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

Phase Separation-Mediated Chromatin Organization and Dynamics: From Imaging-Based Quantitative Characterizations to Functional Implications

As an effective and versatile strategy to compartmentalize cellular components without the need for lipid membranes, phase separation has been found to underpin a wide range of intranuclear processes, particularly those involving chromatin. Many of the unique physico-chemical properties of chromatin-based phase condensates are harnessed by the cell to accomplish complex regulatory functions in a spatially and temporally controlled manner. Here, we survey key recent findings on the mechanistic roles of phase separation in regulating the organization and dynamics of chromatin-based molecular processes across length scales, packing states and intranuclear functions, with a particular emphasis on quantitative characterizations of these condensates enabled by advanced imaging-based approaches. By illuminating the complex interplay between chromatin and various chromatin-interacting molecular species mediated by phase separation, this review sheds light on an emerging multi-scale, multi-modal and multi-faceted landscape that hierarchically regulates the genome within the highly crowded and dynamic nuclear space. Moreover, deficiencies in existing studies also highlight the need for mechanism-specific criteria and multi-parametric approaches for the characterization of chromatin-based phase separation using complementary techniques and call for greater efforts to correlate the quantitative features of these condensates with their functional consequences in close-to-native cellular contexts.

Predicting Genome Architecture: Challenges and Solutions

Genome architecture plays a pivotal role in gene regulation. The use of high-throughput methods for chromatin profiling and 3-D interaction mapping provide rich experimental data sets describing genome organization and dynamics. These data challenge development of new models and algorithms connecting genome architecture with epigenetic marks. In this review, we describe how chromatin architecture could be reconstructed from epigenetic data using biophysical or statistical approaches. We discuss the applicability and limitations of these methods for understanding the mechanisms of chromatin organization. We also highlight the emergence of new predictive approaches for scoring effects of structural variations in human cells.

Polymer compaction and bridging-induced clustering of protein-inspired patchy particles

There are many proteins or protein complexes which have multiple DNA binding domains. This allows them to bind to multiple points on a DNA molecule (or chromatin fibre) at the same time. There are also many proteins which have been found to be able to compact DNAin vitro, and many others have been observed in foci or puncta when fluorescently labelled and imagedin vivo. In this work we study, using coarse-grained Langevin dynamics simulations, the compaction of polymers by simple model proteins and a phenomenon known as the 'bridging-induced attraction'. The latter is a mechanism observed in previous simulations [Brackleyet al2013Proc. Natl Acad. Sci. USA110E3605], where proteins modelled as spheres form clusters via their multivalent interactions with a polymer, even in the absence of any explicit protein-protein attractive interactions. Here we extend this concept to consider more detailed model proteins, represented as simple 'patchy particles' interacting with a semi-flexible bead-and-spring polymer. We find that both the compacting ability and the effect of the bridging-induced attraction depend on the valence of the model proteins. These effects also depend on the shape of the protein, which determines its ability to form bridges.

Chromosome Conformation Capture and Beyond: Toward an Integrative View of Chromosome Structure and Function

Rapidly developing technologies have recently fueled an exciting era of discovery in the field of chromosome structure and nuclear organization. In addition to chromosome conformation capture (3C) methods, new alternative techniques have emerged to study genome architecture and biological processes in the nucleus, often in single or living cells. This sets an unprecedented stage for exploring the mechanisms that link chromosome structure and biological function. Here we review popular as well as emerging approaches to study chromosome organization, focusing on the contribution of complementary methodologies to our understanding of structures revealed by 3C methods and their biological implications, and discuss the next technical and conceptual frontiers.

Bridging-induced microphase separation: photobleaching experiments, chromatin domains and the need for active reactions

We review the mechanism and consequences of the ‘bridging-induced attraction’, a generic biophysical principle that underpins some existing models for chromosome organization in 3D. This attraction, which was revealed in polymer physics-inspired computer simulations, is a generic clustering tendency arising in multivalent chromatin-binding proteins, and it provides an explanation for the biogenesis of nuclear bodies and transcription factories via microphase separation. Including post-translational modification reactions involving these multivalent proteins can account for the fast dynamics of the ensuing clusters, as is observed via microscopy and photobleaching experiments. The clusters found in simulations also give rise to chromatin domains that conform well with the observation of A/B compartments in HiC experiments.

Cross-linker mediated compaction and local morphologies in a model chromosome

Chromatin and associated proteins constitute the highly folded structure of chromosomes. We consider a self-avoiding polymer model of the chromatin, segments of which may get cross-linked via protein binders that repel each other. The binders cluster together via the polymer mediated attraction, in turn, folding the polymer. Using molecular dynamics simulations, and a mean field description, we explicitly demonstrate the continuous nature of the folding transition, characterized by unimodal distributions of the polymer size across the transition. At the transition point the chromatin size and cross-linker clusters display large fluctuations, and a maximum in their negative cross-correlation, apart from a critical slowing down. Along the transition, we distinguish the local chain morphologies in terms of topological loops, inter-loop gaps, and zippering. The topologies are dominated by simply connected loops at the criticality, and by zippering in the folded phase.

Modeling the functions of condensin in chromosome shaping and segregation

The mechanistic details underlying the assembly of rod-shaped chromosomes during mitosis and how they segregate from each other to act as individually mobile units remain largely unknown. Here, we construct a coarse-grained physical model of chromosomal DNA and condensins, a class of large protein complexes that plays key roles in these processes. We assume that condensins have two molecular activities: consecutive loop formation in DNA and inter-condensin attractions. Our simulation demonstrates that both of these activities and their balancing acts are essential for the efficient shaping and segregation of mitotic chromosomes. Our results also demonstrate that the shaping and segregation processes are strongly correlated, implying their mechanistic coupling during mitotic chromosome assembly. Our results highlight the functional importance of inter-condensin attractions in chromosome shaping and segregation.

Immediately before a cell divides, chromosomal DNA in a eukaryotic cell is packaged into a discrete set of rod-shaped chromosomes. This process, known as mitotic chromosome assembly or condensation, secures the faithful segregation of genetic information into daughter cells. Central to this mechanistically complex process is a class of protein complexes known as condensins. However, how condensins support the assembly and segregation of mitotic chromosomes at a mechanistic level remains elusive. Here we construct a coarse-grained physical model of chromosomal DNA fibers and condensin molecules, and study how condensins work in the mitotic chromosome assembly using computer simulations. Our results show that two activities of condensins, formation of consecutive loops in chromosomal DNA fibers and inter-condensin attractions, are necessary for both the shaping and segregation of mitotic chromosomes, and balancing acts of these activities help to coordinate the efficient progress of the processes. Importantly, chromosome shaping and segregation in our results are strongly correlated, implying that they are controlled by the same underlying mechanism mediated by condensins.

Crowding, Entropic Forces, and Confinement: Crucial Factors for Structures and Functions in the Cell Nucleus

The view of the cell nucleus as a crowded system of colloid particles and that chromosomes are giant self-avoiding polymers is stimulating rapid advances in our understanding of its structure and activities, thanks to concepts and experimental methods from colloid, polymer, soft matter, and nano sciences and to increased computational power for simulating macromolecules and polymers. This review summarizes current understanding of some characteristics of the molecular environment in the nucleus, of how intranuclear compartments are formed, and of how the genome is highly but precisely compacted, and underlines the crucial, subtle, and sometimes unintuitive effects on structures and reactions of entropic forces caused by the high concentration of macromolecules in the nucleus.

Ephemeral Protein Binding to DNA Shapes Stable Nuclear Bodies and Chromatin Domains

Fluorescence microscopy reveals that the contents of many (membrane-free) nuclear bodies exchange rapidly with the soluble pool while the underlying structure persists; such observations await a satisfactory biophysical explanation. To shed light on this, we perform large-scale Brownian dynamics simulations of a chromatin fiber interacting with an ensemble of (multivalent) DNA-binding proteins able to switch between an "on" (binding) and an "off" (nonbinding) state. This system provides a model for any DNA-binding protein that can be posttranslationally modified to change its affinity for DNA (e.g., through phosphorylation). Protein switching is a nonequilibrium process, and it leads to the formation of clusters of self-limiting size, where individual proteins in a cluster exchange with the soluble pool with kinetics similar to those seen in photobleaching experiments. This behavior contrasts sharply with that exhibited by nonswitching proteins, which are permanently in the on-state; when these bind to DNA nonspecifically, they form clusters that grow indefinitely in size. To explain these findings, we propose a mean-field theory from which we obtain a scaling relation between the typical cluster size and the protein switching rate. Protein switching also reshapes intrachromatin contacts to give networks resembling those seen in topologically associating domains, as switching markedly favors local (short-range) contacts over distant ones. Our results point to posttranslational modification of chromatin-bridging proteins as a generic mechanism driving the self-assembly of highly dynamic, nonequilibrium, protein clusters with the properties of nuclear bodies.

Simulating topological domains in human chromosomes with a fitting-free model

We discuss a polymer model for the 3D organization of human chromosomes. A chromosome is represented by a string of beads, with each bead being "colored" according to 1D bioinformatic data (e.g., chromatin state, histone modification, GC content). Individual spheres (representing bi- and multi-valent transcription factors) can bind reversibly and selectively to beads with the appropriate color. During molecular dynamics simulations, the factors bind, and the string spontaneously folds into loops, rosettes, and topologically-associating domains (TADs). This organization occurs in the absence of any specified interactions between distant DNA segments, or between transcription factors. A comparison with Hi-C data shows that simulations predict the location of most boundaries between TADs correctly. The model is "fitting-free" in the sense that it does not use Hi-C data as an input; consequently, one of its strengths is that it can - in principle - be used to predict the 3D organization of any region of interest, or whole chromosome, in a given organism, or cell line, in the absence of existing Hi-C data. We discuss how this simple model might be refined to include more transcription factors and binding sites, and to correctly predict contacts between convergent CTCF binding sites.

Modelling genome-wide topological associating domains in mouse embryonic stem cells

Chromosome conformation capture (3C)-based techniques such as chromosome conformation capture carbon copy (5C) and Hi-C revealed that the folding of mammalian chromosomes is highly hierarchical. A fundamental structural unit in the hierarchy is represented by topologically associating domains (TADs), sub-megabase regions of the genome within which the chromatin fibre preferentially interacts. 3C-based methods provide the mean contact probabilities between chromosomal loci, averaged over a large number of cells, and do not give immediate access to the single-cell conformations of the chromatin fibre. However, coarse-grained polymer models based on 5C data can be used to extract the single-cell conformations of single TADs. Here, we extend this approach to analyse around 2500 TADs in murine embryonic stem cells based on high-resolution Hi-C data. This allowed to predict the cell-to-cell variability in single contacts within genome-wide TADs and correlations between them. Based on these results, we predict that TADs are more similar to ideal chains than to globules in terms of their physical size and three-dimensional shape distribution. Furthermore, we show that their physical size and the degree of structural anisotropy of single TADs are correlated with the level of transcriptional activity of the genes that it harbours. Finally, we show that a large number of multiplets of genomic loci co-localize more often than expected by random, and these loci are particularly enriched in promoters, enhancers and CTCF-bound sites. These results provide the first genome-wide structural reconstruction of TADs using polymeric models obeying the laws of thermodynamics and reveal important universal trends in the correlation between chromosome structure and transcription.

Looping probability of random heteropolymers helps to understand the scaling properties of biopolymers

Random heteropolymers are a minimal description of biopolymers and can provide a theoretical framework to the investigate the formation of loops in biophysical experiments. The looping probability as a function of polymer length was observed to display in some biopolymers, like chromosomes in cell nuclei or long RNA chains, anomalous scaling exponents. Combining a two-state model with self-adjusting simulated-tempering calculations, we calculate numerically the looping properties of several realizations of the random interactions within the chain. We find a continuous set of exponents upon varying the temperature, which arises from finite-size effects and is amplified by the disorder of the interactions. We suggest that this could provide a simple explanation for the anomalous scaling exponents found in experiments. In addition, our results have important implications notably for the study of chromosome folding as they show that scaling exponents cannot be the sole criteria for testing hypothesis-driven models of chromosome architecture.

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.

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.

Phase Behavior of DNA in the Presence of DNA-Binding Proteins

To characterize the thermodynamical equilibrium of DNA chains interacting with a solution of nonspecific binding proteins, we implemented a Flory-Huggins free energy model. We explored the dependence on DNA and protein concentrations of the DNA collapse. For physiologically relevant values of the DNA-protein affinity, this collapse gives rise to a biphasic regime with a dense and a dilute phase; the corresponding phase diagram was computed. Using an approach based on Hamiltonian paths, we show that the dense phase has either a molten globule or a crystalline structure, depending on the DNA bending rigidity, which is influenced by the ionic strength. These results are valid at the thermodynamical equilibrium and therefore should be consistent with many biological processes, whose characteristic timescales range typically from 1 ms to 10 s. Our model may thus be applied to biological phenomena that involve DNA-binding proteins, such as DNA condensation with crystalline order, which occurs in some bacteria to protect their chromosome from detrimental factors; or transcription initiation, which occurs in clusters called transcription factories that are reminiscent of the dense phase characterized in this study.