KINETICS OF CONTRACTION OF A STIFF CHAIN

The contraction kinetics of a moderately stiff chain upon sudden undercooling 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 kinetic equation, derived from the appropriate nonequilibrium Langevin equation, yields the time rate of change of the contraction ratios of the Rouse-Zimm normal modes in terms of the current free-energy gradient and of the instantaneous relaxation times. For a large enough undercooling tau = (T - Theta)/T, the kinetics proceeds in two contraction steps separated by a time interval denoted as the induction time, wherein the chain size and especially the free energy remain almost constant. During the induction time, the normal modes slowly adjust to one another in a strongly cooperative process. Eventually, at a well-defined time the final contraction step takes place very quickly, leading to a relatively compact globule. From our calculations with up to 40 repeat units, the induction time scales as N-2((tau-tau(*))/tau(*))(-1.40), tau(*) being the critical undercooling to reach a globular state at equilibrium. Thus, the induction time may be very large for a large-molecular-weight polymer. Conversely, no induction time is found for the opposite process; i.e., the swelling of the collapsed globule to the unperturbed state. Possible connections with protein folding kinetics are briefly pointed out. The specificity of the folding behavior of each protein may be tested against the present results, although, strictly speaking, these apply only to an undifferentiated linear polymer.