Fractal Analysis of Protein Potential Energy Landscapes

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.