A thermodynamic switch for chromosome colocalization

Binder and monomer valencies determine the extent of collapse and reswelling of chromatin

Multivalent DNA-bridging protein-mediated collapse of chromatin polymers have long been established as one of the driving factors in chromatin organization inside cells. These multivalent proteins can bind to distant binding sites along the chromatin backbone and bring them together in spatial proximity, leading to collapsed conformations. Recently, it has been suggested that these proteins not only drive the collapse of the chromatin polymer but also reswelling at higher concentrations. In this study, we investigate the physical mechanisms underlying this unexpected reswelling behavior. We use the Langevin dynamics simulation of a coarse-grained homopolymer to investigate the effects of the valencies of both the binders and the monomers on the polymer conformations. We find that while the extent of collapse of the polymer is strongly dependent on the binder valency, the extent of reswelling is largely determined by the monomer valency. Furthermore, we also discovered two different physical mechanisms that drive the reswelling of the polymer-excluded volume effects and loss of long-range loops. Finally, we obtain a classification map to determine the regimes in which each of these mechanisms is the dominant factor leading to polymer reswelling.

Bridging scales in chromatin organization: Computational models of loop formation and their implications for genome function

Chromatin loop formation plays a crucial role in 3D genome interactions, with misfolding potentially leading to irregular gene expression and various diseases. While experimental tools such as Hi-C have advanced our understanding of genome interactions, the biophysical principles underlying chromatin loop formation remain elusive. This review examines computational approaches to chromatin folding, focusing on polymer models that elucidate chromatin loop mechanics. We discuss three key models: (1) the multi-loop-subcompartment model, which investigates the structural effects of loops on chromatin conformation; (2) the strings and binders switch model, capturing thermodynamic chromatin aggregation; and (3) the loop extrusion model, revealing the role of structural maintenance of chromosome complexes. In addition, we explore advanced models that address chromatin clustering heterogeneity in biological processes and disease progression. The review concludes with an outlook on open questions and current trends in chromatin loop formation and genome interactions, emphasizing the physical and computational challenges in the field.

Effective model of protein-mediated interactions in chromatin

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

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.

Consistencies and contradictions in different polymer models of chromatin architecture

Genetic information is stored in very long DNA molecules, which are folded to form chromatin, a similarly long polymer fibre that is ultimately organised into chromosomes. The organisation of chromatin is fundamental to many cellular functions, from the expression of the genetic information to cell division. As a long polymer, chromatin is very flexible and may adopt a myriad of shapes. Globally, the polymer physics governing chromatin dynamics is very well understood. But chromatin is not uniform and regions of it, with chemical modifications and bound effectors, form domains and compartments through mechanisms not yet clear. Polymer models have been successfully used to investigate these mechanisms to explain cytological observations and build hypothesis for experimental validation. Many different approaches to conceptualise chromatin in polymer models can be envisioned and each reflects different aspects. Here, we compare recent approaches that aim at reproducing prominent features of interphase chromatin organisation: the compartmentalisation into eu- and heterochromatin compartments, the formation of a nucleolus, chromatin loops and the rosette and Rabl conformations of interphase chromosomes. We highlight commonalities and contradictions that point to a modulation of the mechanisms involved to fine degree. Consolidating models will require the inclusion of yet hidden or neglected parameters.

Phase Separation-Mediated Chromatin Organization and Dynamics: From Imaging-Based Quantitative Characterizations to Functional Implications

As an effective and versatile strategy to compartmentalize cellular components without the need for lipid membranes, phase separation has been found to underpin a wide range of intranuclear processes, particularly those involving chromatin. Many of the unique physico-chemical properties of chromatin-based phase condensates are harnessed by the cell to accomplish complex regulatory functions in a spatially and temporally controlled manner. Here, we survey key recent findings on the mechanistic roles of phase separation in regulating the organization and dynamics of chromatin-based molecular processes across length scales, packing states and intranuclear functions, with a particular emphasis on quantitative characterizations of these condensates enabled by advanced imaging-based approaches. By illuminating the complex interplay between chromatin and various chromatin-interacting molecular species mediated by phase separation, this review sheds light on an emerging multi-scale, multi-modal and multi-faceted landscape that hierarchically regulates the genome within the highly crowded and dynamic nuclear space. Moreover, deficiencies in existing studies also highlight the need for mechanism-specific criteria and multi-parametric approaches for the characterization of chromatin-based phase separation using complementary techniques and call for greater efforts to correlate the quantitative features of these condensates with their functional consequences in close-to-native cellular contexts.

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.

Live imaging and biophysical modeling support a button-based mechanism of somatic homolog pairing in Drosophila

Three-dimensional eukaryotic genome organization provides the structural basis for gene regulation. In Drosophila melanogaster, genome folding is characterized by somatic homolog pairing, where homologous chromosomes are intimately paired from end to end; however, how homologs identify one another and pair has remained mysterious. Recently, this process has been proposed to be driven by specifically interacting 'buttons' encoded along chromosomes. Here, we turned this hypothesis into a quantitative biophysical model to demonstrate that a button-based mechanism can lead to chromosome-wide pairing. We tested our model using live-imaging measurements of chromosomal loci tagged with the MS2 and PP7 nascent RNA labeling systems. We show solid agreement between model predictions and experiments in the pairing dynamics of individual homologous loci. Our results strongly support a button-based mechanism of somatic homolog pairing in Drosophila and provide a theoretical framework for revealing the molecular identity and regulation of buttons.

Inference of chromosome 3D structures from GAM data by a physics computational approach

The combination of modelling and experimental advances can provide deep insights for understanding chromatin 3D organization and ultimately its underlying mechanisms. In particular, models of polymer physics can help comprehend the complexity of genomic contact maps, as those emerging from technologies such as Hi-C, GAM or SPRITE. Here we discuss a method to reconstruct 3D structures from Genome Architecture Mapping (GAM) data, based on PRISMR, a computational approach introduced to find the minimal polymer model best describing Hi-C input data from only polymer physics. After recapitulating the PRISMR procedure, we describe how we extended it for treating GAM data. We successfully test the method on a 6 Mb region around the Sox9 gene and, at a lower resolution, on the whole chromosome 7 in mouse embryonic stem cells. The PRISMR derived 3D structures from GAM co-segregation data are finally validated against independent Hi-C contact maps. The method results to be versatile and robust, hinting that it can be similarly applied to different experimental data, such as SPRITE or microscopy distance data.

A Dynamic Folded Hairpin Conformation Is Associated with α-Globin Activation in Erythroid Cells

We investigate the three-dimensional (3D) conformations of the α-globin locus at the single-allele level in murine embryonic stem cells (ESCs) and erythroid cells, combining polymer physics models and high-resolution Capture-C data. Model predictions are validated against independent fluorescence in situ hybridization (FISH) data measuring pairwise distances, and Tri-C data identifying three-way contacts. The architecture is rearranged during the transition from ESCs to erythroid cells, associated with the activation of the globin genes. We find that in ESCs, the spatial organization conforms to a highly intermingled 3D structure involving non-specific contacts, whereas in erythroid cells the α-globin genes and their enhancers form a self-contained domain, arranged in a folded hairpin conformation, separated from intermingling flanking regions by a thermodynamic mechanism of micro-phase separation. The flanking regions are rich in convergent CTCF sites, which only marginally participate in the erythroid-specific gene-enhancer contacts, suggesting that beyond the interaction of CTCF sites, multiple molecular mechanisms cooperate to form an interacting domain.

Structure of the human chromosome interaction network

New Hi-C technologies have revealed that chromosomes have a complex network of spatial contacts in the cell nucleus of higher organisms, whose organisation is only partially understood. Here, we investigate the structure of such a network in human GM12878 cells, to derive a large scale picture of nuclear architecture. We find that the intensity of intra-chromosomal interactions is power-law distributed. Inter-chromosomal interactions are two orders of magnitude weaker and exponentially distributed, yet they are not randomly arranged along the genomic sequence. Intra-chromosomal contacts broadly occur between epigenomically homologous regions, whereas inter-chromosomal contacts are especially associated with regions rich in highly expressed genes. Overall, genomic contacts in the nucleus appear to be structured as a network of networks where a set of strongly individual chromosomal units, as envisaged in the 'chromosomal territory' scenario derived from microscopy, interact with each other via on average weaker, yet far from random and functionally important interactions.

A Polymer Physics Investigation of the Architecture of the Murine Orthologue of the 7q11.23 Human Locus

In the last decade, the developments of novel technologies, such as Hi-C or GAM methods, allowed to discover that chromosomes in the nucleus of mammalian cells have a complex spatial organization, encompassing the functional contacts between genes and regulators. In this work, we review recent progresses in chromosome modeling based on polymer physics to understand chromatin structure and folding mechanisms. As an example, we derive in mouse embryonic stem cells the full 3D structure of the Bmp7 locus, a genomic region that plays a key role in osteoblastic differentiation. Next, as an application to Neuroscience, we present the first 3D model for the mouse orthologoue of the Williams-Beuren syndrome 7q11.23 human locus. Deletions and duplications of the 7q11.23 region generate neurodevelopmental disorders with multi-system involvement and variable expressivity, and with autism. Understanding the impact of such mutations on the rewiring of the interactions of genes and regulators could be a new key to make sense of their related diseases, with potential applications in biomedicine.

Polymer models of the hierarchical folding of the Hox-B chromosomal locus

As revealed by novel technologies, chromosomes in the nucleus of mammalian cells have a complex spatial organization that serves vital functional purposes. Here we use models from polymer physics to identify the mechanisms that control their three-dimensional spatial organization. In particular, we investigate a model of the Hox-B locus, an important genomic region involved in embryo development, to expose the principles regulating chromatin folding and its complex behaviors in mouse embryonic stem cells. We reconstruct with high accuracy the pairwise contact matrix of the Hox-B locus as derived by Hi-C experiments and investigate its hierarchical folding dynamics. We trace back the observed behaviors to general scaling properties of polymer physics.

From single genes to entire genomes: the search for a function of nuclear organization

The existence of different domains within the nucleus has been clear from the time, in the late 1920s, that heterochromatin and euchromatin were discovered. The observation that heterochromatin is less transcribed than euchromatin suggested that microscopically identifiable structures might correspond to functionally different domains of the nucleus. Until 15 years ago, studies linking gene expression and subnuclear localization were limited to a few genes. As we discuss in this Review, new genome-wide techniques have now radically changed the way nuclear organization is analyzed. These have provided a much more detailed view of functional nuclear architecture, leading to the emergence of a number of new paradigms of chromatin folding and how this folding evolves during development.

Polymer Physics of the Large-Scale Structure of Chromatin

We summarize the picture emerging from recently proposed models of polymer physics describing the general features of chromatin large scale spatial architecture, as revealed by microscopy and Hi-C experiments.

Physical mechanisms behind the large scale features of chromatin organization

We review the picture emerging from recently published models of classical polymer physics of the general features of chromatin large scale spatial organization, as revealed by microscopy and Hi-C data.

Models of chromosome structure

Understanding the mechanisms that control chromosome folding in the nucleus of eukaryotes and their contribution to gene regulation is a key open issue in molecular biology. Microscopy and chromatin-capture techniques have shown that chromatin has a complex organization, which dynamically changes across organisms and cell types. The need to make sense of such a fascinating complexity has prompted the development of quantitative models from physics, to find the principles of chromosome folding, its origin and function. Here, we concisely review recent advances in chromosome modeling, focusing on a recently proposed framework, the Strings & Binders Switch (SBS) model, which recapitulates key features of chromosome organization in space and time.

Single-cell states in the estrogen response of breast cancer cell lines

Estrogen responsive breast cancer cell lines have been extensively studied to characterize transcriptional patterns in hormone-responsive tumors. Nevertheless, due to current technological limitations, genome-wide studies have typically been limited to population averaged data. Here we obtain, for the first time, a characterization at the single-cell level of the states and expression signatures of a hormone-starved MCF-7 cell system responding to estrogen. To do so, we employ a recently proposed model that allows for dissecting single-cell states from time-course microarray data. We show that within 32 hours following stimulation, MCF-7 cells traverse, most likely, six states, with a faster early response followed by a progressive deceleration. We also derive the genome-wide transcriptional profiles of such single-cell states and their functional characterization. Our results support a scenario where estrogen promotes cell cycle progression by controlling multiple, sequential regulatory steps, whose single-cell events are here identified.

A polymer model explains the complexity of large-scale chromatin folding

The underlying global organization of chromatin within the cell nucleus has been the focus of intense recent research. Hi-C methods have allowed for the detection of genome-wide chromatin interactions, revealing a complex large-scale organization where chromosomes tend to partition into megabase-sized "topological domains" of local chromatin interactions and intra-chromosomal contacts extends over much longer scales, in a cell-type and chromosome specific manner. Until recently, the distinct chromatin folding properties observed experimentally have been difficult to explain in a single conceptual framework. We reported that a simple polymer-physics model of chromatin, the strings and binders switch (SBS) model, succeeds in describing the full range of chromatin configurations observed in vivo. The SBS model simulates the interactions between randomly diffusing binding molecules and binding sites on a polymer chain. It explains how polymer architectural patterns can be established, how different stable conformations can be produced and how conformational changes can be reliably regulated by simple strategies, such as protein upregulation or epigenetic modifications, via fundamental thermodynamics mechanisms.

Structure-driven homology pairing of chromatin fibers: the role of electrostatics and protein-induced bridging

Chromatin domains formed in vivo are characterized by different types of 3D organization of interconnected nucleosomes and architectural proteins. Here, we quantitatively test a hypothesis that the similarities in the structure of chromatin fibers (which we call "structural homology") can affect their mutual electrostatic and protein-mediated bridging interactions. For example, highly repetitive DNA sequences in heterochromatic regions can position nucleosomes so that preferred inter-nucleosomal distances are preserved on the surfaces of neighboring fibers. On the contrary, the segments of chromatin fiber formed on unrelated DNA sequences have different geometrical parameters and lack structural complementarity pivotal for stable association and cohesion. Furthermore, specific functional elements such as insulator regions, transcription start and termination sites, and replication origins are characterized by strong nucleosome ordering that might induce structure-driven iterations of chromatin fibers. We propose that shape-specific protein-bridging interactions facilitate long-range pairing of chromatin fragments, while for closely-juxtaposed fibers electrostatic forces can in addition yield fine-tuned structure-specific recognition and pairing. These pairing effects can account for some features observed for mitotic and inter-phase chromatins.

Colocalization of multiple DNA loci: a physical mechanism

A variety of important cellular processes require, for functional purposes, the colocalization of multiple DNA loci at specific time points. In most cases, the physical mechanisms responsible for bringing them in close proximity are still elusive. Here we show that the interaction of DNA loci with a concentration of diffusing molecular factors can induce spontaneously their colocalization, through a mechanism based on a thermodynamic phase transition. We consider up to four DNA loci and different valencies for diffusing molecular factors. In particular, our analysis illustrates that a variety of nontrivial stable spatial configurations is allowed in the system, depending on the details of the molecular factor/DNA binding-sites interaction. Finally, we discuss as a case study an application of our model to the pairing of X chromosome at X inactivation, one of the best-known examples of DNA colocalization. We also speculate on the possible links between X colocalization and inactivation.

Complexity of chromatin folding is captured by the strings and binders switch model

Chromatin has a complex spatial organization in the cell nucleus that serves vital functional purposes. A variety of chromatin folding conformations has been detected by single-cell imaging and chromosome conformation capture-based approaches. However, a unified quantitative framework describing spatial chromatin organization is still lacking. Here, we explore the "strings and binders switch" model to explain the origin and variety of chromatin behaviors that coexist and dynamically change within living cells. This simple polymer model recapitulates the scaling properties of chromatin folding reported experimentally in different cellular systems, the fractal state of chromatin, the processes of domain formation, and looping out. Additionally, the strings and binders switch model reproduces the recently proposed "fractal-globule" model, but only as one of many possible transient conformations.

The impact of entropy on the spatial organization of synaptonemal complexes within the cell nucleus

We employ 4Pi-microscopy to study SC organization in mouse spermatocyte nuclei allowing for the three-dimensional reconstruction of the SC's backbone arrangement. Additionally, we model the SCs in the cell nucleus by confined, self-avoiding polymers, whose chain ends are attached to the envelope of the confining cavity and diffuse along it. This work helps to elucidate the role of entropy in shaping pachytene SC organization. The framework provided by the complex interplay between SC polymer rigidity, tethering and confinement is able to qualitatively explain features of SC organization, such as mean squared end-to-end distances, mean squared center-of-mass distances, or SC density distributions. However, it fails in correctly assessing SC entanglement within the nucleus. In fact, our analysis of the 4Pi-microscopy images reveals a higher ordering of SCs within the nuclear volume than what is expected by our numerical model. This suggests that while effects of entropy impact SC organization, the dedicated action of proteins or actin cables is required to fine-tune the spatial ordering of SCs within the cell nucleus.

Diffusion-based DNA target colocalization by thermodynamic mechanisms

In eukaryotic cell nuclei, a variety of DNA interactions with nuclear elements occur, which, in combination with intra- and inter-chromosomal cross-talks, shape a functional 3D architecture. In some cases they are organized by active, i.e. actin/myosin, motors. More often, however, they have been related to passive diffusion mechanisms. Yet, the crucial questions on how DNA loci recognize their target and are reliably shuttled to their destination by Brownian diffusion are still open. Here, we complement the current experimental scenario by considering a physics model, in which the interaction between distant loci is mediated by diffusing bridging molecules. We show that, in such a system, the mechanism underlying target recognition and colocalization is a thermodynamic switch-like process (a phase transition) that only occurs if the concentration and affinity of binding molecules is above a threshold, or else stable contacts are not possible. We also briefly discuss the kinetics of this `passive-shuttling' process, as produced by random diffusion of DNA loci and their binders, and derive predictions based on the effects of genomic modifications and deletions.

The X as model for RNA's niche in epigenomic regulation

The X-linked region now known as the "X-inactivation center" (Xic) was once dominated by protein-coding genes but, with the rise of Eutherian mammals some 150-200 million years ago, became infiltrated by genes that produce long noncoding RNA (ncRNA). Some of the noncoding genes have been shown to play crucial roles during X-chromosome inactivation (XCI), including the targeting of chromatin modifiers to the X. The rapid establishment of ncRNA hints at a possible preference for long transcripts in some aspects of epigenetic regulation. This article discusses the role of RNA in XCI and considers the advantages RNA offers in delivering allelic, cis-limited, and locus-specific control. Unlike proteins and small RNAs, long ncRNAs are tethered to the site of transcription and effectively tag the allele of origin. Furthermore, long ncRNAs are drawn from larger sequence space than proteins and can mark a unique region in a complex genome. Thus, like their small RNA cousins, long ncRNAs may emerge as versatile and powerful regulators of the epigenome.

DNA loci cross-talk through thermodynamics

The recognition and pairing of specific DNA loci, though crucial for a plenty of important cellular processes, are produced by still mysterious physical mechanisms. We propose the first quantitative model from Statistical Mechanics, able to clarify the interaction allowing such “DNA cross-talk” events. Soluble molecules, which bind some DNA recognition sequences, produce an effective attraction between distant DNA loci; if their affinity, their concentration, and the relative DNA binding sites number exceed given thresholds, DNA colocalization occurs as a result of a thermodynamic phase transition. In this paper, after a concise report on some of the most recent experimental results, we introduce our model and carry out a detailed “in silico” analysis of it, by means of Monte Carlo simulations. Our studies, while rationalize several experimental observations, result in very interesting and testable predictions.

Entropic organization of interphase chromosomes

Chromosomes are not distributed randomly in nuclei. Appropriate positioning can activate (or repress) genes by bringing them closer to active (or inactive) compartments like euchromatin (or heterochromatin), and this is usually assumed to be driven by specific local forces (e.g., involving H bonds between nucleosomes or between nucleosomes and the lamina). Using Monte Carlo simulations, we demonstrate that nonspecific (entropic) forces acting alone are sufficient to position and shape self-avoiding polymers within a confining sphere in the ways seen in nuclei. We suggest that they can drive long flexible polymers (representing gene-rich chromosomes) to the interior, compact/thick ones (and heterochromatin) to the periphery, looped (but not linear) ones into appropriately shaped (ellipsoidal) territories, and polymers with large terminal beads (representing centromeric heterochromatin) into peripheral chromocenters. Flexible polymers tend to intermingle less than others, which is in accord with observations that gene-dense (and so flexible) chromosomes make poor translocation partners. Thus, entropic forces probably participate in the self-organization of chromosomes within nuclei.

Symmetry breaking mechanism for epithelial cell polarization

In multicellular organisms, epithelial cells form layers separating compartments responsible for different physiological functions. At the early stage of epithelial layer formation, each cell of an aggregate defines an inner and an outer side by breaking the symmetry of its initial state, in a process known as epithelial polarization. By integrating recent biochemical and biophysical data with stochastic simulations of the relevant reaction-diffusion system, we provide evidence that epithelial cell polarization is a chemical phase-separation process induced by a local bistability in the signaling network at the level of the cell membrane. The early symmetry breaking event triggering phase separation is induced by adhesion-dependent mechanical forces localized in the point of convergence of cell surfaces when a threshold number of confluent cells is reached. The generality of the emerging phase-separation scenario is likely common to many processes of cell polarity formation.

Lessons from X-chromosome inactivation: long ncRNA as guides and tethers to the epigenome

Transcriptome studies are revealing that the eukaryotic genome actively transcribes a diverse repertoire of large noncoding RNAs (ncRNAs), many of which are unannotated and distinct from the small RNAs that have garnered much attention in recent years. Why are they so pervasive, and do they have a function? X-chromosome inactivation (XCI) is a classic epigenetic phenomenon associated with many large ncRNAs. Here, I provide a perspective on how XCI is achieved in mice and suggest how this knowledge can be applied to the rest of the genome. Emerging data indicate that long ncRNAs can function as guides and tethers, and may be the molecules of choice for epigenetic regulation: First, unlike proteins and small RNAs, large ncRNAs remain tethered to the site of transcription, and can therefore uniquely direct allelic regulation. Second, ncRNAs command a much larger sequence space than proteins, and can therefore achieve very precise spatiotemporal control of development. These properties imply that long noncoding transcripts may ultimately rival small RNAs and proteins in their versatility as epigenetic regulators, particularly for locus- and allele-specific control.

Thermodynamic pathways to genome spatial organization in the cell nucleus

The architecture of the eukaryotic genome is characterized by a high degree of spatial organization. Chromosomes occupy preferred territories correlated to their state of activity and, yet, displace their genes to interact with remote sites in complex patterns requiring the orchestration of a huge number of DNA loci and molecular regulators. Far from random, this organization serves crucial functional purposes, but its governing principles remain elusive. By computer simulations of a statistical mechanics model, we show how architectural patterns spontaneously arise from the physical interaction between soluble binding molecules and chromosomes via collective thermodynamics mechanisms. Chromosomes colocalize, loops and territories form, and find their relative positions as stable thermodynamic states. These are selected by thermodynamic switches, which are regulated by concentrations/affinity of soluble mediators and by number/location of their attachment sites along chromosomes. Our thermodynamic switch model of nuclear architecture, thus, explains on quantitative grounds how well-known cell strategies of upregulation of DNA binding proteins or modification of chromatin structure can dynamically shape the organization of the nucleus.

Mechanics and dynamics of X-chromosome pairing at X inactivation

At the onset of X-chromosome inactivation, the vital process whereby female mammalian cells equalize X products with respect to males, the X chromosomes are colocalized along their Xic (X-inactivation center) regions. The mechanism inducing recognition and pairing of the X's remains, though, elusive. Starting from recent discoveries on the molecular factors and on the DNA sequences (the so-called “pairing sites”) involved, we dissect the mechanical basis of Xic colocalization by using a statistical physics model. We show that soluble DNA-specific binding molecules, such as those experimentally identified, can be indeed sufficient to induce the spontaneous colocalization of the homologous chromosomes but only when their concentration, or chemical affinity, rises above a threshold value as a consequence of a thermodynamic phase transition. We derive the likelihood of pairing and its probability distribution. Chromosome dynamics has two stages: an initial independent Brownian diffusion followed, after a characteristic time scale, by recognition and pairing. Finally, we investigate the effects of DNA deletion/insertions in the region of pairing sites and compare model predictions to available experimental data.

Some important cellular processes involve homologous chromosome recognition and pairing. A prominent example is the colocalization of X chromosomes occurring at the onset of X chromosome inactivation, the vital process whereby female mammalian cells silence one of their two X chromosomes to equalize the dosage of X products with respect to males (having just one X). The crucial question on how the Xs recognize each other and come together is, however, still open. Starting from important recent experimental discoveries, we propose a quantitative model, from statistical mechanics, which elucidates the mechanical basis of such phenomena. We demonstrate that a set of soluble molecules binding specific DNA sequences are sufficient to induce recognition and colocalization. This is possible, however, only when their binding energy/concentration exceeds a threshold value, and this suggests how the cell could regulate colocalization. The pairing mechanism that we propose is grounded in general thermodynamic principles, so it could apply to other DNA pairing processes. While we also explore the kinetics of X colocalization, we compare our results to available experimental data and produce testable predictions.

The colocalization transition of homologous chromosomes at meiosis

Meiosis is the specialized cell division required in sexual reproduction. During its early stages, in the mother cell nucleus, homologous chromosomes recognize each other and colocalize in a crucial step that remains one of the most mysterious of meiosis. Starting from recent discoveries on the system molecular components and interactions, we discuss a statistical mechanics model of chromosome early pairing. Binding molecules mediate long-distance interaction of special DNA recognition sequences and, if their concentration exceeds a critical threshold, they induce a spontaneous colocalization transition of chromosomes, otherwise independently diffusing.