Dynamics of heteropolymers in dilute solution: effective equation of motion and relaxation spectrum

Abstract

The dynamics of a heteropolymer chain in solution is studied in the limit of long chain length. Using functional integral representation we derive an effective equation of motion, in which the heterogeneity of the chain manifests itself as a time-dependent excluded volume effect. At the mean field level, the heteropolymer chain is therefore dynamically equivalent to a homopolymer chain with both time-independent and time-dependent excluded volume effects. The perturbed relaxation spectrum is also calculated. We find that heterogeneity also renormalizes the relaxation spectrum. However, we find, to the lowest order in heterogeneity, that the relaxation spectrum does not exhibit any dynamic freezing, at the point when static (equilibrium) ``freezing'' transition occurs in heteropolymer. Namely, the breaking of fluctuation-dissipation theorem (FDT) proposed for spin glass dynamics does not have dynamic effect in heteropolymer, as far as relaxation spectrum is concerned. The implication of this result is discussed.