cgNA+min: computation of sequence-dependent dsDNA energy-minimising minicircle configurations

TL;DR

This paper introduces cgNA+min, a computational method for efficiently predicting the energy-minimizing configurations of sequence-dependent, topologically closed dsDNA minicircles, aiding understanding of DNA mechanics.

Contribution

The paper extends the cgNA+ model to compute energy-minimizing configurations of closed dsDNA minicircles with sequence dependence and various topologies.

Findings

cgNA+min accurately predicts minicircle energies matching experimental data

The method efficiently handles over 120,000 sequences of different lengths

Minicircle shape and energy depend on sequence and linking number

Abstract

DNA minicircles are closed double-stranded DNA (dsDNA) fragments that have been demonstrated to be an important experimental tool to understand supercoiled, or stressed, DNA mechanics, such as nucleosome positioning and DNA-protein interactions. Specific minicircles can be simulated using Molecular Dynamics (MD) simulation. However, the enormous sequence space makes it unfeasible to exhaustively explore the sequence-dependent mechanics of DNA minicircles using either experiment or MD. For linear fragments, the cgNA+ model, a computationally efficient sequence-dependent coarse-grained model using enhanced Curves+ internal coordinates (rigid base plus rigid phosphate) of double-stranded nucleic acids (dsNAs), predicts highly accurate nonlocal sequence-dependent equilibrium distributions for an arbitrary sequence when compared with MD simulations. This article addresses the problem of modeling sequence-dependent topologically closed and, therefore, stressed fragments of dsDNA. We introduce cgNA+min, a computational approach within the cgNA+ framework, which extends the cgNA+ model applicability to compute the sequence-dependent energy minimising configurations of covalently closed dsDNA minicircles of various lengths and linking numbers (Lk). The main idea is to derive the appropriate chain rule to express the cgNA+ energy in absolute coordinates involving quaternions where the closure condition is simple to handle. We also present a semi-analytic method for efficiently computing sequence-dependent initial minicircles having arbitrary Lk and length. For different classes and lengths of sequences, we demonstrate that the dsDNA minicircle energies computed using cgNA+min agree well with the energies approximated from experimentally measured J-factor values. Finally, we present the minicircle shape, energy, and multiplicity of Lk for more than 120K random DNA sequences of different lengths.