An Associative Memory Hamiltonian Model for DNA and Nucleosomes

Abstract

A model for DNA and nucleosomes is introduced with the goal of studying chromosomes from a single base level all the way to higher-order chromatin structures. This model, dubbed the Widely Editable Chromatin Model (WEChroM), is able to reproduce the complex mechanics of the double helix including its bending persistence length and twisting persistence length, and their respective temperature dependence. The WEChroM Hamiltonian is composed of chain connectivity, steric interactions, and associative memory terms representing all remaining interactions leading to the structure, dynamics, and mechanical characteristics of the B-DNA. Several applications of this model are discussed to demonstrate its applicability. WEChroM is used to investigate the behavior of circular DNA in the presence of positive and negative supercoiling. We show that it recapitulates the formation of plectonemes and of structural defects that relax mechanical stress. The model spontaneously manifests an asymmetric behavior with respect to positive or negative supercoiling, similarly to what was previously observed in experiments. Additionally, we show that the associative memory Hamiltonian is also capable of reproducing the free energy of partial DNA unwrapping from nucleosomes. WEChroM can readily emulate the continuously variable mechanical properties of the 10nm fiber and, by virtue of its simplicity, allows the simulation of molecular systems large enough to study the structural ensembles of genes. WEChroM is implemented in the OpenMM simulation toolkits and is freely available for public use. Author SummaryThe structural ensembles of genes have been so far out of the reach of theoretical and computational investigations because genes are molecular complexes too big to be tackled with even the most efficient computational chemistry approaches and yet too strongly affected by heterogeneous molecular factors to be effectively modeled as a simple polymer. In this work, we develop a computationally efficient, easy-to-use, and widely editable chromatin model to study the principles of DNA folding at the gene scale. Using the framework of Associative Memory Hamiltonians, this model reproduces the structural and mechanical properties of double-stranded DNA and accounts for the effects of nucleosome-forming histone octamers and other proteins bound to DNA. Our results open the path to studying the structural and mechanical ensembles of genetic systems as large as tens of kilobases of chromatin, i.e., the size of mammalian genes.