KINETICS OF CONTRACTION OF A STIFF CHAIN

The contraction kinetics of a moderately stiff chain upon sudden under cooling below the Theta temperature is investigated, adopting a freely -rotating chain model subject to intramolecular medium- and long-range interactions. The temperature-dependent two-body interactions, which vanish at T = Theta, provide the driving force to collapse. The kineti c equation, derived from the appropriate nonequilibrium Langevin equat ion, yields the time rate of change of the contraction ratios of the R ouse-Zimm normal modes in terms of the current free-energy gradient an d of the instantaneous relaxation times. For a large enough undercooli ng tau = (T - Theta)/T, the kinetics proceeds in two contraction steps separated by a time interval denoted as the induction time, wherein t he chain size and especially the free energy remain almost constant. D uring the induction time, the normal modes slowly adjust to one anothe r in a strongly cooperative process. Eventually, at a well-defined tim e the final contraction step takes place very quickly, leading to a re latively compact globule. From our calculations with up to 40 repeat u nits, the induction time scales as N-2((tau-tau())/tau(*))(-1.40), ta u() being the critical undercooling to reach a globular state at equi librium. Thus, the induction time may be very large for a large-molecu lar-weight polymer. Conversely, no induction time is found for the opp osite process; i.e., the swelling of the collapsed globule to the unpe rturbed state. Possible connections with protein folding kinetics are briefly pointed out. The specificity of the folding behavior of each p rotein may be tested against the present results, although, strictly s peaking, these apply only to an undifferentiated linear polymer.