Stabilized polypeptide insulin receptor modulators

1. A polypeptide comprising an alpha-helical segment, wherein the polypeptide binds to the insulin receptor, and wherein the polypeptide is of Formula (I-2):

or a pharmaceutically acceptable salt thereof;

wherein:

n=0 or 1;

each instance of independently represents a single bond, a double bond, or a triple bond;

each of R a1 and R a2 , are, independently, hydrogen; acyl; optionally substituted C 1-6 alkyl; or an amino protecting group;

each of R 2a and R 2b is, independently, optionally substituted alkyl; optionally substituted alkenyl; optionally substituted alkynyl; optionally substituted heteroalkyl; optionally substituted carbocyclyl; optionally substituted heterocyclyl;

each of R 3a and R 3b is, independently, optionally substituted alkylene; unsubstituted heteroalkylene; optionally substituted carbocyclylene; or optionally substituted heterocyclylene; or optionally R 2a and R 3a are joined to form a ring; or optionally R 2b and R 3b are joined to form a ring;

L 1 is independently, a bond; optionally substituted C 1-10 alkylene; or C(═O)OR L1 —;

L 2 is independently, a bond; optionally substituted C 1-10 alkylene; or —C(═O)OR L2 —;

each of R L1 and R L2 is independently optionally substituted C 1-10 alkylene;

each instance of R c1 is independently hydrogen; optionally substituted aliphatic; optionally substituted heteroaliphatic; optionally substituted aryl; optionally substituted heteroaryl; acyl; optionally substituted hydroxyl; optionally substituted thiol; optionally substituted amino; azido; cyano; isocyano; halogen; or nitro;

q1 is 0, 1, or 2;

R f is (i) hydrogen; (ii) unsubstituted aliphatic; (iii) acetyl; (iv) acyl; or (v) aliphatic substituted with halogen, ═O, ═S, ═NN(R bb ) 2 , ═NNR bb C(═O)R aa , ═NNR bb C(═O)OR aa , ═NNR bb S(═O) 2 R aa , ═NR bb , ═NOR cc , —CN, —NO 2 , —N 3 , —SO 2 H, —SO 3 H, —OH, —OR aa , —ON(R bb ) 2 , —SH, —SR aa , —SSR cc , —C(═O)R aa , —CO 2 H, —CHO, —C(OR cc ) 2 , —CO 2 R aa , —OC(═O)R aa , —OCO 2 R aa , —C(═O)N(R bb ) 2 , —OC(═O)N(R bb ) 2 , —C(═NR bb )R aa , —C(═NR bb )OR aa , —OC(═NR bb )R aa , —OC(═NR bb )OR aa , —C(═NR bb )N(R bb ) 2 , —OC(═NR bb )N(R bb ) 2 , —C(═O)NR bb SO 2 R aa , —SO 2 N(R bb ) 2 , —SO 2 R aa , —SO 2 OR aa , —OSO 2 R aa , —S(═O)R aa , —OS(═O)R aa , —Si(R aa ) 3 , —OSi(R aa ) 3 , —C(═S)N(R bb ) 2 , —C(═O)SR aa , —C(═S)SR aa , —SC(═S)SR aa , —SC(═O)SR aa , —OC(═O)SR aa , —SC(═O)OR aa , —SC(═O)R aa , —P(═O) 2 R aa , —OP(═O) 2 R aa , —P(═O)(R aa ) 2 , —OP(═O)(R aa ) 2 , —OP(═O)(OR cc ) 2 , —P(═O) 2 N(R bb ) 2 , —OP(═O) 2 N(R bb ) 2 , —P(═O)(NR bb ) 2 , —OP(═O)(NR bb ) 2 , —P(R cc ) 2 , —P(R cc ) 3 , —OP(R cc ) 2 , —OP(R cc ) 3 , —B(R aa ) 2 , —B(OR cc ) 2 , —BR aa (OR cc ), C 1-10 alkyl, C 1-10 perhaloalkyl, C 2-10 alkenyl, C 2-10 alkynyl, C 3-10 carbocyclyl, 3-14 membered heterocyclyl, C 6-14 aryl, or 5-14 membered heteroaryl; wherein each instance of R aa is, independently, C 1-10 alkyl, C 1-10 perhaloalkyl, C 2-10 alkenyl, C 2-10 alkynyl, heteroC 1-10 alkyl, heteroC 2-10 alkenyl, heteroC 2-10 alkynyl, C 3-10 carbocyclyl, 3-14 membered heterocyclyl, C 6-14 aryl, or 5-14 membered heteroaryl, or two R aa groups are joined to form a 3-14 membered heterocyclyl or 5-14 membered heteroaryl ring; wherein each instance of R bb is, independently, hydrogen, —OH, —OR aa , —N(R cc ) 2 , —CN, —C(═O)R aa , —C(═O)N(R cc ) 2 , —CO 2 R aa , —SO 2 R aa , —C(═NR cc )OR aa , —C(═NR cc )N(R cc ) 2 , —SO 2 N(R cc ) 2 , —SO 2 R cc , —SO 2 OR cc , —SOR aa , —C(═S)N(R cc ) 2 , —C(═O)SR cc , —C(═S)SR cc , —P(═O) 2 R aa , —P(═O)(R aa ) 2 , —P(═O) 2 N(R cc ) 2 , —P(═O)(NR cc ) 2 , C 1-10 alkyl, C 1-10 perhaloalkyl, C 2-10 alkenyl, C 2-10 alkynyl, heteroC 1-10 alkyl, heteroC 2-10 alkenyl, heteroC 2-10 alkynyl, C 3-10 carbocyclyl, 3-14 membered heterocyclyl, C 6-14 aryl, or 5-14 membered heteroaryl, or two R bb groups are joined to form a 3-14 membered heterocyclyl or 5-14 membered heteroaryl ring; and wherein each instance of R cc is, independently, hydrogen, C 1-10 alkyl, C 1-10 perhaloalkyl, C 2-10 alkenyl, C 2-10 alkynyl, heteroC 1-10 alkyl, heteroC 2-10 alkenyl, heteroC 2-10 alkynyl, C 3-10 carbocyclyl, 3-14 membered heterocyclyl, C 6-14 aryl, or 5-14 membered heteroaryl, or two R cc groups are joined to form a 3-14 membered heterocyclyl or 5-14 membered heteroaryl ring;

R e is —OR E ; —N(R E ) 2 ; or —SR E , wherein each instance of R E is, independently, (i) hydrogen; (ii) unsubstituted-aliphatic; (iii) unsubstituted-heteroaliphatic; (iv) optionally substituted aryl; (v) optionally substituted heteroaryl; or (vi) aliphatic substituted with —CN, —NO 2 , —N 3 , —SO 2 H, —SO 3 H, —OH, —OR aa , —ON(R bb ) 2 , —N(R bb ) 2 , —N(R bb ) 3 + X − , —N(OR cc )R bb , —SH, —SR aa , —SSR cc , —C(═O)R aa , —CHO, —OC(═O)R aa , —OCO 2 R aa , —OC(═O)N(R bb ) 2 , —NR bb C(═O)R aa , —NR bb CO 2 R aa , —NR bb C(═O)N(R bb ) 2 , —C(═NR bb )R aa , —C(═NR bb )OR aa , —OC(═NR bb )R aa , —OC(═NR bb )OR aa , —OC(═NR bb )N(R bb ) 2 , —NR bb C(═NR bb )N(R bb ) 2 , —NR bb SO 2 R aa , —SO 2 N(R bb ) 2 , —SO 2 R aa , —SO 2 OR aa , —OSO 2 R aa , —S(═O)R aa , —OS(═O)R aa , —Si(R aa ) 3 , —OSi(R aa ) 3 , —C(═S)N(R bb ) 2 , —SC(═S)SR aa , —SC(═O)SR aa , —OC(═O)SR aa , —SC(═O)OR aa , —SC(═O)R aa , —P(═O) 2 R aa , —OP(═O) 2 R aa , —P(═O)(R aa ) 2 , —OP(═O)(R aa ) 2 , —OP(═O)(OR cc ) 2 , —P(═O) 2 N(R bb ) 2 , —OP(═O) 2 N(R bb ) 2 , —P(═O)(NR bb ) 2 , —OP(═O)(NR bb ) 2 , —NR bb P(═O)(OR cc ) 2 , —NR bb P(═O)(NR bb ) 2 , —P(R cc ) 2 , —P(R cc ) 3 , —OP(R cc ) 2 , —OP(R cc ) 3 , —B(R aa ) 2 , —B(OR cc ) 2 , —BR aa (OR cc ), C 1-10 alkyl, C 1-10 perhaloalkyl, C 2-10 alkenyl, C 2-10 alkynyl, heteroC 1-10 alkyl, heteroC 2-10 alkenyl, heteroC 2-10 alkynyl, C 3-10 carbocyclyl, 3-14 membered heterocyclyl, C 6-14 aryl, or 5-14 membered heteroaryl; wherein each instance of R aa is, independently, C 1-10 alkyl, C 1-10 perhaloalkyl, C 2-10 alkenyl, C 2-10 alkynyl, heteroC 1-10 alkyl, heteroC 2-10 alkenyl, heteroC 2-10 alkynyl, C 3-10 carbocyclyl, 3-14 membered heterocyclyl, C 6-14 aryl, or 5-14 membered heteroaryl, or two R aa groups are joined to form a 3-14 membered heterocyclyl or 5-14 membered heteroaryl ring; wherein each instance of R bb is, independently, —OH, —OR aa , —N(R cc ) 2 , —CN, —C(═O)R aa , —C(═O)N(R cc ) 2 , —CO 2 R aa , —SO 2 R aa , —C(═NR cc )OR aa , —C(═NR cc )N(R cc ) 2 , —SO 2 N(R cc ) 2 , —SO 2 R cc , —SO 2 OR cc , —SOR aa , —C(═S)N(R cc ) 2 , —C(═O)SR cc , —C(═S)SR cc , —P(═O) 2 R aa , —P(═O)(R aa ) 2 , —P(═O) 2 N(R cc ) 2 , —P(═O)(NR cc ) 2 , C 1-10 alkyl, C 1-10 perhaloalkyl, C 2-10 alkenyl, C 2-10 alkynyl, heteroC 1-10 alkyl, heteroC 2-10 alkenyl, heteroC 2-10 alkynyl, C 3-10 carbocyclyl, 3-14 membered heterocyclyl, C 6-14 aryl, or 5-14 membered heteroaryl, or two R bb groups are joined to form a 3-14 membered heterocyclyl or 5-14 membered heteroaryl ring; and wherein each instance of R cc is, independently, C 1-10 alkyl, C 1-10 perhaloalkyl, C 2-10 alkenyl, C 2-10 alkynyl, heteroC 1-10 alkyl, heteroC 2-10 alkenyl, heteroC 2-10 alkynyl, C 3-10 carbocyclyl, 3-14 membered heterocyclyl, C 6-14 aryl, or 5-14 membered heteroaryl, or two R cc groups are joined to form a 3-14 membered heterocyclyl or 5-14 membered heteroaryl ring; or (vii) two R E groups taken together form an optionally substituted heterocyclic or optionally substituted heteroaryl ring.

2. The polypeptide of claim 1 , wherein each instance of the cross-linked amino acids is independently of Formula (i-d), (ii-d), (i-e), or (ii-e):

wherein

each of Y 1 and Y 2 is, independently, CR 5 or N;

R 5 is hydrogen, halogen, —NO 2 , —OH, —CN, or C 1-6 alkyl; and

each of j and j1 is, independently, 0, 1, 2, 3, 4, 5, or 6; and

each of k and k1 is, independently, 0 or an integer from 1 to 10, inclusive.

3. The polypeptide of claim 1 , wherein R 3a is of Formula (G-1):

wherein

Y 1 is a bond, —CR 5 R 6 — or —NR 1 —;

each of R 5 and R 6 is, independently, hydrogen, halogen, —NO 2 , —OH, —CN, or C 1-6 alkyl;

R 1 is hydrogen; acyl; optionally substituted C 1-6 alkyl; or an amino protecting group; and

j is 0 or an integer between 1 and 10, inclusive.

4. The polypeptide of claim 1 , wherein L 1 is of Formula (G-4) or Formula (G-5):

wherein each of g and g1 is, independently, 0 or an integer between 1 and 10, inclusive.

5. The polypeptide of claim 1 , wherein R 3b is of Formula (G-6):

wherein

Y 2 is a bond, —CR 5 R 6 —, or —NR 1 —;

each of R 5 and R 6 is independently hydrogen, halogen, —NO 2 , —OH, —CN, or C 1-6 alkyl;

R 1 is hydrogen; acyl; optionally substituted C 1-6 alkyl; or an amino protecting group; and

k is 0 or an integer between 1 and 10, inclusive.

6. The polypeptide of claim 1 , wherein L 2 is of Formula (G-9) or Formula (G-10):

wherein each of h and h1 is, independently, 0 or an integer between 1 and 10, inclusive.

7. The polypeptide of claim 1 , wherein is a single bond or a double bond.

8. An insulin analogue comprising:

(i) a polypeptide of claim 1 ;

(ii) an insulin A-chain polypeptide; and

(ii) an insulin B-chain polypeptide;

wherein

the polypeptide is linked to the insulin A chain polypeptide via a linker; and

the linker is optionally substituted alkylene-C(═O)—, optionally substituted heteroalkylene-C(═O)—, optionally substituted alkenylene-C(═O)—, optionally substituted heteroalkenylene-C(═O)—, optionally substituted alkynylene-C(═O)—, optionally substituted heteroalkynylene-C(═O)—, optionally substituted cycloalkylene-C(═O)—, optionally substituted heterocycloalkylene-C(═O)—, optionally substituted arylene-C(═O)—, optionally substituted heteroarylene-C(═O)—, optionally substituted aralkylene-C(═O)—, or optionally substituted heteroaralkylene-C(═O)—.

9. A pharmaceutical composition comprising a polypeptide of claim 1 or a pharmaceutically acceptable salt thereof and a pharmaceutically acceptable excipient.

10. A method of treating a diabetic condition or a complication thereof comprising administering to a subject in need thereof an effective amount of a polypeptide of claim 1 or a pharmaceutically acceptable salt thereof.

11. A method of treating a diabetic condition or a complication thereof comprising administering to a subject in need thereof an effective amount of an insulin analogue of claim 8 or a pharmaceutically acceptable salt thereof.

12. A method of lowering blood glucose levels in a subject comprising administering to the subject in need thereof an effective amount of a polypeptide of claim 1 or a pharmaceutically acceptable salt thereof.

13. A method of lowering blood glucose levels in a subject comprising administering to the subject in need thereof an effective amount of an insulin analogue of claim 8 or a pharmaceutically acceptable salt thereof.

14. A method of activating an insulin receptor comprising contacting the insulin receptor with an effective amount of a polypeptide of claim 1 or a pharmaceutically acceptable salt thereof.

15. The polypeptide of claim 1 , wherein Rt is hydrogen; unsubstituted aliphatic; acetyl; acyl; or aliphatic substituted with ═O; and R e is —OR E ; —N(R E ) 2 ; or —SR E , wherein each instance of R E is, independently, hydrogen or unsubstituted aliphatic.

16. The polypeptide of claim 1 , wherein n is 1.