Chris A. Brackley

Nonspecific bridging-induced attraction drives clustering of DNA-binding proteins and genome organization

Significance We use molecular dynamics to simulate reversible binding of proteins to DNA and uncover an unexpected force driving DNA compaction and protein aggregation. In the absence of any explicit interactions between proteins, or between templates, we find proteins aggregate spontaneously to locally organize the genome. The simulations reproduce the structures seen experimentally when small bivalent proteins assemble into rows (like bacterial H-NS protein), larger proteins with eight binding sites into irregular strings (like octameric nucleosomal cores in chromatin fibers), and still-larger complexes representing RNA polymerase II and a transcription factor (NFκB) into clusters surrounded by loops (like transcription factories). We suggest clustering is driven by an entropic bridging-induced attraction that minimizes bending and looping penalties in the template. Molecular dynamics simulations are used to model proteins that diffuse to DNA, bind, and dissociate; in the absence of any explicit interaction between proteins, or between templates, binding spontaneously induces local DNA compaction and protein aggregation. Small bivalent proteins form into rows [as on binding of the bacterial histone-like nucleoid-structuring protein (H-NS)], large proteins into quasi-spherical aggregates (as on nanoparticle binding), and cylinders with eight binding sites (representing octameric nucleosomal cores) into irregularly folded clusters (like those seen in nucleosomal strings). Binding of RNA polymerase II and a transcription factor (NFκB) to the appropriate sites on four human chromosomes generates protein clusters analogous to transcription factories, multiscale loops, and intrachromosomal contacts that mimic those found in vivo. We suggest that this emergent behavior of clustering is driven by an entropic bridging-induced attraction that minimizes bending and looping penalties in the template.

Simulated binding of transcription factors to active and inactive regions folds human chromosomes into loops, rosettes and topological domains

Biophysicists are modeling conformations of interphase chromosomes, often basing the strengths of interactions between segments distant on the genetic map on contact frequencies determined experimentally. Here, instead, we develop a fitting-free, minimal model: bivalent or multivalent red and green ‘transcription factors’ bind to cognate sites in strings of beads (‘chromatin’) to form molecular bridges stabilizing loops. In the absence of additional explicit forces, molecular dynamic simulations reveal that bound factors spontaneously cluster—red with red, green with green, but rarely red with green—to give structures reminiscent of transcription factories. Binding of just two transcription factors (or proteins) to active and inactive regions of human chromosomes yields rosettes, topological domains and contact maps much like those seen experimentally. This emergent ‘bridging-induced attraction’ proves to be a robust, simple and generic force able to organize interphase chromosomes at all scales.

Facilitated diffusion on mobile DNA: configurational traps and sequence heterogeneity.

We present Brownian dynamics simulations of the facilitated diffusion of a protein, modeled as a sphere with a binding site on its surface, along DNA, modeled as a semiflexible polymer. We consider both the effect of DNA organization in three dimensions and of sequence heterogeneity. We find that in a network of DNA loops, which are thought to be present in bacterial DNA, the search process is very sensitive to the spatial location of the target within such loops. Therefore, specific genes might be repressed or promoted by changing the local topology of the genome. On the other hand, sequence heterogeneity creates traps which normally slow down facilitated diffusion. When suitably positioned, though, these traps can, surprisingly, render the search process much more efficient.

Predicting the three-dimensional folding of cis-regulatory regions in mammalian genomes using bioinformatic data and polymer models

The three-dimensional (3D) organization of chromosomes can be probed using methods like Capture-C. However, it is unclear how such population-level data relate to the organization within a single cell, and the mechanisms leading to the observed interactions are still largely obscure. We present a polymer modeling scheme based on the assumption that chromosome architecture is maintained by protein bridges, which form chromatin loops. To test the model, we perform FISH experiments and compare with Capture-C data. Starting merely from the locations of protein binding sites, our model accurately predicts the experimentally observed chromatin interactions, revealing a population of 3D conformations.

A simple model for DNA bridging proteins and bacterial or human genomes: bridging-induced attraction and genome compaction

We present computer simulations of the phase behaviour of an ensemble of proteins interacting with a polymer, mimicking non-specific binding to a piece of bacterial DNA or eukaryotic chromatin. The proteins can simultaneously bind to the polymer in two or more places to create protein bridges. Despite the lack of any explicit interaction between the proteins or between DNA segments, our simulations confirm previous results showing that when the protein-polymer interaction is sufficiently strong, the proteins come together to form clusters. Furthermore, a sufficiently large concentration of bridging proteins leads to the compaction of the swollen polymer into a globular phase. Here we characterise both the formation of protein clusters and the polymer collapse as a function of protein concentration, protein-polymer affinity and fibre flexibility.

Models for twistable elastic polymers in Brownian dynamics, and their implementation for LAMMPS.

An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions relating to both bending and twisting of the rod are derived for both continuous and discrete cases, and results are compared with numerical simulations. Finally, two possible implementations of the discretised model in the multi-purpose molecular dynamics software package LAMMPS are described.

Exploiting native forces to capture chromosome conformation in mammalian cell nuclei

Mammalian interphase chromosomes fold into a multitude of loops to fit the confines of cell nuclei, and looping is tightly linked to regulated function. Chromosome conformation capture (3C) technology has significantly advanced our understanding of this structure‐to‐function relationship. However, all 3C‐based methods rely on chemical cross‐linking to stabilize spatial interactions. This step remains a “black box” as regards the biases it may introduce, and some discrepancies between microscopy and 3C studies have now been reported. To address these concerns, we developed “i3C”, a novel approach for capturing spatial interactions without a need for cross‐linking. We apply i3C to intact nuclei of living cells and exploit native forces that stabilize chromatin folding. Using different cell types and loci, computational modeling, and a methylation‐based orthogonal validation method, “TALE‐iD”, we show that native interactions resemble cross‐linked ones, but display improved signal‐to‐noise ratios and are more focal on regulatory elements and CTCF sites, while strictly abiding to topologically associating domain restrictions.

Stochastic Model of Supercoiling-Dependent Transcription

We propose a stochastic model for gene transcription coupled to DNA supercoiling, where we incorporate the experimental observation that polymerases create supercoiling as they unwind the DNA helix and that these enzymes bind more favorably to regions where the genome is unwound. Within this model, we show that when the transcriptionally induced flux of supercoiling increases, there is a sharp crossover from a regime where torsional stresses relax quickly and gene transcription is random, to one where gene expression is highly correlated and tightly regulated by supercoiling. In the latter regime, the model displays transcriptional bursts, waves of supercoiling, and up regulation of divergent or bidirectional genes. It also predicts that topological enzymes which relax twist and writhe should provide a pathway to down regulate transcription.

Extrusion without a motor: a new take on the loop extrusion model of genome organization.

ABSTRACT Chromatin loop extrusion is a popular model for the formation of CTCF loops and topological domains. Recent HiC data have revealed a strong bias in favour of a particular arrangement of the CTCF binding motifs that stabilize loops, and extrusion is the only model to date which can explain this. However, the model requires a motor to generate the loops, and although cohesin is a strong candidate for the extruding factor, a suitable motor protein (or a motor activity in cohesin itself) has yet to be found. Here we explore a new hypothesis: that there is no motor, and thermal motion within the nucleus drives extrusion. Using theoretical modelling and computer simulations we ask whether such diffusive extrusion could feasibly generate loops. Our simulations uncover an interesting ratchet effect (where an osmotic pressure promotes loop growth), and suggest, by comparison to recent in vitro and in vivo measurements, that diffusive extrusion can in principle generate loops of the size observed in the data. Extra View on : C. A. Brackley, J. Johnson, D. Michieletto, A. N. Morozov, M. Nicodemi, P. R. Cook, and D. Marenduzzo “Non-equilibrium chromosome looping via molecular slip-links”, Physical Review Letters 119 138101 (2017)

Topological constraints strongly affect chromatin reconstitution in silico

The fundamental building block of chromatin, and of chromosomes, is the nucleosome, a composite material made up from DNA wrapped around a histone octamer. In this study we provide the first computer simulations of chromatin self-assembly, starting from DNA and histone proteins, and use these to understand the constraints which are imposed by the topology of DNA molecules on the creation of a polynucleosome chain. We take inspiration from the in vitro chromatin reconstitution protocols which are used in many experimental studies. Our simulations indicate that during self-assembly, nucleosomes can fall into a number of topological traps (or local folding defects), and this may eventually lead to the formation of disordered structures, characterised by nucleosome clustering. Remarkably though, by introducing the action of topological enzymes such as type I and II topoisomerase, most of these defects can be avoided and the result is an ordered 10-nm chromatin fibre. These findings provide new insight into the biophysics of chromatin formation, both in the context of reconstitution in vitro and in terms of the topological constraints which must be overcome during de novo nucleosome formation in vivo, e.g. following DNA replication or repair.