RELATED APPLICATION(S)

[0001] This application claims the benefit of U.S. Provisional Application No. 62/884,703, filed on August 9, 2019. The entire teachings of the above application are incorporated herein by reference.

INCORPORATION BY REFERENCE OF MATERIAL IN ASCII TEXT FILE

[0002] This application incorporates by reference the Sequence Listing contained in the following ASCII text file being submitted concurrently herewith:

File name: 57081028001_Sequence_Listing.txt; created August 7, 2020, 57 KB in size.

BACKGROUND

[0003] Parathyroid Hormone Receptor (PTHR or PTH1R, HGNC:9608, human GenelD: 5745, HomoloGene: 267) is a G protein-coupled receptor (GPCR) that is expressed at high levels in bone and kidney and regulates calcium ion homeostasis. PTHR has two natural ligands: parathyroid hormone (PTH) and parathyroid hormone-related peptide (PTHrP). Alterations in PTHR biology play a role in many important diseases, including osteoporosis and other diseases of dysregulated calcium homeostasis. Diseases caused by inactivating mutations in PTHR include, for example, Blomstrand’s lethal chondrodysplasia, Ollier diseases, familial primary failure of tooth eruption, and Eiken syndrome. Diseases caused by imbalances of ligands include brachydactyly type E and hypoparathyroidism. Osteoporosis, an imbalance between bone resorption and bone building processes, is also regulated by signaling through PTHR.

[0004] Therapeutic peptides based on the natural ligands of PTHR have been produced recombinantly and are approved as drugs for the treatment of osteoporosis: teriparatide (corresponding to the amino acids 1-34 of PTH, Eli Lilly) and abaloparatide (amino acids 1-34 of PTHrP, Radius health).

[0005] Despite their FDA approval and clinical use, both natural ligands have severe side effects. Both teriparatide and abaloparatide are marketed with a black-box label warning of the risk of osteosarcoma, and treatment with the drug is not recommended for more than two years over the course of a patient’s lifetime. Additionally, extended exposure to teriparatide often triggers catabolic bone resorption in patients, counteracting the desired outcome of the treatment. Furthermore, these compounds do not address other disorders requiring, for example, antagonist or inverse agonist activity of PTHR.

SUMMARY

[0006] The invention disclosed herein is based, in part, on the discovery that polypeptides of the present invention specifically bind Parathyroid Hormone Receptor (PTHR). Accordingly, the invention generally relates to compositions (e.g., polypeptides, pharmaceutical compositions) and methods that are useful for modulating PTHR-mediated signaling in a cell.

[0007] Provided herein are polypeptides that specifically bind PTHR. In one aspect, the invention provides polypeptides that specifically bind PTHR, wherein the polypeptide comprises a synthetic parathyroid hormone (sPTH).

[0008] In some embodiments, the sPTH comprises a 14-amino acid sequence comprising: a) 1-3 polar residues and, relative to SEQ ID NO: 7, 1-14 amino acid substitutions; b) at least 4 polar residues, at least 1 charged residue, and, relative to SEQ ID NO: 7, 1-14 amino acid substitutions; c) at least 5 polar residues, at least 2 charged residues, and, relative to SEQ ID NO:

7, 1-14 amino acid substitutions; d) at least 5 polar residues, valine at position 2, and, relative to SEQ ID NO: 7, 1-13 amino acid substitutions; or e) at least 6 polar residues and, relative to SEQ ID NO: 7, 1-14 amino acid substitutions.

[0009] In some embodiments, the sPTH comprises a 32-amino acid sequence comprising: a) at most 13 polar residues and, relative to SEQ ID NO: 8, 1-32 amino acid substitutions; b) at least 14 polar residues, valine at position 2, and, relative to SEQ ID NO: 8, 1-31 substitutions; c) at least 14 polar residues and, relative to SEQ ID NO: 8, 22-28 amino acid substitutions; or d) positions 1-14 of SEQ ID NO: 8 and, relative to SEQ ID NO: 5, 1-18 amino acid substitutions at positions 15-32.

[0010] In some embodiments, the sPTH comprises an amino acid sequence having at least about 20% sequence identity to an amino acid sequence selected from SEQ ID NOs: 9- 106 and SEQ ID NOs: 108-160. In some embodiments, the sPTH comprises an amino acid sequence selected from SEQ ID NOs: 9-106 and SEQ ID NOs: 108-160. [0011] In some embodiments, the sPTH comprises an amino acid sequence having at least about 20% sequence identity to an amino acid sequence selected from SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, MO- 143, 145, 147-152, 154, 155 and 157-160. In some embodiments, the sPTH comprises an amino acid sequence selected from SEQ ID NOs: SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160.

[0012] In some embodiments, the sPTH comprises an amino acid sequence having at least about 20% sequence identity to SEQ ID NO: 5.

[0013] In some embodiments, the sPTH comprises an amino acid sequence set forth by SEQ ID NO: 6. In some embodiments, the amino acid sequence set forth by SEQ ID NO: 6 is at the N-terminus of the sPTH. In some embodiments, the sPTH comprises an amino acid sequence having at least about 55% sequence identity to a sequence selected from the group consisting of SEQ ID NOs: 102-106 and SEQ ID NOs: 132-155.

[0014] In some embodiments, the sPTH comprises the amino acid sequence of SEQ ID NO: 107.

[0015] In some embodiments, the sPTH is an agonist of PTHR. In some embodiments, the sPTH is a biased agonist of PTHR. In some embodiments, the sPTH is an inverse agonist of PTHR. In some embodiments, the sPTH is an antagonist of PTHR.

[0016] In some embodiments, the polypeptides of the invention are fusion proteins.

[0017] In other aspects, the invention provides a polynucleotide encoding a polypeptide disclosed herein, a vector comprising such polynucleotide, and a host cell comprising such polynucleotide or vector.

[0018] In another aspect, the invention provides a method of modulating PTHR signaling in a mammalian cell, comprising contacting the mammalian cell with an effective amount of a polypeptide disclosed herein or a composition (e.g., pharmaceutical composition) comprising a polypeptide disclosed herein.

[0019] In another aspect, the invention provides a method of treating a subject in need thereof (e.g., a subject having Osteoporosis), comprising administering to the subject an effective amount of a polypeptide disclosed herein or a composition (e.g., pharmaceutical composition) comprising a polypeptide disclosed herein.

[0020] In another aspect, the invention provides a method of modulating PTHR signaling in a subject in need thereof (e.g., a subject having Osteoporosis), comprising administering to the subject an effective amount of a polypeptide disclosed herein or a composition (e.g., pharmaceutical composition) comprising a polypeptide disclosed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments.

[0022] FIG. 1 depicts results of the b1-arrestin recruitment assay.

[0023] FIG. 2 depicts results of the b2-arrestin recruitment assay.

[0024] FIG. 3 depicts results of the cAMP accumulation assay.

DETAILED DESCRIPTION

[0025] A description of example embodiments follows.

[0026] There is a need for novel ligands to PTHR that can modulate PTHR activity. The invention provides, inter alia , synthetic parathyroid hormones (sPTHs) that can modulate the activity of PTHR, as well as conjugates (e.g., comprising a heterologous moiety), fusion proteins, and compositions comprising the sPTHs, nucleic acids encoding the sPTHs, as well as methods of using the sPTHs, e.g., to modulate PTHR activity, for example, to treat disorders of calcium homeostasis and/or PTHR signaling.

PTH and related peptides

[0027] The native ligand of PTHR, PTH (HGNC: 9606), is a secreted peptide hormone that binds to PTHR. The peptide is comprised of a signal sequence and a pro-peptide fold that is cleaved, leaving an 84-amino acid active molecule (amino acids 32-115). The bioactive sequence for PTH is provided as SEQ ID NO: 1 (Table 1). A review of the biology of PTHR and its role in disease can be found in: Cheloha et al ., Nature Reviews Endocrinology 11(12): 712-24 (2015). [0028] A second native ligand of PTHR, PTHrP (HGNC: 9607), is a secreted peptide hormone that binds to PTHR. The peptide is comprised of a signal peptide, a pro-peptide, and a long chain that is endoproteolytically cleaved into three principal secretory forms, called PTHrP [1-36], PTHrP[38-94], and osteostatin (PTHrP[107-139]). The full sequence of PTHRrP is provided as SEQ ID NO: 2 (Table 1).

[0029] It is known from experimental results that the N-terminal 14 amino acids of PTH, PTH[1-14], engages with the receptor and drives signaling, whereas the C-terminal 20 amino acids, PTH[ 15-34], binds to the extracellular domain of PTHR and confers some amount of receptor specificity (Pioszak & Xu, ProcNatl Acad Sci U S A. 105(13): 5034-39 (2008); Pioszak etal, J Biol Chem. 284(41): 28382-91 (2009)).

[0030] The sequence of the therapeutic peptide teriparatide, corresponding to amino acids 1- 34 of the native ligand PTH is provided as SEQ ID NO: 3 (Table 1).

[0031] The sequence of the therapeutic peptide abaloparatide is provided as SEQ ID NO: 4 (Table 1), and corresponds to the first 20 amino acids of the native ligand PTHrP. Residues 21- 34 have 50% diversity to the C-terminal 14 amino acids of PTHrP, including the unnatural amino acid 2-aminoisobutyric acid (annotated as “X”).

[0032] The structure of PTHR was recently solved in complex with a peptide ligand, LA- PTH, that is a hybrid of PTH and PTHrP. See Zhao LH et al. , Science 364: 148-53 (2019). The sequence of the 32-mer LA-PTH is provided as SEQ ID NO: 5, and the N-terminal 14-mer of LA-PTH is provided as SEQ ID NO: 6 (Table 1).

[0033] Consensus sequences encompassing the foregoing PTH and PTHrP sequences are provided in SEQ ID NO: 7 and SEQ ID NO: 8 (Table 1).

Table 1 sPTHs provided by the invention

[0034] In one aspect, the invention provides a polypeptide that specifically binds PTHR, wherein the polypeptide comprises a synthetic parathyroid hormone (sPTH).

[0035] A “synthetic parathyroid hormone” or “sPTH” or “sPTH(s) provided by the invention” and the like refers to a polypeptide that binds the PTHR, comprises an amino acid sequence similar in size to the bioactive portion of the mature PTH peptide, and does not comprise, consist of, or consist essentially of the amino acid sequence of wild-type PTH (SEQ ID NO: 1), wild-type PTHrP (SEQ ID NO: 2), teriparatide (FORTEO ^® ; SEQ ID NO: 3), abaloparatide (TYMLOS ^® ; SEQ ID NO: 4), or “long acting” PTH (N-terminal 32-mer (SEQ ID NO: 5) or N-terminal 14-mer (SEQ ID NO:6)).

[0036] In certain embodiments, the sPTH provided by the invention does not comprise, consist of, or consist essentially of a consensus amino acid sequence set forth in SEQ ID NO: 7, SEQ ID NO: 8, and/or SEQ ID NO: 107. In some embodiments, the sPTH of the invention does not comprise, consist of, or consist essentially of an amino acid sequence disclosed in US 6,921,750, US 7,803,770, and/or WO/2000/010596. In some embodiments, the sPTH of the invention comprises, consists essentially of, or consists of an amino acid sequence encompassed by the consensus sequence of SEQ ID NO: 7, SEQ ID NO: 8 or SEQ ID NO: 107, and meeting one or more criteria set forth in Table 2. In some embodiments, the sPTH comprises the amino acid sequence of SEQ ID NO: 7. In some embodiments, the sPTH comprises the amino acid sequence of SEQ ID NO: 8. In some embodiments, the sPTH comprises the amino acid sequence of SEQ ID NO: 107.

Table 2. Categorizing Non-Limiting Examples of sPTH Polypeptides of the Invention

[0037] “Polar” amino acid residues include basic, acidic and hydrophilic but uncharged canonical amino acids and non-canonical amino acids. In certain embodiments, the polar residue is a canonical amino acid, e.g., basic (K, R, H), acidic (D, E) or hydrophilic but uncharged (S, T, N, Q, C). In some embodiments, the polar residue is a non-canonical amino acid.

[0038] “Charged” residues include basic and acidic canonical amino acids and non-canonical amino acids. In some embodiments, the charged residue is a canonical amino acid, e.g., basic (K, R, H) or acidic (D, E). In some embodiments, the charged residue is a non-canonical amino acid. [0039] In some embodiments, the sPTH of the invention comprises, consists essentially of, or consists of an amino acid sequence selected from SEQ ID NOs: 9-106 and 108-159 (Table 3), or a variant thereof.

[0040] Table 3. Non-Limiting Examples of sPTH Polypeptides of the Invention

[0041] A “variant of a sPTH” polypeptide (e.g., a “variant” in reference to a sPTH), and the like, comprises an amino acid sequence with, for example, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, or 14 amino acid substitutions (or more, in the case of longer sequences, such as 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, or 31) relative to a reference sequence (e.g, one of SEQ ID NOs: 9-107 or 108-160). In certain embodiments, a variant of an sPTH provided by the invention includes up to 1, 2, 3, 4, 5, 6, or 7 amino acid substitutions, e.g., 1-3 amino acid substitutions. A variety of amino acid substitutions for variants of a sPTH provided by the invention are possible, including substitution with non-canonical amino acids. Non-limiting examples of non-canonical amino acids include the D-isomers of any canonical amino acid (e.g., D-alanine), selenocysteine, pyrrolysine, b-alanine, 4-aminobutyric acid, 6-aminocaproic acid, sarcosine, statine, citrulline, homocitruline, homoserine, norleucine, norvaline, and ornithine. In some embodiments, the amino acid substitution is a conservative amino acid substitution. “Conservative substitutions” relative to a reference sequence means a given amino acid substitution has a value of 0 or greater in BLOSUM62. In some embodiments, the amino acid substitution is a highly conservative amino acid substitution. “Highly conservative substitutions” relative to a reference sequence means a given amino acid substitution has a value of 1 or greater (e.g, in some embodiments, 2, or more) in BLOSUM62.

[0042] In some embodiments, a “variant of a sPTH” polypeptide comprises an amino acid sequence that is at least about 50% identical to a sPTH provided by the invention (e.g., a sPTH of SEQ ID NOs: 9-106 or 108-160 (Table 3)). For example, the variant can be at least about: 50%, 60%, 70%, 71%, 72%, 73%, 74%, 75%, 76%, 77%, 78%, 79%, 80%, 81%, 82%, 83%, 84%, 85%, 86%, 87%, 88%, 89%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98% or 99% identical to a sPTH of any one or more of SEQ ID NOs: 9-106 and 108-160 (Table 3).

[0043] As used herein, the term “sequence identity,” refers to the extent to which two nucleotide sequences, or two amino acid sequences, have the same residues at the same positions when the sequences are aligned to achieve a maximal level of identity, expressed as a percentage. For sequence alignment and comparison, typically one sequence is designated as a reference sequence, to which a test sequences are compared. The sequence identity between reference and test sequences is expressed as the percentage of positions across the entire length of the reference sequence where the reference and test sequences share the same nucleotide or amino acid upon alignment of the reference and test sequences to achieve a maximal level of identity. As an example, two sequences are considered to have 70% sequence identity when, upon alignment to achieve a maximal level of identity, the test sequence has the same nucleotide or amino acid residue at 70% of the same positions over the entire length of the reference sequence.

[0044] Alignment of sequences for comparison to achieve maximal levels of identity can be readily performed by a person of ordinary skill in the art using an appropriate alignment method or algorithm. In some instances, the alignment can include introduced gaps to provide for the maximal level of identity. Examples include the local homology algorithm of Smith & Waterman, Adv. Appl. Math. 2:482 (1981), the homology alignment algorithm of Needleman & Wunsch, J. Mol. Biol. 48:443 (1970), the search for similarity method of Pearson & Lipman, Proc. Nat'l. Acad. Sci. USA 85:2444 (1988), computerized implementations of these algorithms (GAP, BESTFIT, FASTA, and TFASTA in the Wisconsin Genetics Software Package, Genetics Computer Group, 575 Science Dr., Madison, Wis.), and visual inspection (see generally Ausubel et al, Current Protocols in Molecular Biology).

[0045] When using a sequence comparison algorithm, test and reference sequences are input into a computer, subsequent coordinates are designated, if necessary, and sequence algorithm program parameters are designated. The sequence comparison algorithm then calculates the percent sequence identity for the test sequence(s) relative to the reference sequence, based on the designated program parameters. A commonly used tool for determining percent sequence identity is Protein Basic Local Alignment Search Tool (BLASTP) available through National Center for Biotechnology Information, National Library of Medicine, of the United States National Institutes of Health. (Altschul et al., 1990).

[0046] In some embodiments, the sPTH comprises a 14-amino acid sequence comprising: a) 1-3 polar residues and, relative to SEQ ID NO: 7, 1-14 amino acid substitutions; b) at least 4 polar residues, at least 1 charged residue, and, relative to SEQ ID NO: 7, 1-14 amino acid substitutions; c) at least 5 polar residues, at least 2 charged residues, and, relative to SEQ ID NO:

7, 1-14 amino acid substitutions; d) at least 5 polar residues, valine at position 2, and, relative to SEQ ID NO: 7, 1-13 amino acid substitutions; or a) at least 6 polar residues and, relative to SEQ ID NO: 7, 1-14 amino acid substitutions.

[0047] In some embodiments, the sPTH comprises a 32-amino acid sequence comprising: a) at most 13 polar residues and, relative to SEQ ID NO: 8, 1-32 amino acid substitutions; b) at least 14 polar residues, valine at position 2, and, relative to SEQ ID NO: 8, 1-31 substitutions; c) at least 14 polar residues and, relative to SEQ ID NO: 8, 22-28 amino acid substitutions; or d) positions 1-14 of SEQ ID NO: 8 and, relative to SEQ ID NO: 5, 1-18 amino acid substitutions at positions 15-32.

[0048] In some embodiments, the sPTH comprises an amino acid sequence having at least about 20% sequence identity to an amino acid sequence selected from SEQ ID NOs: 9-106 and SEQ ID NOs: 108-160. For example, having at least about: 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 95% or 97%; having about: 20-97%, 25-97%, 25- 95%, 30-95%, 30-90%, 35-90%, 35-85%, 40-85%, 40-80%, 45-75%, 45-70%, 50-70%, 50-65% or 55-65%; or having up to about: 70%, 75%, 80%, 85%, 90%, 95% or 97%, sequence identity to an amino acid sequence selected from SEQ ID NOs: 9-106 and SEQ ID NOs: 108-160. In some embodiments, the sPTH comprises an amino acid sequence having about 50-97% sequence identity to an amino acid sequence selected from SEQ ID NOs: 9-106 and SEQ ID NOs: 108- 160.

[0049] In some embodiments, the sPTH comprises at least 1 amino acid substitution relative to an amino acid sequence selected from SEQ ID NOs: 9-106 and SEQ ID NOs: 108-160. For example, the sPTH comprises at least: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 or 32; or about: 1-32, 1-28, 1-24, 1-20, 1-15, 1-10,

1-5, 2-32, 2-28, 2-24, 2-20, 2-15, 2-10, 2-5, 3-32, 3-28, 3-24, 3-20, 3-15, 3-10, 3-5, 4-32, 4-28, 4- 24, 4-20, 4-15, 4-10 or 4-5 amino acid substitution relative to an amino acid sequence selected from SEQ ID NOs: 9-106 and SEQ ID NOs: 108-160. [0050] In some embodiments, the sPTH comprises up to 32 amino acid substitutions relative to an amino acid sequence selected from SEQ ID NOs: 9-106 and SEQ ID NOs: 108-160. For example, the sPTH comprises up to: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 or 31; or up to: 1-32, 1-28, 1-24, 1-20, 1-15, 1-10, 1-5, 2-32, 2-28, 2-24, 2-20, 2-15, 2-10, 2-5, 3-32, 3-28, 3-24, 3-20, 3-15, 3-10, 3-5, 4-32, 4-28, 4-24, 4-20, 4-15, 4-10 or 4-5 amino acid substitution relative to an amino acid sequence selected from SEQ ID NOs: 9-106 and SEQ ID NOs: 108-160.

[0051] In some embodiments, the sPTH comprises an amino acid sequence selected from SEQ ID NOs: 9-106 and SEQ ID NOs: 108-160.

[0052] In some embodiments, the sPTH comprises an amino acid sequence having at least about 20% sequence identity to an amino acid sequence selected from SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147- 152, 154, 155 and 157-160. For example, having at least about: 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 95% or 97%; having about: 20-97%, 25- 97%, 25-95%, 30-95%, 30-90%, 35-90%, 35-85%, 40-85%, 40-80%, 45-75%, 45-70%, 50-70%, 50-65% or 55-65%; or having up to about: 70%, 75%, 80%, 85%, 90%, 95% or 97%, sequence identity to an amino acid sequence selected from SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101- 103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157- 160. In some embodiments, the sPTH comprises an amino acid sequence having about 50-97% sequence identity to an amino acid sequence selected from SEQ ID NOs: 9, 10, 19, 20, 31, 35,

41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160.

[0053] In some embodiments, the sPTH comprises at least 1 amino acid substitution relative to an amino acid sequence selected from SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103,

108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160. For example, the sPTH comprises at least: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 or 32; or about: 1-32, 1-28, 1-24, 1-20, 1-15, 1- 10, 1-5, 2-32, 2-31, 2-28, 2-24, 2-20, 2-18, 2-15, 2-10, 2-5, 3-32, 3-28, 3-24, 3-20, 3-15, 3-10, 3- 5, 4-32, 4-28, 4-24, 4-20, 4-15, 4-10 or 4-5 amino acid substitution relative to an amino acid sequence selected from SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160.

[0054] In some embodiments, the sPTH comprises up to 32 amino acid substitutions relative to an amino acid sequence selected from SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103,

108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160. For example, the sPTH comprises up to: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 or 31; or up to: 1-32, 1-28, 1-24, 1-20, 1-15, 1-10, 1- 5, 2-32, 2-31, 2-28, 2-24, 2-20, 2-18, 2-15, 2-10, 2-5, 3-32, 3-28, 3-24, 3-20, 3-15, 3-10, 3-5, 4- 32, 4-28, 4-24, 4-20, 4-15, 4-10 or 4-5 amino acid substitution relative to an amino acid sequence selected from SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160.

[0055] In some embodiments, the sPTH comprises an amino acid sequence selected from SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136- 138, 140-143, 145, 147-152, 154, 155 and 157-160.

[0056] In some embodiments, the sPTH comprises an amino acid sequence having at least about 20% sequence identity to an amino acid sequence selected from SEQ ID NOs: 101, 103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160. For example, having at least about: 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 95% or 97%; having about: 20-97%, 25-97%, 25-95%, 30-95%, 30-90%, 35-90%, 35-85%, 40-85%, 40-80%, 45-75%, 45-70%, 50-70%, 50-65% or 55-65%; or having up to about: 70%, 75%, 80%, 85%, 90%, 95% or 97%, sequence identity to an amino acid sequence selected from SEQ ID NOs: 101, 103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143,

145, 147-152, 154, 155 and 157-160. In some embodiments, the sPTH comprises an amino acid sequence having about 50-97% sequence identity to an amino acid sequence selected from SEQ

ID NOs: 101, 103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160.

[0057] In some embodiments, the sPTH comprises at least 1 amino acid substitution relative to an amino acid sequence selected from SEQ ID NOs: 101, 103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160. For example, the sPTH comprises at least: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 or 32; or about: 1-32, 1-28, 1-24, 1-20, 1-15, 1-10, 1-5, 2-32, 2-31, 2-

28, 2-24, 2-20, 2-18, 2-15, 2-10, 2-5, 3-32, 3-28, 3-24, 3-20, 3-15, 3-10, 3-5, 4-32, 4-28, 4-24, 4-

20, 4-15, 4-10 or 4-5 amino acid substitution relative to an amino acid sequence selected from

SEQ ID NOs: 101, 103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147- 152, 154, 155 and 157-160.

[0058] In some embodiments, the sPTH comprises up to 32 amino acid substitutions relative to an amino acid sequence selected from SEQ ID NOs: 101, 103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160. For example, the sPTH comprises up to: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 or 31; or up to: 1-32, 1-28, 1-24, 1-20, 1-15, 1-10, 1-5, 2-32, 2-31, 2-28, 2- 24, 2-20, 2-18, 2-15, 2-10, 2-5, 3-32, 3-28, 3-24, 3-20, 3-15, 3-10, 3-5, 4-32, 4-28, 4-24, 4-20, 4- 15, 4-10 or 4-5 amino acid substitution relative to an amino acid sequence selected from SEQ ID NOs: 101, 103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154,

155 and 157-160.

[0059] In some embodiments, the sPTH comprises an amino acid sequence selected from

SEQ ID NOs: 101, 103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-

152, 154, 155 and 157-160.

[0060] In some embodiments, the sPTH consists of 28-36 amino acids, e.g., 18, 29, 30, 31, 32, 33, 35 or 36 amino acids. In some embodiments, the sPTH consists of 30-34 amino acids. In some embodiments, the sPTH consists of 32 amino acids.

[0061] In some embodiments, the sPTH comprises an amino acid sequence having at least about 20% sequence identity to SEQ ID NO: 5. For example, having at least about: 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 95% or 97%; having about: 20-97%, 25-97%, 25-95%, 30-95%, 30-90%, 35-90%, 35-85%, 40-85%, 40-80%, 45-75%, 45- 70%, 50-70%, 50-65% or 55-65%; or having up to about: 70%, 75%, 80%, 85%, 90%, 95% or 97%, sequence identity to SEQ ID NO: 5. In some embodiments, the sPTH comprises an amino acid sequence having about 50-97% sequence identity to SEQ ID NO: 5.

[0062] In some embodiments, the sPTH comprises at least 1 amino acid substitution relative to SEQ ID NO: 5. For example, the sPTH comprises at least: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 or 32; or about: 1-32, 1-28, 1- 24, 1-20, 1-15, 1-10, 1-5, 2-32, 2-31, 2-28, 2-24, 2-20, 2-18, 2-15, 2-10, 2-5, 3-32, 3-28, 3-24, 3- 20, 3-15, 3-10, 3-5, 4-32, 4-28, 4-24, 4-20, 4-15, 4-10 or 4-5 amino acid substitution relative to SEQ ID NO: 5.

[0063] In some embodiments, the sPTH comprises up to 32 amino acid substitutions relative to SEQ ID NO: 5. For example, the sPTH comprises up to: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 or 31; or up to: 1-32, 1-28, 1-24, 1-20, 1-15, 1-10, 1-5, 2-32, 2-31, 2-28, 2-24, 2-20, 2-18, 2-15, 2-10, 2-5, 3-32, 3-28, 3-24, 3-20, 3-15, 3-10, 3-5, 4-32, 4-28, 4-24, 4-20, 4-15, 4-10 or 4-5 amino acid substitution relative to SEQ ID NO: 5.

[0064] In some embodiments, the sPTH comprises an amino acid sequence set forth by SEQ ID NO: 6. In some embodiments, the amino acid sequence set forth by SEQ ID NO: 6 is at the N-terminus of the sPTH. [0065] In some embodiments, the sPTH comprises an amino acid sequence having at least about 55% sequence identity to a sequence selected from the group consisting of SEQ ID NOs: 102-106 and SEQ ID NOs: 132-155. For example, having at least about: 60%, 65%, 70%, 75%, 80%, 85%, 90%, 95% or 97%; having about: 55-97%, 60-97%, 60-95%, 65-95%, 65-90%, 70- 90%, 70-85% or 80-85%; or having up to about: 70%, 75%, 80%, 85%, 90%, 95% or 97%, sequence identity to a sequence selected from the group consisting of SEQ ID NOs: 102-106 and SEQ ID NOs: 132-155. In some embodiments, the sPTH comprises an amino acid sequence having about 50-97% sequence identity to a sequence selected from the group consisting of SEQ ID NOs: 102-106 and SEQ ID NOs: 132-155. In some embodiments, the sPTH comprises an amino acid sequence having about 75-97% sequence identity to a sequence selected from the group consisting of SEQ ID NOs: 102-106 and SEQ ID NOs: 132-155. In some embodiments, the sPTH comprises an amino acid sequence selected from the group consisting of SEQ ID NOs: 102-106 and SEQ ID NOs: 132-155.

[0066] In some embodiments, the at least amino acid substitution is a conservative substitution. In some embodiments, the at least amino acid substitution is a highly conservative substitution. In some embodiments, the amino acid substitutions are conservative substitutions.

In some embodiments, the amino acid substitutions are highly conservative substitutions.

[0067] In some embodiments, the sPTH binds PTHR with an affinity that is at least about 5% higher than a polypeptide having an amino acid sequence consisting of SEQ ID NO: 1, SEQ ID NO: 2, SEQ ID NO: 3, SEQ ID NO: 4 or SEQ ID NO: 5. For example, the sPTH binds PTHR with an affinity that is at least about: 10%, 15%, 20%, 25%, 30%, 35%, 40%, 50%, 60% or 70% higher than a polypeptide having an amino acid sequence consisting of SEQ ID NO: 1, SEQ ID NO: 2, SEQ ID NO: 3, SEQ ID NO: 4 or SEQ ID NO: 5.

[0068] In some embodiments, the sPTH binds PTHR with an affinity that is at least about 5% lower than a polypeptide having an amino acid sequence consisting of SEQ ID NO: 1, SEQ ID NO: 2, SEQ ID NO: 3, SEQ ID NO: 4 or SEQ ID NO: 5. For example, the sPTH binds PTHR with an affinity that is at least about: 10%, 15%, 20%, 25%, 30%, 35%, 40%, 50%, 60% or 70% lower than a polypeptide having an amino acid sequence consisting of SEQ ID NO: 1, SEQ ID NO: 2, SEQ ID NO: 3, SEQ ID NO: 4 or SEQ ID NO: 5.

[0069] In some embodiments, no more than about 5% lower than a polypeptide having an amino acid sequence consisting of SEQ ID NO: 1, SEQ ID NO: 2, SEQ ID NO: 3, SEQ ID NO:

4 or SEQ ID NO: 5. For example, the sPTH binds PTHR with an affinity that is no more than about: 10%, 15%, 20%, 25%, 30%, 35%, 40%, 50%, 60% or 70% lower than a polypeptide having an amino acid sequence consisting of SEQ ID NO: 1, SEQ ID NO: 2, SEQ ID NO: 3,

SEQ ID NO: 4 or SEQ ID NO: 5.

[0070] In some embodiments, the sPTH provided by the invention or variant thereof includes a post-translational modification, such as one or more post-translational modifications resulting from acetylation, amidation, formylation, glycosylation, hydroxylation, methylation, myristoylation, phosphorylation, deamidation, prenylation (e.g., farnesylation, geranylation, etc.), ubiquitination, ribosylation or sulfation of the sPTH or variant thereof, or any combination of the foregoing.

[0071] The sPTH polypeptide of the invention can function as an agonist (e.g., a biased agonist), an inverse agonist or an antagonist of one or more PTHR signaling pathways. In some embodiments, the one or more PTHR signaling pathways are selected from the group consisting of the Gas-adenylyl cyclase-cAMP-protein kinase A (PKA) pathway (G _s pathway), the Ga _q- phospholipase C (PLC) b-inositol triphosphate-cytoplasmic Ca ²⁺ -protein kinase C pathway (G _q pathway), the Ga _12/13 -phospholipase D-transforming protein RhoA pathway (G12/1 ₃ pathway), the b-arrestin-extracellular signal-regulated kinase 1/2 (ERK1/2) pathway (b-arrestin pathway), and the combinations thereof. In some embodiments, the PTHR signaling pathway comprises the Gas-adenylyl cyclase-cAMP-protein kinase A (PKA) pathway (G _s pathway). In some embodiments, the PTHR signaling pathway comprises the Ga _q- phospholipase C (PLC) b- inositol triphosphate-cytoplasmic Ca ²⁺ -protein kinase C pathway (G _q pathway). In some embodiments, the PTHR signaling pathway comprises the Ga _12/13 -phospholipase D- transforming protein RhoA pathway (G12/1 ₃ pathway). In some embodiments, the PTHR signaling pathway comprises the b-arrestin-extracellular signal-regulated kinase 1/2 (ERK1/2) pathway (b-arrestin pathway). Additional examples of PTHR signaling pathways are described in Cheloha RW et al ., Nat Rev Endocrinol. 11(12): 712-24 (2015), the contents of which are incorporated by reference in their entirety.

[0072] In some embodiments, the sPTH polypeptide of the invention functions as an agonist of one or more PTHR signaling pathways. An “agonist of PTHR” binds to and activates PTHR signaling. An agonist of PTHR provided by the invention can be used, inter alia , to boost bone mass, increase bone formation, and/or reduce fractures in subjects (e.g., human patients) with osteoporosis or at increased risk for osteoporosis.

[0073] In some embodiments, a sPTH polypeptide that is an agonist of PTHR has improved activity (e.g., about: 1.1-fold, 1.2-fold, 1.3-fold, 1.4-fold, 1.5-fold or greater activity) compared to a reference PTH polypeptide (e.g., PTH 1-34). In certain embodiments, a sPTH polypeptide that is an agonist of PTHR has equivalent or similar activity (e.g., about: 90, 95, 97, 98, 99 or 100% activity) compared to a reference PTH polypeptide (e.g., PTH 1-34). Non-limiting examples of activities include signaling activity through, e.g., the Gs pathway, the Gq pathway, the G12/13 pathway, the b-arrestin pathway and combinations thereof.

[0074] In some embodiments, a sPTH polypeptide that is an agonist of PTHR has a lower binding constant (KD) value to PTHR (e.g., about: 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50% or lower) compared to a reference PTH polypeptide (e.g., PTH 1-34). In certain embodiments, a sPTH polypeptide that is an agonist of PTHR has equivalent or similar KD value (e.g., about: 96%, 97%, 98%, 99%, 100%, 102%, 105% or 110%) compared to a reference PTH polypeptide (e.g., PTH 1-34). As used herein the term “KD,” also referred to as “binding constant,” “equilibrium dissociation constant” or “affinity constant,” is a measure of the extent of a reversible association between two molecular species (e.g., antibody and target protein) and includes both the actual binding affinity as well as the apparent binding affinity. Binding affinity can be determined using methods known in the art including, for example, by measurement of surface plasmon resonance, e.g., using a Biolayer interferometry (Octet, ForteBio) or a surface plasmon resonance (Biacore) system and assay. A reference that compares various surface technologies for measuring binding affinity and kinetics is Yang et ah, Analytical Biochemistry 508: 78-96 (2016), the contents of which are incorporated by reference herein in their entirety. [0075] In some embodiments, a sPTH polypeptide that is an agonist of PTHR comprises more than 14 amino acids (e.g., 32 amino acids, 34 amino acids), wherein the N-terminal 14 amino acids of the polypeptide correspond to SEQ ID NO: 6.

[0076] Particular examples of sPTH polypeptides that are agonists of PTHR include SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160. See, e.g., Example 6 herein.

[0077] In some embodiments, the sPTH polypeptide of the invention is selected from the group consisting of SEQ ID NO: 120, SEQ ID NO: 136, SEQ ID NO: 143, SEQ ID NO: 145 and SEQ ID NO: 159. In some embodiments, the sPTH polypeptide of the invention is SEQ ID NO: 145 or SEQ ID NO: 159. In some embodiments, the sPTH polypeptide of the invention is selected from the group consisting of SEQ ID NO: 108, SEQ ID NO: 115, SEQ ID NO: 131,

SEQ ID NO: 136, SEQ ID NO: 137, SEQ ID NO: 138, SEQ ID NO: 139, SEQ ID NO: 140, SEQ ID NO: 141, SEQ ID NO: 143, SEQ ID NO: 149, SEQ ID NO: 155 and SEQ ID NO: 157. In some embodiments, the sPTH polypeptide of the invention is selected from the group consisting of SEQ ID NO: 108, SEQ ID NO: 115, SEQ ID NO: 131, SEQ ID NO: 136, SEQ ID NO: 143, SEQ ID NO: 155 and SEQ ID NO: 157. In some embodiments, the sPTH polypeptide of the invention is selected from the group consisting of SEQ ID NO: 101, SEQ ID NO: 103, SEQ ID NO: 120, SEQ ID NO: 121, SEQ ID NO: 129, SEQ ID NO: 131, SEQ ID NO: 132, SEQ ID NO: 134, SEQ ID NO: 142, SEQ ID NO: 143, SEQ ID NO: 147, SEQ ID NO: 148, SEQ ID NO: 150, SEQ ID NO: 151, SEQ ID NO: 152, SEQ ID NO: 154, SEQ ID NO: 158 and SEQ ID NO: 160. In some embodiments, the sPTH polypeptide of the invention is selected from the group consisting of SEQ ID NO: 101, SEQ ID NO: 120, SEQ ID NO: 121, SEQ ID NO: 129, SEQ ID NO: 131, SEQ ID NO: 147, SEQ ID NO: 148, SEQ ID NO: 150, SEQ ID NO: 151, SEQ ID NO: 152, SEQ ID NO: 154, SEQ ID NO: 158 and SEQ ID NO: 160.

[0078] In some embodiments, the sPTH polypeptide of the invention functions as a biased agonist of one or more PTHR signaling pathways. A “biased agonist of PTHR” binds to PTHR and preferentially activates a distinct subset of the intracellular signaling responses that are usually activated by the parent ligand or induce alterations in the duration and cellular localization of signaling. See, e.g., Cheloha RW et al. , Nat Rev Endocrinol . 11(12): 712-24 (2015) for additional description. In some embodiments, the sPTH polypeptide acting as a PTHR biased agonist induces selective activation of one pathway independently of one or more other pathways. For example, the sPTH polypeptide acting as a PTHR biased agonist induces selective activation of the b-arrestin pathway without inducing activation of one or more of the G protein- coupled signaling mechanisms (G _s pathway, Gq pathway, or G12/13 pathway or any combination of the foregoing). As such, a PTHR biased agonist can be used to selectively induce anabolic bone formation and improve therapeutic efficacy with reduced side effects in subjects (e.g., human patients) with osteoporosis or at increased risk for osteoporosis. In some embodiments, the sPTH polypeptide of the invention is a variant of a reference biased agonist. Non-limiting examples of reference biased agonists include D-Trpl2 (D-Trp at position 12) and Tyr34-PTH (7-34) (Tyr at position 34) on the PTH(7-34) scaffold. See, for example Bohinc BN and Gesty- PalmerD , Mini Rev Med Chem. 12(9): 856-65 (2012).

[0079] In some embodiments, the sPTH polypeptide of the invention functions as an inverse agonist of one or more PTHR signaling pathways. An “inverse agonist of PTHR” is a polypeptide that can bind to PTHR and inhibit a constitutively active PTHR or reduce basal PTHR signaling. See, e.g., Cheloha RW et al, Nat Rev Endocrinol. 11(12): 712-24 (2015). In some embodiments, the sPTH polypeptide acting as a PTHR inverse agonist is used to inhibit and/or reverse excessive activation of PTHR due to gain-of-function mutations. In some embodiments, the sPTH polypeptide acting as a PTHR inverse agonist is used to treat and/or prevent one or more indications. Non-limiting examples of the indication include Jansen's metaphyseal chondrodysplasia, hypercalcemia, hypercalciuria, nephrocalcinosis, and chronic kidney disease. See, for example, Saito H etal. , J Clin Endocrinol Metab . 49: 20-28 (2018). [0080] In some embodiments, the sPTH polypeptide of the invention functions as an antagonist of one or more PTHR signaling pathways. An “antagonist of PTHR” is a polypeptide that binds to PTHR and prevents alterations of PTHR signaling by agonists or inverse agonists. See, e.g., Cheloha RW et al, Nat Rev Endocrinol. 11(12): 712-24 (2015). In some embodiments, the sPTH polypeptide acting as a PTHR antagonistic is used to inhibit excessive activation of PTHR. In some embodiments, the sPTH polypeptide acting as a PTHR antagonistic is used to treat and/or prevent one or more indications. Non-limiting examples of the indication include including hypercalcemia, hyperparathyroidism, parathyroid carcinoma, and metastatic bone disease. See, for example, Mirza AM et al. , AACR Annual Meeting 2017.

[0081] In some embodiments, PTHR signaling is assessed by a luciferase assay, which can be performed according to Hattersly et al., Endocrinology 157(1): 141-49 (2016) or Kumar et al. , 2007, incorporated by reference in their entirety. A sPTH polypeptide mediated effect (e.g., an agonist activity or an inverse agonist activity) on PTHR signaling can be assessed, for example, through a FRET (fluorescence resonance energy transfer) assay. For example, with a luciferase- tagged b-arrestin and a YFP-tagged GPCR. In some embodiments, a sPTH polypeptide mediated effect (e.g., an inverse agonist activity or an antagonist activity) is evaluated by detecting a reduction in cAMP level. In some embodiments (e.g., an inverse agonist activity), a background cAMP level is determined using a constitutively active receptor, e.g., containing one or more constitutive mutations. Non-limiting examples of the constitutive mutations include H223R, T410P, or I458R or a combination thereof, which underlies Jansen’s metaphyseal chondrodysplasia. In some embodiments (e.g., an antagonist activity), a background cAMP level is determined using a native ligand. Detailed descriptions of assays can be found in Example 2B (antagonist activity) and Example 2C (inverse agonist activity).

[0082] In some embodiments, the sPTH polypeptide is conjugated to a heterologous moiety. The term “conjugated” refers to attached, via a covalent or noncovalent interaction. Conjugation can employ any of suitable linking agents. Non-limiting examples include peptide linkers, compound linkers, and chemical cross-linking agents.

[0083] In some embodiments, the heterologous moiety is a therapeutic agent, a diagnostic agent or a combination thereof. In some embodiments, the heterologous moiety is polyethylene glycol (PEG), hexadecanoic acid, hydrogels, nanoparticles, multimerization domains and carrier peptides. [0084] In some embodiments, the nanoparticle is a lipid nanoparticle. In some embodiments, the nanoparticle is a polymer nanoparticle. In some embodiments, the polymer is an amphiphilic polymer. In other embodiments, the polymer is a hydrophobic or hydrophilic polymer. Non limiting examples of polymers include poly(lactic acid)-poly(ethylene glycol), poly(lactic-co- glycolic acid)-poly(ethylene glycol), poly(lactic-co-glycolic) acid (PLGA), poly(lactic-co- glycolic acid)-d-a-tocopheryl polyethylene glycol succinate, poly(lactic-co-glycolic acid)- ethylene oxide fumarate, poly(glycolic acid)-poly(ethylene glycol), polycaprolactone- poly(ethylene glycol), or any salts thereof. In some embodiments, the polymer nanoparticle comprises poly(lactic-co-glycolic) acid (PLGA).

Fusion Proteins

[0085] In another aspect, the invention provides a fusion protein comprising one or more of the SPTHs described herein.

[0086] The term “fusion protein” refers to a synthetic, semi-synthetic or recombinant single protein molecule. A fusion protein can comprise all or a portion of two or more different proteins and/or polypeptides that are attached by covalent bonds (e.g., peptide bonds).

[0087] Fusion proteins of the invention can be produced recombinantly or synthetically, using routine methods and reagents that are well known in the art. For example, a fusion protein of the invention can be produced recombinantly in a suitable host cell (e.g., bacteria) according to methods known in the art. See, e.g., Current Protocols in Molecular Biology, Second Edition, Ausubel etal. eds., John Wiley & Sons, 1992; and Molecular Cloning: a Laboratory Manual, 2nd edition, Sambrook et al., 1989, Cold Spring Harbor Laboratory Press. For example, a nucleic acid molecule comprising a nucleotide sequence encoding a fusion protein described herein can be introduced and expressed in suitable host cell (e.g, E. coli), and the expressed fusion protein can be isolated/purified from the host cell (e.g., in inclusion bodies) using routine methods and readily available reagents. For example, DNA fragments coding for different protein sequences (e.g, a light-responsive domain, a heterologous peptide component) can be ligated together in- frame in accordance with conventional techniques. In another embodiment, the fusion gene can be synthesized by conventional techniques including automated DNA synthesizers.

Alternatively, PCR amplification of nucleic acid fragments can be carried out using anchor primers that give rise to complementary overhangs between two consecutive nucleic acid fragments that can subsequently be annealed and re-amplified to generate a chimeric nucleic acid sequence (see Ausubel et al, Current Protocols in Molecular Biology, 1992). Nucleic Acids. Expression Vectors. Expression Host Cells

[0088] In another aspect, the invention provides one or more polynucleotides encoding any one of the SPTH polypeptides or fusion proteins described herein. In some embodiments, the SPTH polypeptide or fusion protein of the invention is encoded by a single polynucleotide. In some embodiments, the SPTH polypeptide or fusion protein of the invention is encoded by multiple polynucleotides.

[0089] In some embodiments, the SPTH polynucleotide comprises a nucleotide sequence that is codon-optimized for a chosen host cell.

[0090] In another aspect, the invention provides an expression vector comprising any one or more of the polynucleotides described herein.

[0091] The term “expression vector” refers to a replicable nucleic acid from which one or more proteins can be expressed when the expression vector is transformed into a suitable expression host cell.

[0092] In some embodiments, the expression vector further comprises an expression control polynucleotide sequence operably linked to the polynucleotide, a polynucleotide sequence encoding a selectable marker, or both. In some embodiments, the expression control polynucleotide sequence comprises a promoter sequence, an enhancer sequence, or both. In some embodiments, the expression control polynucleotide sequence comprises an inducible promoter sequence. The term “promoter” refers to a region of DNA to which RNA polymerase binds and initiates the transcription of a gene. The term “operably linked” means that the nucleic acid is positioned in the recombinant polynucleotide, e.g ., vector, in such a way that enables expression of the nucleic acid under control of the element (e.g, promoter) to which it is linked. The term “selectable marker element” is an element that confers a trait suitable for artificial selection. Selectable marker elements can be negative or positive selection markers.

[0093] In another aspect, the invention provides an expression host cell comprising any one or more of the polynucleotides or expression vectors described herein.

[0094] The term “expression host cell” refers to a cell useful for receiving, maintaining, reproducing and/or amplifying a vector.

[0095] Non-limiting examples of expression host cells include mammalian cells such as Chinese hamster ovary (CHO) cells, COS cells, human embryonic kidney (HEK), yeast cells such as Pichia pastoris cells, or bacterial cells such as DH5a, etc. Compositions

[0096] In another aspect, the invention provides a composition comprising any one of the polypeptides or fusion proteins described herein. In some embodiments, the composition is a pharmaceutical composition.

[0097] In some embodiments, the composition (e.g., pharmaceutical composition) further comprises pharmaceutically acceptable carriers, excipients, stabilizers, diluents or tonifiers (Remington's Pharmaceutical Sciences 16th edition, Osol, A. Ed. (1980)). Suitable pharmaceutically acceptable carriers, excipients, or stabilizers are nontoxic to recipients at the dosages and concentrations employed. Non-limiting examples of pharmaceutically acceptable carriers, excipients, stabilizers, diluents or tonifiers include buffers (e.g., phosphate, citrate, histidine), antioxidants (e.g., ascorbic acid or methionine), preservatives, proteins (e.g., serum albumin, gelatin or immunoglobulins); hydrophilic polymers, amino acids, carbohydrates (e.g., monosaccharides, disaccharides, glucose, mannose or dextrins); chelating agents (e.g., EDTA), sugars (e.g., sucrose, mannitol, trehalose or sorbitol), salt-forming counter-ions (e.g., sodium), metal complexes (e.g., Zn-protein complexes); non-ionic surfactants (e.g., Tween), PLURONICS™ and polyethylene glycol (PEG).

[0098] In some embodiments, the composition (e.g., pharmaceutical composition) of the invention is formulated for a suitable administration schedule and route. Non-limiting examples of administration routes include oral, rectal, mucosal, intravenous, intramuscular, subcutaneous and topical, etc. In some embodiments, the composition (e.g., pharmaceutical composition) of the invention is stored in the form of an aqueous solution or a dried formulation (e.g., lyophilized).

[0099] In some embodiments, the composition is formulated to be administered by infusion (e.g., intravenous infusion). In some embodiments, the composition is formulated to be administered with a second therapeutic agent as a combination therapy.

Methods of Making a sPTH

[00100] The SPTH polypeptides, the conjugates thereof, the fusion proteins thereof and the compositions of the invention can be produced by any suitable means known in the art. In some embodiments, a method of chemical synthesis is used. In some embodiments, a method of recombinant production/expression is used. In some embodiments, a combination of chemical synthesis and recombinant production/expression is used. For example, the SPTH polypeptide component is recombinantly produced followed by chemically conjugating a heterologous moiety. In some embodiments, a host cell of the invention (e.g., comprising a SPTH polynucleotide or expression vector of the invention) is cultured under suitable conditions to generate the sPTH, which is then isolated from the host cell or culture supernatant, thereby producing the sPTH.

Methods Using a sPTH

[00101] In another aspect, the invention provides a method of modulating PTHR signaling in a cell (e.g., a mammalian cell), comprising contacting the cell with an effective amount of the polypeptide, fusion protein or composition (e.g., pharmaceutical composition) described herein. [00102] In another aspect, the invention provides a method of modulating PTHR signaling in a subject in need thereof, comprising administering an effective amount of the polypeptide, fusion protein or composition (e.g., pharmaceutical composition) described herein to the subject. [00103] In some embodiments, modulating PTHR signaling involves an agonist activity (e.g., a biased agonist activity), an inverse agonist activity, or an antagonist activity of PTHR signaling or a combination of the forgoing. In some embodiments, modulating PTHR signaling involves an agonist activity of PTHR signaling. In some embodiments, modulating PTHR signaling involves a biased agonist activity of PTHR signaling. In some embodiments, modulating PTHR signaling involves an inverse agonist activity of PTHR signaling. In some embodiments, modulating PTHR signaling involves an antagonist activity of PTHR signaling.

[00104] In another aspect, the invention provides a method of treating a subject in need thereof, comprising administering to the subject an effective amount of a pharmaceutical composition described herein to the subject.

[00105] In some embodiments, treating the subject in need thereof involves an agonist activity (e.g., a biased agonist activity), an inverse agonist activity, or an antagonist activity of PTHR signaling or a combination of the forgoing. In some embodiments, treating the subject in need thereof involves an agonist activity of PTHR signaling. In some embodiments, treating the subject in need thereof involves a biased agonist activity of PTHR signaling. In some embodiments, treating the subject in need thereof involves an inverse agonist activity of PTHR signaling. In some embodiments, treating the subject in need thereof involves an antagonist activity of PTHR signaling.

[00106] The term “subject” or “patient” refers to an animal (e.g., a mammal). In some embodiments, the subject is a mammal. In some embodiments, the subject is a human. In some embodiments, the subject is an adult. In some embodiments, the subject is at least 50 years old.

In some embodiments, the subject is a female. In some embodiments, the subject is peri- menopausal, menopausal, or post-menopausal. In some embodiments, the subject is peri- menopausal. In some embodiments, the subject is menopausal. In some embodiments, the subject is post-menopausal.

[00107] A subject to be treated according to the methods described herein may be one who has been diagnosed with a condition, or one at risk of developing such conditions. In some embodiments, the subject has the condition. In some embodiments, the subject has been diagnosed with the condition. In other embodiments, the subject is at risk of developing the condition. Exemplary conditions (indications) treatable by the methods provided by the invention include those described in Tables 4-6 or claims, below, or the enumerated embodiments, supra.

Table 4. Non-limiting Examples of Disorders of Calcium Homeostasis Treatable with Agonist Activity or Biased Agonist Activity of PTHR Signaling.

Table 5. Non-limiting Examples of Disorders of Calcium Homeostasis Treatable with antagonist Activity of PTHR Signaling. Table 6. Non-limiting Examples of Disorders of Calcium Homeostasis Treatable with Inverse Agonist Activity of PTHR Signaling. [00108] In some embodiments, the subject has, or is at risk of developing, dysregulated calcium homeostasis.

[00109] In some embodiments, the subject has, or is at risk of developing, a disorder selected from Osteoporosis, Blomstrand’s chondrodysplasia, Familial primary failure of tooth eruption, Eiken syndrome, Ollier disease, Hypercalcemia, Hyperparathyroidism, Jansen’s metaphyseal chondrodysplasia, Hypercalcemia, Hypercalciuria, Nephrocalcinosis and combinations thereof. [00110] In some embodiments, the subject has, or is at risk of developing, low bone density.

[00111] In some embodiments, the subject has, or is at risk of developing, a disorder selected from Blomstrand’s lethal chondrodysplasia, Ollier disease, familial primary failure of tooth eruption, Eiken syndrome, brachydactyly type E, hypoparathyroidism, osteoporosis and combinations thereof.

[00112] In some embodiments, the subject has, or is at risk of developing, osteoporosis.

[00113] In some embodiments, the subject has, or is at increased risk of developing, a disorder selected from: hypercalcemia, hyperparathyroidism, parathyroid carcinoma, metastatic bone disease and combinations thereof. In some embodiments, the hyperparathyroidism occurs as a complication of parathyroid carcinoma. In some embodiments, the metastatic bone disease occurs with associated hypercalcemia.

[00114] In some embodiments, the subject has, or is at increased risk of developing, a disorder selected from Jansen's metaphyseal chondrodysplasia, hyperparathyroidism, hypercalcemia, hypercalciuria, nephrocalcinosis, chronic kidney disease and combinations thereof. In some embodiments, the chronic kidney disease occurs in conjunction with, or as a result of, hypercalcemia, hypercalciuria, nephrocalcinosis or a combination thereof.

[00115] Diagnosis may be performed by any method or technique known in the art. One skilled in the art will understand that a subject to be treated according to the present disclosure may have been subjected to standard tests or may have been identified, without examination, as one at risk due to the presence of one or more risk factors associated with the disease or condition.

[00116] The sPTHs (and compositions, conjugates (e.g., comprising a heterologous moiety joined or otherwise lined, e.g., by covalent linkage), and fusion proteins containing them; or nucleic acids, vectors, or cells encoding them) provided by the invention can be used in a variety of situations to modulate PTHR signaling, e.g., as: an agonist of PTHR, a biased agonist of PTHR, an inverse agonist of PTHR, or an antagonist of PTHR. The modulation of PTHR signaling can be in vitro , in a cell, or in vivo , e.g., in a subject. Exemplary indications treatable by the methods provided by the invention include those described in Tables 2-4 or claims, below, or the enumerated embodiments, supra.

[00117] In these methods, the sPTH (composition, conjugate, fusion protein, or nucleic acid or cell) is provided to the subject by suitable means in an effective amount. The term “effective amount,” “therapeutically effective amount,” or “sufficient amount” refers to a quantity sufficient to, when administered to a subject, including a mammal (e.g., a human), effect beneficial or desired results, including effects at the cellular level, tissue level, or clinical results, and, as such, an “effective amount” or synonym thereto depends upon the context in which it is being applied. For example, in some embodiments it is an amount of the composition sufficient to achieve a treatment response as compared to the response obtained without administration of the composition. The amount of a given composition described herein that will correspond to such an amount will vary depending upon various factors, such as the given agent, the pharmaceutical formulation, the route of administration, the type of disease or disorder, the identity of the subject (e.g., age, sex, weight) or host being treated, and the like, but can nevertheless be routinely determined by one skilled in the art. Also, as used herein, a “therapeutically effective amount” of a composition of the present disclosure is an amount that results in a beneficial or desired result in a subject as compared to a control. As defined herein, a therapeutically effective amount of a composition of the present disclosure may be readily determined by one of ordinary skill by routine methods known in the art. Dosage regimen and route of administration may be adjusted to provide the optimum therapeutic response.

[00118] In some embodiments, the amount is effective to promote calcium homeostasis, increase, maintain or reduce a decrease of bone mineral density, reduce risk of fracture, promote fracture healing or a combination of the foregoing.

[00119] In some embodiments, the effective amount does not induce catabolic bone resorption.

[00120] “Treatment” and “treating,” as used herein, refer to the medical management of a subject with the intent to improve, ameliorate, stabilize (i.e., not worsen), prevent or cure a disease, pathological condition, or disorder — such as the particular indications exemplified herein. This term includes active treatment (treatment directed to improve the disease, pathological condition, or disorder), causal treatment (treatment directed to the cause of the associated disease, pathological condition, or disorder), palliative treatment (treatment designed for the relief of symptoms), preventative treatment (treatment directed to minimizing or partially or completely inhibiting the development of the associated disease, pathological condition, or disorder); and supportive treatment (treatment employed to supplement another therapy). Treatment also includes diminishment of the extent of the disease or condition; preventing spread of the disease or condition; delay or slowing the progress of the disease or condition; amelioration or palliation of the disease or condition; and remission (whether partial or total), whether detectable or undetectable. “Ameliorating” or “palliating” a disease or condition means that the extent and/or undesirable clinical manifestations of the disease, disorder, or condition are lessened and/or time course of the progression is slowed or lengthened, as compared to the extent or time course in the absence of treatment. “Treatment” can also mean prolonging survival as compared to expected survival if not receiving treatment. Those in need of treatment include those already with the condition or disorder, as well as those prone to have the condition or disorder or those in which the condition or disorder is to be prevented.

[00121] Features of the sPTHs provided by the invention (and conjugates, fusion proteins, and compositions containing them; or nucleic acids, vectors, or cells encoding them) or methods of using them can include one or more of the following enumerated embodiments.

[00122] Embodiment 1 : a polypeptide that specifically binds Parathyroid Hormone Receptor (PTHR), wherein the polypeptide comprises a synthetic parathyroid hormone (sPTH).

[00123] Embodiment 2: the polypeptide of Embodiment 1, wherein the sPTH comprises a 14- amino acid sequence comprising: a) 1-3 polar residues and, relative to SEQ ID NO: 6, 1-14 amino acid substitutions; b) at least 4 polar residues, at least 1 charged residue, and, relative to SEQ ID NO: 7, 1-14 amino acid substitutions; c) at least 5 polar residues, at least 2 charged residues, and, relative to SEQ ID NO:

7, 1-14 amino acid substitutions; d) at least 5 polar residues, valine at position 2, and, relative to SEQ ID NO: 7, 1-13 amino acid substitutions; or e) at least 6 polar residues and, relative to SEQ ID NO: 7, 1-14 amino acid substitutions.

[00124] Embodiment 3: the polypeptide of Embodiment 1, wherein the sPTH comprises a 32- amino acid sequence comprising: a) at most 13 polar residues and, relative to SEQ ID NO: 8, 1-32 amino acid substitutions; b) at least 14 polar residues, valine at position 2, and, relative to SEQ ID NO: 8, 1-31 substitutions; c) at least 14 polar residues and, relative to SEQ ID NO: 8, 22-28 amino acid substitutions; or d) positions 1-14 of SEQ ID NO: 8 and, relative to SEQ ID NO: 5, 1-18 amino acid substitutions at positions 15-32.

[00125] Embodiment 4: the polypeptide of Embodiment 1, wherein the sPTH comprises an amino acid sequence having at least about 20% sequence identity to an amino acid sequence selected from SEQ ID NOs: 9-106 and SEQ ID NOs: 108-160.

[00126] Embodiment 5: the polypeptide of Embodiment 1, wherein the sPTH comprises an amino acid sequence having about 50-97% sequence identity to an amino acid sequence selected from SEQ ID NOs: 9-106 and SEQ ID NOs: 108-160.

[00127] Embodiment 6: the polypeptide of Embodiment 1, wherein the sPTH comprises at least 1 amino acid substitution relative to an amino acid sequence selected from SEQ ID NOs: 9- 106 and SEQ ID NOs: 108-160.

[00128] Embodiment 7: the polypeptide of Embodiment 1, wherein the sPTH comprises up to 2-31 amino acid substitutions relative to an amino acid sequence selected from SEQ ID NOs: 9- 106 and SEQ ID NOs: 108-160.

[00129] Embodiment 8: the polypeptide of Embodiment 1, wherein the sPTH comprises up to 2-18 amino acid substitutions relative to an amino acid sequence selected from SEQ ID NOs: 9- 106 and SEQ ID NOs: 108-160.

[00130] Embodiment 9: the polypeptide of Embodiment 1, wherein the sPTH comprises an amino acid sequence selected from SEQ ID NOs: 9-106 and SEQ ID NOs: 108-160.

[00131] Embodiment 10: the polypeptide of Embodiment 1, wherein the sPTH comprises an amino acid sequence having at least about 20% sequence identity to an amino acid sequence selected from SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160.

[00132] Embodiment 11 : the polypeptide of Embodiment 1, wherein the sPTH comprises an amino acid sequence having about 50-97% sequence identity to an amino acid sequence selected from SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132,

134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160.

[00133] Embodiment 12: the polypeptide of Embodiment 1, wherein the sPTH comprises at least 1 amino acid substitution relative to an amino acid sequence selected from SEQ ID NOs: SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136- 138, 140-143, 145, 147-152, 154, 155 and 157-160. [00134] Embodiment 13: the polypeptide of Embodiment 1, wherein the sPTH comprises up to 2-31 amino acid substitutions relative to an amino acid sequence selected from SEQ ID NOs: SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136- 138, 140-143, 145, 147-152, 154, 155 and 157-160.

[00135] Embodiment 14: the polypeptide of Embodiment 1, wherein the sPTH comprises up to 2-18 amino acid substitutions relative to an amino acid sequence selected from SEQ ID NOs: SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136- 138, 140-143, 145, 147-152, 154, 155 and 157-160.

[00136] Embodiment 15: the polypeptide of Embodiment 1, wherein the sPTH comprises an amino acid sequence selected from SEQ ID NOs: SEQ ID NOs: 9, 10, 19, 20, 31, 35, 41, 88, 101-103, 108, 115, 120, 121, 129, 131, 132, 134, 136-138, 140-143, 145, 147-152, 154, 155 and 157-160.

[00137] Embodiment 16: the polypeptide of Embodiment 1, wherein the sPTH consists of 28- 36 amino acids.

[00138] Embodiment 17: the polypeptide of Embodiment 1, wherein the sPTH consists of 30- 34 amino acids.

[00139] Embodiment 18: the polypeptide of Embodiment 1, wherein the sPTH consists of 32 amino acids.

[00140] Embodiment 19: the polypeptide of any one of Embodiments 16-18, wherein the sPTH comprises an amino acid sequence having at least about 20% sequence identity to SEQ ID NO: 5.

[00141] Embodiment 20: the polypeptide of Embodiment 19, wherein the sPTH comprises an amino acid sequence having about 50-97% sequence identity to SEQ ID NO: 5.

[00142] Embodiment 21 : the polypeptide of Embodiment 19, wherein the sPTH comprises at least 1 amino acid substitution relative to SEQ ID NO: 5.

[00143] Embodiment 22: the polypeptide of Embodiment 19, wherein the sPTH comprises 2- 18 amino acid substitutions relative to SEQ ID NO: 5.

[00144] Embodiment 23: the polypeptide of Embodiment 19, wherein the sPTH comprises an amino acid sequence set forth by SEQ ID NO: 6.

[00145] Embodiment 24: the polypeptide of Embodiment 23, wherein the amino acid sequence set forth by SEQ ID NO: 6 is at the N-terminus of the sPTH.

[00146] Embodiment 25: the polypeptide of Embodiment 19, wherein the sPTH comprises an amino acid sequence having at least about 55% sequence identity to a sequence selected from the group consisting of SEQ ID NOs: 102-106 and SEQ ID NOs: 132-155. [00147] Embodiment 26: the polypeptide of Embodiment 19, wherein the sPTH comprises an amino acid sequence having about 75-97% sequence identity to a sequence selected from the group consisting of SEQ ID NOs: 102-106 and SEQ ID NOs: 132-155.

[00148] Embodiment 27: the polypeptide of Embodiment 1, wherein the sPTH comprises an amino acid sequence selected from the group consisting of SEQ ID NOs: 102-106 and SEQ ID NOs: 132-155.

[00149] Embodiment 28: the polypeptide of Embodiment 1, wherein the sPTH comprises the amino acid sequence of SEQ ID NO: 107.

[00150] Embodiment 29: the polypeptide of any one of Embodiments 6, 12 and 21, wherein the at least 1 amino acid substitution is a conservative substitution.

[00151] Embodiment 30: the polypeptide of Embodiment 29, wherein the at least 1 amino acid substitution is a highly conservative substitution.

[00152] Embodiment 31: the polypeptide of any one of Embodiments 2, 3, 7, 8, 13, 14 and 22, wherein the amino acid substitutions are conservative substitutions.

[00153] Embodiment 32: the polypeptide of Embodiment 31, wherein the amino acid substitutions are highly conservative substitutions.

[00154] Embodiment 33: the polypeptide of any one of Embodiments 1-32, wherein the sPTH binds PTHR with an affinity that is at least about 5% higher than a polypeptide having an amino acid sequence consisting of SEQ ID NO: 1, SEQ ID NO: 2, SEQ ID NO: 3, SEQ ID NO: 4 or SEQ ID NO: 5.

[00155] Embodiment 34: the polypeptide of any one of Embodiments 1-32, wherein the sPTH binds PTHR with an affinity that is at least about 5% lower than a polypeptide having an amino acid sequence consisting of SEQ ID NO: 1, SEQ ID NO: 2, SEQ ID NO: 3, SEQ ID NO: 4 or SEQ ID NO: 5.

[00156] Embodiment 35: the polypeptide of any one of Embodiments 1-32, wherein the sPTH binds PTHR with an affinity that is no more than about 5% lower than a polypeptide having an amino acid sequence consisting of SEQ ID NO: 1, SEQ ID NO: 2, SEQ ID NO: 3, SEQ ID NO:

4 or SEQ ID NO: 5.

[00157] Embodiment 36: the polypeptide of any one of Embodiments 1-35, wherein the sPTH is an agonist of PTHR.

[00158] Embodiment 37: the polypeptide of Embodiment 36, wherein the sPTH is a biased agonist of PTHR.

[00159] Embodiment 38: the polypeptide of any one of Embodiments 1-35, wherein the sPTH is an inverse agonist of PTHR. [00160] Embodiment 39: the polypeptide of any one of Embodiments 1-35, wherein the sPTH is an antagonist of PTHR.

[00161] Embodiment 40: the polypeptide of any one of Embodiments 1-39, wherein the polypeptide is conjugated to a heterologous moiety.

[00162] Embodiment 41 : the polypeptide of Embodiment 40, wherein the heterologous moiety is selected from the group consisting of polyethylene glycol (PEG), hexadecanoic acid, a hydrogel, a lipid nanoparticle, a polymer nanoparticle, and a heterologous polypeptide sequence, or a combination thereof.

[00163] Embodiment 42: the polypeptide of Embodiment 41, wherein the polymer nanoparticle comprises poly(lactic-co-glycolic) acid (PLGA).

[00164] Embodiment 43: the polypeptide of Embodiment 40, wherein the heterologous polypeptide sequence comprises a carrier polypeptide.

[00165] Embodiment 44: the polypeptide of Embodiment 43, wherein the carrier polypeptide is albumin or an Fc polypeptide.

[00166] Embodiment 45: a fusion protein comprising the polypeptide of any one of Embodiments 1-44.

[00167] Embodiment 46: a polynucleotide comprising a sequence encoding the polypeptide of any one of Embodiments 1-44 or the fusion protein of Embodiment 45.

[00168] Embodiment 47: an expression vector comprising the polynucleotide of Embodiment 46.

[00169] Embodiment 48: a host cell comprising the polynucleotide of Embodiment 46 or the expression vector of Embodiment 47.

[00170] Embodiment 49: a composition comprising the polypeptide of any one of Embodiments 1-44 or the fusion protein of Embodiment 45.

[00171] Embodiment 50: the composition of Embodiment 49, further comprising one or more pharmaceutical excipients, diluents, or carriers.

[00172] Embodiment 51 : a method of modulating PTHR signaling in a mammalian cell, comprising contacting the mammalian cell with an effective amount of the composition of Embodiment 49 or 50.

[00173] Embodiment 52: a method of treating a subject in need thereof, comprising administering an effective amount of the composition of Embodiment 49 or 50 to the subject. [00174] Embodiment 53 : a method of modulating PTHR signaling in a subject in need thereof, comprising administering an effective amount of the composition of Embodiment 49 or 50 to the subject. [00175] Embodiment 54: the method of Embodiment 52 or 53, wherein the subject is a mammal.

[00176] Embodiment 55: the method of Embodiment 54, wherein the subject is a human.

[00177] Embodiment 56: the method of any one of Embodiments 52-55, wherein the subject is an adult.

[00178] Embodiment 57: the method of any one of Embodiments 52-56, wherein the subject is at least 50 years old.

[00179] Embodiment 58: the method of any one of Embodiments 52-57, wherein the subject is a female.

[00180] Embodiment 59: the method of Embodiment 58, wherein the subject is peri- menopausal, menopausal, or post-menopausal.

[00181] Embodiment 60: the method of any one of Embodiments 52-59, wherein the subject has, or is at risk of developing, dysregulated calcium homeostasis.

[00182] Embodiment 61 : the method of any one of Embodiments 52-59, wherein the subject has, or is at risk of developing, a disorder selected from Osteoporosis, Blomstrand’s chondrodysplasia, Familial primary failure of tooth eruption, Eiken syndrome, Ollier disease, Hypercalcemia, Hyperparathyroidism, Jansen’s metaphyseal chondrodysplasia, Hypercalcemia, Hypercalciuria, Nephrocalcinosis and combinations thereof.

[00183] Embodiment 62: the method of Embodiment 61, wherein the sPTH is an agonist of PTHR.

[00184] Embodiment 63 : the method of Embodiment 62, wherein the sPTH is a biased agonist of PTHR.

[00185] Embodiment 64: the method of any one of Embodiments 52-63, wherein the subject has, or is at risk of developing, low bone density.

[00186] Embodiment 65: the method of any one of Embodiments 52-59, wherein the subject has, or is at risk of developing, a disorder selected from Blomstrand’s lethal chondrodysplasia, Ollier disease, familial primary failure of tooth eruption, Eiken syndrome, brachydactyly type E, hypoparathyroidism, osteoporosis and combinations thereof.

[00187] Embodiment 66: the method of any one of Embodiments 52-59, wherein the subject has, or is at risk of developing, osteoporosis.

[00188] Embodiment 67: the method of any one of Embodiments 52-66, wherein the amount is effective to promote calcium homeostasis, increase, maintain or reduce a decrease of bone mineral density, reduce risk of fracture, promote fracture healing or a combination of the foregoing. [00189] Embodiment 68: the method of any one of Embodiments 52-67, wherein the effective amount does not induce catabolic bone resorption.

[00190] Embodiment 69: the method of any one of Embodiments 52-59, wherein the subject has, or is at increased risk of developing, a disorder selected from: hypercalcemia, hyperparathyroidism, parathyroid carcinoma, metastatic bone disease and combinations thereof. [00191] Embodiment 70: the method of Embodiment 69, wherein the hyperparathyroidism occurs as a complication of parathyroid carcinoma.

[00192] Embodiment 71 : the method of Embodiment 69 or 70, wherein the metastatic bone disease occurs with associated hypercalcemia.

[00193] Embodiment 72: the method of any one of Embodiments 52-59, wherein the subject has, or is at increased risk of developing, a disorder selected from Jansen's metaphyseal chondrodysplasia, hyperparathyroidism, hypercalcemia, hypercalciuria, nephrocalcinosis, chronic kidney disease and combinations thereof.

[00194] Embodiment 73: the method of Embodiment 72, wherein the chronic kidney disease occurs in conjunction with, or as a result of, hypercalcemia, hypercalciuria, nephrocalcinosis or a combination thereof.

[00195] Examples

[00196] Sequences predicted to bind and activate PTHR were generated using computational models and solved structures of PTHR, including a recent CryoEM report published by Zhao LH et al ., Science 364, 148-53 (2019). Sequences predicted to optimally bind to the receptor while retaining a similar structure to the native ligand. Families of sequences were generated as described in Table 2.

Example 1. Synthesis of peptide

[00197] The peptide is produced using one of two methods known in the art: recombinant production from bacteria or chemical synthesis.

[00198] For recombinant production, the DNA sequences of the peptide is encoded in a suitable DNA vector for bacterial production, e.g. a PET vector. The bacteria are transformed with the plasmid and grown in suitable growth medium. When the bacteria have reached log growth stage the translation of the plasmid is induced, e.g. with IPTG. The protein is harvested from bacteria by lysis and recovery from inclusion bodies.

[00199] For solid phase chemical synthesis, standard methods are described in Stawikowski and Fields, Curr Protoc Protein Sci 2002, Feb. Chapter 18.1, available at the following uniform resource locator: www.ncbi.nlm.nih.gov/pmc/articles/PMC3564544.

Example 2 Testing receptor activity in vitro for agonism. antagonism and inverse agonism [00200] For measuring PTHR activity, standard methods such as cAMP accumulation assays, e.g., as described in Hattersley G etal., Endocrinology , 157(1): 141-49 (2016), are used. These assays are performed at room temperature on cells transfected with plasmid DNA encoding PTHR variants (sPTHRs) provided by the invention. Standard kits, e.g. , cAMP-Glo™ assay by Promega, are used to measure cAMP levels in cells with a homogeneous, bioluminescent and high-throughput assay that monitors cAMP production (see, e.g., Kumar M et al. , Assay Drug Dev Technol. 5(2): 237-45 (2007). The assay is based on the principle that cyclic AMP (cAMP) stimulates protein kinase A (PKA) holoenzyme activity, which in turn decreases available ATP, leading to decreased light production in a coupled luciferase reaction.

[00201] The assay is performed following manufacturer’s protocols. Cells are treated with the peptide at various concentrations. Cells are then lysed with a lysis buffer. After adding a PKA reaction mix, the cell lysates are incubated for 20 minutes. Then a developing buffer containing the Kinase-Glo reagent is added and plates are incubated for 10 minutes. Finally, luminescence is measured using a plate-reading luminometer. [00202] a) Agonist activity

[00203] The produced peptide is tested for activation of the receptor in cell lines that recombinantly express PTHR as described in, for example, Gardella et al. , Endocrinology 137(9): 3936-41 (1996). Briefly, COS-7 cells are cultured in DMEM supplemented with 10% FBS. Cells are transfected with DEAE/dextran and plasmid DNA (100 ng/well) encoding PTHR cDNA. Receptor assays are performed with intact COS-7 cells (500,000 cells/well) three days after transfection.

[00204] To test for agonist activity, cells are treated with the agonist peptide at various concentrations. PTHR activation is then measured using a cAMP accumulation assay (e.g. cAMP-Glo™ assay) as described herein. It is expected that activation of the PTHR by an agonist peptide leads to accumulation of cAMP inside the cell, which is reflected as a higher luminescence reading than in control or untreated cells.

[00205] b) Antagonist activity

[00206] The produced peptide is tested for inhibition of receptor activation in cell lines that recombinantly express PTHR as described in the agonist activity section. To test for antagonist activity, cells are treated with the antagonist peptide at various concentrations together with a validated agonist at a fixed concentration (e.g. PTH 1-34) at 1 nM as described in Shimizu N et al. BiolChem. 280(3): 1797-807 (2005).

[00207] PTHR activity is then measured using a cAMP accumulation assay (e.g. cAMP- Glo™ assay) as described herein. Inhibition of PTHR activation by an antagonist peptide prevents the accumulation of cAMP inside the cell, which is reflected as a lower luminescence reading than in cells treated with a validated agonist.

[00208] c) Inverse agonist activity

[00209] The produced peptide is tested for reducing basal receptor activity in cell lines that recombinantly express a gain-of-function mutant of PTHR as described in, for example, Saito H et al., J Clin Endocrinol Metab. 103(7): 2660-69 (2018). Briefly, HEK293 cells are seeded in 96- well plates at a density of 20,000 cells/well and are cultured in DMEM supplemented with 10% FBS. Cells are transfected with DEAE/dextran and plasmid DNA (100 ng/well) encoding a gain- of-function mutant of PTHR (e.g. H223R). Receptor assays are performed with intact HEK293 cells (100,000 cells/well) two days after transfection.

[00210] Cells are treated with the inverse agonist peptide at various concentrations. Mutant PTHR activation is then measured using a cAMP accumulation assay (e.g. cAMP-Glo™ assay) as described herein. It is expected that a reduction in basal mutant PTHR activity leads to a decrease of cAMP inside the cell, which is reflected as a lower luminescence reading than in control or untreated cells.

Example 3 Testing receptor activity in vitro for biased agonism [00211] To test for biased b-arrestin signaling of PTHR, standard methods measuring b-arrestin recruitment are performed, e.g., as described in Wang T el al ., Bethesda (MD): Eli Lilly & Company and the National Center for Advancing Translational Sciences; 2004-2017 Nov 20. Standard kits include, e.g. PathHunter b-arrestin assay by DiscoverX. A CHO cell line, stably expressing PTHR carboxyl-terminally extended with a peptide fragment of b- galactosidase and a corresponding deletion mutant of b-galactosidase fused to b-arrestin is used. The assay measures the level of reconstituted b-galactosidase with a homogeneous, bioluminescent, and high-throughput assay. The assay is based on the principle that b-arrestin recruitment brings about reconstitution of an active b-galactosidase, which catalyzes a bioluminescence reaction from an exogenous substrate to generate a bioluminescence readout. [00212] The assay is performed following manufacturer’s protocols. Cells are treated with the peptide at various concentrations. Cells are then incubated with the provided Working Detection Solution for 1 hour at room temperate in the dark. Finally, luminescence is measured using a plate-reading luminometer.

[00213] It is expected that an increase in b-arrestin recruitment to PTHR leads to an increase of reconstituted active b-galactosidase inside the cell, which is reflected as a higher luminescence reading than in control or untreated cells.

Example 4 Testing activity in vivo

[00214] The peptides are assessed for functional activity in the standard laboratory model of osteoporosis, namely the ovariectomized rat model. In this model, after surgical ovariectomy, bone resorption exceeds bone formation initially, causing bone loss. Soon thereafter, bone remodeling reaches a steady state, where resorption and formation are balanced. Statistically significant bone loss is seen in the proximal tibial metaphysis after 14 days, in the lumbar vertebral body after 60 days, and in the femoral neck after 30 days (see e.g., Lelovas et al. , Comp Med 58(5): 424-30 (2008)).

[00215] Peptides are administered daily via subcutaneous injections to the laboratory rat (see e.g., Bemhardsson M etal., Acta Orthop 89(6): 674-77 (2018)). Bone density is measured non- invasively by densitometry and micro-computerized tomography (MicroCT), and invasively by histomorphometry and mechanical strength evaluation including three-point bending, four-point bending, and torsion testing.

[00216] It is expected that peptides that signal through PTHR (e.g, agonists or biased signaling agonists of PTHR) lead to less bone loss in the ovariectomized rat, thus increasing bone density and bone strength compared to untreated control animals.

Example 5 Treating a human patient with osteoporosis

[00217] A patient is diagnosed as having or being at risk for osteoporosis, e.g. a postmenopausal woman aged 49 to 86 years with bone mineral density T score less than or equal to -2.5 and greater than -5.0 assessed by dual energy X-ray absorptiometry (see Miller PD et al ., JAMA 316(7): 722-33 (2016)). The patient is prescribed treatment with the peptides described herein, e.g. , an agonist of PTHR or biased signaling agonist of PTHR.

[00218] A method for administration of PTHR agonists and bone density assessment is described, for example, in Miller PD et al. , JAMA 316(7): 722-33 (2016). The peptides are administered daily via subcutaneous injections, and the patient’s bone mineral density is monitored by dual-energy X-ray absorptiometry.

Example 6 Bioluminescence Resonance Energy Transfer (BRET) assays [00219] Synthesis: Peptides were synthesized by Genscript using standard synthesis methods and purified using TFA. Peptides were shipped lyophilized and resuspend in DMSO prior to use.

[00220] a) Measuring b-arrestin recruitment

[00221] HEK293T cells (CRL-3216, ATCC, VA) at a density of 2 million/mL, were transfected with beta-arrestinl or beta-arrestin2-Rluc cDNA (1 ng/well) (Life Technologies Corporation, CA) and Flag-PTHRl-YFP cDNA (199 ng/well) (Genwiz, New Jersey) using polyethylenimine (0.8 mL/well) (Polysciences, PA). 18-24 hours post transfection, the Luciferase substrate Coelenterazine (NanoLight Technologies, AZ) was added to cells, a baseline BRET measurement was taken after 5 minutes incubation, and then serial dilutions of peptides, diluted in PBS (with 0.5mM MgCl ₂ + 0.1% BSA FAF), were added to cells, and BRET signal was measured every 2 minutes for 30 minutes on Hybrid Multi -Mode Reader (Synergy Neo2,

BioTek, VT). Seventy-five peptides were tested in the b-arrestin recruitment assay.

[00222] b) Measuring cAMP accumulation

[00223] CHO-Kl/Gal5/PTHRl (Genscript USA, NJ) cells were cultured in a 10-cm Petri dish and harvested when cell culture confluence reached 80-85%. Cell suspension (5 mL) was seeded in 384-well plates at a density of 3,000 cells/well. Cells were treated with test samples (5 mL) or agonist (PTH 1-34) for 30 minutes at room temperature. cAMP-d2 working solution (5 mL) and anti-cAMP-Cryptate working solution (5 mL) were added to cells and incubated for 60 minutes at room temperature. The signal of the assay plate was read with PheraStar (BMG LABTECH,

NC), an HTRF compatible reader.

[00224] c) Results

[00225] The b-arrestin recruitment and cAMP accumulation assays were performed on designed peptides to determine their ability to activate the PTHR receptor. PTH 1-34 was the positive control in both assays. In the b-arrestinl recruitment assays, many generated peptides were able to elicit similar magnitudes of response as compared to PTH 1-34 (e.g., Rl-101, Rl- 81, R2-13, R2-29 and R2-36), while two peptides demonstrated higher levels of recruitment of b- arrestin 1 (R2-38 and R2-52) (FIG. 1). Similarly, in the b-arrestin2 assay, many peptides demonstrated activity similar to the control peptide (e.g., R2-34, R2-33, R2-31, R2-30 and R2- 42) while nine peptides showed increased activity as compared to control (R2-48, R2-50, R2-8, R2-1, Rl-101, R2-25, R2-36, Rl-81 and R2-29) (FIG. 2). In both B-arrestin assays there were also peptides that showed less activity than the control peptide.

[00226] Varying degrees of activity were also observed for the designed peptides in the cAMP accumulation assay. In this assay there were more peptides demonstrating increased activity as compared to the control peptide (R2-14, R2-40, R2-45, R2-43, R2-44, R2-24, R2-41, R2-22, Rl- 41, Rl-94, R2-51, R2-47, R2-37, Rl-101, and Rl-103) whereas some peptides demonstrated activity similar to the control peptide (e.g., R2-36, R2-35, Rl-96, R2-27 and R2-25) (FIG. 3). [00227] For more details, see Tables 7 and 8.

Table 7 Table 8. [00228] It is expected that treatment with the peptides will lead to reduced bone density loss, reduced risk of fracture, and improvement of the patient’s osteoporosis.

[00229] It should be understood that for all numerical bounds describing some parameter in this application, such as “about,” “at least,” “less than,” and “more than,” the description also necessarily encompasses any range bounded by the recited values. Accordingly, for example, the description “at least 1, 2, 3, 4, or 5” also describes, inter alia , the ranges 1-2, 1-3, 1-4, 1-5, 2-3, 2-4, 2-5, 3-4, 3-5, and 4-5, et cetera.

[00230] For all patents, applications, or other reference cited herein, such as non-patent literature and reference sequence information, it should be understood that they are incorporated by reference in their entirety for all purposes as well as for the proposition that is recited. Where any conflict exists between a document incorporated by reference and the present application, this application will control. All information associated with reference gene sequences disclosed in this application, such as GenelDs or accession numbers (typically referencing NCBI accession numbers), including, for example, genomic loci, genomic sequences, functional annotations, allelic variants, and reference mRNA (including, e.g, exon boundaries or response elements) and protein sequences (such as conserved domain structures), as well as chemical references (e.g, PubChem compound, PubChem substance, or PubChem Bioassay entries, including the annotations therein, such as structures and assays, et cetera), are hereby incorporated by reference in their entirety.

[00231] Headings used in this application are for convenience only and do not affect the interpretation of this application.

[00232] Preferred features of each of the aspects provided by the invention are applicable to all of the other aspects of the invention mutatis mutandis and, without limitation, are exemplified by the dependent claims and also encompass combinations and permutations of individual features (e.g, elements, including numerical ranges and exemplary embodiments) of particular embodiments and aspects of the invention, including the working examples. For example, particular experimental parameters exemplified in the working examples can be adapted for use in the claimed invention piecemeal without departing from the invention. For example, for materials that are disclosed, while specific reference of each of the various individual and collective combinations and permutations of these compounds may not be explicitly disclosed, each is specifically contemplated and described herein. Thus, if a class of elements A, B, and C are disclosed as well as a class of elements D, E, and F and an example of a combination of elements A-D is disclosed, then, even if each is not individually recited, each is individually and collectively contemplated. Thus, in this example, each of the combinations A-E, A-F, B-D, B-E, B-F, C-D, C-E, and C-F are specifically contemplated and should be considered disclosed from disclosure of A, B, and C; D, E, and F; and the example combination A-D. Likewise, any subset or combination of these is also specifically contemplated and disclosed. Thus, for example, the sub-groups of A-E, B-F, and C-E are specifically contemplated and should be considered disclosed from disclosure of A, B, and C; D, E, and F; and the example combination A-D. This concept applies to all aspects of this application, including elements of a composition of matter and steps of method of making or using the compositions.

[00233] The forgoing aspects of the invention, as recognized by the person having ordinary skill in the art following the teachings of the specification, can be claimed in any combination or permutation to the extent that they are novel and non-obvious over the prior art — thus, to the extent an element is described in one or more references known to the person having ordinary skill in the art, they may be excluded from the claimed invention by, inter alia , a negative proviso or disclaimer of the feature or combination of features.

[00234] The teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety.

[00235] While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments encompassed by the appended claims.