Multifractality, Levinthal paradox, and energy hypersurface

Abstract

Multifractal properties in the potential energy hypersurface of polypeptides and proteins are investigated. Characteristic multifractal behavior for different molecular systems is obtained from the $f\left(\alpha \right)$ spectra. The analysis shows that the dimension of the phase space of the problem influences the accessibility to different parts of the potential energy hypersurface. Also, we show that it is necessary to take into account the H-bond formation between amino acids in the conformational-folding search. The present findings indicate that the $f\left(\alpha \right)$ function describes some structural properties of a protein. The behavior of the $f\left(\alpha \right)$ spectra gives an alternative explanation about the Levinthal paradox. Furthermore, the anomalous temperature dependence of the Raman spin-lattice relaxation rates can be related to the perturbations in the secondary structures.