Anomalous diffusion in folding dynamics of minimalist protein landscape

A novel method is proposed to quantify collectivity at different space and time scales in multiscale dynamics of proteins. This is based on the combination of the principal component (PC) and the concept recently developed for multiscale dynamical systems called the finite size Lyapunov exponent. The method can differentiate the well-known apparent correlation along the low-indexed PCs in multidimensional Brownian systems from the correlated motion inherent to the system. As an illustration, we apply the method to a model protein of 46 amino beads with three different types of residues. We show how the motion of the model protein changes depending on the space scales and the choices of degrees of freedom. In particular, anomalous superdiffusion is revealed along the low-indexed PC in the unfolded state. The implication of superdiffusion in the process of folding is also discussed.