Free-energy calculations for semi-flexible macromolecules: Applications to DNA knotting and looping

TL;DR

This paper introduces a novel computational method combining thermodynamic integration and normal-mode analysis to accurately calculate free energies of semi-flexible macromolecules like DNA, enabling exploration of larger fluctuations and complex configurations.

Contribution

The method uses internal coordinates for reference states and allows flexible selection, improving accuracy and applicability to diverse biopolymer systems.

Findings

Validated with high accuracy on DNA knots with L/P=20 and 40

Revealed bifurcation in free-energy landscape of DNA looped complexes

Applied to DNA-protein interactions relevant to gene regulation

Abstract

We present a method to obtain numerically accurate values of configurational free energies of semiflexible macromolecular systems, based on the technique of thermodynamic integration combined with normal-mode analysis of a reference system subject to harmonic constraints. Compared with previous free-energy calculations that depend on a reference state, our approach introduces two innovations, namely the use of internal coordinates to constrain the reference states and the ability to freely select these reference states. As a consequence, it is possible to explore systems that undergo substantially larger fluctuations than those considered in previous calculations, including semiflexible biopolymers having arbitrary ratios of contour length L to persistence length P. To validate the method, high accuracy is demonstrated for free energies of prime DNA knots with L/P=20 and L/P=40, corresponding to DNA lengths of 3000 and 6000 base pairs, respectively. We then apply the method to study the free-energy landscape for a model of a synaptic nucleoprotein complex containing a pair of looped domains, revealing a bifurcation in the location of optimal synapse (crossover) sites. This transition is relevant to target-site selection by DNA-binding proteins that occupy multiple DNA sites separated by large linear distances along the genome, a problem that arises naturally in gene regulation, DNA recombination, and the action of type-II topoisomerases.