Dynamics of the helix-coil transition in biopolymers

Abstract

The dynamics near and far from equilibrium of the linear Ising model of biopolymers is formulated in terms of the concentrations n+l(t) [n−l(t)] of sequences of l subsequent units in the helix [coil] state, investigating the limit of very long chains. The resulting set of kinetic equations can be truncated for large l in a controlled fashion with negligible error, in contrast to previous ’’closure’’ approximations whose accuracy was doubtful. The initial relaxation time τ* is obtained exactly by our method for relaxation near and far from equilibrium, in agreement with previous studies. Analytic approximation formulas are obtained for helix fractions ϑ close to zero or unity, complementing previous work valid for ϑ close to 1/2. For intermediate values of ϑ we solve our set of kinetic equations numerically to study the width of the relaxation spectrum. We find that the relaxation function becomes distinctly nonexponential for ϑ away from 1/2, 1, 0 and cooperativities σ=10−3–10−1. Applications of these results to temperature or pH jump, as well as NMR experiments, etc., are briefly discussed.