Calculation of the potential of mean force using molecular dynamics with linear constraints: An application to a conformational transition in a solvated dipeptide

An algorithm is proposed for the calculation of mean force potentials using molecular dynamics with linear constraints. The new algorithm is based on free energy perturbation and is especially useful when the analytical form of the reaction coordinate is not known (e.g., for a numerically evaluated steepest descent path). It employs only Cartesian coordinates which makes it easy to use for a variety of systems. In particular, it is useful when the reaction coordinate cannot be represented by a single local coordinate or by a combination of a small number of local (internal) coordinates. The linear constraints are solved explicitly and the computational effort required is similar to that of dynamics with no constraints. The potential of mean force for a conformational transition of a solvated valine dipeptide is calculated. In aqueous solution the barriers for the conformational transitions are reduced with respect to the barriers in vacuo, the helix configuration becomes stabilized.