A Simplified Confinement Method for Calculating Absolute Free Energies and Free Energy and Entropy Differences

Abstract:

A simple and robust formulation of the path-​independent confinement method for the calcn. of free energies is presented. The simplified confinement method (SCM) does not require matrix diagonalization or switching off the mol. force field, and has a simple convergence criterion. The method can be readily implemented in mol. dynamics programs with minimal or no code modifications. Because the confinement method is a special case of thermodn. integration, it is trivially parallel over the integration variable. The accuracy of the method is demonstrated using a model diat. mol., for which exact results can be computed anal. The method is then applied to the alanine dipeptide in vacuum, and to the α-​helix ↔ β-​sheet transition in a 16-​residue peptide modeled in implicit solvent. The SCM requires less effort for the calcn. of free energy differences than previous formulations because it does not require computing normal modes. The SCM has a diminished advantage for detg. abs. free energy values, because it requires decreasing the MD integration step to obtain accurate results. An approx. confinement procedure is introduced, which can be used to est. directly the configurational entropy difference between two macrostates, without the need for addnl. computation of the difference in the free energy or enthalpy. The approxn. has convergence properties similar to those of the std. confinement method for the calcn. of free energies. The use of the approxn. requires about 5 times less wall-​clock simulation time than that needed to compute enthalpy differences to similar precision from an MD trajectory. For the biomol. systems considered in this study, the errors in the entropy approxn. are under 10​%. Practical applications of the methods to proteins are currently limited to implicit solvent simulations.