Structural transitions in torsionally constrained DNA and their dependence on solution electrostatics.

Experimental studies on single molecules of DNA have reported a rich variety of structural transitions, including coexistence of three phases, in a torsionally constrained molecule. A comprehensive knowledge of these structural transitions is useful for unraveling the in vivo and in vitro behavior of DNA. Our objective is to understand the structural transitions in a torsionally constrained DNA molecule when it is pulled using optical or magnetic tweezers. We use foundational concepts from the Zimm-Bragg helix-coil transition theory and merge them with ideas from the theory of fluctuating elastic rods to model the mechanics of DNA. We also account for the electrostatic interactions between the ions and the negatively charged phosphate backbone of DNA. Using our model, we calculate the force and torque corresponding to the overstretching transition characterized by a 70% jump in the contour length of the molecule and examine the effect of salt concentration on this transition. We also deduce conditions under which the co-existence of B-, S- and P-DNA is possible. We examine how the cooperativity parameter for each transition affects the force-extension curve or torque-rotation curve. We attempt to rationalize the non-monotonic dependence of external work done on the ion concentration by connecting it to the electrostatic dependence of the interfacial energy between two phases of DNA. Our theoretical results are in agreement with multiple experiments documented in the literature and they generate falsifiable predictions that can be tested in new experiments.

STATEMENT OF SIGNIFICANCE: The overarching objective of this paper is to explore the implications of variation in ion concentration on the structural transitions driven by external forces in a torsionally constrained DNA molecule. A comprehensive understanding of the phase behavior of torsionally constrained DNA is useful because DNA in cells is tightly packaged and is acted upon by molecular machines in different ionic environments. We examine the mechanics of the overstretching transition, characterized by a 70% jump in contour length, wherein a mixture of B- and S-DNA converts into a mixture of S- and P-DNA through a triple point in the phase diagram. Our results are corroborated by experimental data at every step and we make predictions that are experimentally verifiable.