Topical formulations of borinic acid antibiotics and their methods of use

A topical pharmaceutical formulation comprising a pharmaceutically acceptable topical carrier and a compound having the formula:

• and its pharmaceutically acceptable salts,
• wherein:
• R* and R** are members independently selected from substituted or unsubstituted aralkyl, substituted or unsubstituted aryl, substituted or unsubstituted cycloalkyl, and substituted or unsubstituted heterocycle;
• z is 0 or 1, with the proviso, that
• if z is 1, then A is a member selected from CR10 and N, and D is a member selected from N and CR12;
• and with the further proviso, that
• if z is 0, then D is a member selected from O, S, and NR12a.
• E is a member selected from hydrogen, hydroxy, alkoxy, (cycloalkyl)oxy, (cycloheteroalkyl)oxy, carboxy, or alkyloxycarbonyl;
• m is 0 or 1;
• R12 is a member selected from hydrogen, hydroxyalkyl, aminoalkyl, alkylaminoalkyl, dialkylaminoalkyl, carboxy, alkyloxycarbonyl, amido, hydroxy, alkoxy, aryloxy, thio, alkylthio, arylthio, alkylsulfonyl, dialkylaminosulfonyl, alkylaminosulfonyl, aminosulfonyl, sulfo, cyano, halo, nitro, amino, dialkylamino, alkylamino, arylamino, diarylamino, aralkylamino, and diaralkylamino, wherein the alkyl or aryl portion of any moiety recited for R12 is optionally substituted;
• R12a is a member selected from hydrogen, substituted or unsubstituted alkyl, substituted or unsubstituted heteroalkyl, substituted or unsubstituted aralkyl, substituted or unsubstituted aryl, substituted or unsubstituted cycloalkyl, and substituted or unsubstituted heterocycle;
• R9 and R10 are members independently selected from hydrogen, alkyl, cycloalkyl, hydroxyalkyl, aminoalkyl, alkylaminoalkyl, dialkylaminoalkyl, halo, carbonyl, hydroxyimino, carboxy, alkyloxycarbonyl, alkylthio, alkylsulfonyl, arylthio, dialkylaminosulfonyl, alkylaminosulfonyl, aminosulfonyl, amino, alkoxy, nitro, sulfo, and hydroxy, wherein the alkyl or aryl portion of any moiety recited for R9 or R10 is optionally substituted.