Exploring Protein Energy Landscapes with Time-Dependent Principal Component Analysis

Abstract

Protein function crucially depends on protein dynamics. Large-scale molecular dynamics simulations of small globular proteins show an anomalous diffusion behavior for the principal motions of proteins over multiple time scales. Specifically the variance of the essential principal components increases with a power law σ ∼ T α with trajectory length T. This behavior suggests a hierarchical structure of the energy landscape as first proposed by Frauenfelder.To quantify how the anomalous diffusion exponents found in the molecular dynamics simulations give insight into the hierarchical structure of the underlying energy landscape, we compared our results to the simple discrete energy landscape shown in the figure. In this model, a hierarchy of energy barriers separating adjecent states is assumed. This hierarchy is characterized by its “ruggedness” ΔF as shown in the figure. We show that ΔF can be derived from the power law exponent α measured in the simulations via ΔF=log(2)(2/α-1). Typical values of 5-7 kT are obtained.View Large Image | View Hi-Res Image | Download PowerPoint Slide