Mittag-Leffler Correlated Noise and Anomalous Diffusion within a Single Protein Molecule

One of authors (Wang) studied the motion of a particle under the influence of a random force modeled as Gaussian colored noise with arbitrary correlation and with/without external force (Wang et al., Physica A \textbf{265, }341(1999)). The generalized Langevin equation, Generalized Fokker-Planck equation, and the variances of displacement, velocity and cross variance between displacement and velocity are obtained in that paper. Recently, Xie et al. (Phys. Rev. Letters. \textbf{93}, 180603 (2004), \textbf{94}, 198302 (2005)) applied the theory developed by Wang to explaining the anomalous diffusion within a single protein molecule. However, in this presentation, we will show that using Mittag-Leffler correlated noise and generalized Langevin equation can more accurately explain the experimental data of autocorrelation function of distance in a single protein molecule.