Endpoint-restricted adiabatic free energy dynamics approach for the exploration of biomolecular conformational equilibria.

A method for calculating the free energy difference between two structurally defined conformational states of a chemical system is developed. A path is defined using a previously reported collective variable that interpolates between two or more conformations, and a restraint is introduced in order to keep the system close to the path. The evolution of the system along the path, which typically presents a high free energy barrier, is generated using enhanced sampling schemes. Although the formulation of the method in terms of a path is quite general, an important advance in this work is the demonstration that prior knowledge of the path is, in fact, not needed and that the free energy difference can be obtained using a simplified definition of the path collective variable that involves the endpoints. We first validate this method on cyclohexane isomerization. The method is then tested for an extensive conformational change in a realistic molecular system by calculating the free energy difference between the -helix and -hairpin conformations of deca-alanine in solution. Finally, the method is applied to a biologically relevant system to calculate the free energy difference of an observed and a hypothetical conformation of an antigenic peptide bound to a major histocompatibility complex.