Activin receptor type IIa variants and methods of use thereof

Abstract

The invention features polypeptides that include an extracellular ActRlla variant. In some embodiments, a polypeptide of the invention includes an extracellular ActRlla variant fused to an Fc domain monomer or moiety. The invention also features pharmaceutical compositions and methods of using the polypeptides to treat diseases and conditions involving bone damage, e.g., primary osteoporosis, secondary osteoporosis, osteopenia, osteopetrosis, fracture, bone cancer or cancer metastasis-related bone loss, Paget's disease, renal osteodystrophy, treatment-related bone loss, diet-related bone loss, bone loss associated with the treatment of obesity, low gravity-related bone loss, or immobility-related bone loss.

Claims

1. A method of reducing bone resorption, increasing bone formation, increasing bone strength, or reducing risk of bone fracture in a subject having a bone disease, comprising administering to the subject a therapeutically effective amount of a polypeptide comprising an extracellular activin receptor type IIa (ActRIIa) variant, the variant having a sequence of GAILGRSETQECLX.sub.1X.sub.2NANWX.sub.3X.sub.4X.sub.5X.sub.6TNQTGVEX.sub.7CX.sub.8GX.sub.9X.sub.10X.sub.11X.sub.12X.sub.13X.sub.14HCX.sub.15ATWX.sub.16NISGSIEIVX.sub.17X.sub.18GCX.sub.19X.sub.20X.sub.21DX.sub.22NCYDRTDCVEX.sub.23X.sub.24X.sub.25X.sub.26PX.sub.27VYFCCCEGNMCNEKFSYFPEMEVTQPTS (SEQ ID NO: 1), wherein X.sub.1 is F or Y; X.sub.2 is Y; X.sub.3 is E; X.sub.4 is L; X.sub.5 is D or E; X.sub.6 is R; X.sub.7 is P or R; X.sub.8 is E; X.sub.9 is E; X.sub.10 is K or Q; X.sub.11 is D; X.sub.12 is K; X.sub.13 is R; X.sub.14 is L; X.sub.15 is F or Y; X.sub.16 is K, R, or A; X.sub.17 is K; X.sub.18 is K; X.sub.19 is W; X.sub.20 is L; X.sub.21 is D; X.sub.22 is I, F, or A; X.sub.23 is T; X.sub.24 is K or E; X.sub.25 is E; X.sub.26 is N; and X.sub.27 is Q.

2. The method of claim 1, wherein the subject has or is at risk of osteoporosis, osteopenia, osteopetrosis, fracture, bone cancer or cancer metastasis-related bone loss, Paget's disease, renal osteodystrophy, treatment-related bone loss, diet-related bone loss, bone loss associated with the treatment of obesity, low gravity-related bone loss, or immobility-related bone loss.

3. The method of claim 1, wherein the variant has the sequence of any one of SEQ ID NOs: 6-72.

4. The method of claim 1, wherein the ActRIIa variant has the sequence of SEQ ID NO: 6, SEQ ID NO: 38, SEQ ID NO: 41, SEQ ID NO: 44, SEQ ID NO: 58, SEQ ID NO: 69, SEQ ID NO: 70, SEQ ID NO: 71, or SEQ ID NO: 72.

5. The method of claim 1, wherein X.sub.16 is K or R and X.sub.22 is I or F.

6. The method of claim 5, wherein X.sub.1 is F and X.sub.10 is K.

7. The method of claim 1, wherein the polypeptide further comprises a C-terminal extension of one or more amino acids at the C-terminus of the ActRIIa variant.

8. The method of claim 7, wherein the C-terminal extension is NP or NPVTPK (SEQ ID NO: 155).

9. The method of claim 1, wherein the polypeptide further comprises an Fc domain monomer, an Fc domain, an albumin-binding peptide, a fibronectin domain, or a human serum albumin fused to the C-terminus of the ActRIIa variant by way of a linker.

10. The method of claim 9, wherein the polypeptide comprises an Fc domain monomer fused to the C-terminus of the ActRIIa variant by way of a linker.

11. The method of claim 10, wherein the polypeptide is in the form of a homodimer.

12. A method of treating a subject having a bone disease, comprising administering to the subject a therapeutically effective amount of a polypeptide comprising an extracellular activin receptor type IIa (ActRIIa) variant, the variant having a sequence of GAILGRSETQECLX.sub.1X.sub.2NANWX.sub.3X.sub.4X.sub.5X.sub.6TNQTGVEX.sub.7CX.sub.8GX.sub.9X.sub.10X.sub.11X.sub.12X.sub.13X.sub.14HCX.sub.15ATWX.sub.16NISGSIEIVX.sub.17X.sub.18GCX.sub.19X.sub.20X.sub.21DX.sub.22NCYDRTDCVEX.sub.23X.sub.24X.sub.25X.sub.26PX.sub.27VYFCCCEGNMCNEKFSYFPEMEVTQPTS (SEQ ID NO: 1), wherein X.sub.1 is F or Y; X.sub.2 is Y; X.sub.3 is E; X.sub.4 is L; X.sub.5 is D or E; X.sub.6 is R; X.sub.7 is P or R; X.sub.8 is E; X.sub.9 is E; X.sub.10 is K or Q; X.sub.11 is D; X.sub.12 is K; X.sub.13 is R; X.sub.14 is L; X.sub.15 is F or Y; X.sub.16 is K, R, or A; X.sub.17 is K; X.sub.18 is K; X.sub.19 is W; X.sub.20 is L; X.sub.21 is D; X.sub.22 is I, F, or A; X.sub.23 is T; X.sub.24 is K or E; X.sub.25 is E; X.sub.26 is N; and X.sub.27 is Q.

13. The method of claim 12, wherein the bone disease is osteoporosis, osteopenia, osteopetrosis, bone fracture, bone cancer or cancer metastasis-related bone loss, Paget's disease, renal osteodystrophy, treatment-related bone loss, diet-related bone loss, bone loss associated with the treatment of obesity, low gravity-related bone loss, or immobility-related bone loss.

14. The method claim 13, wherein the bone cancer is multiple myeloma.

15. The method of claim 12, wherein the variant has the sequence of any one of SEQ ID NOs: 6-72.

16. The method of claim 12, wherein the ActRIIa variant has the sequence of SEQ ID NO: 6, SEQ ID NO: 38, SEQ ID NO: 41, SEQ ID NO: 44, SEQ ID NO: 58, SEQ ID NO: 69, SEQ ID NO: 70, SEQ ID NO: 71, or SEQ ID NO: 72.

17. The method of claim 12, wherein X.sub.16 is K or R and X.sub.22 is I or F.

18. The method of claim 17, wherein X.sub.1 is F and X.sub.10 is K.

19. The method of claim 12, wherein the polypeptide further comprises a C-terminal extension of one or more amino acids at the C-terminus of the ActRIIa variant.

20. The method of claim 19, wherein the C-terminal extension is NP or NPVTPK (SEQ ID NO: 155).

21. The method of claim 12, wherein the polypeptide further comprises an Fc domain monomer, an Fc domain, an albumin-binding peptide, a fibronectin domain, or a human serum albumin fused to the C-terminus of the ActRIIa variant by way of a linker.

22. The method of claim 21, wherein the polypeptide comprises an Fc domain monomer fused to the C-terminus of the ActRIIa variant by way of a linker.

23. The method of claim 22, wherein the polypeptide is in the form of a homodimer.

Description

DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a sequence alignment showing the wild-type sequences of extracellular ActRIIa and ActRIIb and the amino acid substitutions in ActRIIa variants. Sequences shown in FIG. 1 include an extracellular portion of ActRIIa (amino acids 12-92 of SEQ ID NO: 73), an extracellular portion of ActRIIB (amino acids 10-90 of SEQ ID NO: 74), ActRIIA/B (SEQ ID NO: 69), ActRIIB/A (SEQ ID NO: 149), ActRIIA/Bdelta9 (SEQ ID NO: 58), ActRIIA/Bdelta9min (SEQ ID NO: 6), ActRIIA/B+ (SEQ ID NO: 150), ActRIIa/bdelta9m2 (SEQ ID NO: 38), ActRIIa/bdelta9m3 (SEQ ID NO: 41), ActRIIa/bdelta9m4 (SEQ ID NO: 44), ActRIIa/bmax1 (SEQ ID NO: 70), ActRIIa/bmax2 (SEQ ID NO: 71), and ActRIIa/bmax3 (SEQ ID NO: 72).

(2) FIG. 2 is a series of graphs depicting bone morphometry measurements made after treatment of eight-week old male C57Bl/6 mice with either vehicle or ActRII A/B (SEQ ID NO: 69) at 20 mg/kg biweekly for four weeks. Trabecular bone volume fraction, trabecular number, trabecular thickness, and trabecular spacing data were calculated based on a 50-slice region of scan volume selected immediately distal to the proximal tibial growth plate.

(3) FIG. 3 is graph showing the effect of treatment with ActRIIA/B-Fc on trabecular bone volume fraction in a mouse model of osteoporosis. Treatment with ActRIIA/B-Fc increased bone volume fraction (reduced bone loss) associated with orchiectomy (*=p≤0.05; ****=p≤0.0001).

DETAILED DESCRIPTION OF THE INVENTION

(4) The invention features polypeptides that include an extracellular activin receptor type IIa (ActRIIa) variant. In some embodiments, a polypeptide of the invention includes an extracellular ActRIIa variant fused to a moiety (e.g., Fc domain monomer, a wild-type Fc domain, an Fc domain with amino acid substitutions (e.g., one or more substitutions that reduce dimerization), an albumin-binding peptide, a fibronectin domain, or a human serum albumin). A polypeptide including an extracellular ActRIIa variant fused to an Fc domain monomer may also form a dimer (e.g., homodimer or heterodimer) through the interaction between two Fc domain monomers. The ActRIIa variants described herein have weak binding affinity or no binding affinity to bone morphogenetic protein 9 (BMP9) compared to activins and myostatin. The invention also includes methods of treating bone diseases and conditions involving bone damage by increasing bone mineral density or bone formation or affecting myostatin, activin, and/or BMP9 signaling in a subject by administering to the subject a polypeptide including an extracellular ActRIIa variant described herein.

(5) I. Extracellular Activin Receptor Type IIa Variants

(6) Activin type II receptors are single transmembrane domain receptors that modulate signals for ligands in the transforming growth factor β (TGF-β) superfamily. Ligands in the TGF-β superfamily are involved in a host of physiological processes, such as muscle growth, vascular growth, cell differentiation, homeostasis, and osteogenesis. Ligands in the TGF-β superfamily include, e.g., activin, inhibin, growth differentiation factors (GDFs) (e.g., GDF8, also known as myostatin), and bone morphogenetic proteins (BMPs) (e.g., BMP9). Activins are expressed abundantly in bone tissues and regulate bone formation by controlling both osteoblast and osteoclast functions. Activin has been reported to be upregulated in bone disease and inhibit osteoblast activity. Myostatin is also implicated in bone homeostasis through increasing osteogenesis and inhibiting osteoblast activity. These data suggest that activin receptor ligands (e.g., activin and myostatin), promote bone resorption (e.g., bone loss), which could lead to diseases and conditions involving bone damage, such as primary osteoporosis, secondary osteoporosis, osteopenia, osteopetrosis, fracture, bone cancer or cancer metastasis-related bone loss, Paget's disease, renal osteodystrophy, treatment-related bone loss, diet-related bone loss, bone loss associated with the treatment of obesity, low gravity-related bone loss, or immobility-related bone loss. Methods that reduce or inhibit this signaling could, therefore, be used in the treatment of diseases and conditions involving bone damage.

(7) There exist two types of activin type II receptors: ActRIIa and ActRIIb. Studies have shown that BMP9 binds ActRIIb with about 300-fold higher binding affinity than ActRIIa (see, e.g., Townson et al., J. Biol. Chem. 287:27313, 2012). ActRIIa is known to have a longer half-life compared to ActRIIb. The present invention describes extracellular ActRIIa variants that are constructed by introducing amino acid residues of ActRIIb to ActRIIa, with the goal of imparting physiological properties conferred by ActRIIb, while also maintaining beneficial physiological and pharmacokinetic properties of ActRIIa. The optimum peptides confer significant increases in bone mineral density, while retaining longer serum half-life and low binding-affinity to BMP9, for example. The preferred ActRIIa variants also exhibit improved binding to activins and/or myostatin compared to wild-type ActRIIa, which allows them to compete with endogenous activin receptors for ligand binding and reduce or inhibit endogenous activin receptor signaling. These variants can be used to treat disorders in which activin receptor signaling is elevated, such bone disease, leading to a reduction in bone resorption (e.g., bone loss) or osteoclast activity, and an increase in bone formation, bone mineral density, or bone strength. In some embodiments, amino acid substitutions may be introduced to an extracellular ActRIIa variant to reduce or remove the binding affinity of the variant to BMP9. The wild-type amino acid sequences of the extracellular portions of human ActRIIa and ActRIIb are shown below.

(8) TABLE-US-00003 Human ActRIIa, extracellular portion (SEQ ID NO: 73): GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNIS GSIEIVKQGCWLDDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFP EMEVTQPTS Human ActRIIb, extracellular portion (SEQ ID NO: 74): GRGEAETRECIYYNANWELERTNQSGLERCEGEQDKRLHCYASWRNSSGT IELVKKGCWLDDFNCYDRQECVATEENPQVYFCCCEGNFCNERFTHLPEA GGPEVTYEPPPTAPT

(9) Polypeptides described herein include an extracellular ActRIIa variant having at least one amino acid substitution relative to the wild-type extracellular ActRIIa having the sequence of SEQ ID NO: 73 or the extracellular ActRIIa having any one of the sequences of SEQ ID NOs: 76-96. Possible amino acid substitutions at 27 different positions may be introduced to an extracellular ActRIIa variant (Table 1). In some embodiments, an extracellular ActRIIa variant may have at least 85% (e.g., at least 85%, 87%, 90%, 92%, 95%, 97%, or greater) amino acid sequence identity to the sequence of a wild-type extracellular ActRIIa (SEQ ID NO: 73). An extracellular ActRIIa variant may have one or more (e.g., 1-27, 1-25, 1-23, 1-21, 1-19, 1-17, 1-15, 1-13, 1-11, 1-9, 1-7, 1-5, 1-3, or 1-2; e.g., 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, or 27) amino acid substitutions relative the sequence of a wild-type extracellular ActRIIa (SEQ ID NO: 73). In some embodiments, an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having a sequence of SEQ ID NO: 1) may include amino acid substitutions at all of the 27 positions as listed in Table 1. In some embodiments, an extracellular ActRIIa variant may include amino acid substitutions at a number of positions, e.g., at 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, or 26 out of the 27 positions, as listed in Table 1.

(10) Amino acid substitutions can worsen or improve the activity and/or binding affinity of the ActRIIa variants of the invention. To maintain polypeptide function, it is important that the lysine (K) at position X.sub.17 in the sequences shown in Tables 1 and 2 (SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) be retained. Substitutions at that position can lead to a loss of activity. For example, an ActRIIa variant having the sequence GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCYATWRNISGSIEIVAKGCWLDDFNCYD RTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS (SEQ ID NO: 150) has reduced activity in vivo, indicating that the substitution of alanine (A) for lysine (K) at X.sub.17 is not tolerated. ActRIIa variants of the invention, including variants in Tables 1 and 2 (e.g., SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72), therefore, retain amino acid K at position X.sub.17.

(11) The ActRIIa variants of the invention preferably have reduced, weak, or no substantial binding to BMP9. BMP9 binding is reduced in ActRIIa variants containing the amino acid sequence TEEN (SEQ ID NO: 156) at positions X.sub.23, X.sub.24, X.sub.25, and X.sub.26, as well as in variants that maintain the amino acid K at position X24 and have the amino acid sequence TKEN (SEQ ID NO: 157) at positions X.sub.23, X.sub.24, X.sub.25, and X.sub.26. The sequences TEEN (SEQ ID NO: 156) and TKEN (SEQ ID NO: 157) can be employed interchangeably in the ActRIIa variants (e.g., the variants in Tables 1 and 2, e.g., SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) of the invention to provide reduced BMP9 binding.

(12) The ActRIIa variants of the invention may further include a C-terminal extension (e.g., additional amino acids at the C-terminus). The C-terminal extension can add one or more additional amino acids at the C-terminus (e.g., 1, 2, 3, 4, 5, 6, or more additional amino acids) to any of the variants shown in Tables 1 and 2 (e.g., SEQ ID NOs: 1-70 (e.g., SEQ ID NOs: 6-70)). One potential C-terminal extension that can be included in the ActRIIa variants of the invention is amino acid sequence NP. For example, the sequence including the C-terminal extension is SEQ ID NO: 71 (e.g., SEQ ID NO: 69 with a C-terminal extension of NP). Another exemplary C-terminal extension that can be included in the ActRIIa variants of the invention is amino acid sequence NPVTPK (SEQ ID NO: 155). For example, the sequence including the C-terminal extension is SEQ ID NO: 72 (e.g., SEQ ID NO: 69 with a C-terminal extension of NPVTPK (SEQ ID NO: 155)).

(13) TABLE-US-00004 TABLE 1 Amino acid substitutions in an extracellular ActRIIa variant having a sequence of any one of SEQ ID NOs: 1-5 GAILGRSETQECLX.sub.1X.sub.2NANWX.sub.3X.sub.4X.sub.5X.sub.6TNQTGVEX.sub.7CX.sub.8GX.sub.9X.sub.10X.sub.11 X.sub.12X.sub.13X.sub.14HCX.sub.15ATWX.sub.16NISGSIEIVX.sub.17X.sub.18GCX.sub.19X.sub.20X.sub.21DX.sub.22 NCYDRTDCVEX.sub.23X.sub.24X.sub.25X.sub.26PX.sub.27VYFCCCEGNMCNEKFSYFPEMEVT QPTS (SEQ ID NO: 1) GAILGRSETQECLFX.sub.2NANWX.sub.3X.sub.4X.sub.5X.sub.6TNQTGVEX.sub.7CX.sub.8GX.sub.9KX.sub.11X.sub.12 X.sub.13X.sub.14HCX.sub.15ATWX.sub.16NISGSIEIVX.sub.17X.sub.18GCX.sub.19X.sub.20X.sub.21DX.sub.22NCY DRTDCVEX.sub.23X.sub.24X.sub.25X.sub.26PX.sub.27VYFCCCEGNMCNEKFSYFPEMEVTQPT S (SEQ ID NO: 2) GAILGRSETQECLFX.sub.2NANWEX.sub.4X.sub.5RTNQTGVEX.sub.7CX.sub.8GX.sub.9KDKRX.sub.14HC X.sub.15ATWX.sub.16NISGSIEIVKX.sub.18GCWLDDX.sub.22NCYDRTDCVEX.sub.23X.sub.24X.sub.25 X.sub.26PX.sub.27VYFCCCEGNMCNEKFSYFPEMEVTQPTS (SEQ ID NO: 3) GAILGRSETQECLFX.sub.2NANWEX.sub.4DRTNQTGVEX.sub.7CX.sub.8GX.sub.9KDKRX.sub.14HC X.sub.15ATWX.sub.16NISGSIEIVKX.sub.18GCWLDDX.sub.22NCYDRTDCVEX.sub.23KX.sub.25 X.sub.26PX.sub.27VYFCCCEGNMCNEKFSYFPEMEVTQPTS (SEQ ID NO: 4) GAILGRSETQECLFX.sub.2NANWEX.sub.4DRTNQTGVEPCX.sub.8GX.sub.9KDKRXHHCFAT WKNISGSIEIVKX.sub.18GCWLDDINCYDRTDCVEX.sub.23KX.sub.25X.sub.26PX.sub.27VYFC CCEGNMCNEKFSYFPEMEVTQPTS (SEQ ID NO: 5) X.sub.1 F or Y X.sub.2 F or Y X.sub.3 E or A X.sub.4 K or L X.sub.5 D or E X.sub.6 R or A X.sub.7 P or R X.sub.8 Y or E X.sub.9 D or E X.sub.10 K or Q X.sub.11 D or A X.sub.12 K or A X13 R or A X.sub.14 R or L X.sub.16 F or Y X.sub.16 K, R, or A X.sub.17 K, A, Y, F, or I X.sub.18 Q or K X.sub.19 W or A X.sub.20 L or A X.sub.21 D, K, R, A, F, G, M, N, or I X.sub.22 I, F, or A X.sub.23 K or T X.sub.24 K or E X.sub.26 D or E X.sub.26 S or N X.sub.27 E or Q

(14) In some embodiments of the extracellular ActRIIa variant having the sequence of SEQ ID NO: 2, X.sub.3 is E, X.sub.6 is R, X.sub.11 is D, X.sub.12 is K, X.sub.13 is R, X.sub.16 is K or R, X.sub.17 is K, X.sub.19 is W, X.sub.20 is L, X.sub.21 is D, and X.sub.22 is I or F. In some embodiments of the extracellular ActRIIa variant having the sequence of SEQ ID NO: 1 or 2, X.sub.17 is K. In some embodiments of the extracellular ActRIIa variant having the sequence of SEQ ID NOs: 1-3, X.sub.17 is K, X.sub.23 is T, X.sub.24 is E, X.sub.25 is E, and X.sub.26 is N. In some embodiments of the extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-5, X.sub.17 is K, X.sub.23 is T, X.sub.24 is K, X.sub.25 is E, and X.sub.26 is N.

(15) In some embodiments, a polypeptide described herein includes an extracellular ActRIIa variant having a sequence of any one of SEQ ID NOs: 6-72 (Table 2).

(16) TABLE-US-00005 TABLE 2 Extracellular ActRIIa variants having the sequences of SEQ ID NOs: 6-72 SEQ ID NO Amino Acid Sequence 6 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 7 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 8 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 9 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 10 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 11 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 12 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 13 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 14 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 15 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 16 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 17 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 18 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 19 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 20 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 21 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 22 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 23 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 24 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 25 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 26 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 27 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 28 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 29 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 30 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 31 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 32 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 33 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 34 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 35 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 36 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 37 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 38 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 39 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 40 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 41 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 42 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 43 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCFATWKNISGSIEIVKKGC WLDDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 44 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 45 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 46 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 47 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 48 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDINCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 49 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 50 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 51 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 52 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 53 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCFATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 54 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 55 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 56 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 57 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 58 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 59 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 60 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 61 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 62 GAILGRSETQECLFYNANWELDRTNQTGVEPCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 63 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETKENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 64 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDINCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 65 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCYATWKNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 66 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCFATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 67 GAILGRSETQECLFYNANWELDRTNQTGVERCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 69 GAILGRSETQECLFYNANWELERTNQTGVEPCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 69 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 70 GAILGRSETQECLYYNANWELERTNQTGVERCEGEQDKRLHCYATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS 71 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTSNP 72 GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCYATWRNISGSIEIVKKGCWL DDFNCYDRTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTSNPVTPK

(17) In some embodiments, a polypeptide of the invention including an extracellular ActRIIa variant (e.g., any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) has amino acid K at position X.sub.17. Altering the amino acid at position X.sub.17 can result in reduced activity. For example, an ActRIIa variant having the sequence GAILGRSETQECLFYNANWELERTNQTGVERCEGEKDKRLHCYATWRNISGSIEIVAKGCWLDDFNCYD RTDCVETEENPQVYFCCCEGNMCNEKFSYFPEMEVTQPTS (SEQ ID NO: 150) has reduced activity in vivo, indicating that the substitution of A for K at X.sub.17 is not tolerated.

(18) In some embodiments, a polypeptide of the invention including an extracellular ActRIIa variant (e.g., any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) with the sequence TEEN (SEQ ID NO: 156) at positions X.sub.23, X.sub.24, X.sub.25, and X.sub.26 can have a substitution of the amino acid K for the amino acid E at position X.sub.24. In some embodiments, a polypeptide of the invention including an extracellular ActRIIa variant (e.g., any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) with the sequence TKEN (SEQ ID NO: 157) at positions X.sub.23, X.sub.24, X.sub.25, and X.sub.26 can have a substitution of the amino acid E for the amino acid K at position X.sub.24. Polypeptides having the sequence TEEN (SEQ ID NO: 156) or TKEN (SEQ ID NO: 157) at positions X.sub.23, X.sub.24, X.sub.25, and X.sub.26 have reduced or weak binding to BMP9.

(19) In some embodiments, a polypeptide of the invention including an extracellular ActRIIa variant (e.g., any one of SEQ ID NOs: 1-70 (e.g., SEQ ID NOs: 6-70)) may further include a C-terminal extension (e.g., additional amino acids at the C-terminus). In some embodiments, the C-terminal extension is amino acid sequence NP. For example, the sequence including the C-terminal extension is SEQ ID NO: 71 (e.g., SEQ ID NO: 69 with a C-terminal extension of NP). In some embodiments, the C-terminal extension is amino acid sequence NPVTPK (SEQ ID NO: 155). For example, the sequence including the C-terminal extension is SEQ ID NO: 72 (e.g., SEQ ID NO: 69 with a C-terminal extension of NPVTPK (SEQ ID NO: 155)). The C-terminal extension can add one or more additional amino acids at the C-terminus (e.g., 1, 2, 3, 4, 5, 6, or more additional amino acids).

(20) In some embodiments, a polypeptide of the invention including an extracellular ActRIIa variant may further include a moiety (e.g., Fc domain monomer, a wild-type Fc domain, an Fc domain with amino acid substitutions (e.g., one or more substitutions that reduce dimerization), an albumin-binding peptide, a fibronectin domain, or a human serum albumin), which may be fused to the N- or C-terminus (e.g., C-terminus) of the extracellular ActRIIa variant by way of a linker. In some embodiments, the moiety increases the stability or improves the pharmacokinetic properties of the polypeptide. A polypeptide including an extracellular ActRIIa variant fused to an Fc domain monomer may form a dimer (e.g., homodimer or heterodimer) through the interaction between two Fc domain monomers, which combine to form an Fc domain in the dimer.

(21) In some embodiments, an extracellular ActRIIa variant described herein does not have the sequence of any one of SEQ ID NOs: 76-96 shown in Table 3 below.

(22) TABLE-US-00006 TABLE 3 Excluded Extracellular ActRIIa Variants. SEQ ID NO Amino Acid Sequence 76 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWANISGSIEIVKQGCWL DDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 77 GAILGRSETQECLFFNANWAKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCWL DDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 78 GAILGRSETQECLFFNANWEKDATNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCWL DDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 79 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKAKRRHCFATWKNISGSIEIVKQGCWL DDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 80 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDARRHCFATWKNISGSIEIVKQGCWL DDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 81 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKARHCFATWKNISGSIEIVKQGCWL DDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 82 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVAQGCWL DDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 83 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVYQGCWL DDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 84 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVFQGCWL DDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 85 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVIQGCWL DDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 86 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCAL DDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 87 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCWA DDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 88 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCWL KDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 89 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCWL RDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 90 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCWL ADINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 91 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCWL FDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 92 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCWL GDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 93 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCWL MDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 94 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCWL NDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 95 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCWL IDINCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS 96 GAILGRSETQECLFFNANWEKDRTNQTGVEPCYGDKDKRRHCFATWKNISGSIEIVKQGCWL DDANCYDRTDCVEKKDSPEVYFCCCEGNMCNEKFSYFPEMEVTQPTS

(23) Furthermore, in some embodiments, a polypeptide described herein has a serum half-life of at least 7 days in humans. The polypeptide may bind to bone morphogenetic protein 9 (BMP9) with a K.sub.D of 200 pM or higher. The polypeptide may bind to activin A with a K.sub.D of 10 pM or higher. In some embodiments, the polypeptide does not bind to BMP9 or activin A. In some embodiments, the polypeptide binds to activin and/or myostatin and exhibits reduced (e.g., weak) binding to BMP9. In some embodiments, the polypeptide that has reduced or weak binding to BMP9 has the sequence TEEN (SEQ ID NO: 156) or TKEN (SEQ ID NO: 157) at positions X.sub.23, X.sub.24, X.sub.25, and X.sub.26.

(24) Additionally, in some embodiments, the polypeptide may bind to human BMP9 with a K.sub.D of about 200 pM or higher (e.g., a K.sub.D of about 200, 300, 400, 500, 600, 700, 800, or 900 pM or higher, e.g., a K.sub.D of about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, or 50 nM or higher, e.g., a K.sub.D of between about 200 pM and about 50 nM). In some embodiments, the polypeptide does not substantially bind to human BMP9. In some embodiments, the polypeptide may bind to human activin A with a K.sub.D of about 800 pM or less (e.g., a K.sub.D of about 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 pM or less, e.g., a K.sub.D of between about 800 pM and about 200 pM). In some embodiments, the polypeptide may bind to human activin B with a K.sub.D of 800 pM or less (e.g., a K.sub.D of about 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 pM or less, e.g., a K.sub.D of between about 800 pM and about 200 pM) The polypeptide may also bind to growth and differentiation factor 11 (GDF-11) with a K.sub.D of approximately 5 pM or higher (e.g., a K.sub.D of about 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, or 200 pM or higher).

(25) II. Fc Domains

(26) In some embodiments, a polypeptide described herein may include an extracellular ActRIIa variant fused to an Fc domain monomer of an immunoglobulin or a fragment of an Fc domain to increase the serum half-life of the polypeptide. A polypeptide including an extracellular ActRIIa variant fused to an Fc domain monomer may form a dimer (e.g., homodimer or heterodimer) through the interaction between two Fc domain monomers, which form an Fc domain in the dimer. As conventionally known in the art, an Fc domain is the protein structure that is found at the C-terminus of an immunoglobulin. An Fc domain includes two Fc domain monomers that are dimerized by the interaction between the C.sub.H3 antibody constant domains. A wild-type Fc domain forms the minimum structure that binds to an Fc receptor, e.g., FcγRI, FcγRIIa, FcγRIIb, FcγRIIIa, FcγRIIIb, FcγRIV. In some embodiments, an Fc domain may be mutated to lack effector functions, typical of a “dead” Fc domain. For example, an Fc domain may include specific amino acid substitutions that are known to minimize the interaction between the Fc domain and an Fcγ receptor. In some embodiments, an Fc domain is from an IgG1 antibody and includes amino acid substitutions L234A, L235A, and G237A. In some embodiments, an Fc domain is from an IgG1 antibody and includes amino acid substitutions D265A, K322A, and N434A. The aforementioned amino acid positions are defined according to Kabat (Sequences of Proteins of Immunological Interest, 5th Ed. Public Health Service, National Institutes of Health, Bethesda, Md. (1991)). The Kabat numbering of amino acid residues may be determined for a given antibody by alignment at regions of homology of the sequence of the antibody with a “standard” Kabat numbered sequence. Furthermore, in some embodiments, an Fc domain does not induce any immune system-related response. For example, the Fc domain in a dimer of a polypeptide including an extracellular ActRIIa variant fused to an Fc domain monomer may be modified to reduce the interaction or binding between the Fc domain and an Fcγ receptor. The sequence of an Fc domain monomer that may be fused to an extracellular ActRIIa variant is shown below (SEQ ID NO: 97):

(27) TABLE-US-00007 THTCPPCPAPELLGGPSVFLFPPKPKDTLMISRTPEVTCVVVDVSHEDPE VKFNWYVDGVEVHNAKTKPREEQYNSTYRVVSVLTVLHQDWLNGKEYKCK VSNKALPVPIEKTISKAKGQPREPQVYTLPPSREEMTKNQVSLTCLVKGF YPSDIAVEWESNGQPENNYKTTPPVLDSDGPFFLYSKLTVDKSRWQQGNV FSCSVMHEALHNHYTQKSLSLSPGK

(28) In some embodiments, an Fc domain is from an IgG1 antibody and includes amino acid substitutions L12A, L13A, and G15A, relative to the sequence of SEQ ID NO: 97. In some embodiments, an Fc domain is from an IgG1 antibody and includes amino acid substitutions D43A, K100A, and N212A, relative to the sequence of SEQ ID NO: 97. In some embodiments, an extracellular ActRIIa variant described herein (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) may be fused to the N- or C-terminus of an Fc domain monomer (e.g., SEQ ID NO: 97) through conventional genetic or chemical means, e.g., chemical conjugation. If desired, a linker (e.g., a spacer) can be inserted between the extracellular ActRIIa variant and the Fc domain monomer. The Fc domain monomer can be fused to the N- or C-terminus (e.g., C-terminus) of the extracellular ActRIIa variant.

(29) In some embodiments, a polypeptide described herein may include an extracellular ActRIIa variant fused to an Fc domain. In some embodiments, the Fc domain contains one or more amino acid substitutions that reduce or inhibit Fc domain dimerization. In some embodiments, the Fc domain contains a hinge domain. The Fc domain can be of immunoglobulin antibody isotype IgG, IgE, IgM, IgA, or IgD. Additionally, the Fc domain can be an IgG subtype (e.g., IgG1, IgG2a, IgG2b, IgG3, or IgG4). The Fc domain can also be a non-naturally occurring Fc domain, e.g., a recombinant Fc domain.

(30) Methods of engineering Fc domains that have reduced dimerization are known in the art. In some embodiments, one or more amino acids with large side-chains (e.g., tyrosine or tryptophan) may be introduced to the C.sub.H3-C.sub.H3 dimer interface to hinder dimer formation due to steric clash. In other embodiments, one or more amino acids with small side-chains (e.g., alanine, valine, or threonine) may be introduced to the C.sub.H3-C.sub.H3 dimer interface to remove favorable interactions. Methods of introducing amino acids with large or small side-chains in the C.sub.H3 domain are described in, e.g., Ying et al. (J Biol Chem. 287:19399-19408, 2012), U.S. Patent Publication No. 2006/0074225, U.S. Pat. Nos. 8,216,805 and 5,731,168, Ridgway et al. (Protein Eng. 9:617-612, 1996), Atwell et al. (J Mol Biol. 270:26-35, 1997), and Merchant et al. (Nat Biotechnol. 16:677-681, 1998), all of which are incorporated herein by reference in their entireties.

(31) In yet other embodiments, one or more amino acid residues in the C.sub.H3 domain that make up the C.sub.H3-C.sub.H3 interface between two Fc domains are replaced with positively-charged amino acid residues (e.g., lysine, arginine, or histidine) or negatively-charged amino acid residues (e.g., aspartic acid or glutamic acid) such that the interaction becomes electrostatically unfavorable depending on the specific charged amino acids introduced. Methods of introducing charged amino acids in the C.sub.H3 domain to disfavor or prevent dimer formation are described in, e.g., Ying et al. (J Biol Chem. 287:19399-19408, 2012), U.S. Patent Publication Nos. 2006/0074225, 2012/0244578, and 2014/0024111, all of which are incorporated herein by reference in their entireties.

(32) In some embodiments of the invention, an Fc domain includes one or more of the following amino acid substitutions:T366W, T366Y, T394W, F405W, Y349T, Y349E, Y349V, L351T, L351H, L351 N, L352K, P353S, S354D, D356K, D356R, D356S, E357K, E357R, E357Q, S364A, T366E, L368T, L368Y, L368E, K370E, K370D, K370Q, K392E, K392D, T394N, P395N, P396T, V397T, V397Q, L398T, D399K, D399R, D399N, F405T, F405H, F405R, Y407T, Y407H, Y407I, K409E, K409D, K409T, and K409I, relative to the sequence of human IgG1. In one particular embodiment, an Fc domain includes the amino acid substitution T366W, relative to the sequence of human IgG1. The sequence of wild-type Fc domain is shown in SEQ ID NO: 151.

(33) III. Albumin-Binding Peptide

(34) In some embodiments, a polypeptide described herein may include an extracellular ActRIIa variant fused to a serum protein-binding peptide. Binding to serum protein peptides can improve the pharmacokinetics of protein pharmaceuticals.

(35) As one example, albumin-binding peptides that can be used in the methods and compositions described here are generally known in the art. In one embodiment, the albumin binding peptide includes the sequence DICLPRWGCLW (SEQ ID NO: 152).

(36) In the present invention, albumin-binding peptides may be joined to the N- or C-terminus (e.g., C-terminus) of an extracellular ActRIIa variant described herein (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) to increase the serum half-life of the extracellular ActRIIa variant. In some embodiments, an albumin-binding peptide is joined, either directly or through a linker, to the N- or C-terminus of an extracellular ActRIIa variant.

(37) In some embodiments, an extracellular ActRIIa variant described herein (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) may be fused to the N- or C-terminus of albumin-binding peptide (e.g., SEQ ID NO: 152) through conventional genetic or chemical means, e.g., chemical conjugation. If desired, a linker (e.g., a spacer) can be inserted between the extracellular ActRIIa variant and the albumin-binding peptide. Without being bound to a theory, it is expected that inclusion of an albumin-binding peptide in an extracellular ActRIIa variant described herein may lead to prolonged retention of the therapeutic protein through its binding to serum albumin.

(38) IV. Fibronectin Domain

(39) In some embodiments, a polypeptide described herein may include an extracellular ActRIIa variant fused to fibronectin domains. Binding to fibronectin domains can improve the pharmacokinetics of protein pharmaceuticals.

(40) Fibronectin domain is a high molecular weight glycoprotein of the extracellular matrix, or a fragment thereof, that binds to, e.g., membrane-spanning receptor proteins such as integrins and extracellular matrix components such as collagens and fibrins. In some embodiments of the present invention, a fibronectin domain is joined to the N- or C-terminus (e.g., C-terminus) of an extracellular ActRIIa variant described herein (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) to increase the serum half-life of the extracellular ActRIIa variant. A fibronectin domain can be joined, either directly or through a linker, to the N- or C-terminus of an extracellular ActRIIa variant.

(41) As one example, fibronectin domains that can be used in the methods and compositions described here are generally known in the art. In one embodiment, the fibronectin domain is a fibronectin type III domain (SEQ ID NO: 153) having amino acids 610-702 of the sequence of UniProt ID NO: P02751. In another embodiment, the fibronectin domain is an adnectin protein.

(42) In some embodiments, an extracellular ActRIIa variant described herein (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) may be fused to the N- or C-terminus of a fibronectin domain (e.g., SEQ ID NO: 153) through conventional genetic or chemical means, e.g., chemical conjugation. If desired, a linker (e.g., a spacer) can be inserted between the extracellular ActRIIa variant and the fibronectin domain. Without being bound to a theory, it is expected that inclusion of a fibronectin domain in an extracellular ActRIIa variant described herein may lead to prolonged retention of the therapeutic protein through its binding to integrins and extracellular matrix components such as collagens and fibrins.

(43) V. Serum Albumin

(44) In some embodiments, a polypeptide described herein may include an extracellular ActRIIa variant fused to serum albumin. Binding to serum albumins can improve the pharmacokinetics of protein pharmaceuticals.

(45) Serum albumin is a globular protein that is the most abundant blood protein in mammals. Serum albumin is produced in the liver and constitutes about half of the blood serum proteins. It is monomeric and soluble in the blood. Some of the most crucial functions of serum albumin include transporting hormones, fatty acids, and other proteins in the body, buffering pH, and maintaining osmotic pressure needed for proper distribution of bodily fluids between blood vessels and body tissues. In preferred embodiments, serum albumin is human serum albumin. In some embodiments of the present invention, a human serum albumin is joined to the N- or C-terminus (e.g., C-terminus) of an extracellular ActRIIa variant described herein (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) to increase the serum half-life of the extracellular ActRIIa variant. A human serum albumin can be joined, either directly or through a linker, to the N- or C-terminus of an extracellular ActRIIa variant.

(46) As one example, serum albumins that can be used in the methods and compositions described herein are generally known in the art. In one embodiment, the serum albumin includes the sequence of UniProt ID NO: P02768 (SEQ ID NO: 154).

(47) In some embodiments, an extracellular ActRIIa variant described herein (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) may be fused to the N- or C-terminus of a human serum albumin (e.g., SEQ ID NO: 154) through conventional genetic or chemical means, e.g., chemical conjugation. If desired, a linker (e.g., a spacer) can be inserted between the extracellular ActRIIa variant and the serum albumin. Without being bound to a theory, it is expected that inclusion of a serum albumin in an extracellular ActRIIa variant described herein may lead to prolonged retention of the therapeutic protein.
VI. Linkers

(48) A polypeptide described herein may include an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having a sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) fused to a moiety by way of a linker. In some embodiments, the moiety increases stability of the polypeptide. Exemplary moieties include an Fc domain monomer, a wild-type Fc domain, an Fc domain with amino acid substitutions (e.g., one or more substitutions that reduce dimerization), an albumin-binding peptide, a fibronectin domain, or a human serum albumin. In the present invention, a linker between a moiety (e.g., an Fc domain monomer (e.g., the sequence of SEQ ID NO: 97), a wild-type Fc domain (e.g., SEQ ID NO: 151), an Fc domain with amino acid substitutions (e.g., one or more substitutions that reduce dimerization), an albumin-binding peptide (e.g., SEQ ID NO: 152), a fibronectin domain (e.g., SEQ ID NO: 153), or a human serum albumin (e.g., SEQ ID NO: 154)) and an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)), can be an amino acid spacer including 1-200 amino acids. Suitable peptide spacers are known in the art, and include, for example, peptide linkers containing flexible amino acid residues such as glycine, alanine, and serine. In some embodiments, a spacer can contain motifs, e.g., multiple or repeating motifs, of GA, GS, GG, GGA, GGS, GGG, GGGA (SEQ ID NO: 98), GGGS (SEQ ID NO: 99), GGGG (SEQ ID NO: 100), GGGGA (SEQ ID NO: 101), GGGGS (SEQ ID NO: 102), GGGGG (SEQ ID NO: 103), GGAG (SEQ ID NO: 104), GGSG (SEQ ID NO: 105), AGGG (SEQ ID NO: 106), or SGGG (SEQ ID NO: 107). In some embodiments, a spacer can contain 2 to 12 amino acids including motifs of GA or GS, e.g., GA, GS, GAGA (SEQ ID NO: 108), GSGS (SEQ ID NO: 109), GAGAGA (SEQ ID NO: 110), GSGSGS (SEQ ID NO: 111), GAGAGAGA (SEQ ID NO: 112), GSGSGSGS (SEQ ID NO: 113), GAGAGAGAGA (SEQ ID NO: 114), GSGSGSGSGS (SEQ ID NO: 115), GAGAGAGAGAGA (SEQ ID NO: 116), and GSGSGSGSGSGS (SEQ ID NO: 117). In some embodiments, a spacer can contain 3 to 12 amino acids including motifs of GGA or GGS, e.g., GGA, GGS, GGAGGA (SEQ ID NO: 118), GGSGGS (SEQ ID NO: 119), GGAGGAGGA (SEQ ID NO: 120), GGSGGSGGS (SEQ ID NO: 121), GGAGGAGGAGGA (SEQ ID NO: 122), and GGSGGSGGSGGS (SEQ ID NO: 123). In yet some embodiments, a spacer can contain 4 to 12 amino acids including motifs of GGAG (SEQ ID NO: 104), GGSG (SEQ ID NO: 105), e.g., GGAG (SEQ ID NO: 104), GGSG (SEQ ID NO: 105), GGAGGGAG (SEQ ID NO: 124), GGSGGGSG (SEQ ID NO: 125), GGAGGGAGGGAG (SEQ ID NO: 126), and GGSGGGSGGGSG (SEQ ID NO: 127). In some embodiments, a spacer can contain motifs of GGGGA (SEQ ID NO: 101) or GGGGS (SEQ ID NO: 102), e.g., GGGGAGGGGAGGGGA (SEQ ID NO: 128) and GGGGSGGGGSGGGGS (SEQ ID NO: 129). In some embodiments of the invention, an amino acid spacer between a moiety (e.g., an Fc domain monomer, a wild-type Fc domain, an Fc domain with amino acid substitutions (e.g., one or more substitutions that reduce dimerization), an albumin-binding peptide, a fibronectin domain, or a serum albumin) and an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) may be GGG, GGGA (SEQ ID NO: 98), GGGG (SEQ ID NO: 100), GGGAG (SEQ ID NO: 130), GGGAGG (SEQ ID NO: 131), or GGGAGGG (SEQ ID NO: 132).

(49) In some embodiments, a spacer can also contain amino acids other than glycine, alanine, and serine, e.g., AAAL (SEQ ID NO: 133), AAAK (SEQ ID NO: 134), AAAR (SEQ ID NO: 135), EGKSSGSGSESKST (SEQ ID NO: 136), GSAGSAAGSGEF (SEQ ID NO: 137), AEAAAKEAAAKA (SEQ ID NO: 138), KESGSVSSEQLAQFRSLD (SEQ ID NO: 139), GENLYFQSGG (SEQ ID NO: 140), SACYCELS (SEQ ID NO: 141), RSIAT (SEQ ID NO: 142), RPACKIPNDLKQKVMNH (SEQ ID NO: 143), GGSAGGSGSGSSGGSSGASGTGTAGGTGSGSGTGSG (SEQ ID NO: 144), AAANSSIDLISVPVDSR (SEQ ID NO: 145), or GGSGGGSEGGGSEGGGSEGGGSEGGGSEGGGSGGGS (SEQ ID NO: 146). In some embodiments, a spacer can contain motifs, e.g., multiple or repeating motifs, of EAAAK (SEQ ID NO: 147). In some embodiments, a spacer can contain motifs, e.g., multiple or repeating motifs, of proline-rich sequences such as (XP).sub.n, in which X may be any amino acid (e.g., A, K, or E) and n is from 1-5, and PAPAP (SEQ ID NO: 148).

(50) The length of the peptide spacer and the amino acids used can be adjusted depending on the two protein involved and the degree of flexibility desired in the final protein fusion polypeptide. The length of the spacer can be adjusted to ensure proper protein folding and avoid aggregate formation.

(51) VII. Vectors, Host Cells, and Protein Production

(52) The polypeptides of the invention can be produced from a host cell. A host cell refers to a vehicle that includes the necessary cellular components, e.g., organelles, needed to express the polypeptides and fusion polypeptides described herein from their corresponding nucleic acids. The nucleic acids may be included in nucleic acid vectors that can be introduced into the host cell by conventional techniques known in the art (e.g., transformation, transfection, electroporation, calcium phosphate precipitation, direct microinjection, infection, or the like). The choice of nucleic acid vectors depends in part on the host cells to be used. Generally, preferred host cells are of either eukaryotic (e.g., mammalian) or prokaryotic (e.g., bacterial) origin.

(53) Nucleic Acid Vector Construction and Host Cells

(54) A nucleic acid sequence encoding the amino acid sequence of a polypeptide of the invention may be prepared by a variety of methods known in the art. These methods include, but are not limited to, oligonucleotide-mediated (or site-directed) mutagenesis and PCR mutagenesis. A nucleic acid molecule encoding a polypeptide of the invention may be obtained using standard techniques, e.g., gene synthesis. Alternatively, a nucleic acid molecule encoding a wild-type extracellular ActRIIa may be mutated to include specific amino acid substitutions using standard techniques in the art, e.g., QuikChange™ mutagenesis. Nucleic acid molecules can be synthesized using a nucleotide synthesizer or PCR techniques.

(55) A nucleic acid sequence encoding a polypeptide of the invention may be inserted into a vector capable of replicating and expressing the nucleic acid molecule in prokaryotic or eukaryotic host cells. Many vectors are available in the art and can be used for the purpose of the invention. Each vector may include various components that may be adjusted and optimized for compatibility with the particular host cell. For example, the vector components may include, but are not limited to, an origin of replication, a selection marker gene, a promoter, a ribosome binding site, a signal sequence, the nucleic acid sequence encoding protein of interest, and a transcription termination sequence.

(56) In some embodiments, mammalian cells may be used as host cells for the invention. Examples of mammalian cell types include, but are not limited to, human embryonic kidney (HEK) (e.g., HEK293, HEK 293F), Chinese hamster ovary (CHO), HeLa, COS, PC3, Vero, MC3T3, NS0, Sp2/0, VERY, BHK, MDCK, W138, BT483, Hs578T, HTB2, BT20, T47D, NS0 (a murine myeloma cell line that does not endogenously produce any immunoglobulin chains), CRL7O3O, and HsS78Bst cells. In some embodiments, E. coli cells may also be used as host cells for the invention. Examples of E. coli strains include, but are not limited to, E. coli 294 (ATCC® 31,446), E. coli A 1776 (ATCC® 31,537, E. coli BL21 (DE3) (ATCC® BAA-1025), and E. coli RV308 (ATCC® 31,608). Different host cells have characteristic and specific mechanisms for the posttranslational processing and modification of protein products (e.g., glycosylation). Appropriate cell lines or host systems may be chosen to ensure the correct modification and processing of the polypeptide expressed. The above-described expression vectors may be introduced into appropriate host cells using conventional techniques in the art, e.g., transformation, transfection, electroporation, calcium phosphate precipitation, and direct microinjection. Once the vectors are introduced into host cells for protein production, host cells are cultured in conventional nutrient media modified as appropriate for inducing promoters, selecting transformants, or amplifying the genes encoding the desired sequences. Methods for expression of therapeutic proteins are known in the art, see, for example, Paulina Balbas, Argelia Lorence (eds.) Recombinant Gene Expression: Reviews and Protocols (Methods in Molecular Biology), Humana Press; 2nd ed. 2004 and Vladimir Voynov and Justin A. Caravella (eds.) Therapeutic Proteins: Methods and Protocols (Methods in Molecular Biology) Humana Press; 2nd ed. 2012.

(57) Protein Production, Recovery, and Purification

(58) Host cells used to produce the polypeptides of the invention may be grown in media known in the art and suitable for culturing of the selected host cells. Examples of suitable media for mammalian host cells include Minimal Essential Medium (MEM), Dulbecco's Modified Eagle's Medium (DMEM), Expi293™ Expression Medium, DMEM with supplemented fetal bovine serum (FBS), and RPMI-1640. Examples of suitable media for bacterial host cells include Luria broth (LB) plus necessary supplements, such as a selection agent, e.g., ampicillin. Host cells are cultured at suitable temperatures, such as from about 20° C. to about 39° C., e.g., from 25° C. to about 37° C., preferably 37° C., and CO.sub.2 levels, such as 5 to 10%. The pH of the medium is generally from about 6.8 to 7.4, e.g., 7.0, depending mainly on the host organism. If an inducible promoter is used in the expression vector of the invention, protein expression is induced under conditions suitable for the activation of the promoter.

(59) In some embodiments, depending on the expression vector and the host cells used, the expressed protein may be secreted from the host cells (e.g., mammalian host cells) into the cell culture media. Protein recovery may involve filtering the cell culture media to remove cell debris. The proteins may be further purified. A polypeptide of the invention may be purified by any method known in the art of protein purification, for example, by chromatography (e.g., ion exchange, affinity, and size-exclusion column chromatography), centrifugation, differential solubility, or by any other standard technique for the purification of proteins. For example, the protein can be isolated and purified by appropriately selecting and combining affinity columns such as Protein A column (e.g., POROS Protein A chromatography) with chromatography columns (e.g., POROS HS-50 cation exchange chromatography), filtration, ultra filtration, salting-out and dialysis procedures.

(60) In other embodiments, host cells may be disrupted, e.g., by osmotic shock, sonication, or lysis, to recover the expressed protein. Once the cells are disrupted, cell debris may be removed by centrifugation or filtration. In some instances, a polypeptide can be conjugated to marker sequences, such as a peptide to facilitate purification. An example of a marker amino acid sequence is a hexa-histidine peptide (His-tag), which binds to nickel-functionalized agarose affinity column with micromolar affinity. Other peptide tags useful for purification include, but are not limited to, the hemagglutinin “HA” tag, which corresponds to an epitope derived from influenza hemagglutinin protein (Wilson et al., Cell 37:767, 1984).

(61) Alternatively, the polypeptides of the invention can be produced by the cells of a subject (e.g., a human), e.g., in the context of gene therapy, by administrating a vector (such as a viral vector (e.g., a retroviral vector, adenoviral vector, poxviral vector (e.g., vaccinia viral vector, such as Modified Vaccinia Ankara (MVA)), adeno-associated viral vector, and alphaviral vector)) containing a nucleic acid molecule encoding the polypeptide of the invention. The vector, once inside a cell of the subject (e.g., by transformation, transfection, electroporation, calcium phosphate precipitation, direct microinjection, infection, etc.) will promote expression of the polypeptide, which is then secreted from the cell. If treatment of a disease or disorder is the desired outcome, no further action may be required. If collection of the protein is desired, blood may be collected from the subject and the protein purified from the blood by methods known in the art.

(62) VIII. Pharmaceutical Compositions and Preparations

(63) The invention features pharmaceutical compositions that include the polypeptides described herein (e.g., a polypeptide including an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)). In some embodiments, a pharmaceutical composition of the invention includes a polypeptide including an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-70 (e.g., SEQ ID NOs: 6-70)) with a C-terminal extension (e.g., 1, 2, 3, 4, 5, 6, or more additional amino acids) as the therapeutic protein. In some embodiments, a pharmaceutical composition of the invention includes a polypeptide including an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) fused to a moiety (e.g., a Fc domain monomer, or a dimer thereof, a wild-type Fc domain, an Fc domain with amino acid substitutions (e.g., one or more substitutions that reduce dimerization), an albumin-binding peptide, a fibronectin domain, or a serum albumin) as the therapeutic protein. In some embodiments, a pharmaceutical composition of the invention including a polypeptide of the invention may be used in combination with other agents (e.g., therapeutic biologics and/or small molecules) or compositions in a therapy. In addition to a therapeutically effective amount of the polypeptide, the pharmaceutical composition may include one or more pharmaceutically acceptable carriers or excipients, which can be formulated by methods known to those skilled in the art. In some embodiments, a pharmaceutical composition of the invention includes a nucleic acid molecule (DNA or RNA, e.g., mRNA) encoding a polypeptide of the invention, or a vector containing such a nucleic acid molecule.

(64) Acceptable carriers and excipients in the pharmaceutical compositions are nontoxic to recipients at the dosages and concentrations employed. Acceptable carriers and excipients may include buffers such as phosphate, citrate, HEPES, and TAE, antioxidants such as ascorbic acid and methionine, preservatives such as hexamethonium chloride, octadecyldimethylbenzyl ammonium chloride, resorcinol, and benzalkonium chloride, proteins such as human serum albumin, gelatin, dextran, and immunoglobulins, hydrophilic polymers such as polyvinylpyrrolidone, amino acids such as glycine, glutamine, histidine, and lysine, and carbohydrates such as glucose, mannose, sucrose, and sorbitol. Pharmaceutical compositions of the invention can be administered parenterally in the form of an injectable formulation. Pharmaceutical compositions for injection can be formulated using a sterile solution or any pharmaceutically acceptable liquid as a vehicle. Pharmaceutically acceptable vehicles include, but are not limited to, sterile water, physiological saline, and cell culture media (e.g., Dulbecco's Modified Eagle Medium (DMEM), α-Modified Eagles Medium (α-MEM), F-12 medium). Formulation methods are known in the art, see e.g., Banga (ed.) Therapeutic Peptides and Proteins: Formulation, Processing and Delivery Systems (3rd ed.) Taylor & Francis Group, CRC Press (2015).

(65) The pharmaceutical compositions of the invention may be prepared in microcapsules, such as hydroxylmethylcellulose or gelatin-microcapsule and poly-(methylmethacrylate) microcapsule. The pharmaceutical compositions of the invention may also be prepared in other drug delivery systems such as liposomes, albumin microspheres, microemulsions, nano-particles, and nanocapsules. Such techniques are described in Remington: The Science and Practice of Pharmacy 22.sup.th edition (2012). The pharmaceutical compositions to be used for in vivo administration must be sterile. This is readily accomplished by filtration through sterile filtration membranes.

(66) The pharmaceutical compositions of the invention may also be prepared as a sustained-release formulation. Suitable examples of sustained-release preparations include semipermeable matrices of solid hydrophobic polymers containing the polypeptides of the invention. Examples of sustained release matrices include polyesters, hydrogels, polyactides, copolymers of L-glutamic acid and γ ethyl-L-glutamate, non-degradable ethylene-vinyl acetate, degradable lactic acid-glycolic acid copolymers such as LUPRON DEPOT™, and poly-D-(−)-3-hydroxybutyric acid. Some sustained-release formulations enable release of molecules over a few months, e.g., one to six months, while other formulations release pharmaceutical compositions of the invention for shorter time periods, e.g., days to weeks.

(67) The pharmaceutical composition may be formed in a unit dose form as needed. The amount of active component, e.g., a polypeptide of the invention, included in the pharmaceutical preparations is such that a suitable dose within the designated range is provided (e.g., a dose within the range of 0.01-100 mg/kg of body weight).

(68) The pharmaceutical composition for gene therapy can be in an acceptable diluent, or can include a slow release matrix in which the gene delivery vehicle is imbedded. If hydrodynamic injection is used as the delivery method, the pharmaceutical composition containing a nucleic acid molecule encoding a polypeptide described herein or a vector (e.g., a viral vector) containing the nucleic acid molecule is delivered rapidly in a large fluid volume intravenously. Vectors that may be used as in vivo gene delivery vehicle include, but are not limited to, retroviral vectors, adenoviral vectors, poxviral vectors (e.g., vaccinia viral vectors, such as Modified Vaccinia Ankara), adeno-associated viral vectors, and alphaviral vectors.

(69) IX. Routes, Dosage, and Administration

(70) Pharmaceutical compositions that include the polypeptides of the invention as the therapeutic proteins may be formulated for, e.g., intravenous administration, parenteral administration, subcutaneous administration, intramuscular administration, intra-arterial administration, intrathecal administration, or intraperitoneal administration. The pharmaceutical composition may also be formulated for, or administered via, oral, nasal, spray, aerosol, rectal, or vaginal administration. For injectable formulations, various effective pharmaceutical carriers are known in the art. See, e.g., ASHP Handbook on Injectable Drugs, Toissel, 18th ed. (2014).

(71) In some embodiments, a pharmaceutical composition that includes a nucleic acid molecule encoding a polypeptide of the invention or a vector containing such nucleic acid molecule may be administered by way of gene delivery. Methods of gene delivery are well-known to one of skill in the art. Vectors that may be used for in vivo gene delivery and expression include, but are not limited to, retroviral vectors, adenoviral vectors, poxviral vectors (e.g., vaccinia viral vectors, such as Modified Vaccinia Ankara (MVA)), adeno-associated viral vectors, and alphaviral vectors. In some embodiments, mRNA molecules encoding polypeptides of the invention may be administered directly to a subject.

(72) In some embodiments of the present invention, nucleic acid molecules encoding a polypeptide described herein or vectors containing such nucleic acid molecules may be administered using a hydrodynamic injection platform. In the hydrodynamic injection method, a nucleic acid molecule encoding a polypeptide described herein is put under the control of a strong promoter in an engineered plasmid (e.g., a viral plasmid). The plasmid is often delivered rapidly in a large fluid volume intravenously. Hydrodynamic injection uses controlled hydrodynamic pressure in veins to enhance cell permeability such that the elevated pressure from the rapid injection of the large fluid volume results in fluid and plasmid extravasation from the vein. The expression of the nucleic acid molecule is driven primarily by the liver. In mice, hydrodynamic injection is often performed by injection of the plasmid into the tail vein. In certain embodiments, mRNA molecules encoding a polypeptide described herein may be administered using hydrodynamic injection.

(73) The dosage of the pharmaceutical compositions of the invention depends on factors including the route of administration, the disease to be treated, and physical characteristics, e.g., age, weight, general health, of the subject. A pharmaceutical composition of the invention may include a dosage of a polypeptide of the invention ranging from 0.01 to 500 mg/kg (e.g., 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 100, 150, 200, 250, 300, 350, 400, 450, or 500 mg/kg) and, in a more specific embodiment, about 0.1 to about 30 mg/kg and, in a more specific embodiment, about 0.3 to about 30 mg/kg. The dosage may be adapted by the physician in accordance with conventional factors such as the extent of the disease and different parameters of the subject.

(74) The pharmaceutical compositions are administered in a manner compatible with the dosage formulation and in such amount as is therapeutically effective to result in an improvement or remediation of the symptoms. The pharmaceutical compositions are administered in a variety of dosage forms, e.g., intravenous dosage forms, subcutaneous dosage forms, and oral dosage forms (e.g., ingestible solutions, drug release capsules). Generally, therapeutic proteins are dosed at 0.1-100 mg/kg, e.g., 1-50 mg/kg. Pharmaceutical compositions that include a polypeptide of the invention may be administered to a subject in need thereof, for example, one or more times (e.g., 1-10 times or more) daily, weekly, biweekly, monthly, bimonthly, quarterly, biannually, annually, or as medically necessary. In some embodiments, pharmaceutical compositions that include a polypeptide of the invention may be administered to a subject in need thereof weekly, biweekly, monthly, bimonthly, or quarterly. Dosages may be provided in either a single or multiple dosage regimens. The timing between administrations may decrease as the medical condition improves or increase as the health of the patient declines.

(75) X. Methods of Treatment

(76) The invention is based on the discovery that substituting amino acids from the extracellular portion of ActRIIb into the extracellular portion ActRIIa yields ActRIIa variants with improved properties. The ActRIIa variants generated by introducing residues from ActRIIb into ActRIIa retain the beneficial properties of ActRIIa, such as longer serum half-life and low binding affinity to BMP9, and gain some of the beneficial properties of ActRIIb, such as increased binding to activins A and B (see Table 5). These ActRIIa variant properties produce a polypeptide that can be used therapeutically to compete with endogenous activin receptors for ligand binding. As the ActRIIa variants contain the extracellular portion of the receptor, they are soluble and able to bind to and sequester ligands (e.g., activins A and B, myostatin, GDF11) without activating intracellular signaling pathways. Therefore, the extracellular ActRIIa variants can be used to treat diseases or conditions in which elevated activin signaling has been implicated (e.g., associated with increased expression of activin receptors or activin receptor ligands). For example, activin has been found to be upregulated in bone disease and is known to inhibit osteoblast activity, suggesting that increased activin levels contribute to bone disease. It follows that treatment with a therapeutic agent that binds to activin and reduces its interaction with endogenous receptors could be used to increase bone mineral density and treat subjects with diseases or conditions involving bone damage.

(77) The invention provides compositions and methods of treatment that may be used to increase bone mineral density, increase bone formation, increase bone strength, reduce the risk of bone fracture, or reduce bone resorption (e.g., reduce bone loss) in a subject in need thereof. In some embodiments, the subject may have a disease that results in bone damage (e.g., osteoporosis or osteopenia). In some embodiments, the methods described herein are directed to affecting myostatin, activin, and/or BMP9 signaling in a subject having a disease or condition involving bone damage. In some embodiments, a polypeptide including an extracellular ActRIIa variant described herein reduces or inhibits the binding of myostatin, activin, and/or BMP9 to their receptors, e.g., ActRIIa, ActRIIb, and BMPRII (e.g., ActRIIa). In some embodiments, affecting myostatin, activin, and/or BMP9 signaling (e.g., reducing or inhibiting the binding of myostatin, activin, and/or BMP9 to their receptors, e.g., ActRIIa, ActRIIb, and BMPRII (e.g., ActRIIa)) results in an increase in the subject's bone mineral density or bone formation, or a decrease in the subject's bone resorption (e.g., decreased bone loss).

(78) In some embodiments, the polypeptides described herein (e.g., a polypeptide including an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) may be administered to a subject to increase bone mineral density, to increase bone formation, to increase bone strength, to reduce the risk of bone fracture, to decrease bone resorption (e.g., decrease bone loss), or to affect myostatin, activin, and/or BMP9 signaling in the subject. In some embodiments, the methods described herein increase bone mineral density of the subject. The extracellular ActRIIa variants described herein (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) may increase bone mineral density, increase bone formation, increase bone strength, reduce bone resorption (e.g., bone loss), or reduce the risk of bone fracture compared to measurements obtained prior to treatment or compared to bone mineral density, bone strength, bone formation, bone resorption, or risk of bone fracture typically observed in untreated subjects. In some embodiments, the methods described herein do not cause any vascular complications in the subject, such as increased vascular permeability or leakage. In some embodiments of the methods described herein, the subject has or is at risk of developing a disease or condition involving bone damage (e.g., primary osteoporosis, secondary osteoporosis, osteopenia, osteopetrosis, fracture, bone cancer or cancer metastasis-related bone loss, Paget's disease, renal osteodystrophy, treatment-related bone loss, diet-related bone loss, bone loss associated with the treatment of obesity, low gravity-related bone loss, or immobility-related bone loss).

(79) The invention also includes methods of treating a subject having or at risk of developing primary osteoporosis, secondary osteoporosis, osteopenia, osteopetrosis, fracture, bone cancer or cancer metastasis-related bone loss, Paget's disease, renal osteodystrophy, treatment-related bone loss, diet-related bone loss, bone loss associated with the treatment of obesity, low gravity-related bone loss, or immobility-related bone loss by administering to the subject a polypeptide described herein (e.g., a polypeptide including an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)). In some embodiments, the primary osteoporosis is age-related or hormone-related osteoporosis (e.g., related to a decline in estrogen). In some embodiments, the secondary osteoporosis is immobilization-induced or glucocorticoid-induced osteoporosis. In some embodiments, the bone cancer is multiple myeloma or the cancer metastasis-related bone loss is caused by multiple myeloma. In some embodiments, the treatment-related bone loss occurs due to treatment with FGF-21 or GLP-1, treatment with an FGF-21 or GLP-1 containing therapeutic, or treatment of Type-2 diabetes and/or obesity, or due to cancer therapy (e.g., chemotherapy or radiation). In some embodiments, the diet-related bone loss is rickets (e.g., vitamin D deficiency). In some embodiments, the low-gravity related bone loss is lack of load-related bone loss.

(80) In some embodiments, the polypeptides described herein (e.g., a polypeptide including an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) may be used to prevent the development of a disease or condition involving bone damage (e.g., primary osteoporosis, secondary osteoporosis, osteopenia, osteopetrosis, fracture, bone cancer or cancer metastasis-related bone loss, Paget's disease, renal osteodystrophy, osteopetrosis, treatment-related bone loss, diet-related bone loss, bone loss associated with the treatment of obesity, low gravity-related bone loss, or immobility-related bone loss) and/or to treat patients already diagnosed with a disease or condition involving bone damage. Patients who are likely to develop a disease or condition involving bone damage, e.g., individuals with genetic predisposition, family history of bone damage, or low bone mass, may be administered the polypeptides described herein (e.g., a polypeptide including an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) prophylactically, such that the extracellular ActRIIa polypeptides may prevent or delay the development of bone damage.

(81) In some embodiments, the polypeptides described herein (e.g., a polypeptide including an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) may be administered to a subject to prevent the development of and/or treat patients with a disease or condition involving bone damage (e.g., primary osteoporosis, secondary osteoporosis, osteopenia, osteopetrosis, fracture, bone cancer or cancer metastasis-related bone loss, Paget's disease, renal osteodystrophy, treatment-related bone loss, diet-related bone loss, bone loss associated with the treatment of obesity, low gravity-related bone loss, or immobility-related bone loss), or to affect myostatin, activin, and/or BMP9 signaling in the subject (e.g., to reduce or inhibit the binding of activin, myostatin, and/or BMP9 to their receptors). In some embodiments, the methods described herein increase bone mineral density (e.g., increase bone mass), e.g., increase bone mineral density compared to measurements obtained prior to treatment or compared to bone mineral density typically observed in untreated subjects. In some embodiments, the methods described herein reduce bone resorption (e.g., reduce bone catabolic activity or reduce bone loss), e.g., reduce bone resorption compared to measurements obtained prior to treatment or compared to bone resorption typically observed in untreated subjects. In some embodiments, the methods described herein increase bone formation (e.g., increase bone anabolic activity or increase osteogenesis), e.g., increase bone formation compared to measurements obtained prior to treatment or compared to bone formation typically observed in untreated subjects. In some embodiments, the methods described herein increase osteoblast activity or osteoblastogenesis, e.g., increase osteoblast activity or osteoblastogenesis compared to measurements obtained prior to treatment or compared to osteoblast activity or osteoblastogenesis typically observed in untreated subjects. In some embodiments, the methods described herein decrease osteoclast activity or osteoclastogenesis, e.g., decrease osteoclast activity or osteoclastogenesis compared to measurements obtained prior to treatment or compared to osteoclast activity or osteoclastogenesis typically observed in untreated subjects. In some embodiments, the methods described herein reduce or inhibit the binding of activin and/or myostatin to their receptors. In some embodiments, the methods increase bone formation, increase bone mineral density, or decrease bone resorption (e.g., decrease bone loss) of cortical or trabecular bone.

(82) In any of the methods described herein, a polypeptide including an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-71 (e.g., SEQ ID NOs: 6-71)) that further includes a C-terminal extension of one or more amino acids (e.g., 1, 2, 3, 4, 5, 6, or more amino acids) may be used as the therapeutic protein. In any of the methods described herein, a dimer (e.g., homodimer or heterodimer) of a polypeptide including an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) fused to an Fc domain monomer may be used as the therapeutic protein. In any of the methods described herein, a polypeptide including an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) fused to a moiety (e.g., a wild-type Fc domain, an Fc domain with amino acid substitutions (e.g., one more substitutions that reduce dimerization), an albumin-binding peptide, a fibronectin domain, or a serum albumin) may be used as the therapeutic protein. Nucleic acids encoding the polypeptides described herein, or vectors containing said nucleic acids can also be administered according to any of the methods described herein. In any of the methods described herein, the polypeptide, nucleic acid, or vector can be administered as part of a pharmaceutical composition. Compositions that can be administered to a subject according to the methods described herein are provided in Table 4, below.

(83) TABLE-US-00008 TABLE 4 Row Composition 1 A polypeptide comprising an extracellular activin receptor type IIa (ActRIIa) variant, the variant having a sequence of GAILGRSETQECLX.sub.1X.sub.2NANWX.sub.3X.sub.4X.sub.6X.sub.6TNQTGVEX.sub.7CX.sub.8GX.sub.9X.sub.10X.sub.11X.sub.12X.sub.13X.sub.14HCX.sub.15ATWX.sub.16NI SGSIEIVX.sub.17X.sub.18GCX.sub.19X.sub.20X.sub.21DX.sub.22NCYDRTDCVEX.sub.23X.sub.24X.sub.25X.sub.26PX.sub.27VYFCCCEGNMCNEKFSYF PEMEVTQPTS (SEQ ID NO: 1), wherein X.sub.1, is F or Y; X.sub.2 is F or Y; X.sub.3 is E or A; X.sub.4 is K or L; X.sub.5 is D or E; X.sub.6 is R or A; X.sub.7 is P or R; X.sub.8 is Y or E; X.sub.9 is D or E; X.sub.10 is K or Q; X.sub.11 is D or A; X.sub.12 is K or A; X.sub.13 is R or A; X.sub.14 is R or L; X.sub.15 is F or Y; X.sub.16 is K, R, or A; X.sub.17 is K, A, Y, F, or I; X.sub.18 is Q or K; X.sub.19 is W or A; X.sub.20 is L or A; X.sub.21 is D, K, R, A, F, G, M, N, or I; X.sub.22 is I, F, or A; X.sub.23 is K or T; X.sub.24 is K or E; X.sub.25 is D or E; X.sub.26 is S or N; and X.sub.27 is E or Q, and wherein the variant has at least one amino acid substitution relative to a wild-type extracellular ActRIIa having the sequence of SEQ ID NO: 73 or an extracellular ActRIIa having any one of the sequences of SEQ ID NOs: 76-96. 2 The polypeptide of row 1, wherein the variant has a sequence of GAILGRSETQECLFX.sub.2NANWX.sub.3X.sub.4X.sub.5X.sub.6TNQTGVEX.sub.7CX.sub.8GX.sub.9KX.sub.11X.sub.12X.sub.13X.sub.14HCX.sub.15ATWX.sub.16NIS GSIEIVX.sub.17X.sub.18GCX.sub.19X.sub.20X.sub.21DX.sub.22NCYDRTDCVEX.sub.23X.sub.24X.sub.25X.sub.26PDX.sub.27VYFCCCEGNMCNEKFSYFPEMEVTQP TS (SEQ ID NO: 2), 3 The polypeptide of row 1 or 2, wherein the variant has a sequence of GAILGRSETQECLFX.sub.2NANWEX.sub.4X.sub.5RTNQTGVEX.sub.7CX.sub.8GX.sub.9KDKRX.sub.14HCX.sub.15ATWX.sub.16NISGSIEIV KX.sub.18GOWLDDX.sub.22NCYDRTDCVEX.sub.23X.sub.24X.sub.25X.sub.26PX.sub.27VYFCCCEGNMCNEKFSYFPEMEVTQPTS (SEQ ID NO: 3). 4 The polypeptide of any one of rows 1-3, wherein the variant has a sequence of GAILGRSETQECLFX.sub.2NANWEX.sub.4DRTNQTGVEX.sub.7CX.sub.8GX.sub.9KDKRX.sub.14HCX.sub.15ATWX.sub.16NISGSIEIV KX.sub.18GOWLDDX.sub.22NCYDRTDCVEX.sub.23KX.sub.25X.sub.26PDX.sub.27VYFCCCEGNMCNEKFSYFPEMEVTQPTS (SEQ ID NO: 4). 5 The polypeptide of any one of rows 1-4, wherein the variant has a sequence of GAILGRSETQECLFX.sub.2NANWEX.sub.4DRTNQTGVEPCX.sub.8GX.sub.9KDKRX.sub.14HCFATWKNISGSIEIVKX.sub.18 GCWLDDINCYDRTDCVEX.sub.23KX.sub.25X.sub.26PDX.sub.27VYFCCCEGNMCNEKFSYFPEMEVTQPTS (SEQ ID NO: 5). 6 The polypeptide of row 1, wherein X.sub.1 is F. 7 The polypeptide of row 1, wherein X.sub.1 is Y. 8 The polypeptide of row 1, 6, or 7 wherein X.sub.10 is K. 9 The polypeptide of row 1, 6, or 7 wherein X.sub.10 is Q. 10 The polypeptide of any one of rows 1-9, wherein X.sub.2 is F. 11 The polypeptide of any one of rows 1-9, wherein X.sub.2 is or Y. 12 The polypeptide of any one of rows 1, 2, and 6-11, wherein X.sub.3 is E. 13 The polypeptide of any one of rows 1, 2, and 6-11, wherein X.sub.3 is A. 14 The polypeptide of any one of rows 1-13, wherein X.sub.4 is K. 15 The polypeptide of any one of rows 1-13, wherein X.sub.4 is L. 16 The polypeptide of any one of rows 1, 2, 3, and 6-15, wherein X.sub.5 is D. 17 The polypeptide of any one of rows 1, 2, 3, and 6-15, wherein X.sub.5 is E. 18 The polypeptide of any one of rows 1, 2 and 6-17, wherein X.sub.6 is R. 19 The polypeptide of any one of rows 1, 2 and 6-17, wherein X.sub.6 is A. 20 The polypeptide of any one of rows 1-4 and 6-1 9, wherein X.sub.7 is P. 21 The polypeptide of any one of rows 1-4 and 6-1 9, wherein X.sub.7 is R. 22 The polypeptide of any one of rows 1-21, wherein X.sub.8 is Y. 23 The polypeptide of any one of rows 1-21, wherein X.sub.8 is E. 24 The polypeptide of any one of rows 1-23, wherein X.sub.9 is D. 25 The polypeptide of any one of rows 1-23, wherein X.sub.9 is E. 26 The polypeptide of any one of rows 1, 2 and 6-25, wherein X.sub.11 is D. 27 The polypeptide of any one of rows 1, 2 and 6-25, wherein X.sub.11 is A. 28 The polypeptide of any one of rows 1, 2 and 6-27, wherein X.sub.12 is K. 29 The polypeptide of any one of rows 1, 2 and 6-27, wherein X.sub.12 is A. 30 The polypeptide of any one of rows 1, 2 and 6-29, wherein X.sub.13 is R. 31 The polypeptide of any one of rows 1, 2 and 6-29, wherein X.sub.13 is A. 32 The polypeptide of any one of rows 1-31, wherein X.sub.14 is R. 33 The polypeptide of any one of rows 1-31, wherein X.sub.14 is L. 34 The polypeptide of any one of rows 1-4 and 6-33, wherein X.sub.15 is F. 35 The polypeptide of any one of rows 1-4 and 6-33, wherein X.sub.15 is Y. 36 The polypeptide of any one of rows 1-4 and 6-35, wherein X.sub.16 is K. 37 The polypeptide of any one of rows 1-4 and 6-35, wherein X.sub.16 is R. 38 The polypeptide of any one of rows 1-4 and 6-35, wherein X.sub.16 is A. 39 The polypeptide of any one of rows 1, 2 and 6-38, wherein X.sub.17 is K. 40 The polypeptide of any one of rows 1, 2 and 6-38, wherein X.sub.17 is A. 41 The polypeptide of any one of rows 1, 2 and 6-38, wherein X.sub.17 is Y. 42 The polypeptide of any one of rows 1, 2 and 6-38, wherein X.sub.17 is F. 43 The polypeptide of any one of rows 1, 2 and 6-38, wherein X.sub.17 is I. 44 The polypeptide of any one of rows 1-43, wherein X.sub.18 is Q. 45 The polypeptide of any one of rows 1-43, wherein X.sub.18 is K. 46 The polypeptide of any one of rows 1, 2 and 6-45, wherein X.sub.19 is W. 47 The polypeptide of any one of rows 1, 2 and 6-45, wherein X.sub.19 is A. 48 The polypeptide of any one of rows 1, 2 and 6-47, wherein X.sub.20 is L. 49 The polypeptide of any one of rows 1, 2 and 6-47, wherein X.sub.20 is A. 50 The polypeptide of any one of rows 1, 2 and 6-49, wherein X.sub.21 is D. 51 The polypeptide of any one of rows 1, 2 and 6-49, wherein X.sub.21 is K. 52 The polypeptide of any one of rows 1, 2 and 6-49, wherein X.sub.21 is R. 53 The polypeptide of any one of rows 1, 2 and 6-49, wherein X.sub.21 is A. 54 The polypeptide of any one of rows 1, 2 and 6-49, wherein X.sub.21 is F. 55 The polypeptide of any one of rows 1, 2 and 6-49, wherein X.sub.21 is G. 56 The polypeptide of any one of rows 1, 2 and 6-49, wherein X.sub.21 is M. 57 The polypeptide of any one of rows 1, 2 and 6-49, wherein X.sub.21 is N. 58 The polypeptide of any one of rows 1, 2 and 6-49, wherein X.sub.21 is I. 59 The polypeptide of any one of rows 1-4 and 6-58, wherein X.sub.22 is I. 60 The polypeptide of any one of rows 1-4 and 6-58, wherein X.sub.22 is F. 61 The polypeptide of any one of rows 1-4 and 6-58, wherein X.sub.22 is A. 62 The polypeptide of any one of rows 1-61, wherein X.sub.23 is K. 63 The polypeptide of any one of rows 1-61, wherein X.sub.23 is T. 64 The polypeptide of any one of rows 1, 2, 3, and 6-63, wherein X.sub.24 is K. 65 The polypeptide of any one of rows 1, 2, 3, and 6-63, wherein X.sub.24 is E. 66 The polypeptide of any one of rows 1-65, wherein X.sub.25 is D. 67 The polypeptide of any one of rows 1-65, wherein X.sub.25 is E. 68 The polypeptide of any one of rows 1-67, wherein X.sub.26 is S. 69 The polypeptide of any one of rows 1-67, wherein X.sub.26 is N. 70 The polypeptide of any one of rows 1-69, wherein X.sub.27 is E. 71 The polypeptide of any one of rows 1-69, wherein X.sub.27 is Q. 72 The polypeptide of any one of rows 1-71, wherein X.sub.23 is T, X.sub.24 is E, X.sub.25 is E, and X.sub.26 is N. 73 The polypeptide of any one of rows 1-71, wherein X.sub.23 is T, X.sub.24 is K, X.sub.25 is E, and X.sub.26 is N. 74 The polypeptide of any one of rows 1-73, wherein X.sub.17 is K. 75 The polypeptide of row 1, wherein the variant has the sequence of any one of SEQ ID NOs: 6-72. 76 The polypeptide of row 75, wherein the variant has the sequence of SEQ ID NO: 69. 77 The polypeptide of row 75, wherein the variant has the sequence of SEQ ID NO: 58. 78 The polypeptide of row 75, wherein the variant has the sequence of SEQ ID NO: 6. 79 The polypeptide of row 75, wherein the variant has the sequence of SEQ ID NO: 38. 80 The polypeptide of row 75, wherein the variant has the sequence of SEQ ID NO: 41. 81 The polypeptide of row 75, wherein the variant has the sequence of SEQ ID NO: 44. 82 The polypeptide of row 75, wherein the variant has the sequence of SEQ ID NO: 70. 83 The polypeptide of row 75, wherein the variant has the sequence of SEQ ID NO: 71. 84 The polypeptide of row 75, wherein the variant has the sequence of SEQ ID NO: 72. 85 The polypeptide of any one of rows 1-84, wherein the amino acid at position X.sub.24 is replaced with the amino acid K. 86 The polypeptide of any one of rows 1-85, wherein the amino acid at position X.sub.24 is replaced with the amino acid E. 87 The polypeptide of any one of rows 1-86, further comprising a C-terminal extension of one or more amino acids. 88 The polypeptide of row 87, wherein the C-terminal extension is NP. 89 The polypeptide of row 87, wherein the C-terminal extension is NPVTPK. 90 The polypeptide of any one of rows 1-89, further comprising an Fc domain monomer fused to the C-terminus of the polypeptide by way of a linker. 91 The polypeptide of row 90, wherein the Fc domain monomer comprises the sequence of SEQ  ID NO: 97. 92 The polypeptide of any one of rows 1-89, further comprising a wild-type Fc domain fused to the C-terminus of the polypeptide by way of a linker. 93 The polypeptide of row 92, wherein the wild-type Fc domain comprises the sequence of SEQ  ID NO: 151. 94 The polypeptide of any one of rows 1-89, further comprising an Fc domain with amino acid substitutions fused to the C-terminus of the polypeptide by way of a linker. 95 The polypeptide of row 94, wherein the Fc domain does not form a dimer. 96 The polypeptide of any one of rows 1-89, further comprising an albumin-binding peptide fused to the C-terminus of the polypeptide by way of a linker. 97 The polypeptide of row 96, wherein the albumin-binding peptide comprises the sequence of SEQ ID NO: 152. 98 The polypeptide of any one of rows 1-89, further comprising a fibronectin domain fused to the C-terminus of the polypeptide by way of a linker. 99 The polypeptide of row 98, wherein the fibronectin domain comprises the sequence of SEQ ID NO: 153. 100 The polypeptide of any one of rows 1-89, further comprising a human serum albumin fused to the C-terminus of the polypeptide by way of a linker. 101 The polypeptide of row 100, wherein the human serum albumin comprises the sequence of SEQ ID NO: 154. 102 The polypeptide of row 90 or 91, wherein the polypeptide forms a dimer. 103 The polypeptide of any one of rows 90-102, wherein the linker is an amino acid spacer. 104 The polypeptide of row 103, wherein the amino acid spacer is GGG, GGGA (SEQ ID NO: 98), GGGG (SEQ ID NO: 100), GGGAG (SEQ ID NO: 130), GGGAGG (SEQ ID NO: 131), or GGGAGGG (SEQ ID NO: 132). 105 The polypeptide of any one of rows 1-104, wherein the polypeptide has a serum half-life of at least 7 days. 106 The polypeptide of any one of rows 1-105, wherein the polypeptide binds to human bone morphogenetic protein 9 (BMP9) with a K.sub.D of 200 pM or higher. 107 The polypeptide of row 106, wherein the polypeptide binds to activin and/or myostatin and has reduced or weak binding to human BMP9. 108 The polypeptide of row 106 or 107, wherein the polypeptide does not substantially bind to human BMP9. 109 The polypeptide of any one of rows 1-99, wherein the polypeptide binds to human activin A with a K.sub.D of 800 pM or less. 110 The polypeptide of any one of rows 1-109, wherein the polypeptide binds to human activin B with a K.sub.D of 800 pM or less. 111 The polypeptide of any one of rows 1-110, wherein the polypeptide binds to human GDF-11 with a K.sub.D of 5 pM or higher. 112 A nucleic acid molecule encoding a polypeptide of any one of rows 1-111. 113 A vector comprising the nucleic acid molecule of row 112 114 A host cell that expresses a polypeptide of any one of rows 1-111, wherein the host cell comprises a nucleic acid molecule of row 112 or a vector of row 113, wherein the nucleic acid molecule or vector is expressed in the host cell. 115 A pharmaceutical composition comprising a polypeptide of any one of rows 1-111, a nucleic acid molecule of row 112, or a vector of row 113, and one or more pharmaceutically acceptable carriers or excipients. 116 The pharmaceutical composition of row 115, wherein the polypeptide is in a therapeutically effective amount.

EXAMPLES

Example 1—Evaluation of ActRIIa Variants Binding Affinity by Surface Plasmon Resonance (SPR)

(84) The Biacore 3000 was used to measure the kinetics of the interactions between the ActRIIa variants and the ligands Activin A, Activin B, growth differentiation factor 11 (GDF11), and BMP-9. ActRIIa variants were transiently expressed in HEK293 cells and purified from the conditioned media using Protein-A Sepharose chromatography. The ActRIIa variants were immobilized on the chip (CM4 or CM5) with capture antibodies (anti-mouse from GEGE) in flow cells 2-4 to ensure proper orientation. Flow cell 1 was used as a reference cell to subtract any nonspecific binding and bulk effects. HBS-EP+ buffer from GE Healthcare™ was used as a running buffer. Each ligand was run in a concentration series at 40 μl/min to avoid mass transport effects. The data was analyzed using Scrubber2 by BioLogic™ Software to calculate the K.sub.D of each interaction (Table 5).

(85) TABLE-US-00009 TABLE 5 Comparison of Act RIIa variant binding affinity (Kd) to various ligands Activin A (K.sub.D) Activin B (K.sub.D) GDF-11 (K.sub.D) BMP-9 (K.sub.D) Vehicle N/A N/A N/A N/A ActRIIa 1 nM 373 pM 81 pM 25 nM (SEQ ID NO: 73) ActRIIb 63 pM 23 pM 115 pM 278 pM (SEQ ID NO: 74) ActRIIa/b variant 542 pM 103 pM 186 pM 4 nM (SEQ ID NO: 69) ActRIIb/a variant No No No No (SEQ ID NO: 149) Binding Binding Binding Binding ActRIIa/bΔ9 variant 213 pM 12.3 pM 115 pM 10 nM (SEQ ID NO: 58) ActRIIa/bΔ9 min 310 pM 88 pM 114 pM 17 nM variant (SEQ ID NO: 6) ActRIIa/b+ variant 242 pM 282 pM No 26 nM (SEQ ID NO: 150) dissociation ActRIIa/bΔ9m2 variant 170 pM 104 pM 222 pM 13-18 nM (SEQ ID NO: 38) ActRIIa/bΔ9m3 variant 71 pM 72.5 pM 117 pM 1.2 nM (SEQ ID NO: 41) ActRIIa/bΔ9m4 variant 375 pM 254 pM 394 pM 14-20 nM (SEQ ID NO: 44) ActRIIa/bmax1 variant 232 pM 97 pM 236 pM 5.6 nM (SEQ ID NO: 70) ActRIIa/bmax2 variant 135 pM 39 pM 113 pM 5 nM (SEQ ID NO: 71) ActRIIa/bmax3 variant 89 pM 43 pM 214 pM 3.3 nM (SEQ ID NO: 72)

Example 2—Effect of Extracellular ActRIIa Variants on Bone Mineral Density

(86) Adult male C57/BL6 mice receive either a sham- (SHAM) or castration-surgery (ORX). Both surgery groups are allowed to recover for 14 days post-surgery. All animals are housed in conventional cages with free access to food (regular chow) and water. SHAM and ORX animals are then assigned to either a vehicle-treated group (VEH) or ActRII variant-treated group and receive bi-weekly systemic intraperitoneal administration of vehicle or ActRII variant (10 mg/kg) for 71 d. Body weights are measured twice per week at the time of treatment. Body composition is analyzed at study day 0 then at days 14, 28, 47, and 71 after treatment initiation using the MiniSpec LF50 NMR Analyzer. At study termination date, tissues of interest (muscles, fat depots, and tibias) are surgically removed, weighed, and properly stored for further analysis. At this time, the ORX animals are also examined to confirm complete removal of testes. Cortical morphometry and trabecular structure of the various bones are also evaluated after the experiment termination using micro-computed tomography.

Example 3—Effect of Extracellular ActRIIa Variants on Trabecular Bone

(87) Eight-week old male C57Bl/6 mice were dosed intraperitoneally with either vehicle or ActRII A/B (SEQ ID NO: 69) at 20 mg/kg biweekly for four weeks. Upon completion of dosing, mice were micro-CT imaged at high resolution with the PerkinElmer Quantum FX system (10 mm FOV, 3 min scan, 20 μm voxel-size). Tibia ASBMR bone morphometry parameters were measured in AnalyzePro software from a 50-slice region of scan volume selected immediately distal to the proximal tibial growth plate. From this sub-region trabecular bone fraction, trabecular number, trabecular thickness, and trabecular spacing data were calculated (FIG. 2). Treatment with ActRII A/B (SEQ ID NO: 69) resulted in increased trabecular bone volume fraction, trabecular number, and decreased trabecular spacing. These changes to trabecular bone are associated with increased bone strength and reduced fracture risk.

Example 4—Effect of an Extracellular ActRIIa Variant in a Mouse Model of Osteoporosis

(88) C57BL/6 mice received orchiectomy (ORX) or sham surgery at nine weeks of age. Following a six-week recovery period, during which time the ORX mice developed an osteoporotic phenotype, ORX mice received intraperitoneal injections twice weekly of either vehicle or ActRIIA/B-Fc (SEQ ID NO: 69 fused to an Fc domain, 20 mg/kg). Micro-CT (Perkin Elmer Quantum Fx) imaging was conducted at study-end. ASBMR bone morphometry parameters of each dataset were calculated with AnalyzePro software (AnalyzeDirect, Overland Park KS) using the Bone Morphometry Analysis Add-on. A 50-slice region of CT volume immediately distal to the proximal tibial growth plate was selected to assess changes in trabecular bone parameters. As shown in FIG. 3, Treatment with ActRIIA/B-Fc increased bone volume fraction (reduced bone loss) associated with orchiectomy (*=p≤0.05; ****=p≤0.0001).

Example 5—Treatment of Bone Disease by Administration of an Extracellular ActRIIa Variant

(89) According to the methods disclosed herein, a physician of skill in the art can treat a subject, such as a human patient, having bone disease (e.g., osteoporosis or osteopenia) so as to increase bone mineral density, increase bone formation, reduce bone resorption (e.g., bone loss), or reduce the risk of bone fracture. The method of treatment can include diagnosing or identifying a subject as a candidate for treatment based on standard clinical tests for bone mineral density (e.g., dual X-ray absorptiometry). To treat the subject, a physician of kill in the art can administer to the subject a composition containing an extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)). The composition containing the extracellular ActRIIa variant may be administered to the subject, for example, by parenteral injection (e.g., intravenous injection) to treat bone disease. The extracellular ActRIIa variant (e.g., an extracellular ActRIIa variant having the sequence of any one of SEQ ID NOs: 1-72 (e.g., SEQ ID NOs: 6-72)) is administered in a therapeutically effective amount, such as from 0.01 to 500 mg/kg (e.g., 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 100, 150, 200, 250, 300, 350, 400, 450, or 500 mg/kg). In some embodiments, the extracellular ActRIIa variant is administered bimonthly, once a month, once every two weeks, or at least once a week or more (e.g., 1, 2, 3, 4, 5, 6, or 7 times a week or more). The extracellular ActRIIa variant is administered in an amount sufficient to increase bone mineral density, increase bone formation, reduce bone resorption (e.g., reduce bone loss), or reduce the risk of bone fracture.

(90) Following administration of the composition to a patient, a practitioner of skill in the art can monitor the patient's improvement in response to the therapy by a variety of methods. For example, a physician can monitor the patient's bone mineral density by performing dual X-ray absorptiometry. A finding that the patient exhibits increased bone mineral density, increased bone formation, reduced bone resorption (e.g., reduced bone loss), or a reduced risk of bone fracture following administration of the composition compared to test results prior to administration of the composition indicates that the patient is responding favorably to the treatment. Subsequent doses can be determined and administered as needed.

Other Embodiments

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

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

(93) Other embodiments are within the following claims.