Theoretical study of kinetics of zipping phenomena in biomimetic polymers

In this work we use theory to obtain a mathematical expression for a time correlation function c(l,t) that provides insight into the zipping phenomena along a polymer going through a conformational transition. The polymer is modeled as an Ising-like chain with each segment being in one of two states: bound (+1) or unbound (-1). The time correlation function c(l,t) predicts the correlation between the state of the jth polymer segment at time 0 and the state of the (j+/-l)th polymer segment at time t . The expressions for c(0,t) , c(1,t), and c(2,t) obtained from our theory are dependent on the values of k0 and k1, where 2k0 is the rate coefficient for one segment changing from an unbound state to a bound state when both the neighboring segments are in an unbound state, and 2k1 is the rate coefficient for one segment changing from an unbound state to a bound state when both the neighboring segments are in a bound state. The ratio k1/k0 is an indication of the extent of cooperativity of binding adjacent segments on the polymer. We observe that c(0,t), c(1,t), and c(2,t) decay to 0 (no correlation) more slowly and the maximum values of c(1,t) and c(2,t) are lower for low values of k1/k0 as compared to high values of k1/k0. This is because at low values of k1/k0 the consecutive binding of adjacent segments along the polymer occurs slowly, while at high values of k1/k0 the cooperativity of binding adjacent segments is high and the segments along the polymer bind in a fast zipping mechanism.