Estimating the Ruggedness of Protein Free Energy Landscapes from Molecular Dynamics Simulations

Abstract

The free energy landscape that governs protein dynamics typically exhibits a hierarchical structure, which gives rise to anomalous diffusion. Here we aim at extracting information on the structure of the underlying free energy landscape from molecular dynamics simulations. To this aim, we quantify how anomalous diffusion exponents found in molecular dynamics simulations relate to its hierarchical structure using a simple hierarchical model free energy landscapes with exponentially distributed barriers.This model is characterized by a parameter ΔF which describes its ruggedness. Using a renormalization group approach we show how the anomalous diffusion exponents of these models depend on their ruggedness parameter ΔF.We then carried out microsecond simulation for 500 proteins selected from different function classes and calculated respective anomalous diffusion exponents for each of the 500 proteins. Assuming a similar relation between ruggedness and anomalous diffusion exponents in the simulations, we obtained a comprehensive characterization of their hierarchical free energy landscapes.