Strongly Bent Double-Stranded DNA: Reconciling Theory and Experiment.

Aleksander V Drozdetski,Alexey V Onufriev,Abhishek Mukhopadhyay

doi:10.3389/fphy.2019.00195

Abstract

The strong bending of polymers is poorly understood. We propose a general quantitative framework of polymer bending that includes both the weak and strong bending regimes on the same footing, based on a single general physical principle. As the bending deformation increases beyond a certain (polymer-specific) point, the change in the convexity properties of the effective bending energy of the polymer makes the harmonic deformation energetically unfavorable: in this strong bending regime the energy of the polymer varies linearly with the average bending angle as the system follows the convex hull of the deformation energy function. For double-stranded DNA, the effective bending deformation energy becomes non-convex for bends greater than ~ 2° per base-pair, equivalent to the curvature of a closed circular loop of ~ 160 base pairs. A simple equation is derived for the polymer loop energy that covers both the weak and strong bending regimes. The theory shows quantitative agreement with recent DNA cyclization experiments on short DNA fragments, while maintaining the expected agreement with experiment in the weak bending regime. Counter-intuitively, cyclization probability (j-factor) of very short DNA loops is predicted to increase with decreasing loop length; the j-factor reaches its minimum for loops of ≃ 45 base pairs. Atomistic simulations reveal that the attractive component of the short-range Lennard-Jones interaction between the backbone atoms can explain the underlying non-convexity of the DNA effective bending energy, leading to the linear bending regime. Applicability of the theory to protein-DNA complexes, including the nucleosome, is discussed.

Highlights

Deformation of polymers is ubiquitous, elastic properties of these macromolecules are crucial for their dynamics
Applicability of ECH to protein-DNA complexes will require further rigorous analysis. It is well-established that slightly bent DNA behaves like an elastic rod—the deformation energy is a quadratic function of the deformation
Recent experiments demonstrated that strong bending of small DNA fragments could no longer be described within this classical model

Summary

Introduction

Deformation of polymers is ubiquitous, elastic properties of these macromolecules are crucial for their dynamics. Biopolymers are abundant in nature and play vital roles in many biological processes [1,2,3,4], which depend upon the polymer structure, and on its physical properties [5,6,7]. An all-important example of DNA deformation, relevant to a variety of biological processes that depend on its elastic properties, is DNA looping, which occurs in many prokaryotic [9] and eukaryotic [10] systems. A number of regulatory proteins can loop DNA into various bent conformations, critical for regulation of many biological processes involving DNA [11]. DNA is strongly bent in the nucleosome [12, 13], which is the fundamental

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