Beta-lactamase inhibitors

1. A method of treating an upper or lower respiratory tract infection, a urinary tract infection, an intra-abdominal infection, or a skin infection; the method comprising administering to a subject in need thereof a therapeutically effective amount of a compound of Formula (I) or Formula (Ia), a pharmaceutically acceptable salt, solvate, polymorph, stereoisomer, tautomer, or N oxide, thereof:

wherein:

L is a bond, —CR 1 R 2 —, >C═O, or ═CR 1 —;

M is a bond, —O—, —S—, —S(O)—, >SO 2 , or —N(R 4 )—;

m is 0, 1, or 2;

n is 0, 1, 2, or 3;

provided that

when n is 0, then M is a bond;

p is 0, 1, 2, 3, or 4;

provided that

when p is 0, then L is —CR 1 R 2 — or ═CR 1 —;

X 1 and X 2 are independently selected from —OH, —OR 8 , or F;

Z is >C═O, >C═S, or >SO 2 ;

CycA is an optionally substituted 3-10 membered non-aromatic carbocycle, wherein an optional olefin functionality of the non-aromatic carbocycle is not directly attached to an oxygen, sulfur, or nitrogen substituent;

R a , R b , and R c are independently selected from the group consisting of hydrogen, fluoro, chloro, bromo, optionally substituted C 1 -C 6 alkyl, optionally substituted C 3 -C 6 cycloalkyl, optionally substituted heterocyclyl, optionally substituted aryl, optionally substituted heteroaryl, —OH, —OR 10 , —NR 4 R 5 , and —SR 10 ;

each R 1 and R 2 is independently selected from the group consisting of hydrogen, fluoro, chloro, bromo, optionally substituted C 1 -C 6 alkyl, optionally substituted C 3 -C 6 cycloalkyl, —OH, —OR 10 , —SR 10 , and —NR 4 R 5 ,

or R 1 and R 2 taken together form an oxo, oxime, or an optionally substituted carbocycle or optionally substituted heterocycle with the carbon to which they are attached;

R 3 is hydrogen or optionally substituted C 1 -C 6 alkyl;

each R d , R 4 , and R 5 is independently selected from the group consisting of hydrogen, —OH, —CN, optionally substituted C 1 -C 6 alkyl, optionally substituted alkoxyalkyl, optionally substituted hydroxyalkyl, optionally substituted aminoalkyl, optionally substituted cycloalkyl, optionally substituted heterocyclyl, optionally substituted aryl, optionally substituted heteroaryl, optionally substituted cycloalkylalkyl, optionally substituted heterocyclylalkyl, optionally substituted aralkyl, optionally substituted heteroaralkyl, (poly-ethylene-glycol)-ethyl, and an optionally substituted saccharide;

or R 4 and R 5 taken together form an optionally substituted heterocycle with the nitrogen to which they are attached;

each R 8 is independently selected from the group consisting of optionally substituted C 1 -C 6 alkyl, optionally substituted C 3 -C 6 cycloalkyl, and a pharmaceutically acceptable boronate ester group;

each R 10 is independently selected from the group consisting of optionally substituted C 1 -C 6 alkyl and optionally substituted C 3 -C 6 cycloalkyl;

and each Y is independently —NR 4 R 5 , —NR 4 C(═NR 5 )NR 4 R 5 , —C(═NR 4 )NR 4 R 5 , —N(R 4 )C(═NR 5 )R 6 , —(CR 6 R 7 ) v NR 4 R 5 , —(CR 6 R 7 ) v N(R 4 )C(═NR 5 )NR 4 R 5 , —NR 4 (CR 6 R 7 ) v NR 4 R 5 , —NR 4 (CR 6 R 7 ) v OR 10 , —(CR 6 R 7 ) v NR 4 (CR 6 R 7 ) v NR 4 R 5 , NR 5 C(═NR 5 )NR 4 (CR 6 R 7 ) v NR 4 R 5 , —NR 4 (CR 6 R 7 ) v N(R 4 )C(═NR 5 )NR 4 R 5 , —NR 5 C(O)CR 6 (NR 4 R 5 )(CR 6 R 7 ) v NR 4 R 5 , —(CR 6 R 7 ) v C(═NR 5 )NR 4 R 5 , —(CR 6 R 7 ) v N(R 4 )C(O)(CR 6 R 7 ) v NR 4 R 5 , —C(═NR 4 )NR 4 C(O)R 6 , —NR 4 (CR 6 R 7 ) v Heteroaryl, and —O(CR 6 R 7 ) v NR 4 R 5 ;

each R 6 and R 7 is independently selected from the group consisting of hydrogen, fluoro, chloro, bromo, optionally substituted C 1 -C 6 alkyl, optionally substituted alkoxyalkyl, optionally substituted hydroxyalkyl, optionally substituted C 3 -C 6 cycloalkyl, —OH, —OR 10 , —SR 10 , —NR 4 R 5 , —NR 4 C(O)R 5 , —NR 4 C(O)OR 5 , —NR 4 C(O)NR 5 , —C(O)OR 5 , —C(O)NR 4 R 5 , —C(N=R 5 )NR 4 R 5 —NR 4 SO 2 R 5 , optionally substituted heterocyclyl, optionally substituted aryl, and optionally substituted heteroaryl;

or R 6 and R 7 taken together form an oxo, oxime, or an optionally substituted carbocycle or an optionally substituted heterocycle with the carbon to which they are attached; and

each v is independently 1, 2, 3, or 4.

2. The method of claim 1 , wherein R a , R b , and R c are hydrogen.

3. The method of claim 1 , wherein R 3 is hydrogen.

4. The method of claim 1 , wherein X 1 and X 2 are —OH.

5. The method of claim 1 , wherein R d is hydrogen or C 1 -C 4 -alkyl.

6. The method of claim 1 , wherein Z is >C═O.

7. The method of claim 1 , wherein:

(A) L is —CR 1 R 2 — or ═CR 1 —;

M is —O—, —S—, —SO 2 —, or —N(R 4 )—;

m is 0 or 1; and

n is 1 or 2; or

(B) L is a bond, —CR 1 R 2 —, or ═CR 1 —;

M is a bond or —O—;

m is 0; and

n is 1 or 2; or

(C) L is a bond or >C═O;

M is a bond; and

m and n are 0; or

(D) L is a bond;

M is a bond; and

m or n are 1; or

(E) L is —CR 1 R 2 — or ═CR 1 —;

M is a bond; and

m and n are 0; or

(F) L is —CR 1 R 2 — or ═CR 1 —;

M is a bond; and

m or n are 1.

8. The method of claim 1 , wherein CycA is selected from the group consisting of cyclopropane, cyclobutane, cyclopentane, cyclohexane, cycloheptane, cyclooctane, cyclopentene, cyclohexene, cycloheptene, and cyclooctene, wherein the olefin functionality of the cyclopentene, cyclohexene, cycloheptene, and cyclooctene is not directly attached to an oxygen, sulfur, or nitrogen substituent.

9. The method of claim 8 , wherein CycA is cyclohexane.

10. The method of claim 1 , wherein p is 1 or 2.

11. The method of claim 1 , wherein R 4 and R 5 are independently hydrogen or optionally substituted C 1 -C 6 alkyl.

12. The method of claim 1 , wherein R 6 and R 7 are independently hydrogen, fluoro, or optionally substituted C 1 -C 6 alkyl.

13. The method of claim 1 , wherein the compound is selected from the group represented by the following structures:

or a pharmaceutically acceptable salt, solvate, polymorph, stereoisomer, tautomer, or N-oxide, thereof, wherein the compound is present in a closed, cyclic form according to Formula I and as shown in the structures above, an open, acyclic form according to Formula Ia, or mixtures thereof.

14. The method of claim 1 , further comprising administering a beta-lactam antibiotic.

15. The method of claim 14 , wherein the beta-lactam antibiotic is a penicillin, a cephalosporin, a carbapenem, a monobactam, a bridged monobactam, or a combination thereof.

16. The method of claim 1 , wherein the bacterial infection comprises a bacteria selected from Pseudomonas aeruginosa, Escherichia coli, Citrobacter freundii, Enterobacter cloacae, Enterobacter aerogenes, Klebsiella pneumoniae, Klebsiella oxytoca, Serratia marcescens, Proteus mirabilis, Proteus vulgaris, Providencia alcalifaciens, Providencia rettgeri, Providencia stuartii, Bacteroides fragilis, Bacteroides distasonis, Bacteroides 3452A homology group, Bacteroides vulgatus, Bacteroides ovalus, Bacteroides thetaiotaomicron, Bacteroides uniformis, Bacteroides eggerthii, Bacteroides splanchnicus, Clostridium difficile, Enterococcus faecalis, Enterococcus faecium, Staphylococcus aureus, Staphylococcus epidermidis, Staphylococcus saprophyticus, Staphylococcus intermedius, Staphylococcus hyicus subsp. hyicus, Staphylococcus haemolyticus, Staphylococcus hominis , and Staphylococcus saccharolyticus.