Arg)palm-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His- Leu-lle-Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 27);

[0455] Leu-Leu-His-Lys(Arg)palm-Leu-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His- Leu-lle-Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 28); Leu-Leu-Lys(Arg)palm-Asp-Leu-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His- Leu-lle-Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 29);

[0456] Leu-Lys(Arg)palm-His-Asp-Leu-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His- Leu-lle-Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 30);

[0457] Lys(Arg)palm-Leu-His-Asp-Leu-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His- Leu-lle-Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 31); palm-Leu-Leu-His-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu- lle-Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 32);

[0458] Leu-Nle-His-Gln-Leu-dTrp-Lys(Arg)palm-Trp-lle-Gln-Asp-Ala-Arg-Arg-Arg-Ala-Trp-Leu-His-Lys- Leu-lle-Ala-Glu-lle-His-Thr-Ala-Glu-lle-NH2(SEQ ID NO: 33); or Leu-Leu-His-Asp-Leu-dTrp-Lys(Arg)palm-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His- Leu-lle-Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 34).

[0459] E41 . A method of modulating the activity of PTHR1 in a cell, the method comprising contacting the cell with the conjugate of any one of E1-E40 or a pharmaceutical composition thereof.

[0460] E42. A method of agonizing the activity of PTHR1 in a cell, the method comprising contacting the cell with the conjugate of any one of E1-E14 and E18-E39 or a pharmaceutical composition thereof.

[0461] E43. A method of antagonizing or inversely agonizing the activity of PTHR1 in a cell, the method comprising contacting the cell with the conjugate of any one of E15-E38 and E40 or a pharmaceutical composition thereof.

[0462] E44. The method of any one of E41-E43, wherein the cell is a human cell.

[0463] E45. A method of treating a subject having a disease selected from the group consisting of hypoparathyroidism, hyperphosphatemia, osteoporosis, fracture repair, osteomalacia, arthritis, thrombocytopenia, and chronic kidney disease, the method comprising administering to the subject the conjugate of any one of E1-E14 and E18-E39 or a pharmaceutical composition thereof in an amount sufficient to treat said disease.

[0464] E46. A method of treating a subject with a disease or condition associated with PTHR1 signaling overactivity, the method comprising administering to the subject an effective amount of the conjugate of any one of E15-E38 and E40 or a pharmaceutical composition thereof.

[0465] E47. The method of E46, wherein the disease or condition is hypercalcemia, hypophosphatemia, hyperparathyroidism, or Jansen’s metaphyseal chondrodysplasia.

[0466] E48. The method of E47, wherein the hyperparathyroidism is primary hyperparathyroidism or secondary hyperparathyroidism.

[0467] E49. The method of any one of E46-E48, wherein the conjugate or pharmaceutical composition is administered in an amount sufficient to reduce PTHR1 signaling.

[0468] E50. The method of any one of E45-E49, wherein the administering comprises oral, subcutaneous, intravenous, intranasal, transpulmonary, transdermal, or transmucosal administration of the conjugate or pharmaceutical composition to the subject.

[0469] E51 . The method of E50, wherein the administering comprises oral administration of the conjugate or pharmaceutical composition to the subject. Other embodiments are within the following claims.

Claims

CLAIMS1 . A conjugate, or a pharmaceutically acceptable salt thereof, comprising a polypeptide and a fatty acid acyl, wherein the polypeptide comprises a sequence of formula (I): X01-Val-X03-GIU-lle-Gln-LeU-X08-HiS-Xl0-Xl1-Xl2-Xl3-Xl4-Xl5-Xl6-Xl7-Xl8-Xl9-X20-X21-X22-X23-X24-X25-X26- X27-X28-X29-X30-X31 -X32-X33-X34 (I) , wherein:X01 is ACPC, Ala, or Aib;X03 is Ser, Aib, or Ala;X08 is Met or Nle;X10 is Gin or Asn;X11 is Lys, Arg, Leu, or hArg;X12 is Lys, Ala, Gly, or absent;X13 is Lys or absent;X14 is Lys, His, Trp, or absent;X15 is Tyr, Leu, or absent;X16 is Ala, Asn, or absent;X17 is Ser or absent;Xis is Vai, Met, or absent;X19 is Glu, Arg, or absent;X20 is Arg or absent;X21 is Nle, Vai, or absent;X22 is Gin, Glu, or absent;X23 is Trp or absent;X24 is Leu or absent;X25 is Arg or absent;X26 is Lys or absent;X27 is Lys or absent;X28 is Leu or absent;X29 is Gin or absent;X30 is Asp or absent;X31 is Vai or absent;X32 is His or absent;X33 is Asn or absent; andX34 is Tyr or absent, or a fragment thereof comprising 11 to 15 contiguous amino acid residues, wherein the fatty acid acyl is covalently linked to the side chain amine of a Lys residue at position X11, X12, or X of the polypeptide by way of an amino acid spacer.

2. The conjugate of claim 1 , wherein the polypeptide is a fragment comprising amino acid residues 1 -11 of formula (I).

3. The conjugate of claim 1 , wherein the polypeptide comprises the sequence of ACPC-Val-Aib-Glu-lle- Gln-Leu-Nle-His-Gln-Lys-NH2(SEQ ID NO: 35).

4. The conjugate of claim 1 , wherein the polypeptide is a fragment comprising amino acid residues 1 -12 of formula (I).

5. The conjugate of claim 1 , wherein the polypeptide comprises the sequence of: ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys-NH2(SEQ ID NO: 36); or ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys-Lys-NH2(SEQ ID NO: 37).

6. The conjugate of claim 1 , wherein the polypeptide is a fragment comprising amino acid residues 1 -13 of formula (I).

7. The conjugate of claim 1 , wherein the polypeptide comprises the sequence of: ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys-NH2(SEQ ID NO: 38); or ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys-Ala-Lys-NH2(SEQ ID NO: 39).

8. The conjugate of claim 1 , wherein the polypeptide is a fragment comprising amino acid residues 1 -14 of formula (I).

9. The conjugate of claim 1 , wherein the polypeptide comprises the sequence of ACPC-Val-Aib-Glu-lle- Gln-Leu-Nle-His-Gln-hArg-Ala-Lys-Lys-NH2(SEQ ID NO: 40).

10. The conjugate of claim 1 , wherein the polypeptide is a fragment comprising amino acid residues 1 -15 of formula (I).11 . The conjugate of claim 1 , wherein the polypeptide comprises the sequence of: ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys-Trp-Tyr-NH2(SEQ ID NO: 41); or ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys-Ala-Lys-Trp-Tyr-NH2(SEQ ID NO: 42).

12. The conjugate of claim 1 , wherein the polypeptide is a fragment comprising amino acid residues 1-34 of formula (I).

13. The conjugate of claim 1 , wherein the polypeptide comprises the sequence of: Ala-Val-Ser-Glu-lle-GIn-Leu-Nle-His-Asn-Lys-Gly-Lys-His-Leu-Ala-Ser-Val-Glu-Arg-Nle-GIn-Trp-Leu-Arg- Lys-Lys-Leu-Gln-Asp-Val-His-Asn-Tyr-NH2(SEQ ID NO: 43); or Ala-Val-Ser-Glu-lle-GIn-Leu-Nle-His-Asn-Leu-Gly-Lys-His-Leu-Ala-Ser-Val-Glu-Arg-Nle-GIn-Trp-Leu-Arg- Lys-Lys-Leu-Gln-Asp-Val-His-Asn-Tyr-NH2(SEQ ID NO: 44).

14. The conjugate of claim 1 , wherein the polypeptide is a PTHR1 agonist.

15. A conjugate, or a pharmaceutically acceptable salt thereof, comprising a polypeptide and a fatty acid acyl, wherein the polypeptide comprises a sequence of formula (II):Xo7-Xo8-Xo9-Xio-Xii-Xi2-Lys-Xi4-lle-Gln-Asp-Xi8-Arg-Arg-Arg-X22-Trp-Leu-His-X26-Leu-lle-Ala-Glu-lle-His-Thr-Ala-Glu-X36 (II), wherein X07 is Leu or Lys; Xos is Leu, Lys, or Nle; X09 is His or Lys; X10 is Asp, Lys, Asn, or Gin; X11 is Lys or Leu; X12 is Lys or dTrp; X14 is Lys, Ser, or Trp; Xis is Leu or Ala; X22 is Phe or Ala; X26 is His or Lys; and X36 is Tyr or lie; wherein the fatty acid acyl is covalently linked to:(a) the side chain amine of a Lys residue at position X7, Xs, X9, X10, Xu , X12, X13, or Xi4 of the polypeptide by way of an amino acid spacer; or(b) the N-terminal amine of the polypeptide.

16. The conjugate of claim 15, wherein the polypeptide comprises the sequence of:Leu-Leu-His-Asp-Leu-Lys-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu-lle- His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 45);Leu-Leu-His-Asp-Leu-dTrp-Lys-Lys-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 46);Leu-Leu-His-Asp-Lys-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 47);Leu-Leu-His-Lys-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 48);Leu-Leu-Lys-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 49);Leu-Lys-His-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 50);Lys-Leu-His-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 51);Leu-Leu-His-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala-Glu- lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 52); orLeu-Nle-His-GIn-Leu-dTrp-Lys -Trp-lle-GIn-Asp-Ala-Arg-Arg-Arg-Ala-Trp-Leu-His-Lys-Leu-lle-Ala-Glu-lle-His-Thr-Ala-Glu-lle-NH2(SEQ ID NO: 53).

17. The conjugate of claim 15, wherein the polypeptide is a PTHR1 antagonist or inverse agonist.

18. The conjugate of any one of claims 1-17, wherein the fatty acid acyl is covalently linked to the side chain amine of a Lys residue of the polypeptide by way of an amino acid spacer, wherein the amino acid spacer is Arg, dArg, Glu, or dGlu.

19. The conjugate of any one of claims 1-18, wherein the fatty acid acyl is covalently linked to the side chain amine of a Lys residue of the polypeptide through a linker of formula (III):i wherein X is the amino acid residue side chain of Arg, dArg, Glu, or dGlu, wherein* / ww i _ represents the bond to the side chain amine of the Lys residue, and wherein1represents the bond to the carbonyl carbon of the fatty acid acyl.

20. The conjugate of any one of claims 1-19, wherein the fatty acid acyl is a very long chain fatty acid or a long chain fatty acid acyl.

21. The conjugate of any one of claims 1-20, wherein the fatty acid acyl is a long chain fatty acid acyl.

22. The conjugate of claim 21 , wherein the long chain fatty acid acyl is palmitoyl.

23. The conjugate of claim 21 , wherein the long chain fatty acid acyl is octadecanedioic acid.

24. The conjugate of any one of claims 1-23, wherein the polypeptide is covalently linked to an additional moiety.

25. The conjugate of claim 24, wherein the additional moiety is a dye.

26. The conjugate of claim 25, wherein the dye is conjugated to a Lys residue of the polypeptide.

27. The conjugate of claim 24, wherein the additional moiety is a second fatty acid acyl.

28. The conjugate of claim 27, wherein the second fatty acid acyl is covalently linked to the side chain amine of a second Lys residue of the polypeptide by way of an amino acid spacer.

29. The conjugate of claim 28, wherein the amino acid spacer is Arg, dArg, Glu, or dGlu.

30. The conjugate of claim 28 or 29, wherein the second fatty acid acyl is covalently linked to the side chain amine of a second Lys residue of the polypeptide through a linker of formula (III):% / vw I . wherein X is the amino acid residue side chain of Arg, dArg, Glu, or dGlu, wherein1 1i represents the bond to the side chain amine of the second Lys residue , and whereinrepresents the bond to the carbonyl carbon of the second fatty acid acyl.31 . The conjugate of claim 27, wherein the second fatty acid acyl is covalently linked to the C-terminus of the polypeptide.

32. The conjugate of claim 31 , wherein the second fatty acid acyl is covalently linked to the C-terminus of the polypeptide through a linker of formula (IV):wherein n is an integer from 0 to 10; each of m and q is an integer from 2 to 5; each AAi and each AA2 is independently a proteinogenic amino acid; and R is a bond to the carbonyl carbon of the fatty acid acyl.

33. The conjugate of claim 32, wherein -C(O)-(AAi)m-NH- in the linker structure is -C(O)-EYE-NH- or -C(O)-SYE-NH-.

34. The conjugate of claim 32 or 33, wherein -(AA2)q in the linker structure is -EYE or -ESE.

35. The conjugate of any one of claims 32-34, wherein the C-terminus of -(AA2)q is carboxamide.

36. The conjugate of any one of claims 27-35, wherein the second fatty acid acyl is a very long chain fatty acid or a long chain fatty acid acyl.

37. The conjugate of claim 36, wherein the second fatty acid acyl is a long chain fatty acid.

38. The conjugate of claim 37, wherein the second fatty acid acyl is palmitoyl.

39. The conjugate of claim 1 , wherein the conjugate comprises a sequence of: ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Glu)palm-NH2(SEQ ID NO: 1); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(dGlu)palm-NH2(SEQ ID NO: 2); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-NH2(SEQ ID NO: 3); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(dArg)palm-NH2(SEQ ID NO: 4); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)dioic-NH2(SEQ ID NO: 5); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys(Glu)palm-NH2(SEQ ID NO: 6); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys(dGlu)palm-NH2(SEQ ID NO: 7); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys(Arg)palm-NH2(SEQ ID NO: 8); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Lys(dArg)palm-NH2(SEQ ID NO: 9); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-Lys(TMR)-NH2(SEQ ID NO: 10); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)dioic-Lys(TMR)-NH2(SEQ ID NO: 11); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Glu)palm-NH2(SEQ ID NO: 12); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(dGlu)palm-NH2(SEQ ID NO: 13); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)palm-NH2(SEQ ID NO: 14); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(dArg)palm-NH2(SEQ ID NO: 15); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-Ala-Lys(Arg)palm-NH2(SEQ ID NO: 16); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)dioic-NH2(SEQ ID NO: 17); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)palm-Lys(TMR)-NH2(SEQ ID NO: 18); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)dioic-Lys(TMR)-NH2(SEQ ID NO: 19); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-hArg-Ala-Lys(Arg)palm-Trp-Tyr-NH2(SEQ ID NO: 20); ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-Ala-Lys-Trp-Tyr-NH2(SEQ ID NO: 21);ACPC-Val-Aib-Glu-lle-Gln-Leu-Nle-His-Gln-Lys(Arg)palm-Ala-Lys-Trp-Tyr(PEG2)EYEK(palm)EYE-NH2(SEQ ID NO: 22);Ala-Val-Ser-Glu-lle-Gln-Leu-Nle-His-Asn-Lys(Arg)palm-Gly-Lys-His-Leu-Ala-Ser-Val-Glu-Arg-Nle-Gln- Trp-Leu-Arg-Lys-Lys-Leu-Gln-Asp-Val-His-Asn-Tyr-NH2(SEQ ID NO: 23); orAla-Val-Ser-Glu-lle-Gln-Leu-Nle-His-Asn-Leu-Gly-Lys(Arg)palm-His-Leu-Ala-Ser-Val-Glu-Arg-Nle-Gln- Trp-Leu-Arg-Lys-Lys-Leu-Gln-Asp-Val-His-Asn-Tyr-NH2(SEQ ID NO: 24).

40. The conjugate of claim 15, wherein the conjugate comprises a sequence of:Leu-Leu-His-Asp-Leu-Lys(Arg)palm-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 25);Leu-Leu-His-Asp-Leu-dTrp-Lys-Lys(Arg)palm-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 26);Leu-Leu-His-Asp-Lys(Arg)palm-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 27);Leu-Leu-His-Lys(Arg)palm-Leu-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 28);Leu-Leu-Lys(Arg)palm-Asp-Leu-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 29);Leu-Lys(Arg)palm-His-Asp-Leu-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 30);Lys(Arg)palm-Leu-His-Asp-Leu-dTrp-Lys-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 31); palm-Leu-Leu-His-Asp-Leu-dTrp-Lys-Ser-lle-GIn-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle-Ala- Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 32);Leu-Nle-His-Gln-Leu-dTrp-Lys(Arg)palm-Trp-lle-Gln-Asp-Ala-Arg-Arg-Arg-Ala-Trp-Leu-His-Lys-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-lle-NH2(SEQ ID NO: 33); or Leu-Leu-His-Asp-Leu-dTrp-Lys(Arg)palm-Ser-lle-Gln-Asp-Leu-Arg-Arg-Arg-Phe-Trp-Leu-His-His-Leu-lle- Ala-Glu-lle-His-Thr-Ala-Glu-Tyr-NH2(SEQ ID NO: 34).41 . A method of modulating the activity of PTHR1 in a cell, the method comprising contacting the cell with the conjugate of any one of claims 1-40 or a pharmaceutical composition thereof.

42. A method of agonizing the activity of PTHR1 in a cell, the method comprising contacting the cell with the conjugate of claim 1 or a pharmaceutical composition thereof.

43. A method of antagonizing or inversely agonizing the activity of PTHR1 in a cell, the method comprising contacting the cell with the conjugate of claim 15 or a pharmaceutical composition thereof.

44. The method of any one of claims 41-43, wherein the cell is a human cell.

45. A method of treating a subject having a disease selected from the group consisting of hypoparathyroidism, hyperphosphatemia, osteoporosis, fracture repair, osteomalacia, arthritis, thrombocytopenia, and chronic kidney disease, the method comprising administering to the subject the conjugate of claim 1 or a pharmaceutical composition thereof in an amount sufficient to treat said disease.

46. A method of treating a subject with a disease or condition associated with PTHR1 signaling overactivity, the method comprising administering to the subject an effective amount of the conjugate of claim 15 or a pharmaceutical composition thereof.

47. The method of claim 46, wherein the disease or condition is hypercalcemia, hypophosphatemia, hyperparathyroidism, or Jansen’s metaphyseal chondrodysplasia.

48. The method of claim 47, wherein the hyperparathyroidism is primary hyperparathyroidism or secondary hyperparathyroidism.

49. The method of claim 46, wherein the conjugate or pharmaceutical composition is administered in an amount sufficient to reduce PTHR1 signaling.

50. The method of any one of claims 45-49, wherein the administering comprises oral, subcutaneous, intravenous, intranasal, transpulmonary, transdermal, or transmucosal administration of the conjugate or pharmaceutical composition to the subject.

51. The method of claim 50, wherein the administering comprises oral administration of the conjugate or pharmaceutical composition to the subject.

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