Theory of the Overestimation of Protein-RNA Binding Energies obtained by Molecular Dynamics Simulations with Umbrella Sampling.*

We suggest that Molecular Dynamics (MD) simulations often greatly overestimate the binding free energies between pairs of deformable macromolecules, such as protein-RNA binding energies. This is generally attributed to slow collective modes that do not reach thermal equilibrium on simulation time scales. We present a statistical physics theory of this effect based on the irreversible release of elastic deformation energy. We compare the theory with MD simulations of protein-RNA interactions and present a method to obtain binding free energy by the systematic application of constraints. Conventional soft modes, associated with translation, rotation, and low energy elastic deformations can all be suppressed by the application of constraints. We will discuss that this may not eliminate soft modes associated with irreversible "slipping" between different binding configurations of flexible macromolecules.