On Heteropolymer Shape Dynamics

We investigate the time evolution of the heteropolymer model introduced by Iori, Marinari and Parisi to describe some of the features of protein folding mechanisms. We study how the (folded) shape of the chain evolves in time. We find that for short times the mean square distance (squared) between chain configurations evolves according to a power law, $D\sim t^{\nu }$. We discuss the influence of the quenched disorder (represented by the randomness of the coupling constants in the Lennard-Jones potential) on value of the critical exponent. We find that $\nu$ decreases from $\frac{2}{3}$ to $\frac{1}{2}$ when the strength of the quenched disorder increases.