MEAM Seminar: “Mechanical Models for DNA”

We will discuss two complementary mechanical models for DNA that deal with, respectively two problems: one, phase transitions in a DNA molecule, and two, allosteric interactions between two ligands bound to DNA.

Experimental studies on single molecules of DNA have reported a rich variety of cooperative structural transitions, including coexistence of three phases, when a torsionally constrained DNA molecule is pulled using magnetic or optical tweezers. Our objective is to examine the aforementioned structural transitions using ideas from statistical mechanics and the theory of elasticity. 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. Furthermore, we use Poisson-Boltzmann to 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 over-stretching transition characterized by a 70% jump in the contour length of the molecule and examine the effect of salt concentration on this transition.

In the next part, we present a mechanical model for computing the allosteric interaction energy between two ligands on DNA. This interaction is quantified by measuring the change in free energy as a function of the distance between the binding sites for two ligands. We show that trends in the interaction energy of two ligands binding to DNA can be explained using an elastic birod model which accounts for the elastic deformation of strands and base-pairs as well as the change in stacking energy due to perturbations in position and orientation of the bases caused by the binding of ligands. The strain fields produced by the ligands decay with distance from the binding site. The interaction energy of two ligands decays exponentially with the distance between them and oscillates with the periodicity of the double helix in quantitative agreement with experimental measurements. The trend in the computed interaction energy is similar to that in the perturbation of groove width produced by the binding of a single ligand which is consistent with molecular simulations. Our analysis provides a new framework to understand allosteric interactions in DNA and can be extended to other rod-like macromolecules whose elasticity plays a role in biological functions.

The results from our model are in agreement with multiple experiments documented in the literature and they generate new falsifiable predictions that can be experimentally tested.