Spatial organization of chromosomes leads to heterogeneous chromatin motion and drives the liquid- or gel-like dynamical behavior of chromatin

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.

Delayed Excitations Induce Polymer Looping and Coherent Motion

We consider inhomogeneous polymers driven by energy-consuming active processes which encode temporal patterns of athermal kicks. We find that such temporal excitation programs, propagated by tension along the polymer, can effectively couple distinct polymer loci. Consequently, distant loci exhibit correlated motions that fold the polymer into specific conformations, as set by the local actions of the active processes and their distribution along the polymer. Interestingly, active kicks that are canceled out by a time-delayed echo can induce strong compaction of the active polymer.

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 2Mb 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.

Chromatin structure and dynamics: one nucleosome at a time

Eukaryotic genomes store information on many levels, including their linear DNA sequence, the posttranslational modifications of its constituents (epigenetic modifications), and its three-dimensional folding. Understanding how this information is stored and read requires multidisciplinary collaborations from many branches of science beyond biology, including physics, chemistry, and computer science. Concurrent recent developments in all these areas have enabled researchers to image the genome with unprecedented spatial and temporal resolution. In this review, we focus on what single-molecule imaging and tracking of individual proteins in live cells have taught us about chromatin structure and dynamics. Starting with the basics of single-molecule tracking (SMT), we describe some advantages over in situ imaging techniques and its current limitations. Next, we focus on single-nucleosome studies and what they have added to our current understanding of the relationship between chromatin dynamics and transcription. In celebration of Robert Feulgen's ground-breaking discovery that allowed us to start seeing the genome, we discuss current models of chromatin structure and future challenges ahead.

Transcription regulates the spatio-temporal dynamics of genes through micro-compartmentalization

Although our understanding of the involvement of heterochromatin architectural factors in shaping nuclear organization is improving, there is still ongoing debate regarding the role of active genes in this process. In this study, we utilize publicly-available Micro-C data from mouse embryonic stem cells to investigate the relationship between gene transcription and 3D gene folding. Our analysis uncovers a nonmonotonic - globally positive - correlation between intragenic contact density and Pol II occupancy, independent of cohesin-based loop extrusion. Through the development of a biophysical model integrating the role of transcription dynamics within a polymer model of chromosome organization, we demonstrate that Pol II-mediated attractive interactions with limited valency between transcribed regions yield quantitative predictions consistent with chromosome-conformation-capture and live-imaging experiments. Our work provides compelling evidence that transcriptional activity shapes the 4D genome through Pol II-mediated micro-compartmentalization.

Dynamical phase transition in models that couple chromatin folding with histone modifications

Genomic regions can acquire heritable epigenetic states through unique histone modifications, which lead to stable gene expression patterns without altering the underlying DNA sequence. However, the relationship between chromatin conformational dynamics and epigenetic stability is poorly understood. In this paper, we propose kinetic models to investigate the dynamic fluctuations of histone modifications and the spatial interactions between nucleosomes. Our model explicitly incorporates the influence of chemical modifications on the structural stability of chromatin and the contribution of chromatin contacts to the cooperative nature of chemical reactions. Through stochastic simulations and analytical theory, we have discovered distinct steady-state outcomes in different kinetic regimes, resembling a dynamical phase transition. Importantly, we have validated that the emergence of this transition, which occurs on biologically relevant timescales, is robust against variations in model design and parameters. Our findings suggest that the viscoelastic properties of chromatin and the timescale at which it transitions from a gel-like to a liquidlike state significantly impact dynamic processes that occur along the one-dimensional DNA sequence.

Nucleosome spacing controls chromatin spatial structure and accessibility

Recent research highlights the significance of the three-dimensional structure of chromatin in regulating various cellular processes, particularly transcription. This is achieved through dynamic chromatin structures that facilitate long-range contacts and control spatial accessibility. Chromatin consists of DNA and a variety of proteins, of which histones play an essential structural role by forming nucleosomes. Extensive experimental and theoretical research in recent decades has yielded conflicting results about key factors that regulate the spatial structure of chromatin, which remains enigmatic. By using a computer model that allows us to simulate chromatin volumes containing physiological nucleosome concentrations, we investigated whether nucleosome spacing or nucleosome density is fundamental for three-dimensional chromatin accessibility. Unexpectedly, the regularity of the nucleosome spacing is crucial for determining the accessibility of the chromatin network to diffusive processes, whereas variation in nucleosome concentrations has only minor effects. Using only the basic physical properties of DNA and nucleosomes was sufficient to generate chromatin structures consistent with published electron microscopy data. Contrary to other work, we found that nucleosome density did not substantially alter the properties of chromatin fibers or contact probabilities of genomic loci. No breakup of fiber-like structures was observed at high molar density. These findings challenge previous assumptions and highlight the importance of nucleosome spacing as a key driver of chromatin organization. These results identified changes in nucleosome spacing as a tentative mechanism for altering the spatial chromatin structure and thus genomic functions.

Effect of loops on the mean-square displacement of Rouse-model chromatin

Chromatin polymer dynamics are commonly described using the classical Rouse model. The subsequent discovery, however, of intermediate-scale chromatin organization known as topologically associating domains (TADs) in experimental Hi-C contact maps for chromosomes across the tree of life, together with the success of loop extrusion factor (LEF) model in explaining TAD formation, motivates efforts to understand the effect of loops and loop extrusion on chromatin dynamics. This paper seeks to fulfill this need by combining LEF-model simulations with extended Rouse-model polymer simulations to investigate the dynamics of chromatin with loops and dynamic loop extrusion. We show that loops significantly suppress the averaged mean-square displacement (MSD) of a gene locus, consistent with recent experiments that track fluorescently labeled chromatin loci. We also find that loops reduce the MSD's stretching exponent from the classical Rouse-model value of 1/2 to a loop-density-dependent value in the 0.45-0.40 range. Remarkably, stretching exponent values in this range have also been observed in recent experiments [Weber et al., Phys. Rev. Lett. 104, 238102 (2010)0031-900710.1103/PhysRevLett.104.238102; Bailey et al., Mol. Biol. Cell 34, ar78 (2023)1059-152410.1091/mbc.E23-04-0119]. We also show that the dynamics of loop extrusion itself negligibly affects chromatin mobility. By studying static "rosette" loop configurations, we also demonstrate that chromatin MSDs and stretching exponents depend on the location of the locus in question relative to the position of the loops and on the local friction environment.

Chromatin phase separated nanoregions explored by polymer cross-linker models and reconstructed from single particle trajectories

Phase separated domains (PSDs) are ubiquitous in cell biology, representing nanoregions of high molecular concentration. PSDs appear at diverse cellular domains, such as neuronal synapses but also in eukaryotic cell nucleus, limiting the access of transcription factors and thus preventing gene expression. We develop a generalized cross-linker polymer model, to study PSDs: we show that increasing the number of cross-linkers induces a polymer condensation, preventing access of diffusing molecules. To investigate how the PSDs restrict the motion of diffusing molecules, we compute the mean residence and first escaping times. Finally, we develop a method based on mean-square-displacement of single particle trajectories to reconstruct the properties of PSDs from the continuum range of anomalous exponents. We also show here that PSD generated by polymers do not induces a long-range attracting field (potential well), in contrast with nanodomains at neuronal synapses. To conclude, PSDs can result from condensed chromatin organization, where the number of cross-linkers controls molecular access.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Structure and dynamics of chemically active ring polymers: swelling to collapse

The ring structures are common in many synthetic or natural systems and experience both local and long-range forces by chemical sensing. This work is an effort to investigate the structural and dynamical properties of a chemically active ring in an explicit solvent bath utilizing hybrid molecular dynamics (MD) and multiparticle collision dynamics (MPCD) simulation techniques. We show that by tuning the chemical properties of the ring, it can be converted from a chemo-attractant to a chemo-repellent, thereby changing the steady state to be either collapsed or swelled as compared to its passive limit. We quantify these observations by comparing the scaling laws, local structures and the dynamics of active and passive rings. Furthermore, we show the impact of varying numbers of active sites by calculating the contact probability of the collapse state that highlights diverse structures. We also analyze the dynamics of the ring by finding the relaxation time and the mean square displacement of the centre of mass. A faster relaxation with enhanced diffusion is observed for the active rings.

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.

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.

Polymer folding through active processes recreates features of genome organization

From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.

4D epigenomics: deciphering the coupling between genome folding and epigenomic regulation with biophysical modeling

Recent experimental observations suggest a strong coupling between the 3D nuclear chromosome organization and epigenomics. However, the mechanistic and functional bases of such interplay remain elusive. In this review, we describe how biophysical modeling has been instrumental in characterizing how genome folding may impact the formation of epigenomic domains and, conversely, how epigenomic marks may affect chromosome conformation. Finally, we discuss how this mutual feedback loop between chromatin organization and epigenome regulation, via the formation of physicochemical nanoreactors, may represent a key functional role of 3D compartmentalization in the assembly and maintenance of stable - but yet plastic - epigenomic landscapes.

A polymer chain with dipolar active forces in connection to spatial organization of chromatin

A living cell is an active environment where the organization and dynamics of chromatin are affected by different forms of activity. Optical experiments report that loci show subdiffusive dynamics and the chromatin fiber is seen to be coherent over micrometer-scale regions. Using a bead-spring polymer chain with dipolar active forces, we study how the subdiffusive motion of the loci generate large-scale coherent motion of the chromatin. We show that in the presence of extensile (contractile) activity, the dynamics of the loci grows faster (slower) and the spatial correlation length increases (decreases) compared to the case with no dipolar forces. Hence, both the dipolar active forces modify the elasticity of the chain. Interestingly in our model, the dynamics and organization of such dipolar active chains largely differ from the passive chain with renormalized elasticity.

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.

Unveiling the Machinery behind Chromosome Folding by Polymer Physics Modeling

Understanding the mechanisms underlying the complex 3D architecture of mammalian genomes poses, at a more fundamental level, the problem of how two or multiple genomic sites can establish physical contacts in the nucleus of the cells. Beyond stochastic and fleeting encounters related to the polymeric nature of chromatin, experiments have revealed specific, privileged patterns of interactions that suggest the existence of basic organizing principles of folding. In this review, we focus on two major and recently proposed physical processes of chromatin organization: loop-extrusion and polymer phase-separation, both supported by increasing experimental evidence. We discuss their implementation into polymer physics models, which we test against available single-cell super-resolution imaging data, showing that both mechanisms can cooperate to shape chromatin structure at the single-molecule level. Next, by exploiting the comprehension of the underlying molecular mechanisms, we illustrate how such polymer models can be used as powerful tools to make predictions in silico that can complement experiments in understanding genome folding. To this aim, we focus on recent key applications, such as the prediction of chromatin structure rearrangements upon disease-associated mutations and the identification of the putative chromatin organizing factors that orchestrate the specificity of DNA regulatory contacts genome-wide.

Genome modeling: From chromatin fibers to genes

The intricacies of the 3D hierarchical organization of the genome have been approached by many creative modeling studies. The specific model/simulation technique combination defines and restricts the system and phenomena that can be investigated. We present the latest modeling developments and studies of the genome, involving models ranging from nucleosome systems and small polynucleosome arrays to chromatin fibers in the kb-range, chromosomes, and whole genomes, while emphasizing gene folding from first principles. Clever combinations allow the exploration of many interesting phenomena involved in gene regulation, such as nucleosome structure and dynamics, nucleosome-nucleosome stacking, polynucleosome array folding, protein regulation of chromatin architecture, mechanisms of gene folding, loop formation, compartmentalization, and structural transitions at the chromosome and genome levels. Gene-level modeling with full details on nucleosome positions, epigenetic factors, and protein binding, in particular, can in principle be scaled up to model chromosomes and cells to study fundamental biological regulation.

Nucleus-wide analysis of coherent RNA pol II movement in the context of chromatin dynamics in living cancer cells

Activation of transcription results in coordinated movement of chromatin over a range of micrometers. To investigate how transcriptional regulation affects the mobility of RNA Pol II molecules and whether this movement response depends on the coordinated movement of chromatin, we used our Dense Flow reConstruction and Correlation (DFCC) method. Using DFCC, we studies the nucleus-wide coherent movements of RNA Pol II in the context of DNA in humancancer cells. This study showed the dependance of coherent movements of RNA Pol II molecules (above 1 µm) on transcriptional activity. Here, we share the dataset of this study, includes nucleus-wide live imaging and analysis of DNA and RNA polymerase II in different transcription states, and the code for teh analysis. Our dataset may provide researchers interested in the long-range organization of chromatin in living cell images with the ability to link the structural genomic compartment to dynamic information. .

Cohesin and CTCF control the dynamics of chromosome folding

In mammals, interactions between sequences within topologically associating domains enable control of gene expression across large genomic distances. Yet it is unknown how frequently such contacts occur, how long they last and how they depend on the dynamics of chromosome folding and loop extrusion activity of cohesin. By imaging chromosomal locations at high spatial and temporal resolution in living cells, we show that interactions within topologically associating domains are transient and occur frequently during the course of a cell cycle. Interactions become more frequent and longer in the presence of convergent CTCF sites, resulting in suppression of variability in chromosome folding across time. Supported by physical models of chromosome dynamics, our data suggest that CTCF-anchored loops last around 10 min. Our results show that long-range transcriptional regulation might rely on transient physical proximity, and that cohesin and CTCF stabilize highly dynamic chromosome structures, facilitating selected subsets of chromosomal interactions.

Spatially coherent diffusion of human RNA Pol II depends on transcriptional state rather than chromatin motion

Gene transcription by RNA polymerase II (RNAPol II) is a tightly regulated process in the genomic, temporal, and spatial context. Recently, we have shown that chromatin exhibits spatially coherently moving regions over the entire nucleus, which is enhanced by transcription. Yet, it remains unclear how the mobility of RNA Pol II molecules is affected by transcription regulation and whether this response depends on the coordinated chromatin movement. We applied our Dense Flow reConstruction and Correlation method to analyze nucleus-wide coherent movements of RNA Pol II in living human cancer cells. We observe a spatially coherent movement of RNA Pol II molecules over ≈ 1 μm, which depends on transcriptional activity. Inducing transcription in quiescent cells decreased the coherent motion of RNA Pol II. We then quantify the spatial correlation length of RNA Pol II in the context of DNA motion. RNA Pol II and chromatin spatially coherent motions respond oppositely to transcriptional activities. Our study holds the potential of studying the chromatin environment in different nuclear processes.

Painters in chromatin: a unified quantitative framework to systematically characterize epigenome regulation and memory

In eukaryotes, many stable and heritable phenotypes arise from the same DNA sequence, owing to epigenetic regulatory mechanisms relying on the molecular cooperativity of 'reader-writer' enzymes. In this work, we focus on the fundamental, generic mechanisms behind the epigenome memory encoded by post-translational modifications of histone tails. Based on experimental knowledge, we introduce a unified modeling framework, the painter model, describing the mechanistic interplay between sequence-specific recruitment of chromatin regulators, chromatin-state-specific reader-writer processes and long-range spreading mechanisms. A systematic analysis of the model building blocks highlights the crucial impact of tridimensional chromatin organization and state-specific recruitment of enzymes on the stability of epigenomic domains and on gene expression. In particular, we show that enhanced 3D compaction of the genome and enzyme limitation facilitate the formation of ultra-stable, confined chromatin domains. The model also captures how chromatin state dynamics impact the intrinsic transcriptional properties of the region, slower kinetics leading to noisier expression. We finally apply our framework to analyze experimental data, from the propagation of γH2AX around DNA breaks in human cells to the maintenance of heterochromatin in fission yeast, illustrating how the painter model can be used to extract quantitative information on epigenomic molecular processes.

DNA damage reduces heterogeneity and coherence of chromatin motions

Chromatin motions depend on and may regulate genome functions, in particular the DNA damage response. In yeast, DNA double-strand breaks (DSBs) globally increase chromatin diffusion, whereas in higher eukaryotes the impact of DSBs on chromatin dynamics is more nuanced. We mapped the motions of chromatin microdomains in mammalian cells using diffractive optics and photoactivatable chromatin probes and found a high level of spatial heterogeneity. DNA damage reduces heterogeneity and imposes spatially defined shifts in motions: Distal to DNA breaks, chromatin motions are globally reduced, whereas chromatin retains higher mobility at break sites. These effects are driven by context-dependent changes in chromatin compaction. Photoactivated lattices of chromatin microdomains are ideal to quantify microscale coupling of chromatin motion. We measured correlation distances up to 2 µm in the cell nucleus, spanning chromosome territories, and speculate that this correlation distance between chromatin microdomains corresponds to the physical separation of A and B compartments identified in chromosome conformation capture experiments. After DNA damage, chromatin motions become less correlated, a phenomenon driven by phase separation at DSBs. Our data indicate tight spatial control of chromatin motions after genomic insults, which may facilitate repair at the break sites and prevent deleterious contacts of DSBs, thereby reducing the risk of genomic rearrangements.

Chromosome Changes in Soma and Germ Line: Heritability and Evolutionary Outcome

The origin and inheritance of chromosome changes provide the essential foundation for natural selection and evolution. The evolutionary fate of chromosome changes depends on the place and time of their emergence and is controlled by checkpoints in mitosis and meiosis. Estimating whether the altered genome can be passed to subsequent generations should be central when we consider a particular genome rearrangement. Through comparative analysis of chromosome rearrangements in soma and germ line, the potential impact of macromutations such as chromothripsis or chromoplexy appears to be fascinating. What happens with chromosomes during the early development, and which alterations lead to mosaicism are other poorly studied but undoubtedly essential issues. The evolutionary impact can be gained most effectively through chromosome rearrangements arising in male meiosis I and in female meiosis II, which are the last divisions following fertilization. The diversity of genome organization has unique features in distinct animals; the chromosome changes, their internal relations, and some factors safeguarding genome maintenance in generations under natural selection were considered for mammals.