CONFIGURATIONAL DIFFUSION ON A LOCALLY CONNECTED CORRELATED ENERGY LANDSCAPE - APPLICATION TO FINITE, RANDOM HETEROPOLYMERS

We study the time scale for diffusion on a correlated energy landscape using models based on the generalized random energy model (GREM) stud ied earlier in the context of spin glasses (Derrida B. and Gardner E., J. Phys. C 19 (1986) 2253) with kinetically local connections. The es cape barrier and mean escape time are significantly reduced from the u ncorrelated landscape (REM) values. Results for the mean escape time f rom a kinetic trap are obtained for two models approximating random he teropolymers in different regimes, with linear and bi-linear approxima tions to the configurational entropy versus similarity q with a given state. In both cases, a correlated landscape results in a shorter esca pe time from a meta-stable state than in the uncorrelated model (Bryng elson J.D. and Wolynes P.G., J. Phys. Chem. 93 (1989) 6902). Results a re compared to simulations of the diffusion constant for 27-mers. In g eneral, there is a second transition temperature above the thermodynam ic glass temperature, at and above which kinetics becomes non-activate d. In the special case of an entropy linear in q, there is no escape b arrier for a model preserving ultrametricity. However, in real heterop olymers a barrier can result from the breaking of ultrametricity, as s een in our non-ultrametric model. The distribution of escape times for a model preserving microscopic ultrametricity is also obtained, and f ound to reduce to the uncorrelated landscape in well-defined limits.