Fractal Analysis of Protein Potential Energy Landscapes

TL;DR

This study investigates the fractal properties of potential energy landscapes in proteins, revealing a universal fractal dimension influenced by dynamical noise and weakly dependent on protein type and landscape topology.

Contribution

It demonstrates the near universality of the fractal dimension in protein energy landscapes and links it to self-generated dynamical noise from anharmonic intermode coupling.

Findings

Fractal dimension is nearly independent of temperature.

Fractal dimension increases with time and is larger for smaller proteins.

Global topological features have little effect on fractal behavior.

Abstract

The fractal properties of the total potential energy V as a function of time t are studied for a number of systems, including realistic models of proteins (PPT, BPTI and myoglobin). The fractal dimension of V(t), characterized by the exponent \gamma, is almost independent of temperature and increases with time, more slowly the larger the protein. Perhaps the most striking observation of this study is the apparent universality of the fractal dimension, which depends only weakly on the type of molecular system. We explain this behavior by assuming that fractality is caused by a self-generated dynamical noise, a consequence of intermode coupling due to anharmonicity. Global topological features of the potential energy landscape are found to have little effect on the observed fractal behavior.