Combined collapse by bridging and self-adhesion in a prototypical polymer model inspired by the bacterial nucleoid

Polymer Physics Models Reveal Structural Folding Features of Single-Molecule Gene Chromatin Conformations

Here, we employ polymer physics models of chromatin to investigate the 3D folding of a 2 Mb wide genomic region encompassing the human LTN1 gene, a crucial DNA locus involved in key cellular functions. Through extensive Molecular Dynamics simulations, we reconstruct in silico the ensemble of single-molecule LTN1 3D structures, which we benchmark against recent in situ Hi-C 2.0 data. The model-derived single molecules are then used to predict structural folding features at the single-cell level, providing testable predictions for super-resolution microscopy experiments.

A mean-field theory for predicting single polymer collapse induced by neutral crowders

Macromolecular crowding can induce the collapse of a single long polymer into a globular form due to depletion forces of entropic nature. This phenomenon has been shown to play a significant role in compacting the genome within the bacterium Escherichia coli into a well-defined region of the cell known as the nucleoid. Motivated by the biological significance of this process, numerous theoretical and computational studies have searched for the primary determinants of the behavior of polymer-crowder phases. However, our understanding of this process remains incomplete and there is debate on a quantitatively unified description. In particular, different simulation studies with explicit crowders have proposed different order parameters as potential predictors for the collapse transition. In this work, we present a comprehensive analysis of published simulation data obtained from different sources. Based on the common behavior we find in this data, we develop a unified phenomenological model that we show to be predictive. Finally, to further validate the accuracy of the model, we conduct new simulations on polymers of various sizes, and investigate the role of jamming of the crowders.

Chromatin structure from high resolution microscopy: Scaling laws and microphase separation

Recent advances in experimental fluorescence microscopy allow high accuracy determination (resolution of 50 nm) of the three-dimensional physical location of multiple (up to ∼10^{2}) tagged regions of the chromosome. We investigate publicly available microscopy data for two loci of the human Chr21 obtained from multiplexed fluorescence in situ hybridization (FISH) methods for different cell lines and treatments. Inspired by polymer physics models, our analysis centers around distance distributions between different tags with the aim being to unravel the chromatin conformational arrangements. We show that for any specific genomic site, there are (at least) two different conformational arrangements of chromatin, implying coexisting distinct topologies which we refer to as phase α and phase β. These two phases show different scaling behaviors: the former is consistent with a crumpled globule, while the latter indicates a confined, but more extended conformation, such as a looped domain. The identification of these distinct phases sheds light on the coexistence of multiple chromatin topologies and provides insights into the effects of cellular context and/or treatments on chromatin structure.

Modeling the compaction of bacterial chromosomes by biomolecular crowding and the cross-linking protein H-NS

Cells orchestrate the action of various molecules toward organizing their chromosomes. Using a coarse-grained computational model, we study the compaction of bacterial chromosomes by the cross-linking protein H-NS and cellular crowders. In this work, H-NS, modeled as a mobile "binder," can bind to a chromosome-like polymer with a characteristic binding energy. The simulation results reported here clarify the relative role of biomolecular crowding and H-NS in condensing a bacterial chromosome in a quantitative manner. In particular, they shed light on the nature and degree of crowder and H-NS synergetics: while the presence of crowders enhances H-NS binding to a chromosome-like polymer, the presence of H-NS makes crowding effects more efficient, suggesting two-way synergetics in chain compaction. Also, the results show how crowding effects promote clustering of bound H-NS. For a sufficiently large concentration of H-NS, the cluster size increases with the volume fraction of crowders.

Polymer architecture orchestrates the segregation and spatial organization of replicating E. coli chromosomes in slow growth

The mechanism of chromosome segregation and organization in the bacterial cell cycle of E. coli is one of the least understood aspects in its life cycle. The E. coli chromosome is often modelled as a bead spring ring polymer. We introduce cross-links in the DNA-ring polymer, resulting in the formation of loops within each replicating bacterial chromosome. We use simulations to show that the chosen polymer-topology ensures its self-organization along the cell long-axis, such that various chromosomal loci get spatially localized as seen in vivo. The localization of loci arises due to entropic repulsion between polymer loops within each daughter DNA confined in a cylinder. The cellular addresses of the loci in our model are in fair agreement with those seen in experiments as given in J. A. Cass et al., Biophys. J., 2016, 110, 2597-2609. We also show that the adoption of such modified polymer architectures by the daughter DNAs leads to an enhanced propensity of their spatial segregation. Secondly, we match other experimentally reported results, including observation of the cohesion time and the ter-transition. Additionally, the contact map generated from our simulations reproduces the macro-domain like organization as seen in the experimentally obtained Hi-C map. Lastly, we have also proposed a plausible reconciliation of the 'Train Track' and the 'Replication Factory' models which provide conflicting descriptions of the spatial organization of the replication forks. Thus, we reconcile observations from complementary experimental techniques probing bacterial chromosome organization.

Cooperative effects on the compaction of DNA fragments by the nucleoid protein H-NS and the crowding agent PEG probed by Magnetic Tweezers

BACKGROUND

DNA bridging promoted by the H-NS protein, combined with the compaction induced by cellular crowding, plays a major role in the structuring of the E. coli genome. However, only few studies consider the effects of the physical interplay of these two factors in a controlled environment.

METHODS

We apply a single molecule technique (Magnetic Tweezers) to study the nanomechanics of compaction and folding kinetics of a 6 kb DNA fragment, induced by H-NS bridging and/or PEG crowding.

RESULTS

In the presence of H-NS alone, the DNA shows a step-wise collapse driven by the formation of multiple bridges, and little variations in the H-NS concentration-dependent unfolding force. Conversely, the DNA collapse force observed with PEG was highly dependent on the volume fraction of the crowding agent. The two limit cases were interpreted considering the models of loop formation in a pulled chain and pulling of an equilibrium globule respectively.

CONCLUSIONS

We observed an evident cooperative effect between H-NS activity and the depletion of forces induced by PEG.

GENERAL SIGNIFICANCE

Our data suggest a double role for H-NS in enhancing compaction while forming specific loops, which could be crucial in vivo for defining specific mesoscale domains in chromosomal regions in response to environmental changes.

Nonequilibrium Theory of Epigenomic Microphase Separation in the Cell Nucleus

Understanding the spatial organization of the genome in the cell nucleus is one of the current grand challenges in biophysics. Certain biochemical-or epigenetic-marks that are deposited along the genome are thought to play an important, yet poorly understood, role in determining genome organization and cell identity. The physical principles underlying the interplay between epigenetic dynamics and genome folding remain elusive. Here we propose and study a theory that assumes a coupling between epigenetic mark and genome densities, and which can be applied at the scale of the whole nucleus. We show that equilibrium models are not compatible with experiments and a qualitative agreement is recovered by accounting for nonequilibrium processes that can stabilize microphase separated epigenomic domains. We finally discuss the potential biophysical origin of these terms.

Dilution of contact frequency between superenhancers by loop extrusion at interfaces

The loop extrusion theory predicts that cohesin acts as a molecular motor that extrudes chromatin fibers to produce loops. Hi-C experiments have detected relatively high contact frequencies between superenhancers. These probably result from the fact that superenhancers are localized at condensates of transcriptional activators and coactivators. The contact frequency between superenhancers is enhanced by auxin treatment that removes cohesin from chromatin. Motivated by these experimental results, we here treat chromatin at the surface of a condensate as a loop extruding polymer brush. Our theory predicts that the lateral pressure generated by the brush decreases with decreasing the loading rate of cohesin. This is because loop extrusion actively transfers chain segments at the vicinity of the interface. Our theory thus predicts that the increase of contact frequency by auxin treatment results from the fact that suppressing the loop extrusion process induces the dissolution of molecular components to the nucleoplasm, decreasing the average distance between superenhancers.

Universality of the collapse transition of sticky polymers

The universality of the swelling of the radius of gyration of a homopolymer relative to its value in the θ state, independent of polymer-solvent chemistry, in the crossover regime between θ and athermal solvent conditions, is well known. Here we study, by Brownian dynamics, a polymer model where a subset of monomers is labelled as "stickers". The mutual interaction of the stickers is more attractive than those of the other ("backbone") monomers, and has an additional important characteristic of "functionality" φ, i.e., the maximum number of stickers that can locally bind to a given sticker. A saturated bond formed in this manner remains bound until it breaks due to thermal fluctuations, a requirement which can be viewed as an additional Boolean degree of freedom that describes the bonding. This, in turn, makes the question of the order of the collapse transition a non-trivial one. Nevertheless, for the parameters that we have studied (in particular, φ = 1), we find a standard second-order θ collapse, using a renormalised solvent quality parameter that takes into account the increased average attraction due to the presence of stickers. We examine the swelling of the radius of gyration of such a sticky polymer relative to its value in the altered θ state, using a novel potential to model the various excluded volume interactions that occur between the monomers on the chain. We find that the swelling of such sticky polymers is identical to the universal swelling of homopolymers in the thermal crossover regime. Additionally, for our model, the Kuhn segment length under θ conditions is found to be the same for chains with and without stickers.

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.

From 1D sequence to 3D chromatin dynamics and cellular functions: a phase separation perspective

The high-order chromatin structure plays a non-negligible role in gene regulation. However, the mechanism, especially the sequence dependence for the formation of varied chromatin structures in different cells remains to be elucidated. As the nucleotide distributions in human and mouse genomes are highly uneven, we identified CGI (CpG island) forest and prairie genomic domains based on CGI densities of a species, dividing the genome into two sequentially, epigenetically, and transcriptionally distinct regions. These two megabase-sized domains also spatially segregate to different extents in different cell types. Forests and prairies show enhanced segregation from each other in development, differentiation, and senescence, meanwhile the multi-scale forest-prairie spatial intermingling is cell-type specific and increases in differentiation, helping to define cell identity. We propose that the phase separation of the 1D mosaic sequence in space serves as a potential driving force, and together with cell type specific epigenetic marks and transcription factors, shapes the chromatin structure in different cell types. The mosaicity in genome of different species in terms of forests and prairies could relate to observations in their biological processes like development and aging. In this way, we provide a bottoms-up theory to explain the chromatin structural and epigenetic changes in different processes.

Improved inference of chromosome conformation from images of labeled loci

We previously published a method that infers chromosome conformation from images of fluorescently-tagged genomic loci, for the case when there are many loci labeled with each distinguishable color.  Here we build on our previous work and improve the reconstruction algorithm to address previous limitations.  We show that these improvements 1) increase the reconstruction accuracy and 2) allow the method to be used on large-scale problems involving several hundred labeled loci.  Simulations indicate that full-chromosome reconstructions at 1/2 Mb resolution are possible using existing labeling and imaging technologies.  The updated reconstruction code and the script files used for this paper are available at:  https://github.com/heltilda/align3d.

A segregative phase separation scenario of the formation of the bacterial nucleoid

The mechanism responsible for the compaction of the genomic DNA of bacteria inside a structure called the nucleoid is a longstanding but still lively debated question. Most puzzling is the fact that the nucleoid occupies only a small fraction of the cell, although it is not separated from the rest of the cytoplasm by any membrane and would occupy a volume about a thousand times larger outside the cell. Here, by performing numerical simulations using coarse-grained models, we elaborate on the conjecture that the formation of the nucleoid may result from a segregative phase separation mechanism driven by the demixing of the DNA coil and non-binding globular macromolecules present in the cytoplasm, presumably functional ribosomes. Simulations performed with crowders having a spherical, dumbbell or octahedral geometry highlight the sensitive dependence of the level of DNA compaction on the dissymmetry of DNA/DNA, DNA/crowder, and crowder/crowder repulsive interactions, thereby supporting the segregative phase separation scenario. Simulations also consistently predict a much stronger DNA compaction close to the jamming threshold. Moreover, simulations performed with crowders of different sizes suggest that the final density distribution of each species results from the competition between thermodynamic forces and steric hindrance, so that bigger crowders are expelled selectively from the nucleoid only at moderate total crowder concentrations. This work leads to several predictions, which may eventually be tested experimentally.

Kinetic Signature of Cooperativity in the Irreversible Collapse of a Polymer

We investigate the kinetics of a polymer collapse due to the formation of irreversible cross-links between its monomers. Using the contact probability P(s) as a scale-dependent order parameter depending on the chemical distance s, our simulations show the emergence of a cooperative pearling instability. Namely, the polymer undergoes a sharp conformational transition to a set of absorbing states characterized by a length scale ξ corresponding to the mean pearl size. This length and the transition time depend on the polymer equilibrium dynamics and the cross-linking rate. We confirm experimentally this transition using a DNA conformation capture experiment in yeast.

Spontaneous domain formation in disordered copolymers as a mechanism for chromosome structuring

Motivated by the problem of domain formation in chromosomes, we studied a co-polymer model where only a subset of the monomers feel attractive interactions. These monomers are displaced randomly from a regularly-spaced pattern, thus introducing some quenched disorder in the system. Previous work has shown that in the case of regularly-spaced interacting monomers this chain can fold into structures characterized by multiple distinct domains of consecutive segments. In each domain, attractive interactions are balanced by the entropy cost of forming loops. We show by advanced replica-exchange simulations that adding disorder in the position of the interacting monomers further stabilizes these domains. The model suggests that the partitioning of the chain into well-defined domains of consecutive monomers is a spontaneous property of heteropolymers. In the case of chromosomes, evolution could have acted on the spacing of interacting monomers to modulate in a simple way the underlying domains for functional reasons.

Entropic elasticity and dynamics of the bacterial chromosome: A simulation study

We study the compression and extension dynamics of a DNA-like polymer interacting with non-DNA binding and DNA-binding proteins, by means of computer simulations. The geometry we consider is inspired by recent experiments probing the compressional elasticity of the bacterial nucleoid (DNA plus associated proteins), where DNA is confined into a cylindrical container and subjected to the action of a "piston"-a spherical bead to which an external force is applied. We quantify the effect of steric interactions (excluded volume) on the force-extension curves as the polymer is compressed. We find that non-DNA-binding proteins, even at low densities, exert an osmotic force which can be a lot larger than the entropic force exerted by the compressed DNA. The trends we observe are qualitatively robust with respect to changes in protein sizes and are similar for neutral and charged proteins (and DNA). We also quantify the dynamics of DNA expansion following removal of the "piston": while the expansion is well fitted by power laws, the apparent exponent depends on protein concentration and protein-DNA interaction in a significant way. We further highlight an interesting kinetic process which we observe during the expansion of DNA interacting with DNA-binding proteins when the interaction strength is intermediate: the proteins bind while the DNA is packaged by the compression force, but they "pop-off" one-by-one as the force is removed, leading to a slow unzipping kinetics. Finally, we quantify the importance of supercoiling, which is an important feature of bacterial DNA in vivo.

Features of genomic organization in a nucleotide-resolution molecular model of the Escherichia coli chromosome

We describe structural models of the Escherichia coli chromosome in which the positions of all 4.6 million nucleotides of each DNA strand are resolved. Models consistent with two basic chromosomal orientations, differing in their positioning of the origin of replication, have been constructed. In both types of model, the chromosome is partitioned into plectoneme-abundant and plectoneme-free regions, with plectoneme lengths and branching patterns matching experimental distributions, and with spatial distributions of highly-transcribed chromosomal regions matching recent experimental measurements of the distribution of RNA polymerases. Physical analysis of the models indicates that the effective persistence length of the DNA and relative contributions of twist and writhe to the chromosome's negative supercoiling are in good correspondence with experimental estimates. The models exhibit characteristics similar to those of ‘fractal globules,’ and even the most genomically-distant parts of the chromosome can be physically connected, through paths combining linear diffusion and inter-segmental transfer, by an average of only ∼10 000 bp. Finally, macrodomain structures and the spatial distributions of co-expressed genes are analyzed: the latter are shown to depend strongly on the overall orientation of the chromosome. We anticipate that the models will prove useful in exploring other static and dynamic features of the bacterial chromosome.

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.

Formation of Chromosomal Domains by Loop Extrusion

Topologically associating domains (TADs) are fundamental structural and functional building blocks of human interphase chromosomes, yet the mechanisms of TAD formation remain unclear. Here, we propose that loop extrusion underlies TAD formation. In this process, cis-acting loop-extruding factors, likely cohesins, form progressively larger loops but stall at TAD boundaries due to interactions with boundary proteins, including CTCF. Using polymer simulations, we show that this model produces TADs and finer-scale features of Hi-C data. Each TAD emerges from multiple loops dynamically formed through extrusion, contrary to typical illustrations of single static loops. Loop extrusion both explains diverse experimental observations-including the preferential orientation of CTCF motifs, enrichments of architectural proteins at TAD boundaries, and boundary deletion experiments-and makes specific predictions for the depletion of CTCF versus cohesin. Finally, loop extrusion has potentially far-ranging consequences for processes such as enhancer-promoter interactions, orientation-specific chromosomal looping, and compaction of mitotic chromosomes.

Dynamics of a polymer in an active and viscoelastic bath

We study the dynamics of an ideal polymer chain in a viscoelastic medium and in the presence of active forces. The motion of the center of mass and of individual monomers is calculated. On time scales that are comparable to the persistence time of the active forces, monomers can move superdiffusively, while on larger time scales subdiffusive behavior occurs. The difference between this subdiffusion and that in the absence of active forces is quantified. We show that the polymer swells in response to active processes and determine how this swelling depends on the viscoelastic properties of the environment. Our results are compared to recent experiments on the motion of chromosomal loci in bacteria.

Modeling chromosomes: Beyond pretty pictures

Recently, Chromosome Conformation Capture (3C) based experiments have highlighted the importance of computational models for the study of chromosome organization. In this review, we propose that current computational models can be grouped into roughly four classes, with two classes of data-driven models: consensus structures and data-driven ensembles, and two classes of de novo models: structural ensembles and mechanistic ensembles. Finally, we highlight specific questions mechanistic ensembles can address.

Gene expression homeostasis and chromosome architecture

In rapidly growing populations of bacterial cells, including those of the model organism Escherichia coli, genes essential for growth--such as those involved in protein synthesis--are expressed at high levels; this is in contrast to many horizontally-acquired genes, which are maintained at low transcriptional levels. (1) This balance in gene expression states between 2 distinct classes of genes is established by a galaxy of transcriptional regulators, including the so-called nucleoid associated proteins (NAP) that contribute to shaping the chromosome. (2) Besides these active players in gene regulation, it is not too far-fetched to anticipate that genome organization in terms of how genes are arranged on the chromosome, (3) which is the result of long-drawn transactions among genome rearrangement processes and selection, and the manner in which it is structured inside the cell, plays a role in establishing this balance. A recent study from our group has contributed to the literature investigating the interplay between global transcriptional regulators and genome organization in establishing gene expression homeostasis. (4) In particular, we address a triangle of functional interactions among genome organization, gene expression homeostasis and horizontal gene transfer.

The role of loops on the order of eukaryotes and prokaryotes

The study of the three-dimensional organization of chromatin has recently gained much focus in the context of novel techniques for detecting genome-wide contacts using next-generation sequencing. These chromosome conformation capture-based methods give a deep topological insight into the architecture of the genome inside the nucleus. Several recent studies observe a compartmentalization of chromatin interactions into spatially confined domains. This structural feature of interphase chromosomes is not only supported by conventional studies assessing the interaction data of millions of cells, but also by analysis on the level of a single cell. We first present and examine the different models that have been proposed to elucidate these topological domains in eukaryotes. Then we show that a model which relies on the dynamic formation of loops within domains can account for the experimentally observed contact maps. Interestingly, the topological domain structure is not only found in mammalian genomes, but also in bacterial chromosomes.