Chromosome disentanglement driven via optimal compaction of loop-extruded brush structures

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.

Formation and resolution of meiotic chromosome entanglements and interlocks

Interactions between parental chromosomes during the formation of gametes can lead to entanglements, entrapments and interlocks between unrelated chromosomes. If unresolved, these topological constraints can lead to misregulation of exchanges between chromosomes and to chromosome mis-segregation. Interestingly, these configurations are largely resolved by the time parental chromosomes are aligned during pachytene. In this Review, we highlight the inevitability of topologically complex configurations and discuss possible mechanisms to resolve them. We focus on the dynamic nature of a conserved chromosomal interface - the synaptonemal complex - and the chromosome movements that accompany meiosis as potential mechanisms to resolve topological constraints. We highlight the advantages of the nematode Caenorhabditis elegans for understanding biophysical features of the chromosome axis and synaptonemal complex that could contribute to mechanisms underlying interlock resolution. In addition, we highlight advantages of using the zebrafish, Danio rerio, as a model to understand how entanglements and interlocks are avoided and resolved.

Multi-omics analysis reveals the dynamic interplay between Vero host chromatin structure and function during vaccinia virus infection

The genome folds into complex configurations and structures thought to profoundly impact its function. The intricacies of this dynamic structure-function relationship are not well understood particularly in the context of viral infection. To unravel this interplay, here we provide a comprehensive investigation of simultaneous host chromatin structural (via Hi-C and ATAC-seq) and functional changes (via RNA-seq) in response to vaccinia virus infection. Over time, infection significantly impacts global and local chromatin structure by increasing long-range intra-chromosomal interactions and B compartmentalization and by decreasing chromatin accessibility and inter-chromosomal interactions. Local accessibility changes are independent of broad-scale chromatin compartment exchange (~12% of the genome), underscoring potential independent mechanisms for global and local chromatin reorganization. While infection structurally condenses the host genome, there is nearly equal bidirectional differential gene expression. Despite global weakening of intra-TAD interactions, functional changes including downregulated immunity genes are associated with alterations in local accessibility and loop domain restructuring. Therefore, chromatin accessibility and local structure profiling provide impactful predictions for host responses and may improve development of efficacious anti-viral counter measures including the optimization of vaccine design.

Helical chromonema coiling is conserved in eukaryotes

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

Three factors ParA, TipN, and DnaA-mediated chromosome replication initiation are contributors of centromere segregation in Caulobacter crescentus

The ability of bacteria to maintain chromosomal integrity throughout their life cycle is crucial for survival. In Caulobacter crescentus, the polar factor TipN has been proposed to be involved with the partitioning system ParABS. Cells with tipN knocked out display subtle segregation defects of the centromere-like region parS. We hypothesized that TipN's role with parS segregation is obscured by other forces that are ParABS-independent. To test our hypothesis, we removed one of those forces - chromosome replication - and analyzed the role of TipN with ParA. We first confirm that ParA retains its ability to transport the centromeric region parS from the stalked pole to the opposite pole in the absence of chromosome replication. Our data revealed that in the absence of chromosome replication, TipN becomes essential for ParA's ability to transport parS. Furthermore, we identify a potential connection between the replication initiator DnaA and TipN. Although TipN is not essential for viability, tipN knockout cells lose viability when the regulation of DnaA levels is altered. Our data suggest that the DnaA-dependent susceptibility of tipN knockout cells is connected to parS segregation. Collectively, this work provides insights into the complex regulation involved in the coordination of chromosome replication and segregation in bacteria.

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

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

Four-Dimensional Mesoscale Liquid Model of Nucleus Resolves Chromatin's Radial Organization

Recent advances chromatin capture, imaging techniques, and polymer modeling have dramatically enhanced quantitative understanding of chromosomal folding. However, the dynamism inherent in genome architectures due to physical and biochemical forces and their impact on nuclear architecture and cellular functions remains elusive. While imaging of chromatin in four dimensions is becoming more common, there is a conspicuous lack of physics-based computational tools appropriate for revealing the forces that shape nuclear architecture and dynamics. To this end, we have developed a multiphase liquid model of the nucleus, which can resolve chromosomal territories, compartments, and nuclear lamina using a physics-based and data-informed free-energy function. The model enables rapid hypothesis-driven prototyping of nuclear dynamics in four dimensions, thereby facilitating comparison with whole nucleus imaging experiments. As an application, we model the Drosophila nucleus and map phase diagram of various possible nuclear morphologies. We shed light on the interplay of adhesive and cohesive interactions which give rise to distinct radial organization seen in conventional, inverted, and senescent nuclear architectures. The results also show the highly dynamic nature of the radial organization, the disruption of which leads to significant variability in domain coarsening dynamics and consequently variability of chromatin architecture. The model also highlights the impact of oblate nuclear geometry and heterochromatin-subtype interactions on the global chromatin architecture and local asymmetry of chromatin compartments.

TipN's involvement with centromere segregation in Caulobacter crescentus

Bacteria's ability to maintain chromosomal integrity throughout their life cycle is crucial for their survival. In Caulobacter crescentus, the polar factor TipN has been proposed to be involved with the partitioning system ParABS. However, cells with tipN knocked out display subtle parS segregation defects. We hypothesized that TipN's role with parS segregation is obscured by other forces that are ParABS-independent. To test our hypothesis, we removed one of those forces - chromosome replication - and analyzed the role of TipN with ParA. We first demonstrate that ParA retains its ability to transport the centromeric region parS from the stalked pole to the opposite pole in the absence of chromosome replication. Our data revealed that in the absence of chromosome replication, TipN becomes essential for ParA's ability to transport parS. Furthermore, we identify a potential connection between the replication initiator DnaA and TipN. Although TipN is not essential for viability, tipN knockout cells lose viability when the regulation of DnaA levels is altered. Our data suggest that the DnaA-dependent susceptibility of tipN knockout cells is connected to parS segregation. Collectively, this work provides insights into the complex regulation involved in the coordination of chromosome replication and segregation in bacteria.

Crumpled polymer with loops recapitulates key features of chromosome organization

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

Dynamics of chromosome organization in a minimal bacterial cell

Computational models of cells cannot be considered complete unless they include the most fundamental process of life, the replication and inheritance of genetic material. By creating a computational framework to model systems of replicating bacterial chromosomes as polymers at 10 bp resolution with Brownian dynamics, we investigate changes in chromosome organization during replication and extend the applicability of an existing whole-cell model (WCM) for a genetically minimal bacterium, JCVI-syn3A, to the entire cell-cycle. To achieve cell-scale chromosome structures that are realistic, we model the chromosome as a self-avoiding homopolymer with bending and torsional stiffnesses that capture the essential mechanical properties of dsDNA in Syn3A. In addition, the conformations of the circular DNA must avoid overlapping with ribosomes identitied in cryo-electron tomograms. While Syn3A lacks the complex regulatory systems known to orchestrate chromosome segregation in other bacteria, its minimized genome retains essential loop-extruding structural maintenance of chromosomes (SMC) protein complexes (SMC-scpAB) and topoisomerases. Through implementing the effects of these proteins in our simulations of replicating chromosomes, we find that they alone are sufficient for simultaneous chromosome segregation across all generations within nested theta structures. This supports previous studies suggesting loop-extrusion serves as a near-universal mechanism for chromosome organization within bacterial and eukaryotic cells. Furthermore, we analyze ribosome diffusion under the influence of the chromosome and calculate in silico chromosome contact maps that capture inter-daughter interactions. Finally, we present a methodology to map the polymer model of the chromosome to a Martini coarse-grained representation to prepare molecular dynamics models of entire Syn3A cells, which serves as an ultimate means of validation for cell states predicted by the WCM.

Function and Evolution of the Loop Extrusion Machinery in Animals

Structural maintenance of chromosomes (SMC) complexes are essential proteins found in genomes of all cellular organisms. Essential functions of these proteins, such as mitotic chromosome formation and sister chromatid cohesion, were discovered a long time ago. Recent advances in chromatin biology showed that SMC proteins are involved in many other genomic processes, acting as active motors extruding DNA, which leads to the formation of chromatin loops. Some loops formed by SMC proteins are highly cell type and developmental stage specific, such as SMC-mediated DNA loops required for VDJ recombination in B-cell progenitors, or dosage compensation in Caenorhabditis elegans and X-chromosome inactivation in mice. In this review, we focus on the extrusion-based mechanisms that are common for multiple cell types and species. We will first describe an anatomy of SMC complexes and their accessory proteins. Next, we provide biochemical details of the extrusion process. We follow this by the sections describing the role of SMC complexes in gene regulation, DNA repair, and chromatin topology.

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.

Regulation of the mitotic chromosome folding machines

Over the last several years enormous progress has been made in identifying the molecular machines, including condensins and topoisomerases that fold mitotic chromosomes. The discovery that condensins generate chromatin loops through loop extrusion has revolutionized, and energized, the field of chromosome folding. To understand how these machines fold chromosomes with the appropriate dimensions, while disentangling sister chromatids, it needs to be determined how they are regulated and deployed. Here, we outline the current understanding of how these machines and factors are regulated through cell cycle dependent expression, chromatin localization, activation and inactivation through post-translational modifications, and through associations with each other, with other factors and with the chromatin template itself. There are still many open questions about how condensins and topoisomerases are regulated but given the pace of progress in the chromosome folding field, it seems likely that many of these will be answered in the years ahead.

Dispersive forces and resisting spot welds by alternative homolog conjunction govern chromosome shape in Drosophila spermatocytes during prophase I

The bivalent chromosomes that are generated during prophase of meiosis I comprise a pair of homologous chromosomes. Homolog pairing during prophase I must include mechanisms that avoid or eliminate entanglements between non-homologous chromosomes. In Drosophila spermatocytes, non-homologous associations are disrupted by chromosome territory formation, while linkages between homologous chromosomes are maintained by special conjunction proteins. These proteins function as alternative for crossovers that link homologs during canonical meiosis but are absent during the achiasmate Drosophila male meiosis. How and where within bivalents the alternative homolog conjunction proteins function is still poorly understood. To clarify the rules that govern territory formation and alternative homolog conjunction, we have analyzed spermatocytes with chromosomal aberrations. We examined territory formation after acute chromosome cleavage by Cas9, targeted to the dodeca satellite adjacent to the centromere of chromosome 3 specifically in spermatocytes. Moreover, we studied territory organization, as well as the eventual orientation of chromosomes during meiosis I, in spermatocytes with stable structural aberrations, including heterozygous reciprocal autosomal translocations. Our observations indicate that alternative homolog conjunction is applied in a spatially confined manner. Comparable to crossovers, only a single conjunction spot per chromosome arm appears to be applied usually. These conjunction spots resist separation by the dispersing forces that drive apart homologous pericentromeric heterochromatin and embedded centromeres within territories, as well as the distinct chromosomal entities into peripheral, maximally separated territories within the spermatocyte nucleus.

Already the primordial eukaryote appears to have used meiosis for sexual reproduction, because this sophisticated process follows a canonical program in lineages ranging from unicellular organisms to plants and animals. The maternal and paternal copies of a particular chromosome, i.e., the homologs, are first physically linked into a bivalent before the first meiotic division. Linkage is essential for error-free chromosome segregation. In canonical meiosis, linkage is achieved by crossovers. These are regulated so that each chromosome pair is linked, but only by very few crossovers. Surprisingly, crossovers are absent during meiosis in males of the fruit fly Drosophila melanogaster. Instead, an alternative homolog conjunction system is used. It is not yet clear how this functions. Here, we demonstrate that the alternative chromosome glue appears to be applied in a locally restricted manner rather than all along the paired homologs. Just two spots of glue appear to conjoin the two homologous chromosomes usually, with one spot linking the left and another the right chromosome arm. Thus, number and location of linkages appear to be similar as crossovers, raising the possibility of mechanistic similarities in the establishment of the two distinct types of homolog linkage.

Uncovering the statistical physics of 3D chromosomal organization using data-driven modeling

In recent years, much effort has been devoted to understanding the three-dimensional (3D) organization of the genome and how genomic structure mediates nuclear function. The development of experimental techniques that combine DNA proximity ligation with high-throughput sequencing, such as Hi-C, have substantially improved our knowledge about chromatin organization. Numerous experimental advancements, not only utilizing DNA proximity ligation but also high-resolution genome imaging (DNA tracing), have required theoretical modeling to determine the structural ensembles consistent with such data. These 3D polymer models of the genome provide an understanding of the physical mechanisms governing genome architecture. Here, we present an overview of the recent advances in modeling the ensemble of 3D chromosomal structures by employing the maximum entropy approach combined with polymer physics. Particularly, we discuss the minimal chromatin model (MiChroM) along with the "maximum entropy genomic annotations from biomarkers associated with structural ensembles" (MEGABASE) model, which have been remarkably successful in the accurate modeling of chromosomes consistent with both Hi-C and DNA-tracing data.

Mechanisms of Chromosome Folding and Nuclear Organization: Their Interplay and Open Questions

Microscopy and genomic approaches provide detailed descriptions of the three-dimensional folding of chromosomes and nuclear organization. The fundamental question is how activity of molecules at the nanometer scale can lead to complex and orchestrated spatial organization at the scale of chromosomes and the whole nucleus. At least three key mechanisms can bridge across scales: (1) tethering of specific loci to nuclear landmarks leads to massive reorganization of the nucleus; (2) spatial compartmentalization of chromatin, which is driven by molecular affinities, results in spatial isolation of active and inactive chromatin; and (3) loop extrusion activity of SMC (structural maintenance of chromosome) complexes can explain many features of interphase chromatin folding and underlies key phenomena during mitosis. Interestingly, many features of chromosome organization ultimately result from collective action and the interplay between these mechanisms, and are further modulated by transcription and topological constraints. Finally, we highlight some outstanding questions that are critical for our understanding of nuclear organization and function. We believe many of these questions can be answered in the coming years.

Loop extrusion driven volume phase transition of entangled chromosomes

Experiments on reconstituted chromosomes have revealed that mitotic chromosomes are assembled even without nucleosomes. When topoisomerase II (topo II) is depleted from such reconstituted chromosomes, these chromosomes are not disentangled and form "sparklers," where DNA and linker histone are condensed in the core and condensin is localized at the periphery. To understand the mechanism of the assembly of sparklers, we here take into account the loop extrusion by condensin in an extension of the theory of entangled polymer gels. The loop extrusion stiffens an entangled DNA network because DNA segments in the elastically effective chains are translocated to loops, which are elastically ineffective. Our theory predicts that the loop extrusion by condensin drives the volume phase transition that collapses a swollen entangled DNA gel because the stiffening of the network destabilizes the swollen phase. This may be an important piece to understand the mechanism of the assembly of mitotic chromosomes.

Formulation of Chromatin Mobility as a Function of Nuclear Size during C. elegans Embryogenesis Using Polymer Physics Theories

During early embryogenesis of the nematode, Caenorhabditis elegans, the chromatin motion markedly decreases. Despite its biological implications, the underlying mechanism for this transition was unclear. By combining theory and experiment, we analyze the mean-square displacement (MSD) of the chromatin loci, and demonstrate that MSD-vs-time relationships in various nuclei collapse into a single master curve by normalizing them with the mesh size and the corresponding time scale. This enables us to identify the onset of the entangled dynamics with the size of tube diameter of chromatin polymer in the C. elegans embryo. Our dynamical scaling analysis predicts the transition between unentangled and entangled dynamics of chromatin polymers, the quantitative formula for MSD as a function of nuclear size and timescale, and provides testable hypotheses on chromatin mobility in other cell types and species.

Shaping the genome via lengthwise compaction, phase separation, and lamina adhesion

The link between genomic structure and biological function is yet to be consolidated, it is, however, clear that physical manipulation of the genome, driven by the activity of a variety of proteins, is a crucial step. To understand the consequences of the physical forces underlying genome organization, we build a coarse-grained polymer model of the genome, featuring three fundamentally distinct classes of interactions: lengthwise compaction, i.e., compaction of chromosomes along its contour, self-adhesion among epigenetically similar genomic segments, and adhesion of chromosome segments to the nuclear envelope or lamina. We postulate that these three types of interactions sufficiently represent the concerted action of the different proteins organizing the genome architecture and show that an interplay among these interactions can recapitulate the architectural variants observed across the tree of life. The model elucidates how an interplay of forces arising from the three classes of genomic interactions can drive drastic, yet predictable, changes in the global genome architecture, and makes testable predictions. We posit that precise control over these interactions in vivo is key to the regulation of genome architecture.

The Physical Behavior of Interphase Chromosomes: Polymer Theory and Coarse-Grain Computer Simulations

Fluorescence in situ hybridization and chromosome conformation capture methods point to the same conclusion: that chromosomes appear to the external observer as compact structures with a highly nonrandom three-dimensional organization. In this work, we recapitulate the efforts made by us and other groups to rationalize this behavior in terms of the mathematical language and tools of polymer physics. After a brief introduction dedicated to some crucial experiments dissecting the structure of interphase chromosomes, we discuss at a nonspecialistic level some fundamental aspects of theoretical and numerical polymer physics. Then, we inglobe biological and polymer aspects into a polymer model for interphase chromosomes which moves from the observation that mutual topological constraints, such as those typically present between polymer chains in ordinary melts, induce slow chain dynamics and "constraint" chromosomes to resemble double-folded randomly branched polymer conformations. By explicitly turning these ideas into a multi-scale numerical algorithm which is described here in full details, we can design accurate model polymer conformations for interphase chromosomes and offer them for systematic comparison to experiments. The review is concluded by discussing the limitations of our approach and pointing to promising perspectives for future work.

Computer simulations of melts of ring polymers with nonconserved topology: A dynamic Monte Carlo lattice model

We present computer simulations of a dynamic Monte Carlo algorithm for polymer chains on a fcc lattice which explicitly takes into account the possibility to overcome topological constraints by controlling the rate at which nearby polymer strands may cross through each other. By applying the method to systems of interacting ring polymers at melt conditions, we characterize their structure and dynamics by measuring, in particular, the amounts of knots and links which are formed during the relaxation process. In comparison with standard melts of unknotted and unconcatenated rings, our simulations demonstrate that the mechanism of strand crossing makes polymer dynamics faster provided the characteristic timescale of the process is smaller than the typical timescale for chain relaxation in the unperturbed state, in agreement with recent experiments employing solutions of DNA rings in the presence of the type II topoisomerase enzyme. In the opposite case of slow rates the melt is shown to become slower, and this prediction may be easily validated experimentally.

Linker histone H1.8 inhibits chromatin binding of condensins and DNA topoisomerase II to tune chromosome length and individualization

DNA loop extrusion by condensins and decatenation by DNA topoisomerase II (topo II) are thought to drive mitotic chromosome compaction and individualization. Here, we reveal that the linker histone H1.8 antagonizes condensins and topo II to shape mitotic chromosome organization. In vitro chromatin reconstitution experiments demonstrate that H1.8 inhibits binding of condensins and topo II to nucleosome arrays. Accordingly, H1.8 depletion in Xenopus egg extracts increased condensins and topo II levels on mitotic chromatin. Chromosome morphology and Hi-C analyses suggest that H1.8 depletion makes chromosomes thinner and longer through shortening the average loop size and reducing the DNA amount in each layer of mitotic loops. Furthermore, excess loading of condensins and topo II to chromosomes by H1.8 depletion causes hyper-chromosome individualization and dispersion. We propose that condensins and topo II are essential for chromosome individualization, but their functions are tuned by the linker histone to keep chromosomes together until anaphase.

Mechanisms for Chromosome Segregation in Bacteria

The process of DNA segregation, the redistribution of newly replicated genomic material to daughter cells, is a crucial step in the life cycle of all living systems. Here, we review DNA segregation in bacteria which evolved a variety of mechanisms for partitioning newly replicated DNA. Bacterial species such as Caulobacter crescentus and Bacillus subtilis contain pushing and pulling mechanisms that exert forces and directionality to mediate the moving of newly synthesized chromosomes to the bacterial poles. Other bacteria such as Escherichia coli lack such active segregation systems, yet exhibit a spontaneous de-mixing of chromosomes due to entropic forces as DNA is being replicated under the confinement of the cell wall. Furthermore, we present a synopsis of the main players that contribute to prokaryotic genome segregation. We finish with emphasizing the importance of bottom-up approaches for the investigation of the various factors that contribute to genome segregation.

Scaling Laws for Mitotic Chromosomes

During mitosis in higher eukaryotes, each chromosome condenses into a pair of rod-shaped chromatids. This process is co-regulated by the activity of several gene families, and the underlying biophysics remains poorly understood. To better understand the factors regulating chromosome condensation, we compiled a database of mitotic chromosome size and DNA content from the tables and figures of >200 published papers. A comparison across vertebrate species shows that chromosome width, length and volume scale with DNA content to the powers ∼1/4, ∼1/2, and ∼1, respectively. Angiosperms (flowering plants) show a similar length scaling, so this result is not specific to vertebrates. Chromosome shape and size thus satisfy two conditions: (1) DNA content per unit volume is approximately constant and (2) the cross-sectional area increases proportionately with chromosome length. Since viscous drag forces during chromosome movement are expected to scale with length, we hypothesize that the cross-section increase is necessary to limit the occurrence of large chromosome elongations that could slow or stall mitosis. Lastly, we note that individual vertebrate karyotypes typically exhibit a wider range of chromosome lengths as compared with angiosperms.

Reflections on the organization and the physical state of chromatin in eukaryotic cells

In recent years, our perception of chromatin structure and organization in the cell nucleus has changed in fundamental ways. The 30 nm chromatin fiber has lost its status as an essential in vivo structure. Hi-C and related biochemical methods, advanced electron and super-resolved fluorescence microscopy, together with concepts from soft matter physics, have revolutionized the field. A comprehensive understanding of the structural and functional interactions that regulate cell cycle and cell type specific nuclear functions appears within reach, but it requires the integration of top-down and bottom-up approachs. In this review, I present an update on nuclear architecture studies with an emphasis on organization and the controversy regarding the physical state of chromatin in cells.

The Accidental Ally: Nucleosome Barriers Can Accelerate Cohesin-Mediated Loop Formation in Chromatin

An important question in the context of the three-dimensional organization of chromosomes is the mechanism of formation of large loops between distant basepairs. Recent experiments suggest that the formation of loops might be mediated by loop extrusion factor proteins such as cohesin. Experiments on cohesin have shown that cohesins walk diffusively on the DNA and that nucleosomes act as obstacles to the diffusion, lowering the permeability and hence reducing the effective diffusion constant. An estimation of the times required to form the loops of typical sizes seen in Hi-C experiments using these low-effective-diffusion constants leads to times that are unphysically large. The puzzle then is the following: how does a cohesin molecule diffusing on the DNA backbone achieve speeds necessary to form the large loops seen in experiments? We propose a simple answer to this puzzle and show that although at low densities, nucleosomes act as barriers to cohesin diffusion, beyond a certain concentration they can reduce loop formation times because of a subtle interplay between the nucleosome size and the mean linker length. This effect is further enhanced on considering stochastic binding kinetics of nucleosomes on the DNA backbone and leads to predictions of lower loop formation times than might be expected from a naive obstacle picture of nucleosomes.

Multi-contact 3C reveals that the human genome during interphase is largely not entangled

During interphase the eukaryotic genome is organized into chromosome territories that are spatially segregated into compartment domains. The extent to which interacting domains or chromosomes are entangled is not known. We analyze series of co-occurring chromatin interactions using multi-contact 3C (MC-3C) in human cells to provide insights into the topological entanglement of chromatin. Multi-contact interactions represent percolation paths (C-walks) through 3D chromatin space. We find that the order of interactions within C-walks that occur across interfaces where chromosomes or compartment domains interact is not random. Polymer simulations show that such C-walks are consistent with distal domains being topologically insulated, i.e. not catenated. Simulations show that even low levels of random strand passage, e.g. by topoisomerase II, would result in entanglements, increased mixing at domain interfaces and an order of interactions within C-walks not consistent with experimental MC-3C data. Our results indicate that during interphase entanglements between chromosomes and chromosomal domains are rare.

Light microscopy of proteins in their ultrastructural context

Resolving the distribution of specific proteins at the nanoscale in the ultrastructural context of the cell is a major challenge in fluorescence microscopy. We report the discovery of a new principle for an optical contrast equivalent to electron microscopy (EM) which reveals the ultrastructural context of the cells with a conventional confocal microscope. By decrowding the intracellular space through 13 to 21-fold physical expansion while simultaneously retaining the proteins, bulk (pan) labeling of the proteome resolves local protein densities and reveals the cellular nanoarchitecture by standard light microscopy.

Chromosome organization by one-sided and two-sided loop extrusion

SMC complexes, such as condensin or cohesin, organize chromatin throughout the cell cycle by a process known as loop extrusion. SMC complexes reel in DNA, extruding and progressively growing DNA loops. Modeling assuming two-sided loop extrusion reproduces key features of chromatin organization across different organisms. In vitro single-molecule experiments confirmed that yeast condensins extrude loops, however, they remain anchored to their loading sites and extrude loops in a 'one-sided' manner. We therefore simulate one-sided loop extrusion to investigate whether 'one-sided' complexes can compact mitotic chromosomes, organize interphase domains, and juxtapose bacterial chromosomal arms, as can be done by 'two-sided' loop extruders. While one-sided loop extrusion cannot reproduce these phenomena, variants can recapitulate in vivo observations. We predict that SMC complexes in vivo constitute effectively two-sided motors or exhibit biased loading and propose relevant experiments. Our work suggests that loop extrusion is a viable general mechanism of chromatin organization.

Physics and Biology (of Chromosomes)

Advances in molecular biology, optics, genetics, and bioinformatics have opened the door to mapping, in molecular detail, processes inside living cells. With the ability to observe the individual moving parts of cellular machinery, concepts formerly confined to physics are entering mainstream biology. This article discusses a few ideas of this sort related to chromosome biology, to illustrate what kinds of insights physics might yet bring to our understanding of living systems.