Rouse model with transient intramolecular contacts on a timescale of seconds recapitulates folding and fluctuation of yeast chromosomes

Activity-driven chromatin organization during interphase: Compaction, segregation, and entanglement suppression

In mammalian cells, the cohesin protein complex is believed to translocate along chromatin during interphase to form dynamic loops through a process called active loop extrusion. Chromosome conformation capture and imaging experiments have suggested that chromatin adopts a compact structure with limited interpenetration between chromosomes and between chromosomal sections. We developed a theory demonstrating that active loop extrusion causes the apparent fractal dimension of chromatin to cross-over between two and four at contour lengths on the order of 30 kilo-base pairs. The anomalously high fractal dimension [Formula: see text] is due to the inability of extruded loops to fully relax during active extrusion. Compaction on longer contour length scales extends within topologically associated domains (TADs), facilitating gene regulation by distal elements. Extrusion-induced compaction segregates TADs such that overlaps between TADs are reduced to less than 35% and increases the entanglement strand of chromatin by up to a factor of 50 to several Mega-base pairs. Furthermore, active loop extrusion couples cohesin motion to chromatin conformations formed by previously extruding cohesins and causes the mean square displacement of chromatin loci during lag times ([Formula: see text]) longer than tens of minutes to be proportional to [Formula: see text]. We validate our results with hybrid molecular dynamics-Monte Carlo simulations and show that our theory is consistent with experimental data. This work provides a theoretical basis for the compact organization of interphase chromatin, explaining the physical reason for TAD segregation and suppression of chromatin entanglements which contribute to efficient gene regulation.

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.

Activity-driven chromatin organization during interphase: compaction, segregation, and entanglement suppression

In mammalian cells, the cohesin protein complex is believed to translocate along chromatin during interphase to form dynamic loops through a process called active loop extrusion. Chromosome conformation capture and imaging experiments have suggested that chromatin adopts a compact structure with limited interpenetration between chromosomes and between chromosomal sections. We developed a theory demonstrating that active loop extrusion causes the apparent fractal dimension of chromatin to cross over between two and four at contour lengths on the order of 30 kilo-base pairs (kbp). The anomalously high fractal dimension D = 4 is due to the inability of extruded loops to fully relax during active extrusion. Compaction on longer contour length scales extends within topologically associated domains (TADs), facilitating gene regulation by distal elements. Extrusion-induced compaction segregates TADs such that overlaps between TADs are reduced to less than 35% and increases the entanglement strand of chromatin by up to a factor of 50 to several Mega-base pairs. Furthermore, active loop extrusion couples cohesin motion to chromatin conformations formed by previously extruding cohesins and causes the mean square displacement of chromatin loci during lag times ( Δ t ) longer than tens of minutes to be proportional to Δ t 1 / 3 . We validate our results with hybrid molecular dynamics - Monte Carlo simulations and show that our theory is consistent with experimental data. This work provides a theoretical basis for the compact organization of interphase chromatin, explaining the physical reason for TAD segregation and suppression of chromatin entanglements which contribute to efficient gene regulation.

The power of weak, transient interactions across biology: A paradigm of emergent behavior

A growing list of diverse biological systems and their equally diverse functionalities provides realizations of a paradigm of emergent behavior. In each of these biological systems, pervasive ensembles of weak, short-lived, spatially local interactions act autonomously to convey functionalities at larger spatial and temporal scales. In this article, a range of diverse systems and functionalities are presented in a cursory manner with literature citations for further details. Then two systems and their properties are discussed in more detail: yeast chromosome biology and human respiratory mucus.

Multi-Scale Imaging of the Dynamic Organization of Chromatin

Chromatin is now regarded as a heterogeneous and dynamic structure occupying a non-random position within the cell nucleus, where it plays a key role in regulating various functions of the genome. This current view of chromatin has emerged thanks to high spatiotemporal resolution imaging, among other new technologies developed in the last decade. In addition to challenging early assumptions of chromatin being regular and static, high spatiotemporal resolution imaging made it possible to visualize and characterize different chromatin structures such as clutches, domains and compartments. More specifically, super-resolution microscopy facilitates the study of different cellular processes at a nucleosome scale, providing a multi-scale view of chromatin behavior within the nucleus in different environments. In this review, we describe recent imaging techniques to study the dynamic organization of chromatin at high spatiotemporal resolution. We also discuss recent findings, elucidated by these techniques, on the chromatin landscape during different cellular processes, with an emphasis on the DNA damage response.

Elasticity control of entangled chromosomes: Crosstalk between condensin complexes and nucleosomes

Condensin-mediated loop extrusion is now considered as the main driving force of mitotic chromosome assembly. Recent experiments have shown, however, that a class of mutant condensin complexes deficient in loop extrusion can assemble chromosome-like structures in Xenopus egg extracts, although these structures are somewhat different from those assembled by wild-type condensin complexes. In the absence of topoisomerase II (topo II), the mutant condensin complexes produce an unusual round-shaped structure termed a bean, which consists of a DNA-dense central core surrounded by a DNA-sparse halo. The mutant condensin complexes accumulate in the core, whereas histones are more concentrated in the halo than in the core. We consider that this peculiar structure serves as a model system to study how DNA entanglements, nucleosomes, and condensin functionally crosstalk with each other. To gain insight into how the bean structure is formed, here we construct a theoretical model. Our theory predicts that the core is formed by attractive interactions between mutant condensin complexes, whereas the halo is stabilized by the energy reduction through the selective accumulation of nucleosomes. The formation of the halo increases the elastic free energy due to the DNA entanglement in the core, but the latter free energy is compensated by condensin complexes that suppress the assembly of nucleosomes.

HP1-driven phase separation recapitulates the thermodynamics and kinetics of heterochromatin condensate formation

The spatial segregation of pericentromeric heterochromatin (PCH) into distinct, membrane-less nuclear compartments involves the binding of Heterochromatin Protein 1 (HP1) to H3K9me2/3-rich genomic regions. While HP1 exhibits liquid-liquid phase separation properties in vitro, its mechanistic impact on the structure and dynamics of PCH condensate formation in vivo remains largely unresolved. Here, using a minimal theoretical framework, we systematically investigate the mutual coupling between self-interacting HP1-like molecules and the chromatin polymer. We reveal that the specific affinity of HP1 for H3K9me2/3 loci facilitates coacervation in nucleo and promotes the formation of stable PCH condensates at HP1 levels far below the concentration required to observe phase separation in purified protein assays in vitro. These heterotypic HP1-chromatin interactions give rise to a strong dependence of the nucleoplasmic HP1 density on HP1-H3K9me2/3 stoichiometry, consistent with the thermodynamics of multicomponent phase separation. The dynamical cross talk between HP1 and the viscoelastic chromatin scaffold also leads to anomalously slow equilibration kinetics, which strongly depend on the genomic distribution of H3K9me2/3 domains and result in the coexistence of multiple long-lived, microphase-separated PCH compartments. The morphology of these complex coacervates is further found to be governed by the dynamic establishment of the underlying H3K9me2/3 landscape, which may drive their increasingly abnormal, aspherical shapes during cell development. These findings compare favorably to 4D microscopy measurements of HP1 condensate formation in live Drosophila embryos and suggest a general quantitative model of PCH formation based on the interplay between HP1-based phase separation and chromatin polymer mechanics.

Polymeric nature of tandemly repeated genes enhances assembly of constitutive heterochromatin in fission yeast

Motivated by our recent experiments that demonstrate that the tandemly repeated genes become heterochromatin, here we show a theory of heterochromatin assembly by taking into account the connectivity of these genes along the chromatin in the kinetic equations of small RNA production and histone methylation, which are the key biochemical reactions involved in the heterochromatin assembly. Our theory predicts that the polymeric nature of the tandemly repeated genes ensures the steady production of small RNAs because of the stable binding of nascent RNAs produced from the genes to RDRC/Dicers at the surface of nuclear membrane. This theory also predicts that the compaction of the tandemly repeated genes suppresses the production of small RNAs, consistent with our recent experiments. This theory can be extended to the small RNA-dependent gene silencing in higher organisms.

Chromosome and protein folding: In search for unified principles

Structural biology has traditionally focused on the structures of proteins, short nucleic acids, small molecules, and their complexes. However, it is now widely recognized that the 3D organization of chromosomes should also be included in this list, despite significant differences in scale and complexity of organization. Here we highlight some notable similarities between the folding processes that shape proteins and chromosomes. Both biomolecules are folded by two types of processes: the affinity-mediated interactions, and by active (ATP-dependent) processes. Both chromosome and proteins in vivo can have partially unstructured and non-equilibrium ensembles with yet to be understood functional roles. By analyzing these biological systems in parallel, we can uncover universal principles of biomolecular organization that transcend specific biopolymers.

The Material Properties of the Cell Nucleus: A Matter of Scale

Chromatin regulatory processes physically take place in the environment of the cell nucleus, which is filled with the chromosomes and a plethora of smaller biomolecules. The nucleus contains macromolecular assemblies of different sizes, from nanometer-sized protein complexes to micrometer-sized biomolecular condensates, chromosome territories, and nuclear bodies. This multiscale organization impacts the transport processes within the nuclear interior, the global mechanical properties of the nucleus, and the way the nucleus senses and reacts to mechanical stimuli. Here, we discuss recent work on these aspects, including microrheology and micromanipulation experiments assessing the material properties of the nucleus and its subcomponents. We summarize how the properties of multiscale media depend on the time and length scales probed in the experiment, and we reconcile seemingly contradictory observations made on different scales. We also revisit the concept of liquid-like and solid-like material properties for complex media such as the nucleus. We propose that the nucleus can be considered a multiscale viscoelastic medium composed of three major components with distinct properties: the lamina, the chromatin network, and the nucleoplasmic fluid. This multicomponent organization enables the nucleus to serve its different functions as a reaction medium on the nanoscale and as a mechanosensor and structural scaffold on the microscale.

Theory of chromatin organization maintained by active loop extrusion

The active loop extrusion hypothesis proposes that chromatin threads through the cohesin protein complex into progressively larger loops until reaching specific boundary elements. We build upon this hypothesis and develop an analytical theory for active loop extrusion which predicts that loop formation probability is a nonmonotonic function of loop length and describes chromatin contact probabilities. We validate our model with Monte Carlo and hybrid Molecular Dynamics-Monte Carlo simulations and demonstrate that our theory recapitulates experimental chromatin conformation capture data. Our results support active loop extrusion as a mechanism for chromatin organization and provide an analytical description of chromatin organization that may be used to specifically modify chromatin contact probabilities.

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.

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.

Chromatin dynamics controls epigenetic domain formation

In multicellular organisms, nucleosomes carry epigenetic information that defines distinct patterns of gene expression, which are inherited over multiple generations. The enhanced capacity for information storage arises by nucleosome modifications, which are triggered by enzymes. Modified nucleosomes can transfer the mark to others that are in proximity by a positive-feedback (modification begets modification) mechanism. We created a generic polymer model, referred to as 3DSpreader, in which each bead, representing a nucleosome, stochastically switches between unmodified (U) and modified (M) states depending on the states of the neighbors. Modification begins at a specific nucleation site (NS) that is permanently in the M state, and could spread to other loci that is dictated by chromatin dynamics. Transfer of marks among the non-nucleation loci occurs stochastically as chromatin evolves in time. If the spreading rate is slower than the chromatin relaxation rate, which is biologically pertinent, then finite-sized domains form, driven by contacts between nucleosomes through a three-dimensional looping mechanism. Surprisingly, simulations based on the 3DSpreader model result in finite bounded domains that arise without the need for any boundary elements. Maintenance of spatially and temporally stable domains requires the presence of the NS, whose removal eliminates finite-sized modified domains. The theoretical predictions are in excellent agreement with experimental data for H3K9me3 spreading in mouse embryonic stem cells.

Modeling cell biological features of meiotic chromosome pairing to study interlock resolution

During meiosis, homologous chromosomes become associated side by side in a process known as homologous chromosome pairing. Pairing requires long range chromosome motion through a nucleus that is full of other chromosomes. It remains unclear how the cell manages to align each pair of chromosomes quickly while mitigating and resolving interlocks. Here, we use a coarse-grained molecular dynamics model to investigate how specific features of meiosis, including motor-driven telomere motion, nuclear envelope interactions, and increased nuclear size, affect the rate of pairing and the mitigation/resolution of interlocks. By creating in silico versions of three yeast strains and comparing the results of our model to experimental data, we find that a more distributed placement of pairing sites along the chromosome is necessary to replicate experimental findings. Active motion of the telomeric ends speeds up pairing only if binding sites are spread along the chromosome length. Adding a meiotic bouquet significantly speeds up pairing but does not significantly change the number of interlocks. An increase in nuclear size slows down pairing while greatly reducing the number of interlocks. Interestingly, active forces increase the number of interlocks, which raises the question: How do these interlocks resolve? Our model gives us detailed movies of interlock resolution events which we then analyze to build a step-by-step recipe for interlock resolution. In our model, interlocks must first translocate to the ends, where they are held in a quasi-stable state by a large number of paired sites on one side. To completely resolve an interlock, the telomeres of the involved chromosomes must come in close proximity so that the cooperativity of pairing coupled with random motion causes the telomeres to unwind. Together our results indicate that computational modeling of homolog pairing provides insight into the specific cell biological changes that occur during meiosis.

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.

Anomalous Dynamics in Macromolecular Liquids

Macromolecular liquids display short-time anomalous behaviors in disagreement with conventional single-molecule mean-field theories. In this study, we analyze the behavior of the simplest but most realistic macromolecular system that displays anomalous dynamics, i.e., a melt of short homopolymer chains, starting from molecular dynamics simulation trajectories. Our study sheds some light on the microscopic molecular mechanisms responsible for the observed anomalous behavior. The relevance of the correlation hole, a unique property of polymer liquids, in relation to the observed subdiffusive dynamics, naturally emerges from the analysis of the van Hove distribution functions and other properties.

Mechanisms of DNA Mobilization and Sequestration

The entire genome becomes mobilized following DNA damage. Understanding the mechanisms that act at the genome level requires that we embrace experimental and computational strategies to capture the behavior of the long-chain DNA polymer, which is the building block for the chromosome. Long-chain polymers exhibit constrained, sub-diffusive motion in the nucleus. Cross-linking proteins, including cohesin and condensin, have a disproportionate effect on genome organization in their ability to stabilize transient interactions. Cross-linking proteins can segregate the genome into sub-domains through polymer–polymer phase separation (PPPS) and can drive the formation of gene clusters through small changes in their binding kinetics. Principles from polymer physics provide a means to unravel the mysteries hidden in the chains of life.

Polymer Modeling of 3D Epigenome Folding: Application to Drosophila

Mechanistic modeling in biology allows to investigate, based on first principles, if putative hypotheses are compatible with observations and to drive further experimental works. Along this line, polymer modeling has been instrumental in 3D genomics to better understand the impact of key mechanisms on the spatial genome organization. Here, I describe how polymer-based models can be practically used to study the role of epigenome in chromosome folding. I illustrate this methodology in the context of Drosophila epigenome folding.

Assessing the Polymer Coil-Globule State from the Very First Spectral Modes

The determination of the coil-globule transition of a polymer is generally based on the reconstruction of scaling laws, implying the need for samples from a rather wide range of different polymer lengths N. The spectral point of view developed in this work allows for a very parsimonious description of all the aspects of the finite-size coil-globule transition on the basis of the first two Rouse (cosine) modes only, shedding new light on polymer theory and reintroducing well-established spectral methods that have been surprisingly neglected in this field so far. Capturing the relevant configuration path features, the proposed approach enables one to determine the state of a polymer without the need of any information about the polymer length or interaction strength. Importantly, we propose an experimental implementation of our analysis that can be easily performed with modern fluorescent imaging techniques and would allow differentiation of coil or globule conformations by simply recording the positions of at least three discernible loci on the polymer.

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

Chromosome organization and dynamics are involved in regulating many fundamental processes such as gene transcription and DNA repair. Experiments unveiled that chromatin motion is highly heterogeneous inside cell nuclei, ranging from a liquid-like, mobile state to a gel-like, rigid regime. Using polymer modeling, we investigate how these different physical states and dynamical heterogeneities may emerge from the same structural mechanisms. We found that the formation of topologically associating domains (TADs) is a key driver of chromatin motion heterogeneity. In particular, we showed that the local degree of compaction of the TAD regulates the transition from a weakly compact, fluid state of chromatin to a more compact, gel state exhibiting anomalous diffusion and coherent motion. Our work provides a comprehensive study of chromosome dynamics and a unified view of chromatin motion enabling interpretation of the wide variety of dynamical behaviors observed experimentally across different biological conditions, suggesting that the "liquid" or "solid" state of chromatin are in fact two sides of the same coin.

How important are fluctuations in the treatment of internal friction in polymers?

The Rouse model with internal friction (RIF), a widely used theoretical framework to interpret the effects of internal friction on conformational transitions in biomolecules, is shown to be an approximate treatment that is based on preaveraging internal friction. By comparison with Brownian dynamics simulations of an exact coarse-grained model that incorporates fluctuations in internal friction, the accuracy of the preaveraged model predictions is examined both at and away from equilibrium. While the two models predict intrachain autocorrelations that approach each other for long enough chain segments, they differ in their predictions for shorter segments. Furthermore, the two models differ qualitatively in their predictions for the chain extension and viscosity in shear flow, which is taken to represent a prototypical out-of-equilibrium condition.

Slow chromatin dynamics enhances promoter accessibility to transcriptional condensates

Enhancers are DNA sequences at a long genomic distance from target genes. Recent experiments suggest that enhancers are anchored to the surfaces of condensates of transcription machinery and that the loop extrusion process enhances the transcription level of their target genes. Here, we theoretically study the polymer dynamics driven by the loop extrusion of the linker DNA between an enhancer and the promoter of its target gene to calculate the contact probability of the promoter to the transcription machinery in the condensate. Our theory predicts that when the loop extrusion process is active, the contact probability increases with increasing linker DNA length. This finding reflects the fact that the relaxation time, with which the promoter stays in proximity to the surface of the transcriptional condensate, increases as the length of the linker DNA increases. This contrasts the equilibrium case for which the contact probability between the promoter and the transcription machineries is smaller for longer linker DNA lengths.

Nucleosome-induced homology recognition in chromatin

One of the least understood properties of chromatin is the ability of its similar regions to recognize each other through weak interactions. Theories based on electrostatic interactions between helical macromolecules suggest that the ability to recognize sequence homology is an innate property of the non-ideal helical structure of DNA. However, this theory does not account for the nucleosomal packing of DNA. Can homologous DNA sequences recognize each other while wrapped up in the nucleosomes? Can structural homology arise at the level of nucleosome arrays? Here, we present a theoretical model for the recognition potential well between chromatin fibres sliding against each other. This well is different from the one predicted for bare DNA; the minima in energy do not correspond to literal juxtaposition, but are shifted by approximately half the nucleosome repeat length. The presence of this potential well suggests that nucleosome positioning may induce mutual sequence recognition between chromatin fibres and facilitate the formation of chromatin nanodomains. This has implications for nucleosome arrays enclosed between CTCF-cohesin boundaries, which may form stiffer stem-like structures instead of flexible entropically favourable loops. We also consider switches between chromatin states, e.g. through acetylation/deacetylation of histones, and discuss nucleosome-induced recognition as a precursory stage of genetic recombination.

Random sub-diffusion and capture of genes by the nuclear pore reduces dynamics and coordinates inter-chromosomal movement

Hundreds of genes interact with the yeast nuclear pore complex (NPC), localizing at the nuclear periphery and clustering with co-regulated genes. Dynamic tracking of peripheral genes shows that they cycle on and off the NPC and that interaction with the NPC slows their sub-diffusive movement. Furthermore, NPC-dependent inter-chromosomal clustering leads to coordinated movement of pairs of loci separated by hundreds of nanometers. We developed fractional Brownian motion simulations for chromosomal loci in the nucleoplasm and interacting with NPCs. These simulations predict the rate and nature of random sub-diffusion during repositioning from nucleoplasm to periphery and match measurements from two different experimental models, arguing that recruitment to the nuclear periphery is due to random sub-diffusion and transient capture by NPCs. Finally, the simulations do not lead to inter-chromosomal clustering or coordinated movement, suggesting that interaction with the NPC is necessary, but not sufficient, to cause clustering.

Dynamics of chromosomal target search by a membrane-integrated one-component receptor

Membrane proteins account for about one third of the cellular proteome, but it is still unclear how dynamic they are and how they establish functional contacts with cytoplasmic interaction partners. Here, we consider a membrane-integrated one-component receptor that also acts as a transcriptional activator, and analyze how it kinetically locates its specific binding site on the genome. We focus on the case of CadC, the pH receptor of the acid stress response Cad system in E. coli. CadC is a prime example of a one-component signaling protein that directly binds to its cognate target site on the chromosome to regulate transcription. We combined fluorescence microscopy experiments, mathematical analysis, and kinetic Monte Carlo simulations to probe this target search process. Using fluorescently labeled CadC, we measured the time from activation of the receptor until successful binding to the DNA in single cells, exploiting that stable receptor-DNA complexes are visible as fluorescent spots. Our experimental data indicate that CadC is highly mobile in the membrane and finds its target by a 2D diffusion and capture mechanism. DNA mobility is constrained due to the overall chromosome organization, but a labeled DNA locus in the vicinity of the target site appears sufficiently mobile to randomly come close to the membrane. Relocation of the DNA target site to a distant position on the chromosome had almost no effect on the mean search time, which was between four and five minutes in either case. However, a mutant strain with two binding sites displayed a mean search time that was reduced by about a factor of two. This behavior is consistent with simulations of a coarse-grained lattice model for the coupled dynamics of DNA within a cell volume and proteins on its surface. The model also rationalizes the experimentally determined distribution of search times. Overall our findings reveal that DNA target search does not present a much bigger kinetic challenge for membrane-integrated proteins than for cytoplasmic proteins. More generally, diffusion and capture mechanisms may be sufficient for bacterial membrane proteins to establish functional contacts with cytoplasmic targets.

Adaptation to changing environments is vital to bacteria and is enabled by sophisticated signal transduction systems. While signal transduction by two-component systems is well studied, the signal transduction of membrane-integrated one-component systems, where one protein performs both sensing and response regulation, are insufficiently understood. How can a membrane-integrated protein bind to specific sites on the genome to regulate transcription? Here, we study the kinetics of this process, which involves both protein diffusion within the membrane and conformational fluctuations of the genomic DNA. A well-suited model system for this question is CadC, the signaling protein of the E. coli Cad system involved in pH stress response. Fluorescently labeled CadC forms visible spots in single cells upon stable DNA-binding, marking the end of the protein-DNA search process. Moreover, the start of the search is triggered by a medium shift exposing cells to pH stress. We probe the underlying mechanism by varying the number and position of DNA target sites. We combine these experiments with mathematical analysis and kinetic Monte Carlo simulations of lattice models for the search process. Our results suggest that CadC diffusion in the membrane is pivotal for this search, while the DNA target site is just mobile enough to reach the membrane.

4D nucleome modeling

The intrinsic dynamic nature of chromosomes is emerging as a fundamental component in regulating DNA transcription, replication, and damage-repair among other nuclear functions. With this increased awareness, reinforced over the last ten years, many new experimental techniques, mainly based on microscopy and chromosome conformation capture, have been introduced to study the genome in space and time. Owing to the increasing complexity of these cutting-edge techniques, computational approaches have become of paramount importance to interpret, contextualize, and complement such experiments with new insights. Hence, it is becoming crucial for experimental biologists to have a clear understanding of the diverse theoretical modeling approaches available and the biological information each of them can provide.

Navigating the crowd: visualizing coordination between genome dynamics, structure, and transcription

The eukaryotic genome is hierarchically structured yet highly dynamic. Regulating transcription in this environment demands a high level of coordination to permit many proteins to interact with chromatin fiber at appropriate sites in a timely manner. We describe how recent advances in quantitative imaging techniques overcome caveats of sequencing-based methods (Hi-C and related) by enabling direct visualization of transcription factors and chromatin at high resolution, from single genes to the whole nucleus. We discuss the contribution of fluorescence imaging to deciphering the principles underlying this coordination within the crowded nuclear space in living cells and discuss challenges ahead.

Fission yeast condensin contributes to interphase chromatin organization and prevents transcription-coupled DNA damage

BACKGROUND

Structural maintenance of chromosomes (SMC) complexes are central organizers of chromatin architecture throughout the cell cycle. The SMC family member condensin is best known for establishing long-range chromatin interactions in mitosis. These compact chromatin and create mechanically stable chromosomes. How condensin contributes to chromatin organization in interphase is less well understood.

RESULTS

Here, we use efficient conditional depletion of fission yeast condensin to determine its contribution to interphase chromatin organization. We deplete condensin in G2-arrested cells to preempt confounding effects from cell cycle progression without condensin. Genome-wide chromatin interaction mapping, using Hi-C, reveals condensin-mediated chromatin interactions in interphase that are qualitatively similar to those observed in mitosis, but quantitatively far less prevalent. Despite their low abundance, chromatin mobility tracking shows that condensin markedly confines interphase chromatin movements. Without condensin, chromatin behaves as an unconstrained Rouse polymer with excluded volume, while condensin constrains its mobility. Unexpectedly, we find that condensin is required during interphase to prevent ongoing transcription from eliciting a DNA damage response.

CONCLUSIONS

In addition to establishing mitotic chromosome architecture, condensin-mediated long-range chromatin interactions contribute to shaping chromatin organization in interphase. The resulting structure confines chromatin mobility and protects the genome from transcription-induced DNA damage. This adds to the important roles of condensin in maintaining chromosome stability.

Polymer Modeling Predicts Chromosome Reorganization in Senescence

Lamina-associated domains (LADs) cover a large part of the human genome and are thought to play a major role in shaping the nuclear architectural landscape. Here, we perform polymer simulations, microscopy, and mass spectrometry to dissect the roles played by heterochromatin- and lamina-mediated interactions in nuclear organization. Our model explains the conventional organization of heterochromatin and euchromatin in growing cells and the pathological organization found in oncogene-induced senescence and progeria. We show that the experimentally observed changes in the locality of contacts in senescent and progeroid cells can be explained as arising due to phase transitions in the system. Within our simulations, LADs are highly stochastic, as in experiments. Our model suggests that, once established, the senescent phenotype should be metastable even if lamina-mediated interactions were reinstated. Overall, our simulations uncover a generic physical mechanism that can regulate heterochromatin segregation and LAD formation in a wide range of mammalian nuclei.

Advances in Continuous Microfluidics-Based Technologies for the Study of HIV Infection

HIV-1 is the causative agent of acquired immunodeficiency syndrome (AIDS). It affects millions of people worldwide and the pandemic persists despite the implementation of highly active antiretroviral therapy. A wide spectrum of techniques has been implemented in order to diagnose and monitor AIDS progression over the years. Besides the conventional approaches, microfluidics has provided useful methods for monitoring HIV-1 infection. In this review, we introduce continuous microfluidics as well as the fabrication and handling of microfluidic chips. We provide a review of the different applications of continuous microfluidics in AIDS diagnosis and progression and in the basic study of the HIV-1 life cycle.

Bottom-Up Meets Top-Down: The Crossroads of Multiscale Chromatin Modeling

Chromatin can be viewed as a hierarchically structured fiber that regulates gene expression. It consists of a complex network of DNA and proteins whose characteristic dynamical modes facilitate compaction and rearrangement in the cell nucleus. These modes stem from chromatin's fundamental unit, the nucleosome, and their effects are propagated across length scales. Understanding the effects of nucleosome dynamics on the chromatin fiber, primarily through post-translational modifications that occur on the histones, is of central importance to epigenetics. Within the last decade, imaging and chromosome conformation capture techniques have revealed a number of structural and statistical features of the packaged chromatin fiber at a hitherto unavailable level of resolution. Such experiments have led to increased efforts to develop polymer models that aim to reproduce, explain, and predict the contact probability scaling and density heterogeneity. At nanometer scales, available models have focused on the role of the nucleosome and epigenetic marks on local chromatin structure. At micrometer scales, existing models have sought to explain scaling laws and density heterogeneity. Less work, however, has been done to reconcile these two approaches: bottom-up and top-down models of chromatin. In this perspective, we highlight the multiscale simulation models that are driving toward an understanding of chromatin structure and function, from the nanometer to the micron scale, and we highlight areas of opportunity and some of the prospects for new frameworks that bridge these two scales. Taken together, experimental and modeling advances over the last few years have established a robust platform for the study of chromatin fiber structure and dynamics, which will be of considerable use to the chromatin community in developing an understanding of the interplay between epigenomic regulation and molecular structure.

Nonequilibrium Theory of Epigenomic Microphase Separation in the Cell Nucleus

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

Quantification of the dynamic behaviour of ribosomal DNA genes and nucleolus during yeast Saccharomyces cerevisiae cell cycle

Spatial organisation of chromosomes is a determinant of genome stability and is required for proper mitotic segregation. However, visualization of individual chromatids in living cells and quantification of their geometry, remains technically challenging. Here, we used live cell imaging to quantitate the three-dimensional conformation of yeast Saccharomyces cerevisiae ribosomal DNA (rDNA). rDNA is confined within the nucleolus and is composed of about 200 copies representing about 10% of the yeast genome. To fluorescently label rDNA in living cells, we generated a set of nucleolar proteins fused to GFP or made use of a tagged rDNA, in which lacO repetitions were inserted in each repeat unit. We could show that nucleolus is not modified in appearance, shape or size during interphase while rDNA is highly reorganized. Computationally tracing 3D rDNA paths allowed us to quantitatively assess rDNA size, shape and geometry. During interphase, rDNA was progressively reorganized from a zig-zag segmented line of small size (5,5 µm) to a long, homogeneous, line-like structure of 8,7 µm in metaphase. Most importantly, whatever the cell-cycle stage considered, rDNA fibre could be decomposed in subdomains, as previously suggested for 3D chromatin organisation. Finally, we could determine that spatial reorganisation of these subdomains and establishment of rDNA mitotic organisation is under the control of the cohesin complex.

Magnetic polymer models for epigenetics-driven chromosome folding

Epigenetics is a driving force of important and ubiquitous phenomena in nature such as cell differentiation or even metamorphosis. Opposite to its widespread role, understanding the biophysical principles that allow epigenetics to control and rewire gene regulatory networks remains an open challenge. In this work we study the effects of epigenetic modifications on the spatial folding of chromosomes-and hence on the expression of the underlying genes-by mapping the problem to a class of models known as magnetic polymers. In this work we show that a first order phase transition underlies the simultaneous spreading of certain epigenetic marks and the conformational collapse of a chromosome. Further, we describe Brownian dynamics simulations of the model in which the topology of the polymer and thermal fluctuations are fully taken into account and that confirm our mean field predictions. Extending our models to allow for nonequilibrium terms yields new stable phases which qualitatively agrees with observations in vivo. Our results show that statistical mechanics techniques applied to models of magnetic polymers can be successfully exploited to rationalize the outcomes of experiments designed to probe the interplay between a dynamic epigenetic landscape and chromatin organization.

Mesoscale Liquid Model of Chromatin Recapitulates Nuclear Order of Eukaryotes

The nuclear envelope segregates the genome of Eukaryota from the cytoplasm. Within the nucleus, chromatin is further compartmentalized into architectures that change throughout the lifetime of the cell. Epigenetic patterns along the chromatin polymer strongly correlate with chromatin compartmentalization and, accordingly, also change during the cell life cycle and at differentiation. Recently, it has been suggested that subnuclear chromatin compartmentalization might result from a process of liquid-liquid phase separation orchestrated by the epigenetic marking and operated by proteins that bind to chromatin. Here, we translate these observations into a diffuse interface model of chromatin, which we named the mesoscale liquid model of nucleus. Using this streamlined continuum model of the genome, we study the large-scale rearrangements of chromatin that happen at different stages of the growth and senescence of the cell and during nuclear inversion events. In particular, we investigate the role of droplet diffusion, fluctuations, and heterochromatin-lamina interactions during nuclear remodeling. Our results indicate that the physical process of liquid-liquid phase separation, together with surface effects, is sufficient to recapitulate much of the large-scale morphology and dynamics of chromatin along the life cycle of cells.