A compound of formula, or a pharmaceutically acceptable salt thereof, wherein: R 1 is R 2a, R 2b, and R 2c are each independently -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 -X 2 -C(=Y 4)C 1-15 alkyl, C 3-17 alkyl, -X 2 -C 2-16 alkyl, - CH 2 -X 2 -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 is -OSO 3 H,-OP 2, or -OCH 2 P 2; R 3b is hydrogen or COOH, or an ester thereof; R 3d is H; R 4a is CH 2 OH, CO 2 H, CH 2 OSO 3 H, CH 2 CO 2 H, CH 2 P 2, H, or an ester of the CO 2 H, CH 2 SO 3 H, CH 2 CO 2 H, or CH 2 P 2; R 5 and R 6 are H; X 1 and X 2, at each occurrence, are independently O, S, or NH; X 3 is O; 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 is 1. R 1 is R 2a, R 2b, and R 2c are each independently -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 -X 2 -C(=Y 4)C 1-15 alkyl, C 3-17 alkyl, -X 2 -C 2-16 alkyl, - CH 2 -X 2 -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 is -OSO 3 H,-OP 2, or -OCH 2 P 2; R 3b is hydrogen or COOH, or an ester thereof; R 3d is H; R 4a is CH 2 OH, CO 2 H, CH 2 OSO 3 H, CH 2 CO 2 H, CH 2 P 2, H, or an ester of the CO 2 H, CH 2 SO 3 H, CH 2 CO 2 H, or CH 2 P 2; R 5 and R 6 are H; X 1 and X 2, at each occurrence, are independently O, S, or NH; X 3 is O; 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 is 1.