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

Abstract

262-273Developing free energy estimates of biological molecules starting from a molecular description of the solute, solvent and the salt, is currently in the 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 enzyme necessitates free energy estimates. We present here a computationally expedient and rigorous methodology to develop and analyse the thermodynamics of enzyme-inhibitor binding starting from crystal structures. The complexes of carboxypeptidase A with five inhibitors with known structural and binding constant data have been adopted for this study as illustrative cases. The standard free energy of complexation is considered in terms of a thermodynamic cycle of six distinct steps decomposed into a total of 18 well -defined components. The model we employ involves explicit all atom accounts of the energetics of electrostatic interactions, solvent screening effects, van der Waals components and cavitation effects of solvation combined with a Debye- Huckel treatment of salt effects. Estimates of entropy loss due to decreased translational and rotational degrees of freedom in the complex relative to the unbound species based on classical statistical mechanics are included, as well as corresponding changes in the vibrational and configurational entropy. The magnitudes and signs of the various components are estimated using the AMBER parm94 force field, generalized Born theory and solvent accessibility measures. The calculated standard free energies of formation agree with experiment in these systems to within 5-12 kcal/mol. This generates considerable optimism in the potential viability of the methodology for drug design. Fine tuning of the computational protocols, inclusion of structural adaptation effects and a careful examination and minimization of possible errors are some areas for further research. The net binding free energies are a resultant of several competing contributions with 7 out of the 18 terms favouring complexation. A component-wise analysis of the binding free energy for the five carboxypeptidase A-inhibitor complexes studied here indicates that the nonelectrostatic contributions, i.e. the net vander Waals interactions and the differential cavitation effects 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 structural modifications to be attempted to accomplish optimal binding besides presenting a molecular energetic perspective of induced-fit mechanisms