Single and multiple topologically driven structural transitions in DNA.

Abstract

We derive some exact general results concerning the behavior of topological absorbers (i.e., sequences undergoing topologically driven structural transitions) in closed circular DNA molecules. Starting from the formal physical framework that covers all known structural transitions, like those from standard B-DNA to nonstandard conformers Z-DNA, H-DNA, cruciform-DNA, melt-DNA or others, we develop a reduced state space description that leads to an analytically simplified "black box" view of absorbers. The latter contains only a single state variable-the total sequence unwinding u describing the topological state of the absorber. We show that the statistical mechanics of u is determined by the (one-dimensional) absorption free energy function G(abs) and find explicit expressions for G(abs) and for moments in terms of the standard experimental observable-the absorption function alpha:= . The reduced state space method is then applied to systems consisting of several interacting topologically coupled absorbers and a formula predicting their collective behavior (superposition) in terms of their individual absorptions is derived. Using these results we formulate and discuss solution methods for two basic types of inverse problems that turn out to be fundamental for future absorber construction.