Physical Modeling of Dynamic Coupling between Chromosomal Loci

High-resolution dynamic imaging of chromatin DNA communication using Oligo-LiveFISH

Three-dimensional (3D) genome dynamics are crucial for cellular functions and disease. However, real-time, live-cell DNA visualization remains challenging, as existing methods are often confined to repetitive regions, suffer from low resolution, or require complex genome engineering. Here, we present Oligo-LiveFISH, a high-resolution, reagent-based platform for dynamically tracking non-repetitive genomic loci in diverse cell types, including primary cells. Oligo-LiveFISH utilizes fluorescent guide RNA (gRNA) oligo pools generated by computational design, in vitro transcription, and chemical labeling, delivered as ribonucleoproteins. Utilizing machine learning, we characterized the impact of gRNA design and chromatin features on imaging efficiency. Multi-color Oligo-LiveFISH achieved 20-nm spatial resolution and 50-ms temporal resolution in 3D, capturing real-time enhancer and promoter dynamics. Our measurements and dynamic modeling revealed two distinct modes of chromatin communication, and active transcription slows enhancer-promoter dynamics at endogenous genes like FOS. Oligo-LiveFISH offers a versatile platform for studying 3D genome dynamics and their links to cellular processes and disease.

Organization and Dynamics of Chromosomes

How long thread-like eukaryotic chromosomes fit tidily in the small volume of the nucleus without significant entanglement is just beginning to be understood, thanks to major advances in experimental techniques. Several polymer models, which reproduce contact maps that measure the probabilities that two loci are in spatial contact, have predicted the 3D structures of interphase chromosomes. Data-driven approaches, using contact maps as input, predict that mitotic helical chromosomes are characterized by a switch in handedness, referred to as perversion. By using experimentally derived effective interactions between chromatin loci in simulations, structures of conventional and inverted nuclei have been accurately predicted. Polymer theory and simulations show that the dynamics of individual loci in chromatin exhibit subdiffusive behavior but the diffusion exponents are broadly distributed, which accords well with experiments. Although coarse-grained models are successful, many challenging problems remain, which require the creation of new experimental and computational tools to understand genome biology.

Transcription-dependent mobility of single genes and genome-wide motions in live human cells

The human genome is highly dynamic across all scales. At the gene level, chromatin is persistently remodeled and rearranged during active processes such as transcription, replication and DNA repair. At the genome level, chromatin moves in micron-scale domains that break up and re-form over seconds, but the origin of these coherent motions is unknown. Here, we investigate the connection between genomic motions and gene-level activity. Simultaneous mapping of single-gene and genome-wide motions shows that the coupling of gene transcriptional activity to flows of the nearby genome is modulated by chromatin compaction. A motion correlation analysis suggests that a single active gene drives larger-scale motions in low-compaction regions, but high-compaction chromatin drives gene motion regardless of its activity state. By revealing unexpected connections among gene activity, spatial heterogeneities of chromatin and its emergent genome-wide motions, these findings uncover aspects of the genome's spatiotemporal organization that directly impact gene regulation and expression.

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.

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.

Leveraging polymer modeling to reconstruct chromatin connectivity from live images

Chromosomal dynamics plays a central role in a number of critical biological processes, such as transcriptional regulation, genetic recombination, and DNA replication. However, visualization of chromatin is generally limited to live imaging of a few fluorescently labeled chromosomal loci or high-resolution reconstruction of multiple loci from a single time frame. To aid in mapping the underlying chromosomal structure based on parsimonious experimental measurements, we present an exact analytical expression for the evolution of the polymer configuration based on a flexible-polymer model, and we propose an algorithm that tracks the polymer configuration from live images of chromatin marked with several fluorescent marks. Our theory identifies the resolution of microscopy needed to achieve high-accuracy tracking for a given spacing of markers, establishing the statistical confidence in the assignment of genome identity to the visualized marks. We then leverage experimental data of locus-tracking measurements to demonstrate the validity of our modeling approach and to establish a basis for the design of experiments with a desired resolution. Altogether, this work provides a computational approach founded on polymer physics that vastly improves the interpretation of in vivo measurements of biopolymer dynamics.

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.

First-passage time analysis of diffusion-controlled reactions in single-molecule detection

Single-molecule detection (SMD) aims to achieve the ultimate limit-of-detection (LOD) in biosensing. This method detects a countable number of targeted analyte molecules in solution, where the dynamics of molecule diffusion, capturing, identification and delivery greatly impact the SMD's efficiency and accuracy. In this study, we adopt the first-passage time method to investigate the diffusion-controlled reaction process in SMD. We analyze the influence of detection conditions on incubation time and the expected coefficient of variation (CV) under three SMD molecule capturing strategies, including solid-phase capturing (one-dimensional solid-liquid interface fixation), liquid-phase magnetic bead (MB) capturing, and liquid-phase direct fluorescence pair labeling. We find that inside a finite-sized reaction chamber, a finite average reaction time exists in all three capturing strategies, while the liquid-phase strategies are in general more efficient than the solid-phase approaches. CV can be estimated by averaging first-passage time solely in all three strategies, and the CV reduction is achievable given an extended reaction time. To further enable zeptomolar detection, extra treatments, such as adopting liquid-phase fluorescence pairs with high diffusion rates to label the molecule, or designing specific sensing devices with large effective sensing areas would be required. This framework provides solid theoretical support to guide the design of SMD sensing strategies and sensor structures to achieve desired measurement time and CV.

Single-chromosome dynamics reveals locus-dependent dynamics and chromosome territory orientation

Dynamic chromatin organization instantly influences DNA accessibility through modulating local macromolecular density and interactions, driving changes in transcription activities. Chromatin dynamics have been reported to be locally confined but contribute to coherent chromatin motion across the entire nucleus. However, the regulation of dynamics, nuclear orientation and compaction of subregions along a single chromosome are not well-understood. We used CRISPR-based real-time single-particle tracking and polymer models to characterize the dynamics of specific genomic loci and determine compaction levels of large human chromosomal domains. Our studies showed that chromosome compaction changed during interphase and that compactions of two arms on chromosome 19 were different. The dynamics of genomic loci were subdiffusive and dependent on chromosome regions and transcription states. Surprisingly, the correlation between locus-dependent nuclear localization and mobility was negligible. Strong tethering interactions detected at the pericentromeric region implies local condensation or associations with organelles within local nuclear microenvironments, such as chromatin-nuclear body association. Based on our findings, we propose a 'guided radial model' for the nuclear orientation of the long arm of chromosome 19.

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.

Active and thermal fluctuations in multi-scale polymer structure and dynamics

The presence of athermal noise or biological fluctuations control and maintain crucial life-processes. In this work, we present an exact analytical treatment of the dynamic behavior of a flexible polymer chain that is subjected to both thermal and active forces. Our model for active forces incorporates temporal correlation associated with the characteristic time scale and processivity of enzymatic function (driven by ATP hydrolysis), leading to an active-force time scale that competes with relaxation processes within the polymer chain. We analyze the structure and dynamics of an active-Brownian polymer using our exact results for the dynamic structure factor and the looping time for the chain ends. The spectrum of relaxation times within a polymer chain implies two different behaviors at small and large length scales. Small length-scale relaxation is faster than the active-force time scale, and the dynamic and structural behavior at these scales are oblivious to active forces and, are thus governed by the true thermal temperature. Large length-scale behavior is governed by relaxation times that are much longer than the active-force time scale, resulting in an effective active-Brownian temperature that dramatically alters structural and dynamic behavior. These complex multi-scale effects imply a time-dependent temperature that governs living and non-equilibrium systems, serving as a unifying concept for interpreting and predicting their physical behavior.

Hi-C embedded polymer model of Escherichia coli reveals the origin of heterogeneous subdiffusion in chromosomal loci

Underneath its apparently simple architecture, the circular chromosome of Escherichia coli is known for displaying complex dynamics in its cytoplasm, with past investigations hinting at inherently diverse mobilities of chromosomal loci across the genome. To decipher its origin, we simulate the dynamics of genome-wide spectrum of E. coli chromosomal loci, via integrating its experimentally derived Hi-C interaction matrix within a polymer-based model. Our analysis demonstrates that, while the dynamics of the chromosome is subdiffusive in a viscoelastic media, the diffusion constants are strongly dependent of chromosomal loci coordinates and diffusive exponents (α) are widely heterogenous with α ≈ 0.36-0.60. The loci-dependent heterogeneous dynamics and mean first-passage times of interloci encounter were found to be modulated via genetically distant interloci communications and is robust even in the presence of active, ATP-dependent noises. Control investigations reveal that the absence of Hi-C-derived interactions in the model would have abolished the traits of heterogeneous loci diffusion, underscoring the key role of loci-specific genetically distant interaction in modulating the underlying heterogeneity of the loci diffusion.

Diffusion and distal linkages govern interchromosomal dynamics during meiotic prophase

SignificanceEssential for sexual reproduction, meiosis is a specialized cell division required for the production of haploid gametes. Critical to this process are the pairing, recombination, and segregation of homologous chromosomes (homologs). While pairing and recombination are linked, it is not known how many linkages are sufficient to hold homologs in proximity. Here, we reveal that random diffusion and the placement of a small number of linkages are sufficient to establish the apparent "pairing" of homologs. We also show that colocalization between any two loci is more dynamic than anticipated. Our study provides observations of live interchromosomal dynamics during meiosis and illustrates the power of combining single-cell measurements with theoretical polymer modeling.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells' migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

Mechanical stress affects dynamics and rheology of the human genome

Material properties of the genome are critical for proper cellular function - they directly affect timescales and length scales of DNA transactions such as transcription, replication and DNA repair, which in turn impact all cellular processes via the central dogma of molecular biology. Hence, elucidating the genome's rheology in vivo may help reveal physical principles underlying the genome's organization and function. Here, we present a novel noninvasive approach to study the genome's rheology and its response to mechanical stress in form of nuclear injection in live human cells. Specifically, we use Displacement Correlation Spectroscopy to map nucleus-wide genomic motions pre/post injection, during which we deposit rheological probes inside the cell nucleus. While the genomic motions inform on the bulk rheology of the genome pre/post injection, the probe's motion informs on the local rheology of its surroundings. Our results reveal that mechanical stress of injection leads to local as well as nucleus-wide changes in the genome's compaction, dynamics and rheology. We find that the genome pre-injection exhibits subdiffusive motions, which are coherent over several micrometers. In contrast, genomic motions post-injection become faster and uncorrelated, moreover, the genome becomes less compact and more viscous across the entire nucleus. In addition, we use the injected particles as rheological probes and find the genome to condense locally around them, mounting a local elastic response. Taken together, our results show that mechanical stress alters both dynamics and material properties of the genome. These changes are consistent with those observed upon DNA damage, suggesting that the genome experiences similar effects during the injection process.

Electrostatically Driven Topological Freezing of Polymer Diffusion at Intermediate Confinements

Breaking the paradigm that polymers in crowded aqueous media obey Einstein's law of diffusion, we report a localized nondiffusive hierarchical metastable state at intermediate confinements. Combining electrostatic and topological effects, we can tune the propensity of this new universality class in a quasicoacervate gel system consisting of guest polyamino acid chains inside an oppositely charged host hydrogel. Our observations offer strategies for controlled release and retention of macromolecules in aqueous crowded media, while opening a new direction for understanding topologically frustrated dynamics in polymers and other soft matter systems.

Tracking and interpreting long-range chromatin interactions with super-resolution live-cell imaging

Mammalian genomes are organized and regulated through long-range chromatin interactions. Structural loops formed by CCCTC-binding factor (CTCF) and cohesin fold the genome into domains, while enhancers interact with promoters across vast genomic distances to regulate gene expression. Although genomics and fixed-cell imaging approaches help illuminate many aspects of chromatin interactions, temporal information is usually lost. Here, we discuss how 3D super-resolution live-cell imaging (SRLCI) can resolve open questions on the dynamic formation and dissolution of chromatin interactions. We discuss SRLCI experimental design, implementation strategies, and data interpretation and highlight associated pitfalls. We conclude that, while technically demanding, SRLCI approaches will likely emerge as a critical tool to dynamically probe 3D genome structure and function and to study enhancer–promoter interactions and chromatin looping.

Understanding and Engineering Chromatin as a Dynamical System across Length and Timescales

Connecting the molecular structure and function of chromatin across length and timescales remains a grand challenge to understanding and engineering cellular behaviors. Across five orders of magnitude, dynamic processes constantly reshape chromatin structures, driving spaciotemporal patterns of gene expression and cell fate. Through the interplay of structure and function, the genome operates as a highly dynamic feedback control system. Recent experimental techniques have provided increasingly detailed data that revise and augment the relatively static, hierarchical view of genomic architecture with an understanding of how dynamic processes drive organization. Here, we review how novel technologies from sequencing, imaging, and synthetic biology refine our understanding of chromatin structure and function and enable chromatin engineering. Finally, we discuss opportunities to use these tools to enhance understanding of the dynamic interrelationship of chromatin structure and function.

Cytosolic Crowding Drives the Dynamics of Both Genome and Cytosol in Escherichia coli Challenged with Sub-lethal Antibiotic Treatments

In contrast to their molecular mode of action, the system-level effect of antibiotics on cells is only beginning to be quantified. Molecular crowding is expected to be a relevant global regulator, which we explore here through the dynamic response phenotypes in Escherichia coli, at single-cell resolution, under sub-lethal regimes of different classes of clinically relevant antibiotics, acting at very different levels in the cell. We measure chromosomal mobility through tracking of fast (<15 s timescale) fluctuations of fluorescently tagged chromosomal loci, and we probe the fluidity of the cytoplasm by tracking cytosolic aggregates. Measuring cellular density, we show how the overall levels of macromolecular crowding affect both quantities, regardless of antibiotic-specific effects. The dominant trend is a strong correlation between the effects in different parts of the chromosome and between the chromosome and cytosol, supporting the concept of an overall global role of molecular crowding in cellular physiology.

The rich inner life of the cell nucleus: dynamic organization, active flows, and emergent rheology

The cell nucleus stores the genetic material essential for life, and provides the environment for transcription, maintenance, and replication of the genome. Moreover, the nucleoplasm is filled with subnuclear bodies such as nucleoli that are responsible for other vital functions. Overall, the nucleus presents a highly heterogeneous and dynamic environment with diverse functionality. Here, we propose that its biophysical complexity can be organized around three inter-related and interactive facets: heterogeneity, activity, and rheology. Most nuclear constituents are sites of active, ATP-dependent processes and are thus inherently dynamic: The genome undergoes constant rearrangement, the nuclear envelope flickers and fluctuates, nucleoli migrate and coalesce, and many of these events are mediated by nucleoplasmic flows and interactions. And yet there is spatiotemporal organization in terms of hierarchical structure of the genome, its coherently moving regions and membrane-less compartmentalization via phase-separated nucleoplasmic constituents. Moreover, the non-equilibrium or activity-driven nature of the nucleus gives rise to emergent rheology and material properties that impact all cellular processes via the central dogma of molecular biology. New biophysical insights into the cell nucleus can come from appreciating this rich inner life.

The self-stirred genome: large-scale chromatin dynamics, its biophysical origins and implications

The organization and dynamics of human genome govern all cellular processes - directly impacting the central dogma of biology - yet are poorly understood, especially at large length scales. Chromatin, the functional form of DNA in cells, undergoes frequent local remodeling and rearrangements to accommodate processes such as transcription, replication and DNA repair. How these local activities contribute to nucleus-wide coherent chromatin motion, where micron-scale regions of chromatin move together over several seconds, remains unclear. Activity of nuclear enzymes was found to drive the coherent chromatin dynamics, however, its biological nature and physical mechanism remain to be revealed. The coherent dynamics leads to a perpetual stirring of the genome, leading to collective gene dynamics over microns and seconds, thus likely contributing to local and global gene-expression patterns. Hence, a possible biological role of chromatin coherence may involve gene regulation.

Chromatin Viscoelasticity Measured by Local Dynamic Analysis

The nucleus in eukaryotic cells is a crowded environment that consists of genetic code along the DNA, together with a condensed solution of proteins, RNA, and other molecules. It is subjected to highly dynamic processes, including cell division, transcription, and DNA repair. In addition, the genome in the nucleus is subjected to external forces applied by the cytoplasmic skeleton and neighboring cells, as well as to internal nuclear forces. These forces oppose the need to maintain the genome order, which may be compensated by the internal nuclear viscoelastic properties that can restrain these forces. The structural and mechanical properties of chromatin inside the nucleus are still not fully clear; however, their importance for the proper functioning of the cells is unquestionable. Different approaches have been developed for this aim, ranging from directly measuring the dynamic and elastic properties of chromatin to studying the interactions of chromatin with the surrounding envelope and nuclear bodies. Although the elasticity of naked DNA in vitro is well characterized, the elasticity of chromatin in live cells is more complex and is still not fully understood. Here, we studied the elastic properties of chromatin by dynamic measurements in live cells, followed by viscoelastic modeling. We measured the trajectories of single chromatin loci, centromeres, and telomeres in live cells and analyzed their dynamics using the Langevin formalism. We assumed that the overall effect of the chromatin network forces can be modeled for each locus by a local harmonic potential and calculated the effective force constant. In addition, we assumed that this harmonic force results from the chromatin network formed by the internal polymer structure together with cross-links formed by the protein complex. We show that lamin A has the greatest effect on chromatin viscoelasticity and that its removal leads to a significant reduction in the local harmonic force.

Gene expression in E. coli influences the position and motion of the lac operon and vicinal loci

Transcription and translation of active genes play an important role in determining the global organization of the chromosome. To further elucidate this phenomenon, we examined how the expression of either the lacY or the cfp gene in the native lac operon influences adjacent chromosomal segments by fluorescently labeling loci upstream and downstream of the expressed gene. Based on the positions and motile behaviors of these loci, our results reveal that the local organization of the vicinal chromosomal segments and its position in the nucleoid are both influenced by gene expression. Furthermore, we found that the effects on local organization depend on whether the expressed gene encodes a membrane protein or a cytoplasmic protein. Our measurements showing the movement of loci toward the membrane and the correlation between the motions of the upstream and downstream loci support the conclusion that the expression of genes encoding membrane proteins greatly influences chromosome dynamics.

Advances Using Single-Particle Trajectories to Reconstruct Chromatin Organization and Dynamics

Chromatin organization remains complex and far from understood. In this article, we review recent statistical methods of extracting biophysical parameters from in vivo single-particle trajectories of loci to reconstruct chromatin reorganization in response to cellular stress such as DNA damage. We look at methods for analyzing both single locus and multiple loci tracked simultaneously and explain how to quantify and describe chromatin motion using a combination of extractable parameters. These parameters can be converted into information about chromatin dynamics and function. Furthermore, we discuss how the timescale of recurrent encounter between loci can be extracted and interpreted. We also discuss the effect of sampling rate on the estimated parameters. Finally, we review a polymer method to reconstruct chromatin structure using crosslinkers between chromatin sites. We list and refer to some software packages that are now publicly available to simulate polymer motion. To conclude, chromatin organization and dynamics can be reconstructed from locus trajectories and predicted based on polymer models.

Active dynamics and spatially coherent motion in chromosomes subject to enzymatic force dipoles

Inspired by recent experiments on chromosomal dynamics, we introduce an exactly solvable model for the interaction between a flexible polymer and a set of motorlike enzymes. The enzymes can bind and unbind to specific sites of the polymer and produce a dipolar force on two neighboring monomers when bound. We study the resulting nonequilibrium dynamics of the polymer and find that the motion of the monomers has several properties that were observed experimentally for chromosomal loci: a subdiffusive mean-square displacement and the appearance of regions of correlated motion. We also determine the velocity autocorrelation of the monomers and find that the underlying stochastic process is not fractional Brownian motion. Finally, we show that the active forces swell the polymer by an amount that becomes constant for large polymers.

Chain organization of human interphase chromosome determines the spatiotemporal dynamics of chromatin loci

We investigate spatiotemporal dynamics of human interphase chromosomes by employing a heteropolymer model that incorporates the information of human chromosomes inferred from Hi-C data. Despite considerable heterogeneities in the chromosome structures generated from our model, chromatins are organized into crumpled globules with space-filling (SF) statistics characterized by a single universal scaling exponent (ν = 1/3), and this exponent alone can offer a quantitative account of experimentally observed, many different features of chromosome dynamics. The local chromosome structures, whose scale corresponds to that of topologically associated domains (∼ 0.1 − 1 Mb), display dynamics with a fast relaxation time (≲ 1 − 10 sec); in contrast, the long-range spatial reorganization of the entire chromatin (≳O(102) Mb) occurs on a much slower time scale (≳ hour), providing the dynamic basis of cell-to-cell variability and glass-like behavior of chromosomes. Biological activities, modeled using stronger isotropic white noises added to active loci, accelerate the relaxation dynamics of chromatin domains associated with the low frequency modes and induce phase segregation between the active and inactive loci. Surprisingly, however, they do not significantly change the dynamics at local scales from those obtained under passive conditions. Our study underscores the role of chain organization of chromosome in determining the spatiotemporal dynamics of chromatin loci.

Chromosomes are giant chain molecules made of hundreds of megabase-long DNA intercalated with proteins. Structure and dynamics of interphase chromatin in space and time hold the key to understanding the cell type-dependent gene regulation. In this study, we establish that the crumpled and space-filling (SF) organization of chromatin fiber in the chromosome territory, characterized by a single scaling exponent, is sufficient to explain the complex spatiotemporal hierarchy in chromatin dynamics as well as the subdiffusive motion of the chromatin loci. While seemingly a daunting problem at a first glance, our study shows that relatively simple principles, rooted in polymer physics, can be used to grasp the essence of dynamical properties of the interphase chromatin.

Effective Hamiltonian of topologically stabilized polymer states

Topologically stabilized polymer conformations in melts of nonconcatenated polymer rings and crumpled globules are considered to be a good candidate for the description of the spatial structure of mitotic chromosomes. Despite significant efforts, the microscopic Hamiltonian capable of describing such systems still remains unknown. We describe a polymer conformation by a Gaussian network - a system with a Hamiltonian quadratic in all coordinates - and show that by tuning interaction constants, one can obtain equilibrium conformations with any fractal dimension between 2 (an ideal polymer chain) and 3 (a crumpled globule). Monomer-to-monomer distances in topologically stabilized states, according to available numerical data, fit very well the Gaussian distribution, giving an additional argument in support of the quadratic Hamiltonian model. Mathematically, the polymer conformations are mapped onto the trajectories of a subdiffusive fractal Brownian particle. Moreover, we explicitly show that the quadratic Hamiltonian with a hierarchical set of coupling constants provides the microscopic background for the description of the path integral of the fractional Brownian motion with an algebraically decaying kernel.

Anomalous diffusion, spatial coherence, and viscoelasticity from the energy landscape of human chromosomes

The nucleus of a eukaryotic cell is a nonequilibrium system where chromatin is subjected to active processes that continuously rearrange it over the cell's life cycle. Tracking the motion of chromosomal loci provides information about the organization of the genome and the physical processes shaping that organization. Optical experiments report that loci move with subdiffusive dynamics and that there is spatially coherent motion of the chromatin. We recently showed that it is possible to predict the 3D architecture of genomes through a physical model for chromosomes that accounts for the biochemical interactions mediated by proteins and regulated by epigenetic markers through a transferable energy landscape. Here, we study the temporal dynamics generated by this quasi-equilibrium energy landscape assuming Langevin dynamics at an effective temperature. Using molecular dynamics simulations of two interacting human chromosomes, we show that the very same interactions that account for genome architecture naturally reproduce the spatial coherence, viscoelasticity, and the subdiffusive behavior of the motion in interphase chromosomes as observed in numerous experiments. The agreement between theory and experiments suggests that even if active processes are involved, an effective quasi-equilibrium landscape model can largely mimic their dynamical effects.

Model of chromosomal loci dynamics in bacteria as fractional diffusion with intermittent transport

The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous work has shown that such rapid motions are ubiquitous, we still have little grasp on their physical nature, and no positive model is available that describes them. Here, we propose a minimal theoretical model for loci movements as a fractional Brownian motion subject to a constant but intermittent driving force, and compare simulations and analytical calculations to data from high-resolution dynamic tracking in E. coli. This analysis yields the characteristic time scales for intermittency. Finally, we discuss the possible shortcomings of this model, and show that an increase in the effective local noise felt by the chromosome associates to the active relocations.

Two loci single particle trajectories analysis: constructing a first passage time statistics of local chromatin exploration

Stochastic single particle trajectories are used to explore the local chromatin organization. We present here a statistical analysis of the first contact time distributions between two tagged loci recorded experimentally. First, we extract the association and dissociation times from data for various genomic distances between loci, and we show that the looping time occurs in confined nanometer regions. Second, we characterize the looping time distribution for two loci in the presence of multiple DNA damages. Finally, we construct a polymer model, that accounts for the local chromatin organization before and after a double-stranded DNA break (DSB), to estimate the level of chromatin decompaction. This novel passage time statistics method allows extracting transient dynamic at scales varying from one to few hundreds of nanometers, it predicts the local changes in the number of binding molecules following DSB and can be used to characterize the local dynamic of the chromatin.