'Sequence' dependent elasticity and local stiffness of a random heteropolymer

Abstract

We study the 'sequence' distribution of thermally averaged global and local elastic properties of a random heteropolymer of fixed length N, within the framework of a disordered Kratky–Porod (KP) model. We arrive at a number of qualitative results on the form of the distribution function of the thermally averaged end-to-end distance langR2rang, and its moments. For long N\to \infty chains, this distribution is a Gaussian; for shorter chains, there is a crossover to an exponential distribution, with the most probable end-to-end distance deviating significantly from the mean. Further, the distributions of local quantities related to the thermally averaged tangent–tangent correlator are typically broad, even in the thermodynamic limit, i.e., they do not self-average. This is consistent with the general consensus that DNA–protein binding/unbinding strengths and rates are sensitive to local elastic distortion which is 'sequence' dependent.