Dynamics of Random Hydrophobic-Hydrophilic Copolymers with Implications for Protein Folding

We study the dynamics of a single amphiphilic random copolymer chain. The dynamical treatment shows that in addition to the collapse temperature, $T_{\Theta }$, there exists a scale dependent glass transition temperature $T_G\left(l\right)$. Distinct scenarios for the glassy behavior emerges depending on the relative values of $T_{\Theta }$ and $T_G\left(l\right)$. The possible implications of our results for protein folding, including an estimate of the dependence of the ratio of the folding transition temperature to $T_G\left(l\right)$ on the length of the chain, are sketched.