Confinement Method

Equilibrated structures of the 16-residue peptide from protein G in (a) α-helical conformation, and (b) β-sheet conformation. Complex biomolecular systems such as proteins evolve on rugged potential energy surfaces, on which configurational transitions between local minima are rare events. For such systems, direct calculations of conformational free energy differences from equilibrium molecular dynamics simulations are impractical. Because conformational transitions underlie many processes of biological significance (e.g., protein conformational changes in response to the binding of a ligand) and are relevant for finding the most stable configuration of a molecular system (e.g., structure refinement), algorithms to calculate conformational free energy differences in an accessible time using computer simulations continue to be a research focus. Path-based methods for conformational free energy calculation require the user to specify a reaction coordinate and/or a physical transition path that connects different conformations. For cases in which suitable reaction coordinates or transition paths are unknown, it is important to be able to calculate free energy differences by a path-independent method. Path independent methods can also be used to provide estimates of the free energy to validate other methods. Confinement analysis is one such path-independent method.

The essential idea of confinement analysis is to relate the free energy of a system of interest with 3N degrees of freedom to the free energy of 3N harmonic oscillators (HOs), which is known analytically. We described a simplified confinement method that is very well suited to computing free energy differences (rather than absolute free energies), which is the quantity of interest in most biological processes. The method can be readily implemented in molecular dynamics programs with minimal or no code modifications. Because the confinement method is a special case of thermodynamic integration, it is trivially parallel over the integration variable. The accuracy of the method is demonstrated using a model diatomic molecule, for which exact results can be computed analytically. The method is applied to the alanine dipeptide in vacuum, and to the α-helix ↔ β-sheet transition in a 16residue peptide modeled in implicit solvent.

Efficient extensions of the confinement method to simulations in explicit solvent are currently under development.

Reference:

V. Ovchinnikov, M. Cecchini, and M. Karplus. A Simplified Confinement Method (SCM) for Calculating Absolute Free Energies and Free Energy and Entropy Differences. J. Phys. Chem. B, 117:750–762, 2013 (preprint)