Fractional Relaxation Equations for Protein Dynamics

Due to a large amount of conformational substates, relaxation processes in proteins are governed by many time constants and therefore, they decay more slowly than a Debye relaxation. For processes occurring on different time scales in a self-similar manner, we derive and solve a fractional order differential equation for the relaxation function. Solutions of this well-posed initial value problem are given in terms of a Mittag-Leffler function. Applications to ligand rebinding data of myoglobin are presented leading to a 3-parameter fractional model.