Theoretical analysis of heteropolymeric transitions in superhelical DNA molecules of specified sequence

Abstract

This paper develops accurate and computationally tractable, theoretical methods to analyze equilibrium heteropolymeric transitions in superhelical DNAs of specified sequence and kilo-base length. Although these methods are generally applicable, their development here is focused primarily on superhelical strand separation, a heteropolymeric transition of great biological importance to which every base pair in a duplex DNA molecule is susceptible. Because the total number of states of this transition grows exponentially with molecular length, exact analytic methods that consider all possible states are not feasible for DNAs of practical interest. First, an approximate statistical mechanical analysis is developed in which all states are considered whose free energies do not exceed that of the minimum energy state by more than a specified threshold amount. An approximate partition function is constructed using these states, from which estimates of the equilibrium values of important transition parameters are calculated. Next, a density of states analysis is performed to estimate the influence of the neglected, high energy states. Its results are used to refine the computed equilibrium parameter values, correcting for the effects of the neglected states. Only the transition profile (the probability of transition of each base pair in the sequence) cannot be refined in this manner, although its overall accuracy can be assessed. Sample calculations analyzing the strand separation transition in superhelical pBR322 DNA show that the analytic methods developed here yield accurate results in a computationally feasible manner. Moreover, the predictions of this analysis agree closely with experimental results.