Toll-like receptor ligands

1. A compound of formula (I), or a pharmaceutically acceptable salt thereof,

wherein:

R 1 is

R 2a , R 2b , and R 2c are each independently C 4-22 alkyl, —X 1 —C 3-21 alkyl, —CH 2 —X 1 —C 2-20 alkyl, or —CH(R 10 )(R 11 );

R 10 , at each occurrence, is independently C 1-21 alkyl, —X 1 —C 2-20 alkyl, or —CH 2 —X 1 —C 1-19 alkyl;

R 11 , at each occurrence, is independently C 3-17 alkyl, —X 2 —C 2-16 alkyl, —CH 2 —X 2 —C 1-15 alkyl, —X 2 —C(═Y 4 )C 1-15 alkyl, —CH 2 —C(═Y 4 )C 1-15 alkyl, —X 2 —C(═Y 4 )C 1-15 alkylene-Z 1 —C 1-15 alkyl, —CH 2 —C(═Y 4 )C 1-15 alkylene-Z 1 —C 1-15 alkyl, —C 3-17 alkylene-Z 1 —C 1-15 alkyl, —X 2 —C 2-16 alkylene-Z 1 —C 1-15 alkyl, —CH 2 —X 2 —C 1-15 alkylene-Z 1 —C 1-15 alkyl, —X 2 —C(═Y 4 )C 1-15 alkylene-Z 2 , or —X 2 —C 2-16 alkylene-Z 2 ;

R 3a , R 3b , and R 3c are each independently CO 2 H, —OSO 3 H, —OP(O)(OH) 2 , —C 1-6 alkylene-CO 2 H, —C 1-6 alkylene-OSO 3 H, —C 1-6 alkylene-OP(O)(OH) 2 , —OC 1-6 alkylene-P(O)(OH) 2 , —C 1-6 alkylene-P(O)(OH) 2 , —C 1-6 haloalkylene-P(O)(OH) 2 , H, or an ester of the CO 2 H, —OSO 3 H, —OP(O)(OH) 2 , —C 1-6 alkylene-CO 2 H, —C 1-6 alkylene-OSO 3 H, —C 1-6 alkylene-OP(O)(OH) 2 , —OC 1-6 alkylene-P(O)(OH) 2 , —C 1-6 alkylene-P(O)(OH) 2 , or —C 1-6 haloalkylene-P(O)(OH) 2 , ;

R 3d is CO 2 H, —SO 3 H, —P(O)(OH) 2 , —C 1-6 alkylene-CO 2 H, —C 1-6 alkylene-OSO 3 H, —C 1-6 alkylene-OP(O)(OH) 2 , —OC 1-6 alkylene-P(O)(OH) 2 , —C 1-6 alkylene-P(O)(OH) 2 , —C 1-6 haloalkylene-P(O)(OH) 2 , H, C 1-6 alkyl, C 1-6 haloalkyl, C 3-8 cycloalkyl, or an ester of the CO 2 H, —OSO 3 H, —OP(O)(OH) 2 , —C 1-6 alkylene-CO 2 H, —C 1-6 alkylene-OSO 3 H, —C 1-6 alkylene-OP(O)(OH) 2 , —OC 1-6 alkylene-P(O)(OH) 2 , —C 1-6 alkylene-P(O)(OH) 2 , or —C 1-6 haloalkylene-P(O)(OH) 2 ;

R 4a is CO 2 H, CH 2 OSO 3 H, CH 2 CO 2 H, CH 2 P(O)(OH) 2 , CH 2 OH, H, or an ester of the CO 2 H, CH 2 SO 3 H, CH 2 CO 2 H, or CH 2 P(O)(OH) 2 ;

R 4b , at each occurrence, is independently CO 2 H, CH 2 OSO 3 H, CH 2 CO 2 H, CH 2 P(O)(OH) 2 , CH 2 OH, H, or an ester of the CO 2 H, CH 2 SO 3 H, CH 2 CO 2 H, or CH 2 P(O)(OH) 2 ;

R 5 and R 6 , at each occurrence, are independently H, C 1-6 alkyl, C 1-6 haloalkyl, —O—C 1-6 alkyl, or —C 1-6 alkylene-OH;

X 1 and X 2 , at each occurrence, are independently O, S, or NH;

X 3 is O, S, NH, or CH 2 ;

Y 1 , Y 2 , and Y 3 are independently O, S, NH, or H 2 ;

Y 4 , at each occurrence, is independently O, S, or NH;

Z 1 , at each occurrence, is independently phenylene or 5- to 6-membered heteroarylene, the phenylene and heteroarylene being optionally substituted with 1-4 substituents independently selected from C 1-4 alkyl, C 1-4 haloalkyl, —OC 1-4 alkyl, —OC 1-4 haloalkyl, cyano, and halogen;

Z 2 , at each occurrence, is independently phenyl or a 5- to 6-membered heteroaryl, wherein Z 2 is optionally substituted with 1-5 substituents independently selected from C 1-4 alkyl, C 1-4 haloalkyl, —OC 1-4 alkyl, —OC 1-4 haloalkyl, cyano, and halogen; and

k and q are each independently an integer from 0-4.

2. The compound of claim 1 , or a pharmaceutically acceptable salt thereof, wherein

R 2a , R 2b , and R 2c are each independently —CH(R 10 )(R 11 ).

3. The compound of claim 2 , or a pharmaceutically acceptable salt thereof, wherein at least one occurrence of R 10 is C 1-21 alkyl.

4. The compound of claim 3 , or a pharmaceutically acceptable salt thereof, wherein at least one occurrence of R 11 is —X 2 —C(═Y 4 )C 1-15 alkyl, —X 2 —C(═Y 4 )C 1-15 alkylene-Z 2 , —X 2 —C 2-16 alkylene-Z 2 , —X 2 —C 2-16 alkyl, or —CH 2 —X 2 —C 1-15 alkyl.

5. The compound of claim 4 , or a pharmaceutically acceptable salt thereof, wherein Y 4 is O.

6. The compound of claim 5 , or a pharmaceutically acceptable salt thereof, wherein X 2 is O.

7. The compound of claim 6 , or a pharmaceutically acceptable salt thereof, wherein Y 1 , Y 2 , and Y 3 are O.

8. The compound of claim 7 , or a pharmaceutically acceptable salt thereof, wherein X 3 is O.

9. The compound of claim 8 , or a pharmaceutically acceptable salt thereof, wherein R 3a is —OP(O)(OH) 2 , —OSO 3 H, or —OCH 2 P(O)(OH) 2 .

10. The compound of claim 8 , or a pharmaceutically acceptable salt thereof, wherein R 4a is CH 2 OH.

11. The compound of claim 8 , or a pharmaceutically acceptable salt thereof, wherein

R 1 is

k is 1;

R 3b is hydrogen or COOH, or an ester thereof; and

R 3d , R 5 , and R 6 are each hydrogen.

12. The compound of claim 8 , or a pharmaceutically acceptable salt thereof, wherein

R 1 is

13. The compound of claim 1 , selected from the group consisting of

or a pharmaceutically acceptable salt thereof.

14. A pharmaceutical composition comprising the compound of claim 1 , or a pharmaceutically acceptable salt thereof, and a pharmaceutically acceptable carrier.

15. A kit comprising:

the compound of claim 1 , or a pharmaceutically acceptable salt thereof; and

instructions for use.

16. The compound of claim 11 of formula (I-a), or a pharmaceutically acceptable salt thereof

wherein R 3a is —OP(O)(OH) 2 , —OSO 3 H, or —OCH 2 P(O)(OH) 2 .

17. The compound of claim 16 , or a pharmaceutically acceptable salt thereof, wherein R 10 , at each occurrence, is independently C 8-14 alkyl.

18. The compound of claim 17 , or a pharmaceutically acceptable salt thereof, wherein R 10 , at each occurrence, is independently C 11 alkyl.

19. The compound of claim 18 , or a pharmaceutically acceptable salt thereof, wherein R 10 , at each occurrence, is independently straight chain C 11 alkyl.

20. The compound claim 18 , or a pharmaceutically acceptable salt thereof, wherein R 11 , at each occurrence, is independently —O—C(═O)C 9 alkyl, —O—C 10 alkyl,

O—C(═O)C 7 alkylene-Z 2 , or —O—C 8-9 alkylene-Z 2 .

21. The compound of claim 20 , or a pharmaceutically acceptable salt thereof, wherein

—CH(R 10 )(R 11 ) is

22. The compound or pharmaceutically acceptable salt thereof, of claim 13 , wherein

the compound is

23. The compound, or pharmaceutically acceptable salt thereof, of claim 13 , wherein

the compound is