Analysis of affinities of penicillins for a class C beta-lactamase by molecular dynamics simulations

We present a calculation for the binding free energy difference between two complexes of the class C beta-lactamase from Enterobacter cloacae with foramidocillin (FOPC) and with piperacillin (PIPC). The calculation was carried out by means of the thermodynamic integration (TI) method implemented with molecular dynamics (MD). By use of the available crystal structure of the class C beta-lactamase from E. cloacae, the structures of the beta-lactamase-FOPC (FOPC complex) and beta-lactamase-PIPC (PIPC complex) complexes were built by molecular modeling and equilibrated with MD simulations. FOPC were gradually converted into PIPC in both the solution and the enzyme system by means of MD/TI methods during the MD simulation. The structure of the PIPC complex as derived by the MD/TI simulation was similar to that of the PIPC complex obtained from molecular modeling. The calculated difference in the free energy of binding (deltadeltaGbind) was -2.2 kcal/mol. This compares well with the experimental value of -1.5 kcal/mol. The results indicate that the binding affinity of FOPC is lower than that of PIPC because of the greater difficulty of desolvation for FOPC upon binding to the enzyme. This calculation suggests that the desolvation of the ligand, as well as its interaction with the beta-lactamase, is important in understanding the relative affinity of the ligands with beta-lactamase.