Free energy analysis of enzyme-inhibitor binding: The carboxypeptidase A-inhibitor complexes

Developing free energy estimates of biological molecules starting from a mo lecular description of the solute, solvent and the salt, is currently in th e domain of computationally intractable problems. However, structure based drug design efforts involving for instance, designing a suitable inhibitor molecule with desired binding attributes targeted to an active site on an e nzyme necessitates free energy estimates. We present here a computationally expedient and rigorous methodology to develop and analyse the thermodynami cs of enzyme inhibitor binding starting from crystal structures. The comple xes of carboxypeptidase A with five inhibitors with known structural and bi nding constant data have been adopted for this study as illustrative cases. The standard free energy of complexation is considered in terms of a therm odynamic cycle of six distinct steps decomposed into a total of 18 well-def ined components. The model we employ involves explicit all atom accounts of the energetics of electrostatic interactions, solvent screening effects, v an der Waals components and cavitation effects of solvation combined with a Debye-Huckel treatment of salt effects. Estimates of entropy loss due to d ecreased translational and rotational degrees of freedom in the complex rel ative to the unbound species based on classical statistical mechanics are i ncluded, as well as corresponding changes in the vibrational and configurat ional entropy. The magnitudes and signs of the various components are estim ated using the AMBER parm94 force field, generalized Born theory and solven t accessibility measures. The calculated standard free energies of formatio n agree with experiment in these systems to within 5-12 kcal/mol. This gene rates the various components considerable optimism in the potential viabili ty of the methodology for drug design. Fine tuning of the computational pro tocols, inclusion of structural adaptation effects and a careful examinatio n and minimization of possible errors are some areas for further research. The net binding free energies are a resultant of several competing contribu tions with 7 out of the 18 terms favouring complexation. A component-wise a nalysis of the binding free energy for the five carboxypeptidase A-inhibito r complexes studied here indicates that the nonelectrostatic contributions, i.e. the net van der Waals interactions and the differential cavitation ef fects are favourable to binding. Electrostatic contributions averaged over the five systems turn out to be favourable despite the desolvation expense incurred during binding. Analyses on these lines yield pointers to structur al modifications to be attempted to accomplish optimal binding besides pres enting a molecular energetic perspective of induced-fit mechanisms.