RELAXATIONAL DYNAMICS OF A RANDOM HETEROPOLYMER

We have investigated the relaxational dynamics of a random heteropolym er after a temperature quench using extensive molecular dynamics simul ation. The interaction between all monomers is taken to be a purely re pulsive Lennard-Jones potential plus a random potential with a 1/r(6) behavior. An equilibrium ''phase diagram'' is determined which allows us to find a characteristic temperature T-Theta which separates extend ed states from folded states of the heteropolymer. This temperature is an increasing function of the random interaction strength, and it per mits us to determine appropriate initial and final temperatures for th e quenches. Within the extended states the relaxation is found to be a pure exponential. It is a stretched exponential when quenching across the characteristic temperature. In particular, for long chains the re laxation is a two-stage process; both stages are of stretched form wit h different stretched exponents which we determine numerically for var ious system parameters. Our simulation clearly shows the nature of the relaxation process where a local folding takes place first followed b y a global folding of the local blobs leading to the two folding stage s. The results are discussed in relation to protein folding and to pre vious investigations.