From Macroscopic to Mesoscopic Models of Chromatin Folding

Abstract

An overview of the evolution of computer models for simulation of chromatin folding is presented. Chromatin is the protein/nucleic acid fiber that stores the genetic material in higher organisms. Many biological questions concerning the fiber structure and its dependence on internal and external factors remain a puzzle. Modeling and simulation can in theory provide molecular view for analysis, but the sheer size and range of spatial and temporal scales involved require tailored multiscale models. Our first-generation, macroscopic models ignored histone tail flexibility but generated insights into preferred zigzag configurations and folding/unfolding dynamics at univalent salt. The second-generation mesoscale models incorporated histone tail flexibility, linker histones, and the presence of divalent ions. Recent results reveal the profound compaction induced by linker histones and the polymorphic fiber structure at divalent salt environments, with a small fraction of the linker DNAs bent rather than straight for ultimate compaction. Our chromatin model can be extended further to study many important questions dealing with histone tail post-translational modifications, the effects of variations in linker DNA length and of histone variants on chromatin structure, and the nature of higher-order fiber structures. IntroductionOne of the current challenges in scientific computing is model development that entails bridging the resolution among different spatial and temporal scales. In biological applications, a wide range of spatial scales defines systems, from the quantum particles to atomic, molecular, cellular, organ, system and genome entities. Temporal scales range from sub-femtosecond for electronic motion to billions of years of evolutionary changes. As our computing power and algorithms have improved, problems of greater scientific significance can be addressed with enhanced confidence and accuracy. However, developing appropriate molecular models and simulation algorithms to answer specific biological questions that require bridging all-atom details with the macroscopic view of activity on the cellular level remains an ad-hoc endeavor which requires as much art as science.As a special volume of SIAM's journal on Multiscale Modeling and Simulation illustrated [1], multiscale biology is being developed by many varied techniques and applied to a variety of problems, such as involving protein and RNA threedimensional structures, DNA supercoiling, ribosomal motions, DNA packaging in viruses, heart muscle motion, RNA translation, or fruit fly circadian rhythm. For these applications, techniques involve hierarchical methods that transform fast, low-resolution to slower, higher-resolution models; dynamics propagation using projection of standard molecular dynamics to longer timescales using master-equation methods; rigid-body dynamics; elastic or normal-mode models; and coarse-grained studies of slow, large-scale motions and features using differential equations for global properties or statistical methods.Thi...

Biomolecular modeling and simulation: a field coming of age

“…( a ) QM/MM pathway (from top left to bottom right) of DNA repair enzyme polymerase β nucleotide incorporation (Radhakrishnan & Schlick, 2006); ( b ) superimposed MD configurations from a solvated dodecamer simulation ; ( c ) mesoscale oligonucleosome model with nucleosome cores in grey and tails and linker histones in color (see Arya & Schlick, 2009; Schlick, 2009a for details) ; ( d ) top three principal component motions in the thumb and finger subdomains of DNA polymerase β (Arora & Schlick, 2004); ( e ) representative Monte Carlo snapshots in the sampling of 48-unit oligonucleosomes at three different salt environments using the model shown in ( c ) ; and ( f ) minimized water clusters.…”

Monte Carlo, harmonic approximation, and coarse-graining approaches for enhanced sampling of biomolecular structure

“…Thus, the work rigorously connects equilibrium ensembles of all-atom and multiscale models. Many interesting applications of multiscale models in various scientific fields are collected in a special volume [ 53 ].…”