Discrimination between native and intentionally misfolded conformations of proteins: ES/IS, a new method for calculating conformational free energy that uses both dynamics simulations with an explicit solvent and an implicit solvent continuum model

Abstract

A new method for calculating the total conformational free energy of proteins in water solvent is presented. The method consists of a relatively brief simulation by molecular dynamics with explicit solvent (ES) molecules to produce a set of microstates of the macroscopic conformation. Conformational energy and entropy are obtained from the simulation, the latter in the quasi-harmonic approximation by analysis of the covariance matrix. The implicit solvent (IS) dielectric continuum model is used to calculate the average solvation free energy as the sum of the free energies of creating the solute-size hydrophobic cavity, of the van der Waals solute-solvent interactions, and of the polarization of water solvent by the solute's charges. The reliability of the solvation free energy depends on a number of factors: the details of arrangement of the protein's charges, especially those near the surface; the definition of the molecular surface; and the method chosen for solving the Poisson equation. Molecular dynamics simulation in explicit solvent relaxes the protein's conformation and allows polar surface groups to assume conformations compatible with interaction with solvent, while averaging of internal energy and solvation free energy tend to enhance the precision. Two recently developed methods--SIMS, for calculation of a smooth invariant molecular surface, and FAMBE, for solution of the Poisson equation via a fast adaptive multigrid boundary element--have been employed. The SIMS and FAMBE programs scale linearly with the number of atoms. SIMS is superior to Connolly's MS (molecular surface) program: it is faster, more accurate, and more stable, and it smooths singularities of the molecular surface. Solvation free energies calculated with these two programs do not depend on molecular position or orientation and are stable along a molecular dynamics trajectory. We have applied this method to calculate the conformational free energy of native and intentionally misfolded globular conformations of proteins (the EMBL set of deliberately misfolded proteins) and have obtained good discrimination in favor of the native conformations in all instances.

Electrostatic contributions to protein–protein interactions: Fast energetic filters for docking and their physical basis

“…An important finding in our paper is that, for the bound problem, a binding free energy calculation based on continuum electrostatics (the FDPB method) and a surface area-based method of evaluating the nonpolar contribution to binding (Froloff et al 1997), reliably identifies the native conformation as well as near-native conformations generated by the docking algorithm. Related approaches have been used to discriminate native protein structures from misfolded decoys (Janardhan and Vajda 1998;Vorobjev et al 1998;Lazaridis and Karplus 1999;Petrey and Honig 2000). These results, together with other studies of protein-protein docking (Jiang and Kim 1991;Katchalski-Katzir et al 1992;Meyer et al 1996;Gabb et al 1997), indicate that the physical chemical forces that control protein folding and protein-protein interactions are reasonably well understood.…”

Free Energy Simulations Come of Age: Protein−Ligand Recognition

“…72,73 Sensitivity analysis and charge optimization have been used to analyze or alter binding specificity. 74,75 Two studies employed free energy functions consisting of a Poisson-Boltzmann electrostatic solvation term, plus additional contributions (a cavity term proportional to surface area, a molecular mechanics solute energy, and a harmonic or quasiharmonic solute vibrational entropy 70,76 ). With this PBFE variant ("MM-PBSA"), reasonable agreement with experiment was obtained in several studies involving proteins and small ligands, using solute dielectrics of 1 30 …”

Calculating Structures and Free Energies of Complex Molecules: Combining Molecular Mechanics and Continuum Models

“…The ability to calculate structure and free energy, initiated by the papers by Srinivasan et al, 10 Hermans et al, 11 and Jayaram et al 12 in 1998, heralds the beginning of a fourth era of macromolecular MD. This era combines the advances of the second and third eras, in that we can now calculate structure and free energy.…”