The fractal globule as a model of chromatin architecture in the cell

ENT3C: an entropy-based similarity measure for Hi-C and micro-C derived contact matrices

Hi-C and micro-C sequencing have shed light on the profound importance of 3D genome organization in cellular function by probing 3D contact frequencies across the linear genome. The resulting contact matrices are extremely sparse and susceptible to technical- and sequence-based biases, making their comparison challenging. The development of reliable, robust and efficient methods for quantifying similarity between contact matrices is crucial for investigating variations in the 3D genome organization in different cell types or under different conditions, as well as evaluating experimental reproducibility. We present a novel method, ENT3C, which measures the change in pattern complexity in the vicinity of contact matrix diagonals to quantify their similarity. ENT3C provides a robust, user-friendly Hi-C or micro-C contact matrix similarity metric and a characteristic entropy signal that can be used to gain detailed biological insights into 3D genome organization.

Wet Conformation of Prion-Like Domain and Intimate Correlation of Hydration and Conformational Fluctuations

Proteins with prion-like domains (PLDs) are involved in neurodegeneration-associated aggregation and are prevalent in liquid-like membrane-less organelles. These PLDs contain amyloidogenic stretches but can maintain dynamic disordered conformations, even in the condensed phase. However, the molecular mechanism underlying such intricate conformational properties of PLDs remains elusive. Here we employed molecular dynamics simulations to investigate the conformational properties of a prototypical PLD system (i.e., FUS PLD). According to our simulation results, PLD adopts a wet collapsed conformation, wherein most residues maintain sufficient hydration with the abundance of internal water. These internal water molecules can rapidly exchange between the protein interior and the bulk, enabling intensive coupling of the entire protein with its hydration environment. The dynamic exchange of water molecules is intimately correlated to the overall conformational fluctuations of PLD. Furthermore, the abundance of dynamic internal water suppresses the formation of aggregation-prone ordered structures. These results collectively elucidate the crucial role of internal water in sustaining the dynamic disordered conformation of the PLD and inhibiting its aggregation propensity.

Modeling properties of chromosome territories using polymer filaments in diverse confinement geometries

Interphase chromosomes reside within distinct nuclear regions known as chromosome territories (CTs). Recent observations from Hi-C analyses, a method mapping chromosomal interactions, have revealed varied decay in contact probabilities among different chromosomes. Our study explores the relationship between this contact decay and the particular shapes of the chromosome territories they occupy. For this, we employed molecular dynamics (MD) simulations to examine how confined polymers, resembling chromosomes, behave within different confinement geometries similar to chromosome territory boundaries. Our simulations unveil so far unreported relationships between contact probabilities and end-to-end distances varying based on different confinement geometries. These findings highlight the crucial impact of chromosome territories on shaping the larger-scale properties of 3D genome organization. They emphasize the intrinsic connection between the shapes of these territories and the contact behaviors exhibited by chromosomes. Understanding these correlations is key to accurately interpret Hi-C and microscopy data, and offers vital insights into the foundational principles governing genomic organization.

How Transcription Factor Clusters Shape the Transcriptional Landscape

In eukaryotic cells, gene transcription typically occurs in discrete periods of promoter activity, interspersed with intervals of inactivity. This pattern deviates from simple stochastic events and warrants a closer examination of the molecular interactions that activate the promoter. Recent studies have identified transcription factor (TF) clusters as key precursors to transcriptional bursting. Often, these TF clusters form at chromatin segments that are physically distant from the promoter, making changes in chromatin conformation crucial for promoter-TF cluster interactions. In this review, I explore the formation and constituents of TF clusters, examining how the dynamic interplay between chromatin architecture and TF clustering influences transcriptional bursting. Additionally, I discuss techniques for visualizing TF clusters and provide an outlook on understanding the remaining gaps in this field.

Motorized chain models of the ideal chromosome

An array of motor proteins consumes chemical energy in setting up the architectures of chromosomes. Here, we explore how the structure of ideal polymer chains is influenced by two classes of motors. The first class which we call "swimming motors" acts to propel the chromatin fiber through three-dimensional space. They represent a caricature of motors such as RNA polymerases. Previously, they have often been described by adding a persistent flow onto Brownian diffusion of the chain. The second class of motors, which we call "grappling motors" caricatures the loop extrusion processes in which segments of chromatin fibers some distance apart are brought together. We analyze these models using a self-consistent variational phonon approximation to a many-body Master equation incorporating motor activities. We show that whether the swimming motors lead to contraction or expansion depends on the susceptibility of the motors, that is, how their activity depends on the forces they must exert. Grappling motors in contrast to swimming motors lead to long-ranged correlations that resemble those first suggested for fractal globules and that are consistent with the effective interactions inferred by energy landscape analyses of Hi-C data on the interphase chromosome.

Heterogeneous flexibility can contribute to chromatin segregation in the cell nucleus

The highly and slightly condensed forms of chromatin, heterochromatin and euchromatin, respectively, segregate in the cell nucleus. Heterochromatin is more abundant in the nucleus periphery. Here we study the mechanism of heterochromatin segregation by modeling interphase chromosomes as diblock ring copolymers confined in a rigid spherical shell using molecular dynamics simulations. In our model, heterochromatin and euchromatin are distinguished by their bending stiffnesses only, while an interaction potential between the spherical shell and chromatin is used to model lamin-associated proteins. Our simulations indicate that in the absence of attractive interactions between the nuclear shell and the chromatin, most heterochromatin segregates towards the nuclear interior due to the depletion of less flexible heterochromatin segments from the nuclear periphery. This inverted chromatin distribution,which is opposite to the conventional case with heterochromatin dominating at the periphery, is in accord with experimental observations in rod cells. This "inversion" is also found to be independent of the heterochromatin concentration and chromosome number. The chromatin distribution at the periphery found in vivo can be recovered by further increasing the bending stiffness of heterochromatin segments or by turning on attractive interactions between the nuclear shell and heterochromatin. Our results indicate that the bending stiffness of chromatin could be a contributor to chromosome organization along with differential effects of HP1α-driven phase segregation and of loop extruders and interactions with the nuclear envelope and topological constraints.

Local Volume Concentration, Packing Domains and Scaling Properties of Chromatin

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions. The SR-EV rules of return generate conformationally-defined domains observed by single cell imaging techniques. From nucleosome to chromosome scales, the model captures the overall chromatin organization as a corrugated system, with dense and dilute regions alternating in a manner that resembles the mixing of two disordered bi-continuous phases. This particular organizational topology is a consequence of the multiplicity of interactions and processes occurring in the nuclei, and mimicked by the proposed return rules. Single configuration properties and ensemble averages show a robust agreement between theoretical and experimental results including chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. Model and experimental results suggest that there is an inherent chromatin organization regardless of the cell character and resistant to an external forcing such as Rad21 degradation.

Nonequilibrium switching of segmental states can influence compaction of chromatin

Knowledge about the dynamic nature of chromatin organization is essential to understand the regulation of processes like DNA transcription and repair. The existing models of chromatin assume that protein organization and chemical states along chromatin are static and the 3D organization is purely a result of protein-mediated intra-chromatin interactions. Here we present a new hypothesis that certain nonequilibrium processes, such as switching of chemical and physical states due to nucleosome assembly/disassembly or gene repression/activation, can also simultaneously influence chromatin configurations. To understand the implications of this inherent nonequilibrium switching, we present a block copolymer model of chromatin, with switching of its segmental states between two states, mimicking active/repressed or protein unbound/bound states. We show that competition between switching timescale Tt, polymer relaxation timescale τp, and segmental relaxation timescale τs can lead to non-trivial changes in chromatin organization, leading to changes in local compaction and contact probabilities. As a function of the switching timescale, the radius of gyration of chromatin shows a non-monotonic behavior with a prominent minimum when Tt ≈ τp and a maximum when Tt ≈ τs. We find that polymers with a small segment length exhibit a more compact structure than those with larger segment lengths. We also find that the switching can lead to higher contact probability and better mixing of far-away segments. Our study also shows that the nature of the distribution of chromatin clusters varies widely as we change the switching rate.

Effective model of protein-mediated interactions in chromatin

Protein-mediated interactions are ubiquitous in the cellular environment, and particularly in the nucleus, where they are responsible for the structuring of chromatin. We show through molecular-dynamics simulations of a polymer surrounded by binders that the strength of the binder-polymer interaction separates an equilibrium from a nonequilibrium regime. In the equilibrium regime, the system can be efficiently described by an effective model in which the binders are traced out. Even in this case, the polymers display features that are different from those of a standard homopolymer interacting with two-body interactions. We then extend the effective model to deal with the case where binders cannot be regarded as in equilibrium and a new phenomenology appears, including local blobs in the polymer. An effective description of this system can be useful in elucidating the fundamental mechanisms that govern chromatin structuring in particular and indirect interactions in general.

Helical chromonema coiling is conserved in eukaryotes

Efficient chromatin condensation is required to transport chromosomes during mitosis and meiosis, forming daughter cells. While it is well accepted that these processes follow fundamental rules, there has been a controversial debate for more than 140 years on whether the higher-order chromatin organization in chromosomes is evolutionarily conserved. Here, we summarize historical and recent investigations based on classical and modern methods. In particular, classical light microscopy observations based on living, fixed, and treated chromosomes covering a wide range of plant and animal species, and even in single-cell eukaryotes suggest that the chromatids of large chromosomes are formed by a coiled chromatin thread, named the chromonema. More recently, these findings were confirmed by electron and super-resolution microscopy, oligo-FISH, molecular interaction data, and polymer simulation. Altogether, we describe common and divergent features of coiled chromonemata in different species. We hypothesize that chromonema coiling in large chromosomes is a fundamental feature established early during the evolution of eukaryotes to handle increasing genome sizes.

Multiplexed chromatin imaging reveals predominantly pairwise long-range coordination between Drosophila Polycomb genes

Polycomb (Pc) group proteins are transcriptional regulators with key roles in development, cell identity, and differentiation. Pc-bound chromatin regions form repressive domains that interact in 3D to assemble repressive nuclear compartments. Here, we use multiplexed chromatin imaging to investigate whether Pc compartments involve the clustering of multiple Pc domains during Drosophila development. Notably, 3D proximity between Pc targets is rare and involves predominantly pairwise interactions. These 3D proximities are particularly enhanced in segments where Pc genes are co-repressed. In addition, segment-specific expression of Hox Pc targets leads to their spatial segregation from Pc-repressed genes. Finally, non-Hox Pc targets are more proximal in regions where they are co-expressed. These results indicate that long-range Pc interactions are temporally and spatially regulated during differentiation and development but do not induce frequent clustering of multiple distant Pc genes.

Correlative single molecule lattice light sheet imaging reveals the dynamic relationship between nucleosomes and the local chromatin environment

In the nucleus, biological processes are driven by proteins that diffuse through and bind to a meshwork of nucleic acid polymers. To better understand this interplay, we present an imaging platform to simultaneously visualize single protein dynamics together with the local chromatin environment in live cells. Together with super-resolution imaging, new fluorescent probes, and biophysical modeling, we demonstrate that nucleosomes display differential diffusion and packing arrangements as chromatin density increases whereas the viscoelastic properties and accessibility of the interchromatin space remain constant. Perturbing nuclear functions impacts nucleosome diffusive properties in a manner that is dependent both on local chromatin density and on relative location within the nucleus. Our results support a model wherein transcription locally stabilizes nucleosomes while simultaneously allowing for the free exchange of nuclear proteins. Additionally, they reveal that nuclear heterogeneity arises from both active and passive processes and highlight the need to account for different organizational principles when modeling different chromatin environments.

The probability of chromatin to be at the nuclear lamina has no systematic effect on its transcription level in fruit flies

BACKGROUND

Multiple studies have demonstrated a negative correlation between gene expression and positioning of genes at the nuclear envelope (NE) lined by nuclear lamina, but the exact relationship remains unclear, especially in light of the highly stochastic, transient nature of the gene association with the NE.

RESULTS

In this paper, we ask whether there is a causal, systematic, genome-wide relationship between the expression levels of the groups of genes in topologically associating domains (TADs) of Drosophila nuclei and the probabilities of TADs to be found at the NE. To investigate the nature of this possible relationship, we combine a coarse-grained dynamic model of the entire Drosophila nucleus with genome-wide gene expression data; we analyze the TAD averaged transcription levels of genes against the probabilities of individual TADs to be in contact with the NE in the control and lamins-depleted nuclei. Our findings demonstrate that, within the statistical error margin, the stochastic positioning of Drosophila melanogaster TADs at the NE does not, by itself, systematically affect the mean level of gene expression in these TADs, while the expected negative correlation is confirmed. The correlation is weak and disappears completely for TADs not containing lamina-associated domains (LADs) or TADs containing LADs, considered separately. Verifiable hypotheses regarding the underlying mechanism for the presence of the correlation without causality are discussed. These include the possibility that the epigenetic marks and affinity to the NE of a TAD are determined by various non-mutually exclusive mechanisms and remain relatively stable during interphase.

CONCLUSIONS

At the level of TADs, the probability of chromatin being in contact with the nuclear envelope has no systematic, causal effect on the transcription level in Drosophila. The conclusion is reached by combining model-derived time-evolution of TAD locations within the nucleus with their experimental gene expression levels.

Rules of engagement for condensins and cohesins guide mitotic chromosome formation

During mitosis, interphase chromatin is rapidly converted into rod-shaped mitotic chromosomes. Using Hi-C, imaging, proteomics and polymer modeling, we determine how the activity and interplay between loop-extruding SMC motors accomplishes this dramatic transition. Our work reveals rules of engagement for SMC complexes that are critical for allowing cells to refold interphase chromatin into mitotic chromosomes. We find that condensin disassembles interphase chromatin loop organization by evicting or displacing extrusive cohesin. In contrast, condensin bypasses cohesive cohesins, thereby maintaining sister chromatid cohesion while separating the sisters. Studies of mitotic chromosomes formed by cohesin, condensin II and condensin I alone or in combination allow us to develop new models of mitotic chromosome conformation. In these models, loops are consecutive and not overlapping, implying that condensins do not freely pass one another but stall upon encountering each other. The dynamics of Hi-C interactions and chromosome morphology reveal that during prophase loops are extruded in vivo at ~1-3 kb/sec by condensins as they form a disordered discontinuous helical scaffold within individual chromatids.

The scales, mechanisms, and dynamics of the genome architecture

Even when split into several chromosomes, DNA molecules that make up our genome are too long to fit into the cell nuclei unless massively folded. Such folding must accommodate the need for timely access to selected parts of the genome by transcription factors, RNA polymerases, and DNA replication machinery. Here, we review our current understanding of the genome folding inside the interphase nuclei. We consider the resulting genome architecture at three scales with a particular focus on the intermediate (meso) scale and summarize the insights gained from recent experimental observations and diverse computational models.

Attractive crowding effect on passive and active polymer looping kinetics

Loop formation in complex environments is crucially important to many biological processes in life. In the present work, we adopt three-dimensional Langevin dynamics simulations to investigate passive and active polymer looping kinetics in crowded media featuring polymer-crowder attraction. We find polymers undergo a remarkable coil-globule-coil transition, highlighted by a marked change in the Flory scaling exponent of the gyration radius. Meanwhile, looping time as a function of the crowder's volume fraction demonstrates an apparent non-monotonic alteration. A small number of crowders induce a compact structure, which largely facilitates the looping process. While a large number of crowders heavily impede end-to-end diffusion, looping kinetics is greatly inhibited. For a self-propelled chain, we find that the attractive crowding triggers an unusual activity effect on looping kinetics. Once a globular state is formed, activity takes an effort to open the chain from the compact structure, leading to an unexpected activity-induced inhibition of looping. If the chain maintains a coil state, the dominant role of activity is to enhance diffusivity and, thus, speed up looping kinetics. The novel conformational change and looping kinetics of both passive and active polymers in the presence of attractive crowding highlight a rather distinct scenario that has no analogy in a repulsive crowding counterpart. The underlying mechanism enriches our understanding of the crucial role of attractive interactions in modulating polymer structure and dynamics.

Multiplex DNA fluorescence in situ hybridization to analyze maternal vs. paternal C. elegans chromosomes

Recent advances in microscopy have enabled studying chromosome organization at the single-molecule level, yet little is known about inherited chromosome organization. Here we adapt single-molecule chromosome tracing to distinguish two C. elegans strains (N2 and HI) and find that while their organization is similar, the N2 chromosome influences the folding parameters of the HI chromosome, in particular the step size, across generations. Furthermore, homologous chromosomes overlap frequently, but alignment between homologous regions is rare, suggesting that transvection is unlikely. We present a powerful tool to investigate chromosome architecture and to track the parent of origin.

Single-cell multiplex chromatin and RNA interactions in aging human brain

The dynamically organized chromatin complexes often involve multiplex chromatin interactions and sometimes chromatin-associated RNA (caRNA) 1-3. Chromatin complex compositions change during cellular differentiation and aging, and are expected to be highly heterogeneous among terminally differentiated single cells 4-7. Here we introduce the Multi-Nucleic Acid Interaction Mapping in Single Cell (MUSIC) technique for concurrent profiling of multiplex chromatin interactions, gene expression, and RNA-chromatin associations within individual nuclei. Applied to 14 human frontal cortex samples from elderly donors, MUSIC delineates diverse cortical cell types and states. We observed the nuclei exhibiting fewer short-range chromatin interactions are correlated with an "older" transcriptomic signature and with Alzheimer's pathology. Furthermore, the cell type exhibiting chromatin contacts between cis expression quantitative trait loci (cis eQTLs) and a promoter tends to be the cell type where these cis eQTLs specifically affect their target gene's expression. Additionally, the female cortical cells exhibit highly heterogeneous interactions between the XIST non-coding RNA and Chromosome X, along with diverse spatial organizations of the X chromosomes. MUSIC presents a potent tool for exploring chromatin architecture and transcription at cellular resolution in complex tissues.

Polycomb repression of Hox genes involves spatial feedback but not domain compaction or phase transition

Polycomb group proteins have a critical role in silencing transcription during development. It is commonly proposed that Polycomb-dependent changes in genome folding, which compact chromatin, contribute directly to repression by blocking the binding of activating complexes. Recently, it has also been argued that liquid-liquid demixing of Polycomb proteins facilitates this compaction and repression by phase-separating target genes into a membraneless compartment. To test these models, we used Optical Reconstruction of Chromatin Architecture to trace the Hoxa gene cluster, a canonical Polycomb target, in thousands of single cells. Across multiple cell types, we find that Polycomb-bound chromatin frequently explores decompact states and partial mixing with neighboring chromatin, while remaining uniformly repressed, challenging the repression-by-compaction or phase-separation models. Using polymer simulations, we show that these observed flexible ensembles can be explained by 'spatial feedback'-transient contacts that contribute to the propagation of the epigenetic state (epigenetic memory), without inducing a globular organization.

Steric repulsion introduced by loop constraints modulates the microphase separation of chromatins

Within the confines of a densely populated cell nucleus, chromatin undergoes intricate folding, forming loops, domains, and compartments under the governance of topological constraints and phase separation. This coordinated process inevitably introduces interference between different folding strategies. In this study, we model interphase chromatins as block copolymers with hetero-hierarchical loops within a confined system. Employing dissipative particle dynamics simulations and scaling analysis, we aim to explain how the structure and distribution of loop domains modulate the microphase separation of chromatins. Our results highlight the correlation between the microphase separation of the copolymer and the length, heterogeneity, and hierarchically nested levels of the loop domains. This correlation arises from steric repulsion intrinsic to loop domains. The steric repulsion induces variations in chain stiffness (including local orientation correlations and the persistence length), thereby influencing the degree of phase separation. Through simulations of block copolymers with distinct groups of hetero-hierarchical loop anchors, we successfully reproduce changes in phase separation across diverse cell lines, under fixed interaction parameters. These findings, in qualitative alignment with Hi-C data, suggest that the variations of loop constraints alone possess the capacity to regulate higher-order structures and the gene expressions of interphase chromatins.

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.

Confinement effect of inter-arm interactions on glass formation in star polymer melts

We utilized molecular dynamic simulation to investigate the glass formation of star polymer melts in which the topological complexity is varied by altering the number of star arms (f). Emphasis was placed on how the "confinement effect" of repulsive inter-arm interactions within star polymers influences the thermodynamics and dynamics of star polymer melts. All the characteristic temperatures of glass formation were found to progressively increase with increasing f, but unexpectedly the fragility parameter KVFT was found to decrease with increasing f. As previously observed, stars having more than 5 or 6 arms adopt an average particle-like structure that is more contracted relative to the linear polymer size having the same mass and exhibit a strong tendency for intermolecular and intramolecular segregation. We systematically analyzed how varying f alters collective particle motion, dynamic heterogeneity, the decoupling exponent ζ phenomenologically linking the slow β- and α-relaxation times, and the thermodynamic scaling index γt. Consistent with our hypothesis that the segmental dynamics of many-arm star melts and thin supported polymer films should exhibit similar trends arising from the common feature of high local segmental confinement, we found that ζ increases considerably with increasing f, as found in supported polymer films with decreasing thickness. Furthermore, increasing f led to greatly enhanced elastic heterogeneity, and this phenomenon correlates strongly with changes in ζ and γt. Our observations should be helpful in building a more rational theoretical framework for understanding how molecular topology and geometrical confinement influence the dynamics of glass-forming materials more broadly.

The Risk Function of Breast and Ovarian Cancers in the Avrami-Dobrzyński Cellular Phase-Transition Model

Specifying the role of genetic mutations in cancer development is crucial for effective screening or targeted treatments for people with hereditary cancer predispositions. Our goal here is to find the relationship between a number of cancerogenic mutations and the probability of cancer induction over the lifetime of cancer patients. We believe that the Avrami-Dobrzyński biophysical model can be used to describe this mechanism. Therefore, clinical data from breast and ovarian cancer patients were used to validate this model of cancer induction, which is based on a purely physical concept of the phase-transition process with an analogy to the neoplastic transformation. The obtained values of model parameters established using clinical data confirm the hypothesis that the carcinogenic process strongly follows fractal dynamics. We found that the model's theoretical prediction and population clinical data slightly differed for patients with the age below 30 years old, and that might point to the existence of an ancillary protection mechanism against cancer development. Additionally, we reveal that the existing clinical data predict breast or ovarian cancers onset two years earlier for patients with BRCA1/2 mutations.

An in silico procedure for generating protein-mediated chromatin interaction data and comparison of significant interaction calling methods

The ability to simulate high-throughput data with high fidelity to real experimental data is fundamental for benchmarking methods used to detect true long-range chromatin interactions mediated by a specific protein. Yet, such tools are not currently available. To fill this gap, we develop an in silico experimental procedure, ChIA-Sim, which imitates the experimental procedures that produce real ChIA-PET, Hi-ChIP, or PLAC-seq data. We show the fidelity of ChIA-Sim to real data by using guiding characteristics of several real datasets to generate data using the simulation procedure. We also used ChIA-Sim data to demonstrate the use of our in silico procedure in benchmarking methods for significant interactions analysis by evaluating four methods for significant interaction calling (SIC). In particular, we assessed each method's performance in terms of correct identification of long-range interactions. We further analyzed four experimental datasets from publicly available databases and shew that the trend of the results are consistent with those seen in data generated from ChIA-Sim. This serves as additional evidence that ChIA-Sim closely resembles data produced from the experimental protocols it models after.

Internal friction as a factor in the anomalous chain length dependence of DNA transcriptional dynamics

Recent experiments by Brückner et al. [Science 380, 1357 (2023)] have observed an anomalous chain length dependence of the time of near approach of widely separated pairs of genomic elements on transcriptionally active chromosomal DNA. In this paper, I suggest that the anomaly may have its roots in internal friction between neighboring segments on the DNA backbone. The basis for this proposal is a model of chain dynamics formulated in terms of a continuum scaled Brownian walk (sBw) of polymerization index N. The sBw is an extension of the simple Brownian walk model widely used in path integral calculations of polymer properties, differing from it in containing an additional parameter H (the Hurst index) that can be tuned to produce varying degrees of correlation between adjacent monomers. A calculation using the sBw of the mean time τc for chain closure predicts-under the Wilemski-Fixman approximation for diffusion-controlled reactions-that at early times, τc varies as the 2/3 power of N, in close agreement with the findings of the Brückner et al. study. Other scaling relations of that study, including those related to the probability of loop formation and the mean square displacements of terminal monomers, are also satisfactorily accounted for by the model.

Forecasting histone methylation by Polycomb complexes with minute-scale precision

Animals use the Polycomb system to epigenetically repress developmental genes. The repression requires trimethylation of lysine 27 of histone H3 (H3K27me3) by Polycomb Repressive Complex 2 (PRC2), but the dynamics of this process is poorly understood. To bridge the gap, we developed a computational model that forecasts H3K27 methylation in Drosophila with high temporal resolution and spatial accuracy of contemporary experimental techniques. Using this model, we show that pools of methylated H3K27 in dividing cells are defined by the effective concentration of PRC2 and the replication frequency. We find that the allosteric stimulation by preexisting H3K27me3 makes PRC2 better in methylating developmental genes as opposed to indiscriminate methylation throughout the genome. Applied to Drosophila development, our model argues that, in this organism, the intergenerationally inherited H3K27me3 does not "survive" rapid cycles of embryonic chromatin replication and is unlikely to transmit the memory of epigenetic repression to the offspring. Our model is adaptable to other organisms, including mice and humans.

Interplay between epigenome and 3D chromatin structure

Epigenetic mechanisms, primarily mediated through histone and DNA modifications, play a pivotal role in orchestrating the functional identity of a cell and its response to environmental cues. Similarly, the spatial arrangement of chromatin within the threedimensional (3D) nucleus has been recognized as a significant factor influencing genomic function. Investigating the relationship between epigenetic regulation and 3D chromatin structure has revealed correlation and causality between these processes, from the global alignment of average chromatin structure with chromatin marks to the nuanced correlations at smaller scales. This review aims to dissect the biological significance and the interplay between the epigenome and 3D chromatin structure, while also exploring the underlying molecular mechanisms. By synthesizing insights from both experimental and modeling perspectives, we seek to provide a comprehensive understanding of cellular functions. [BMB Reports 2023; 56(12): 633-644].

Correlative single molecule lattice light sheet imaging reveals the dynamic relationship between nucleosomes and the local chromatin environment

In the nucleus, biological processes are driven by proteins that diffuse through and bind to a meshwork of nucleic acid polymers. To better understand this interplay, we developed an imaging platform to simultaneously visualize single protein dynamics together with the local chromatin environment in live cells. Together with super-resolution imaging, new fluorescent probes, and biophysical modeling, we demonstrated that nucleosomes display differential diffusion and packing arrangements as chromatin density increases whereas the viscoelastic properties and accessibility of the interchromatin space remain constant. Perturbing nuclear functions impacted nucleosome diffusive properties in a manner that was dependent on local chromatin density and supportive of a model wherein transcription locally stabilizes nucleosomes while simultaneously allowing for the free exchange of nuclear proteins. Our results reveal that nuclear heterogeneity arises from both active and passive process and highlights the need to account for different organizational principals when modeling different chromatin environments.

Quantifying the large-scale chromosome structural dynamics during the mitosis-to-G1 phase transition of cell cycle

Cell cycle is known to be regulated by the underlying gene network. Chromosomes, which serve as the scaffold for gene expressions, undergo significant structural reorganizations during mitosis. Understanding the mechanism of the cell cycle from the chromosome structural perspective remains a grand challenge. In this study, we applied an integrated theoretical approach to investigate large-scale chromosome structural dynamics during the mitosis-to-G1 phase transition. We observed that the chromosome structural expansion and adaptation of the structural asphericity do not occur synchronously and attributed this behaviour to the unique unloading sequence of the two types of condensins. Furthermore, we observed that the coherent motions between the chromosomal loci are primarily enhanced within the topologically associating domains (TADs) as cells progress to the G1 phase, suggesting that TADs can be considered as both structural and dynamical units for organizing the three-dimensional chromosome. Our analysis also reveals that the quantified pathways of chromosome structural reorganization during the mitosis-to-G1 phase transition exhibit high stochasticity at the single-cell level and show nonlinear behaviours in changing TADs and contacts formed at the long-range regions. Our findings offer valuable insights into large-scale chromosome structural dynamics after mitosis.

DNA supercoiling in bacteria: state of play and challenges from a viewpoint of physics based modeling

DNA supercoiling is central to many fundamental processes of living organisms. Its average level along the chromosome and over time reflects the dynamic equilibrium of opposite activities of topoisomerases, which are required to relax mechanical stresses that are inevitably produced during DNA replication and gene transcription. Supercoiling affects all scales of the spatio-temporal organization of bacterial DNA, from the base pair to the large scale chromosome conformation. Highlighted in vitro and in vivo in the 1960s and 1970s, respectively, the first physical models were proposed concomitantly in order to predict the deformation properties of the double helix. About fifteen years later, polymer physics models demonstrated on larger scales the plectonemic nature and the tree-like organization of supercoiled DNA. Since then, many works have tried to establish a better understanding of the multiple structuring and physiological properties of bacterial DNA in thermodynamic equilibrium and far from equilibrium. The purpose of this essay is to address upcoming challenges by thoroughly exploring the relevance, predictive capacity, and limitations of current physical models, with a specific focus on structural properties beyond the scale of the double helix. We discuss more particularly the problem of DNA conformations, the interplay between DNA supercoiling with gene transcription and DNA replication, its role on nucleoid formation and, finally, the problem of scaling up models. Our primary objective is to foster increased collaboration between physicists and biologists. To achieve this, we have reduced the respective jargon to a minimum and we provide some explanatory background material for the two communities.

Determination of DNA architecture of bacteria under various types of stress, methodological approaches, problems, and solutions

Actively growing cells maintain a dynamic, far from equilibrium order through metabolism. Under starvation stress or under stress of exposure to the analog of the anabiosis autoinducer (4-hexylresorcinol), cells go into a dormant state (almost complete lack of metabolism) or even into a mummified state. In a dormant state, cells are forced to use the physical mechanisms of DNA protection. The architecture of DNA in the dormant and mummified state of cells was studied by x-ray diffraction of synchrotron radiation and transmission electron microscopy (TEM). Diffraction experiments indicate the appearance of an ordered organization of DNA. TEM made it possible to visualize the type of DNA ordering. Intracellular nanocrystalline, liquid-crystalline, and folded nucleosome-like structures of DNA have been found. The structure of DNA within a cell in an anabiotic dormant state and dormant state (starvation stress) coincides (forms nanocrystalline structures). Data suggest the universality of DNA condensation by a protein Dps for a dormant state, regardless of the type of stress. The mummified state is very different in structure from the dormant state (has no ordering within a cell). It turned out that it is possible to visualize DNA conformation in toroidal and liquid crystal structures in which there is either no or a very small amount of the Dps protein. Observation of the DNA conformation in nanocrystals and folded nucleosome-like structures so far has been inconclusive. The methodological advances described will facilitate high-resolution visualization of the DNA conformation in the near future.

Crumpled polymer with loops recapitulates key features of chromosome organization

Chromosomes are exceedingly long topologically-constrained polymers compacted in a cell nucleus. We recently suggested that chromosomes are organized into loops by an active process of loop extrusion. Yet loops remain elusive to direct observations in living cells; detection and characterization of myriads of such loops is a major challenge. The lack of a tractable physical model of a polymer folded into loops limits our ability to interpret experimental data and detect loops. Here, we introduce a new physical model - a polymer folded into a sequence of loops, and solve it analytically. Our model and a simple geometrical argument show how loops affect statistics of contacts in a polymer across different scales, explaining universally observed shapes of the contact probability. Moreover, we reveal that folding into loops reduces the density of topological entanglements, a novel phenomenon we refer as "the dilution of entanglements". Supported by simulations this finding suggests that up to ~ 1 - 2Mb chromosomes with loops are not topologically constrained, yet become crumpled at larger scales. Our theoretical framework allows inference of loop characteristics, draws a new picture of chromosome organization, and shows how folding into loops affects topological properties of crumpled polymers.

Mapping robust multiscale communities in chromosome contact networks

To better understand DNA's 3D folding in cell nuclei, researchers developed chromosome capture methods such as Hi-C that measure the contact frequencies between all DNA segment pairs across the genome. As Hi-C data sets often are massive, it is common to use bioinformatics methods to group DNA segments into 3D regions with correlated contact patterns, such as Topologically associated domains and A/B compartments. Recently, another research direction emerged that treats the Hi-C data as a network of 3D contacts. In this representation, one can use community detection algorithms from complex network theory that group nodes into tightly connected mesoscale communities. However, because Hi-C networks are so densely connected, several node partitions may represent feasible solutions to the community detection problem but are indistinguishable unless including other data. Because this limitation is a fundamental property of the network, this problem persists regardless of the community-finding or data-clustering method. To help remedy this problem, we developed a method that charts the solution landscape of network partitions in Hi-C data from human cells. Our approach allows us to scan seamlessly through the scales of the network and determine regimes where we can expect reliable community structures. We find that some scales are more robust than others and that strong clusters may differ significantly. Our work highlights that finding a robust community structure hinges on thoughtful algorithm design or method cross-evaluation.

Hi-TrAC detects active sub-TADs and reveals internal organizations of super-enhancers

The spatial folding of eukaryotic genome plays a key role in genome function. We report here that our recently developed method, Hi-TrAC, which specializes in detecting chromatin loops among accessible genomic regions, can detect active sub-TADs with a median size of 100 kb, most of which harbor one or two cell specifically expressed genes and regulatory elements such as super-enhancers organized into nested interaction domains. These active sub-TADs are characterized by highly enriched histone mark H3K4me1 and chromatin-binding proteins, including Cohesin complex. Deletion of selected sub-TAD boundaries have different impacts, such as decreased chromatin interaction and gene expression within the sub-TADs or compromised insulation between the sub-TADs, depending on the specific chromatin environment. We show that knocking down core subunit of the Cohesin complex using shRNAs in human cells or decreasing the H3K4me1 modification by deleting the H3K4 methyltransferase Mll4 gene in mouse Th17 cells disrupted the sub-TADs structure. Our data also suggest that super-enhancers exist as an equilibrium globule structure, while inaccessible chromatin regions exist as a fractal globule structure. In summary, Hi-TrAC serves as a highly sensitive and inexpensive approach to study dynamic changes of active sub-TADs, providing more explicit insights into delicate genome structures and functions.

Mapping the semi-nested community structure of 3D chromosome contact networks

Mammalian DNA folds into 3D structures that facilitate and regulate genetic processes such as transcription, DNA repair, and epigenetics. Several insights derive from chromosome capture methods, such as Hi-C, which allow researchers to construct contact maps depicting 3D interactions among all DNA segment pairs. These maps show a complex cross-scale organization spanning megabase-pair compartments to short-ranged DNA loops. To better understand the organizing principles, several groups analyzed Hi-C data assuming a Russian-doll-like nested hierarchy where DNA regions of similar sizes merge into larger and larger structures. Apart from being a simple and appealing description, this model explains, e.g., the omnipresent chequerboard pattern seen in Hi-C maps, known as A/B compartments, and foreshadows the co-localization of some functionally similar DNA regions. However, while successful, this model is incompatible with the two competing mechanisms that seem to shape a significant part of the chromosomes' 3D organization: loop extrusion and phase separation. This paper aims to map out the chromosome's actual folding hierarchy from empirical data. To this end, we take advantage of Hi-C experiments and treat the measured DNA-DNA interactions as a weighted network. From such a network, we extract 3D communities using the generalized Louvain algorithm. This algorithm has a resolution parameter that allows us to scan seamlessly through the community size spectrum, from A/B compartments to topologically associated domains (TADs). By constructing a hierarchical tree connecting these communities, we find that chromosomes are more complex than a perfect hierarchy. Analyzing how communities nest relative to a simple folding model, we found that chromosomes exhibit a significant portion of nested and non-nested community pairs alongside considerable randomness. In addition, by examining nesting and chromatin types, we discovered that nested parts are often associated with active chromatin. These results highlight that cross-scale relationships will be essential components in models aiming to reach a deep understanding of the causal mechanisms of chromosome folding.

Stochastic motion and transcriptional dynamics of pairs of distal DNA loci on a compacted chromosome

Chromosomes in the eukaryotic nucleus are highly compacted. However, for many functional processes, including transcription initiation, the pairwise motion of distal chromosomal elements such as enhancers and promoters is essential and necessitates dynamic fluidity. Here, we used a live-imaging assay to simultaneously measure the positions of pairs of enhancers and promoters and their transcriptional output while systematically varying the genomic separation between these two DNA loci. Our analysis reveals the coexistence of a compact globular organization and fast subdiffusive dynamics. These combined features cause an anomalous scaling of polymer relaxation times with genomic separation leading to long-ranged correlations. Thus, encounter times of DNA loci are much less dependent on genomic distance than predicted by existing polymer models, with potential consequences for eukaryotic gene expression.

FIREBALL: A tool to fit protein phase diagrams based on mean-field theories for polymer solutions

Biomolecular condensates form via phase transitions of condensate-specific biomacromolecules. Intrinsically disordered regions featuring the appropriate sequence grammars can contribute via homotypic and heterotypic interactions to the driving forces for phase separation of multivalent proteins. Experiments and computations have matured to the point where the concentrations of coexisting dense and dilute phases can be measured or computed for individual intrinsically disordered regions in complex milieus. For a macromolecule such as a disordered protein in a solvent, the locus of points that connects concentrations of the two coexisting phases defines a phase boundary, or binodal. Often, only a few points along the binodal are accessible via measurements. In such cases, and for quantitative and comparative analysis of parameters that describe the driving forces for phase separation, it is useful to fit measured or computed binodals to mean-field free energies for polymer solutions. The nonlinearity of the underlying free energy functions makes it challenging to put mean-field theories into practice. Here, we present FIREBALL, a suite of computational tools designed to enable efficient construction, analysis, and fitting to experimental or computed data of binodals. We show that depending on the theory being used, one can also extract information regarding coil-to-globule transitions of individual macromolecules.

Locality of contacts determines the subdiffusion exponents in polymeric models of chromatin

Loop extrusion by motor proteins mediates the attractive interactions in chromatin on the length scale of megabases, providing the polymer with a well-defined structure and at the same time determining its dynamics. The mean-square displacement of chromatin loci varies from a Rouse-like scaling to a more constrained subdiffusion, depending on cell type, genomic region, and time scale. With a simple polymeric model, we show that such a Rouse-like dynamics occurs when the parameters of the model are chosen so that contacts are local along the chain, while in the presence of nonlocal contacts we observe subdiffusion at short time scales with exponents smaller than 0.5. Such exponents are independent of the detailed choice of the parameters and build a master curve that depends only on the mean locality of the resulting contacts. We compare the loop-extrusion model with a polymeric model with static links, showing that also in this case only the presence of nonlocal contacts can produce low-exponent subdiffusion. We interpret these results in terms of a simple analytical model.

Strong interactions between highly dynamic lamina-associated domains and the nuclear envelope stabilize the 3D architecture of Drosophila interphase chromatin

BACKGROUND

Interactions among topologically associating domains (TADs), and between the nuclear envelope (NE) and lamina-associated domains (LADs) are expected to shape various aspects of three-dimensional (3D) chromatin structure and dynamics; however, relevant genome-wide experiments that may provide statistically significant conclusions remain difficult.

RESULTS

We have developed a coarse-grained dynamical model of D. melanogaster nuclei at TAD resolution that explicitly accounts for four distinct epigenetic classes of TADs and LAD-NE interactions. The model is parameterized to reproduce the experimental Hi-C map of the wild type (WT) nuclei; it describes time evolution of the chromatin over the G1 phase of the interphase. The simulations include an ensemble of nuclei, corresponding to the experimentally observed set of several possible mutual arrangements of chromosomal arms. The model is validated against multiple structural features of chromatin from several different experiments not used in model development. Predicted positioning of all LADs at the NE is highly dynamic-the same LAD can attach, detach and move far away from the NE multiple times during interphase. The probabilities of LADs to be in contact with the NE vary by an order of magnitude, despite all having the same affinity to the NE in the model. These probabilities are mostly determined by a highly variable local linear density of LADs along the genome, which also has the same strong effect on the predicted positioning of individual TADs -- higher probability of a TAD to be near NE is largely determined by a higher linear density of LADs surrounding this TAD. The distribution of LADs along the chromosome chains plays a notable role in maintaining a non-random average global structure of chromatin. Relatively high affinity of LADs to the NE in the WT nuclei substantially reduces sensitivity of the global radial chromatin distribution to variations in the strength of TAD-TAD interactions compared to the lamin depleted nuclei, where a small (0.5 kT) increase of cross-type TAD-TAD interactions doubles the chromatin density in the central nucleus region.

CONCLUSIONS

A dynamical model of the entire fruit fly genome makes multiple genome-wide predictions of biological interest. The distribution of LADs along the chromatin chains affects their probabilities to be in contact with the NE and radial positioning of highly mobile TADs, playing a notable role in creating a non-random average global structure of the chromatin. We conjecture that an important role of attractive LAD-NE interactions is to stabilize global chromatin structure against inevitable cell-to-cell variations in TAD-TAD interactions.

Mesoscale, long-time mixing of chromosomes and its connection to polymer dynamics

Chromosomes are arranged in distinct territories within the nucleus of animal cells. Recent experiments have shown that these territories overlap at their edges, suggesting partial mixing during interphase. Experiments that knock-down of condensin II proteins during interphase indicate increased chromosome mixing, which demonstrates control of the mixing. In this study, we use a generic polymer simulation to quantify the dynamics of chromosome mixing over time. We introduce the chromosome mixing index, which quantifies the mixing of distinct chromosomes in the nucleus. We find that the chromosome mixing index in a small confinement volume (as a model of the nucleus), increases as a power-law of the time, with the scaling exponent varying non-monotonically with self-interaction and volume fraction. By comparing the chromosome mixing index with both monomer subdiffusion due to (non-topological) intermingling of chromosomes as well as even slower reptation, we show that for relatively large volume fractions, the scaling exponent of the chromosome mixing index is related to Rouse dynamics for relatively weak chromosome attractions and to reptation for strong attractions. In addition, we extend our model to more realistically account for the situation of the Drosophila chromosome by including the heterogeneity of the polymers and their lengths to account for microphase separation of euchromatin and heterochromatin and their interactions with the nuclear lamina. We find that the interaction with the lamina further impedes chromosome mixing.

Morphological profiling by high-throughput single-cell biophysical fractometry

Complex and irregular cell architecture is known to statistically exhibit fractal geometry, i.e., a pattern resembles a smaller part of itself. Although fractal variations in cells are proven to be closely associated with the disease-related phenotypes that are otherwise obscured in the standard cell-based assays, fractal analysis with single-cell precision remains largely unexplored. To close this gap, here we develop an image-based approach that quantifies a multitude of single-cell biophysical fractal-related properties at subcellular resolution. Taking together with its high-throughput single-cell imaging performance (~10,000 cells/sec), this technique, termed single-cell biophysical fractometry, offers sufficient statistical power for delineating the cellular heterogeneity, in the context of lung-cancer cell subtype classification, drug response assays and cell-cycle progression tracking. Further correlative fractal analysis shows that single-cell biophysical fractometry can enrich the standard morphological profiling depth and spearhead systematic fractal analysis of how cell morphology encodes cellular health and pathological conditions.

Recent progress and challenges in single-cell imaging of enhancer-promoter interaction

In the past two years, approaches relying on high-resolution microscopy and live-cell imaging have increasingly contributed to our understanding of the 3D genome organization and its importance for transcriptional control. Here, we describe recent progress that has highlighted how flexible and heterogeneous 3D chromatin structure is, on the length scales relevant to transcriptional control. We describe work that has investigated how robust transcriptional outcomes may be derived from such flexible organization without the need for clearly distinct structures in active and silent cells. We survey the latest state of the art in directly observing the dynamics of chromatin interactions, and suggest how some recent, apparently contradictory conclusions may be reconciled.

Stochastic motion and transcriptional dynamics of pairs of distal DNA loci on a compacted chromosome

Chromosomes in the eukaryotic nucleus are highly compacted. However, for many functional processes, including transcription initiation, the 3D pair-wise motion of distal chromosomal elements, such as enhancers and promoters, is essential and necessitates dynamic fluidity. Therefore, the interplay of chromosome organization and dynamics is crucial for gene regulation. Here, we use a live imaging assay to simultaneously measure the positions of pairs of enhancers and promoters and their transcriptional output in the developing fly embryo while systematically varying the genomic separation between these two DNA loci. Our analysis reveals a combination of a compact globular organization and fast subdiffusive dynamics. These combined features cause an anomalous scaling of polymer relaxation times with genomic separation and lead to long-ranged correlations compared to existing polymer models. This scaling implies that encounter times of DNA loci are much less dependent on genomic separation than predicted by existing polymer models, with potentially significant consequences for eukaryotic gene expression.

Hypothesis-driven probabilistic modelling enables a principled perspective of genomic compartments

The Hi-C method has revolutionized the study of genome organization, yet interpretation of Hi-C interaction frequency maps remains a major challenge. Genomic compartments are a checkered Hi-C interaction pattern suggested to represent the partitioning of the genome into two self-interacting states associated with active and inactive chromatin. Based on a few elementary mechanistic assumptions, we derive a generative probabilistic model of genomic compartments, called deGeco. Testing our model, we find it can explain observed Hi-C interaction maps in a highly robust manner, allowing accurate inference of interaction probability maps from extremely sparse data without any training of parameters. Taking advantage of the interpretability of the model parameters, we then test hypotheses regarding the nature of genomic compartments. We find clear evidence of multiple states, and that these states self-interact with different affinities. We also find that the interaction rules of chromatin states differ considerably within and between chromosomes. Inspecting the molecular underpinnings of a four-state model, we show that a simple classifier can use histone marks to predict the underlying states with 87% accuracy. Finally, we observe instances of mixed-state loci and analyze these loci in single-cell Hi-C maps, finding that mixing of states occurs mainly at the cell level.

The spatial organization of transcriptional control

In animals, the sequences for controlling gene expression do not concentrate just at the transcription start site of genes, but are frequently thousands to millions of base pairs distal to it. The interaction of these sequences with one another and their transcription start sites is regulated by factors that shape the three-dimensional (3D) organization of the genome within the nucleus. Over the past decade, indirect tools exploiting high-throughput DNA sequencing have helped to map this 3D organization, have identified multiple key regulators of its structure and, in the process, have substantially reshaped our view of how 3D genome architecture regulates transcription. Now, new tools for high-throughput super-resolution imaging of chromatin have directly visualized the 3D chromatin organization, settling some debates left unresolved by earlier indirect methods, challenging some earlier models of regulatory specificity and creating hypotheses about the role of chromatin structure in transcriptional regulation.

Insights into the cell fate decision-making processes from chromosome structural reorganizations

The cell fate decision-making process, which provides the capability of a cell transition to a new cell type, involves the reorganizations of 3D genome structures. Currently, the high temporal resolution picture of how the chromosome structural rearrangements occur and further influence the gene activities during the cell-state transition is still challenging to acquire. Here, we study the chromosome structural reorganizations during the cell-state transitions among the pluripotent embryonic stem cell, the terminally differentiated normal cell, and the cancer cell using a nonequilibrium landscape-switching model implemented in the molecular dynamics simulation. We quantify the chromosome (de)compaction pathways during the cell-state transitions and find that the two pathways having the same destinations can merge prior to reaching the final states. The chromosomes at the merging states have similar structural geometries but can differ in long-range compartment segregation and spatial distribution of the chromosomal loci and genes, leading to cell-type-specific transition mechanisms. We identify the irreversible pathways of chromosome structural rearrangements during the forward and reverse transitions connecting the same pair of cell states, underscoring the critical roles of nonequilibrium dynamics in the cell-state transitions. Our results contribute to the understanding of the cell fate decision-making processes from the chromosome structural perspective.

Topological gelation of reconnecting polymers

Shuffling of genetic material via reconnection of proximal DNA segments is seen in meiosis and some cancers. In contrast with textbook pictures, reconnections are performed within an entangled environment and can result in knotting or linking, detrimental for cells. By performing Brownian dynamics simulations of reconnecting polymers under confinement, modeling the genome in vivo, we find a topological transition between a gas or liquid of unlinked rings and a gel-like structure with a large number of polydisperse linked rings. This transition can be triggered by increasing polymer stiffness or confinement. Our results suggest ways to design future topological materials, such as DNA-based gels involving recombinase proteins.

DNA recombination is a ubiquitous process that ensures genetic diversity. Contrary to textbook pictures, DNA recombination, as well as generic DNA translocations, occurs in a confined and highly entangled environment. Inspired by this observation, here, we investigate a solution of semiflexible polymer rings undergoing generic cutting and reconnection operations under spherical confinement. Our setup may be realized using engineered DNA in the presence of recombinase proteins or by considering micelle-like components able to form living (or reversibly breakable) polymer rings. We find that in such systems, there is a topological gelation transition, which can be triggered by increasing either the stiffness or the concentration of the rings. Flexible or dilute polymers break into an ensemble of short, unlinked, and segregated rings, whereas sufficiently stiff or dense polymers self-assemble into a network of long, linked, and mixed loops, many of which are knotted. We predict that the two phases should behave qualitatively differently in elution experiments monitoring the escape dynamics from a permeabilized container. Besides shedding some light on the biophysics and topology of genomes undergoing DNA reconnection in vivo, our findings could be leveraged in vitro to design polymeric complex fluids—e.g., DNA-based complex fluids or living polymer networks—with desired topologies.

Nucleus size and its effect on nucleosome stability in living cells

DNA architectural proteins play a major role in organization of chromosomal DNA in living cells by packaging it into chromatin, whose spatial conformation is determined by an intricate interplay between the DNA-binding properties of architectural proteins and physical constraints applied to the DNA by a tight nuclear space. Yet, the exact effects of the nucleus size on DNA-protein interactions and chromatin structure currently remain obscure. Furthermore, there is even no clear understanding of molecular mechanisms responsible for the nucleus size regulation in living cells. To find answers to these questions, we developed a general theoretical framework based on a combination of polymer field theory and transfer-matrix calculations, which showed that the nucleus size is mainly determined by the difference between the surface tensions of the nuclear envelope and the endoplasmic reticulum membrane as well as the osmotic pressure exerted by cytosolic macromolecules on the nucleus. In addition, the model demonstrated that the cell nucleus functions as a piezoelectric element, changing its electrostatic potential in a size-dependent manner. This effect has been found to have a profound impact on stability of nucleosomes, revealing a previously unknown link between the nucleus size and chromatin structure. Overall, our study provides new insights into the molecular mechanisms responsible for regulation of the nucleus size, as well as the potential role of nuclear organization in shaping the cell response to environmental cues.

Dynamical modeling of the H3K27 epigenetic landscape in mouse embryonic stem cells

The Polycomb system via the methylation of the lysine 27 of histone H3 (H3K27) plays central roles in the silencing of many lineage-specific genes during development. Recent experimental evidence suggested that the recruitment of histone modifying enzymes like the Polycomb repressive complex 2 (PRC2) at specific sites and their spreading capacities from these sites are key to the establishment and maintenance of a proper epigenomic landscape around Polycomb-target genes. Here, to test whether such mechanisms, as a minimal set of qualitative rules, are quantitatively compatible with data, we developed a mathematical model that can predict the locus-specific distributions of H3K27 modifications based on previous biochemical knowledge. Within the biological context of mouse embryonic stem cells, our model showed quantitative agreement with experimental profiles of H3K27 acetylation and methylation around Polycomb-target genes in wild-type and mutants. In particular, we demonstrated the key role of the reader-writer module of PRC2 and of the competition between the binding of activating and repressing enzymes in shaping the H3K27 landscape around transcriptional start sites. The predicted dynamics of establishment and maintenance of the repressive trimethylated H3K27 state suggest a slow accumulation, in perfect agreement with experiments. Our approach represents a first step towards a quantitative description of PcG regulation in various cellular contexts and provides a generic framework to better characterize epigenetic regulation in normal or disease situations.