Beta-lactamase inhibitors

A compound of Formula (I) or Formula (Ia), or a pharmaceutically acceptable salt, polymorph, solvate, N-oxide, or isomer thereof:

• wherein:
• M is a bond, —O—, —S—, —S(O)—, SO2—, or —N(R4)—;
• 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 2;
• X1 and X2 are independently selected from —OH, —OR8, or F;
• Z is >C═O, >C═S, or >SO2;
• ArA is an optionally substituted aromatic or heteroaromatic ring system;
• each Y is selected from the group consisting of
• —NR4R5, —NR4C(═NR5)NR4R5, —C(═NR4)NR4R5, —N(R4)C(═NR5)R6, —(CR6R7)vNR4R5, —(CR6R7)vN(R4)C(═NR5)NR4R5, —NR4(CR6R7)vNR4R5, —NR4(CR6R7)vOR10, —(CR6R7)vNR4(CR6R7)vNR4R5, NR5C(═NR5)NR4(CR6R7)vNR4R5, —NR4(CR6R7)vN(R4)C(═NR5)NR4R5, —NR5C(O)CR6(NR4R5)(CR6R7)vNR4R5, —(CR6R7)vC(═NR5)NR4R5, —(CR6R7)vN(R4)C(O)(CR6R7)vNR4R5, —C(═NR4)NR4C(O)R6, —NR4(CR6R7)vHeteroaryl, and —O(CR6R7)vNR4R5;
• v is 1-4;
• or two Ys taken together with the carbon atoms to which they are attached form an optionally substituted carbocycle or an optionally substituted heterocycle;
• Ra, Rb, and Rc are independently selected from the group consisting of hydrogen, fluoro, chloro, bromo, optionally substituted C1-C6 alkyl, optionally substituted C3-C6 cycloalkyl, optionally substituted heterocyclyl, optionally substituted aryl, optionally substituted heteroaryl, —OH, —OR10, —NR4R5, and —SR10;
• R1 and R2 are independently selected from the group consisting of hydrogen, fluoro, chloro, bromo, optionally substituted C1-C6 alkyl, optionally substituted C3-C6 cycloalkyl, —OH, —OR10, —SR10, and —NR4R5,
• or R1 and R2 taken together form an oxo, oxime, or an optionally substituted carbocycle or optionally substituted heterocycle with the carbon to which they are attached;
• R3 is hydrogen, or optionally substituted C1-C6 alkyl;
• Rd, R4 and R5 are independently selected from the group consisting of hydrogen, —OH, —CN, optionally substituted C1-C6 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 R4 and R5 taken together form an optionally substituted heterocycle with the nitrogen to which they are attached;
• R6 and R7 are independently selected from the group consisting of hydrogen, fluoro, chloro, bromo, optionally substituted C1-C6 alkyl, optionally substituted alkoxyalkyl, optionally substituted hydroxyalkyl, optionally substituted C3-C6 cycloalkyl, —OH, —OR10, —SR10, —NR4R5, —NR4C(O)R5, —C(O)NR4R5, —NR4SO2R5, optionally substituted heterocyclyl, optionally substituted aryl, and optionally substituted heteroaryl;
• or R6 and R7 taken together form an oxo, oxime, or an optionally substituted carbocycle or an optionally substituted heterocycle with the carbon to which they are attached;
• R8 is optionally substituted C1-C6 alkyl, optionally substituted C3-C6 cycloalkyl, or a pharmaceutically acceptable boronate ester group;
• R10 is optionally substituted C1-C6 alkyl or optionally substituted C3-C6 cycloalkyl.