Compaction and segregation of sister chromatids via active loop extrusion

Bridging-mediated compaction of mitotic chromosomes

Within living cells, chromosome shapes undergo a striking morphological transition, from loose and uncondensed fibers during interphase to compacted and cylindrical structures during mitosis. ATP driven loop extrusion performed by a specialized protein complex, condensin, has recently emerged as a key driver of this transition. However, while this mechanism can successfully recapitulate the compaction of chromatids during the early stages of mitosis, it cannot capture structures observed after prophase. Here we hypothesize that a condensin bridging activity plays an additional important role, and review evidence - obtained largely through molecular dynamics simulations - that, in combination with loop extrusion, it can generate compact metaphase cylinders. Additionally, the resulting model qualitatively explains the unusual elastic properties of mitotic chromosomes observed in micromanipulation experiments and provides insights into the role of condensins in the formation of abnormal chromosome structures associated with common fragile sites.

Nanoscale DNA tracing reveals the self-organization mechanism of mitotic chromosomes

How genomic DNA is folded during cell division to form the characteristic rod-shaped mitotic chromosomes essential for faithful genome inheritance is a long-standing open question in biology. Here, we use nanoscale DNA tracing in single dividing cells to directly visualize how the 3D fold of genomic DNA changes during mitosis at scales from single loops to entire chromosomes. Our structural analysis reveals a characteristic genome scaling minimum of 6-8 megabases in mitosis. Combined with data-driven modeling and molecular perturbations, we can show that very large and strongly overlapping loops formed by condensins are the fundamental structuring principle of mitotic chromosomes. These loops compact chromosomes locally and globally to the limit set by chromatin self-repulsion. The characteristic length, density, and increasingly overlapping structure of mitotic loops we observe in 3D fully explain how the rod-shaped mitotic chromosome structure emerges by self-organization during cell division.

Coarse-grained chromatin dynamics by tracking multiple similarly labeled gene loci

The "holy grail" of chromatin research would be to follow the chromatin configuration in individual live cells over time. One way to achieve this goal would be to track the positions of multiple loci arranged along the chromatin polymer with fluorescent labels. Using distinguishable labels would define each locus uniquely in a microscopic image but would restrict the number of loci that could be observed simultaneously due to experimental limits to the number of distinguishable labels. Using the same label for all loci circumvents this limitation but requires a (currently lacking) framework for how to establish each observed locus identity, i.e., to which genomic position it corresponds. Here, we analyze theoretically, using simulations of Rouse model polymers, how single-particle tracking of multiple identically labeled loci enables the determination of loci identity. We show that the probability of correctly assigning observed loci to genomic positions converges exponentially to unity as the number of observed loci configurations increases. The convergence rate depends only weakly on the number of labeled loci, so that even large numbers of loci can be identified with high fidelity by tracking them across about eight independent chromatin configurations. In the case of two distinct labels that alternate along the chromatin polymer, we find that the probability of the correct assignment converges faster than for same-labeled loci, requiring observation of fewer independent chromatin configurations to establish loci identities. Finally, for a modified Rouse model polymer, which realizes a population of dynamic loops, we find that the success probability also converges to unity exponentially as the number of observed loci configurations increases, albeit slightly more slowly than for a classical Rouse model polymer. Altogether, these results establish particle tracking of multiple identically or alternately labeled loci over time as a feasible way to infer temporal dynamics of the coarse-grained configuration of the chromatin polymer in individual living cells.

Barrier effects on the kinetics of cohesin-mediated loop extrusion

Chromosome organization mediated by structural maintenance of chromosome complexes is crucial in many organisms. Cohesin extrudes chromatin into loops that are thought to lengthen until it is obstructed by CTCF proteins. In complex cellular environments, the loop extrusion machinery may encounter other chromatin-binding proteins. How these proteins interfere with the cohesin-meditated extrusion process is largely unexplored, but recent experiments have shown that some proteins serve as physical barriers that block cohesin translocation. Other proteins containing a cohesin-interaction motif serve as chemical barriers to induce cohesin pausing through interactions with it. Here, we develop an analytically solvable approach for the loop extrusion model incorporating barriers to investigate the effect of the barrier on the passive extrusion process. To further quantify the impact of barriers, we calculate the mean looping time it takes for cohesin to translocate to form a stable loop before dissociation. Our finding reveals that the physical barrier can accelerate the loop formation, and the degree of acceleration is closely related to the impedance strength of the physical barrier. In particular, the synergy of the cohesin loading site and the physical barrier site accelerates loop formation more significantly. The proximity of the cohesin loading site to the barrier site facilitates the rapid formation of stable loops in long genomes, which implies loop extrusion and chromatin-binding proteins might shape functional genomic organization. Conversely, chemical barriers consistently impede loop formation, with increasing impedance strength of the chemical barrier leading to longer loop formation time. Our study contributes to a more comprehensive understanding of the complexity of the loop extrusion process, providing a new perspective on the potential mechanisms of gene regulation.

Solution AFM Imaging and Coarse-grained Molecular Modeling of Yeast Condensin Structural Variation Coupled to the ATP Hydrolysis Cycle

Condensin is a protein complex that regulates chromatin structural changes during mitosis. It varies the molecular conformation through the ATP hydrolysis cycle and extrudes DNA loops into its ring-like structure as a molecular motor. Condensin contains Smc2 and Smc4, in which a coiled-coil arm tethers the hinge and head domains and dimerizes at the hinge. ATPs bind between the heads, induce their engagement, and are hydrolyzed to promote their disengagement. Previously, we performed solution atomic force microscopy (AFM) imaging of yeast condensin holo-complex with ATP and conducted flexible molecular fitting, obtaining the hinge structure with open conformation. However, it has yet to be clarified how the opening/closing of the hinge is coupled to the ATP hydrolysis cycle. In this study, we performed solution AFM imaging in the presence and absence of varying nucleotides, including AMP-PNP, ATPγS, and ADP. Furthermore, we conducted molecular dynamics simulations of an Smc2/4 heterodimer and selected the structure best representing each AFM image. Our results suggested that head engagement upon ATP binding is coupled to hinge opening and that the N-terminal region of Brn1, one of the accessory subunits, re-associates to the Smc2 head after ADP release.

SRBD1, a highly conserved gene required for chromosome individualization

Despite significant progress made in functional genomics, the roles of a relatively small number of essential genes remain enigmatic. Here, we characterize S1 RNA-binding domain-containing protein 1 (SRBD1), an essential gene with no previously assigned function. Through genetic, proteomic, and functional approaches, we discovered that SRBD1 is a DNA-binding protein and a key component of the mitotic chromatid axis. The loss of SRBD1 results in a pronounced defect in sister chromatid segregation that strikingly resembles the phenotype observed when sister chromatid decatenation is perturbed by topoisomerase IIα (TOP2A) dysfunction. Using genetic screens, we uncovered that the requirement for SRBD1 depends on the presence of condensin II but not condensin I. Moreover, we found that SRBD1 activity is most critical during prophase, when chromosome condensation is established. Taking these results together, we propose that SRBD1 acts during prophase to safeguard the decatenation process to prevent the formation of difficult-to-resolve DNA structures, thereby averting severe chromosome missegregations.

Rules of engagement for condensins and cohesins guide mitotic chromosome formation

We used Hi-C, imaging, proteomics, and polymer modeling to define rules of engagement for SMC (structural maintenance of chromosomes) complexes as cells refold interphase chromatin into rod-shaped mitotic chromosomes. First, condensin disassembles interphase chromatin loop organization by evicting or displacing extrusive cohesin. Second, condensin bypasses cohesive cohesins, thereby maintaining sister chromatid cohesion as sisters separate. Studies of mitotic chromosomes formed by cohesin, condensin II, and condensin I alone or in combination lead to refined models of mitotic chromosome conformation. In these models, loops are consecutive and not overlapping, implying that condensins stall upon encountering each other. The dynamics of Hi-C interactions and chromosome morphology reveal that during prophase, loops are extruded in vivo at ∼1 to 3 kilobases per second by condensins as they form a disordered discontinuous helical scaffold within individual chromatids.

Nuclear exclusion of condensin I in prophase coordinates mitotic chromosome reorganization to ensure complete sister chromatid resolution

During early mitosis, chromosomes transition from their unfolded interphase state to the distinct rod-shaped structures characteristic of mitosis. This process allows correct segregation of replicated sister chromatids to the opposite spindle poles during anaphase. Two protein complexes, named condensin I and condensin II, facilitate mitotic chromosome organization. Condensin II is important for achieving sister chromatid separation (resolution), while condensin I is required for chromosome condensation (folding). Although sister chromatid resolution occurs earlier than chromosome folding, it is not yet clear how these events are coordinated through time or whether this is important for correct chromosome segregation. In this study, we tested the hypothesis that temporal control is achieved through differential localization of the two condensin complexes; i.e., while condensin II localizes in the nucleus, condensin I is excluded from the nucleus in interphase and prophase. We engineered the localization of condensin I to the nucleus and monitored sister chromatid resolution and chromosome folding by real-time imaging. We found that localization of condensin I to the nucleus led to precocious chromosome folding during prophase, with similar timing to sister chromatid resolution. Furthermore, this change led to incomplete sister chromatid resolution in prometaphase/metaphase and frequent chromosome missegregation in anaphase, in which most missegregated chromosomes consisted of lagging chromosomes involving both sister chromatids. We conclude that, in a physiological context, the exclusion of condensin I from the nucleus during prophase delays chromosome folding and allows condensin II to complete sister chromatid resolution, which ensures correct chromosome segregation later in mitosis.

A unified model for cohesin function in sisterchromatid cohesion and chromatin loop formation

The ring-shaped cohesin complex topologically entraps two DNAs to establish sister chromatid cohesion. Cohesin also shapes the interphase chromatin landscape by forming DNA loops, which it is thought to achieve using an in vitro-observed loop extrusion mechanism. However, recent studies revealed that loop-extrusion-deficient cohesin retains its ability to form chromatin loops, suggesting a divergence of in vitro and in vivo loop formation. Instead of loop extrusion, we examine whether cohesin forms chromatin loops by a mechanism akin to sister chromatid cohesion establishment: sequential topological capture of two DNAs. We explore similarities and differences between the "loop capture" and the "loop extrusion" model, how they compare at explaining experimental observations, and how future approaches can delineate their possible respective contributions. We extend our DNA-DNA capture model for cohesin function to related structural maintenance of chromosomes (SMC) family members, condensin, the Smc5-Smc6 complex, and bacterial SMC complexes.

The DEAD-box helicase eIF4A1/2 acts as RNA chaperone during mitotic exit enabling chromatin decondensation

During mitosis, chromosomes condense and decondense to segregate faithfully and undamaged. The exact molecular mechanisms are not well understood. We identify the DEAD-box helicase eIF4A1/2 as a critical factor in this process. In a cell-free condensation assay eIF4A1/2 is crucial for this process, relying on its RNA-binding ability but not its ATPase activity. Reducing eIF4A1/2 levels in cells consistently slows down chromatin decondensation during nuclear reformation. Conversely, increasing eIF4A1/2 concentration on mitotic chromosomes accelerates their decondensation. The absence of eIF4A1/2 affects the perichromatin layer, which surrounds the chromosomes during mitosis and consists of RNA and mainly nucleolar proteins. In vitro, eIF4A1/2 acts as an RNA chaperone, dissociating biomolecular condensates of RNA and perichromatin proteins. During mitosis, the chaperone activity of eIF4A1/2 is required to regulate the composition and fluidity of the perichromatin layer, which is crucial for the dynamic reorganization of chromatin as cells exit mitosis.

Coarse-grained chromatin dynamics by tracking multiple similarly labeled gene loci

The "holy grail" of chromatin research would be to follow the chromatin configuration in individual live cells over time. One way to achieve this goal would be to track the positions of multiple loci arranged along the chromatin polymer with fluorescent labels. Use of distinguishable labels would define each locus uniquely in a microscopic image but would restrict the number of loci that could be observed simultaneously, because of experimental limits to the number of distinguishable labels. Use of the same label for all loci circumvents this limitation but requires a (currently lacking) framework for how to establish each observed locus identity, i.e. to which genomic position it corresponds. Here we analyze theoretically, using simulations of Rouse-model polymers, how single-particle-tracking of multiple identically-labeled loci enables determination of loci identity. We show that the probability of correctly assigning observed loci to genomic positions converges exponentially to unity as the number of observed loci configurations increases. The convergence rate depends only weakly on the number of labeled loci, so that even large numbers of loci can be identified with high fidelity by tracking them across about 8 independent chromatin configurations. In the case of two distinct labels that alternate along the chromatin polymer, we find that the probability of the correct assignment converges faster than for same-labeled loci, requiring observation of fewer independent chromatin configurations to establish loci identities. Finally, for a modified Rouse-model polymer, that realizes a population of dynamic loops, we find that the success probability also converges to unity exponentially as the number of observed loci configurations increases, albeit slightly more slowly than for a classical Rouse model polymer. Altogether, these results establish particle tracking of multiple identically- or alternately-labeled loci over time as a feasible way to infer temporal dynamics of the coarse-grained configuration of the chromatin polymer in individual living cells.

Emerging Roles for Transcription Factors During Mitosis

The genome is dynamically reorganized, partitioned, and divided during mitosis. Despite their role in organizing interphase chromatin, transcription factors were largely believed to be mitotic spectators evicted from chromatin during mitosis, only able to reestablish their position on DNA upon entry into G1. However, a panoply of evidence now contradicts this early belief. Numerous transcription factors are now known to remain active during mitosis to achieve diverse purposes, including chromosome condensation, regulation of the centromere/kinetochore function, and control of centrosome homeostasis. Inactivation of transcription factors during mitosis results in chromosome segregation errors, key features of cancer. Moreover, active transcription and the production of centromere-derived transcripts during mitosis are also known to play key roles in maintaining chromosomal stability. Finally, many transcription factors are associated with chromosomal instability through poorly defined mechanisms. Herein, we will review the emerging roles of transcription factors and transcription during mitosis with a focus on their role in promoting the faithful segregation of sister chromatids.

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.

Sequence-dependent activity and compartmentalization of foreign DNA in a eukaryotic nucleus

In eukaryotes, DNA-associated protein complexes coevolve with genomic sequences to orchestrate chromatin folding. We investigate the relationship between DNA sequence and the spontaneous loading and activity of chromatin components in the absence of coevolution. Using bacterial genomes integrated into Saccharomyces cerevisiae, which diverged from yeast more than 2 billion years ago, we show that nucleosomes, cohesins, and associated transcriptional machinery can lead to the formation of two different chromatin archetypes, one transcribed and the other silent, independently of heterochromatin formation. These two archetypes also form on eukaryotic exogenous sequences, depend on sequence composition, and can be predicted using neural networks trained on the native genome. They do not mix in the nucleus, leading to a bipartite nuclear compartmentalization, reminiscent of the organization of vertebrate nuclei.

SMC motor proteins extrude DNA asymmetrically and can switch directions

Structural maintenance of chromosomes (SMC) complexes organize the genome via DNA loop extrusion. Although some SMCs were reported to do so symmetrically, reeling DNA from both sides into the extruded DNA loop simultaneously, others perform loop extrusion asymmetrically toward one direction only. The mechanism underlying this variability remains unclear. Here, we examine the directionality of DNA loop extrusion by SMCs using in vitro single-molecule experiments. We find that cohesin and SMC5/6 do not reel in DNA from both sides, as reported before, but instead extrude DNA asymmetrically, although the direction can switch over time. Asymmetric DNA loop extrusion thus is the shared mechanism across all eukaryotic SMC complexes. For cohesin, direction switches strongly correlate with the turnover of the subunit NIPBL, during which DNA strand switching may occur. Apart from expanding by extrusion, loops frequently diffuse and shrink. The findings reveal that SMCs, surprisingly, can switch directions.

SMC-mediated chromosome organization: Does loop extrusion explain it all?

In recent years, loop extrusion has attracted much attention as a general mechanism of chromosome organization mediated by structural maintenance of chromosomes (SMC) protein complexes, such as condensin and cohesin. Despite accumulating evidence in support of this mechanism, it is not fully established whether or how loop extrusion operates under physiological conditions, or whether any alternative or additional SMC-mediated mechanisms operate in the cell. In this review, we summarize non-loop extrusion mechanisms proposed in the literature and clarify unresolved issues to further enrich our understanding of how SMC protein complexes work.

In vitro dynamics of DNA loop extrusion by structural maintenance of chromosomes complexes

Genomic DNA inside the cell's nucleus is highly organized and tightly controlled by the structural maintenance of chromosomes (SMC) protein complexes. These complexes fold genomes by creating and processively enlarging loops, a process called loop extrusion. After more than a decade of accumulating indirect evidence, recent in vitro single-molecule studies confirmed loop extrusion as an evolutionarily conserved function among eukaryotic and prokaryotic SMCs. These studies further provided important insights into mechanisms and regulations of these universal molecular machines, which will be discussed in this minireview.

Interphase chromatin biophysics and mechanics: new perspectives and open questions

The physical organization and properties of chromatin within the interphase nucleus are intimately linked to a wide range of functional DNA-based processes. In this context, interphase chromatin mechanics - that is, how chromatin, physically, responds to forces - is gaining increasing attention. Recent methodological advances for probing the force-response of chromatin in cellulo open new avenues for research, as well as new questions. This review discusses emerging views from these approaches and others, including recent in vitro single-molecule studies of cohesin and condensin motor activities, providing insights into physical and material aspects of chromatin, its plasticity in the context of functional processes, its nonequilibrium or 'active matter' properties, and the importance of factors such as chromatin fiber tension and stiffness. This growing field offers exciting opportunities to better understand the interplay between interphase chromosome structure, dynamics, mechanics, and functions.

Ipsilateral restriction of chromosome movement along a centrosome, and apical-basal axis during the cell cycle

Little is known about how distance between homologous chromosomes are controlled during the cell cycle. Here, we show that the distribution of centromere components display two discrete clusters placed to either side of the centrosome and apical/basal axis from prophase to G1 interphase. 4-Dimensional live cell imaging analysis of centromere and centrosome tracking reveals that centromeres oscillate largely within one cluster, but do not cross over to the other cluster. We propose a model of an axis-dependent ipsilateral restriction of chromosome oscillations throughout mitosis.

Stiff extracellular matrix drives the differentiation of mesenchymal stem cells toward osteogenesis by the multiscale 3D genome reorganization

Extracellular matrix (ECM) stiffness is a major driver of stem cell fate. However, the involvement of the three-dimensional (3D) genomic reorganization in response to ECM stiffness remains unclear. Here, we generated comprehensive 3D chromatin landscapes of mesenchymal stem cells (MSCs) exposed to various ECM stiffness. We found that there were more long-range chromatin interactions, but less compartment A in MSCs cultured on stiff ECM than those cultured on soft ECM. However, the switch from compartment B in MSCs cultured on soft ECM to compartment A in MSCs cultured on stiff ECM included genes encoding proteins primarily enriched in cytoskeleton organization. At the topologically associating domains (TADs) level, stiff ECM tends to have merged TADs on soft ECM. These merged TADs on stiff ECM include upregulated genes encoding proteins enriched in osteogenesis, such as SP1, ETS1, and DCHS1, which were validated by quantitative real-time polymerase chain reaction and found to be consistent with the increase of alkaline phosphatase staining. Knockdown of SP1 or ETS1 led to the downregulation of osteogenic marker genes, including COL1A1, RUNX2, ALP, and OCN in MSCs cultured on stiff ECM. Our study provides an important insight into the stiff ECM-mediated promotion of MSC differentiation towards osteogenesis, emphasizing the influence of mechanical cues on the reorganization of 3D genome architecture and stem cell fate.

Understanding and Simulating the Dynamics of a Polymer-Like Chromatin

Chromatin modeling enables the characterization of chromatin architecture at a resolution so far unachievable with experimental techniques. Polymer models fill our knowledge gap on a wide range of structures, from chromatin loops to nuclear compartments. Many physical properties already known for polymers can thus explain the dynamics of chromatin. With molecular simulations, it is possible to probe an ensemble of conformations, which attest to the variability observed in individual cells and the general behavior of a population of cells. In this review, we describe universal characteristics of polymers that chromatin carries. We introduce how these characteristics can be assessed with polymer simulations while also addressing specific aspects of chromatin and its environment. Finally, we give examples of plant chromatin models that, despite their paucity, augur well for the future of polymer simulations to plant chromosome biology.

Multiscale molecular modeling of chromatin with MultiMM: From nucleosomes to the whole genome

Motivation: We present a user-friendly 3D chromatin simulation model for the human genome based on OpenMM, addressing the challenges posed by existing models with use-specific implementations. Our approach employs a multi-scale energy minimization strategy, capturing chromatin's hierarchical structure. Initiating with a Hilbert curve-based structure, users can input files specifying nucleosome positioning, loops, compartments, or subcompartments. Results: The model utilizes an energy minimization approach with a large choice of numerical integrators, providing the entire genome's structure within minutes. Output files include the generated structures for each chromosome, offering a versatile and accessible tool for chromatin simulation in bioinformatics studies. Furthermore, MultiMM is capable of producing nucleosome-resolution structures by making simplistic geometric assumptions about the structure and the density of nucleosomes on the DNA. Code availability: Open-source software and the manual are freely available on https://github.com/SFGLab/MultiMM or via pip https://pypi.org/project/MultiMM/.

Cohesin distribution alone predicts chromatin organization in yeast via conserved-current loop extrusion

BACKGROUND

Inhomogeneous patterns of chromatin-chromatin contacts within 10-100-kb-sized regions of the genome are a generic feature of chromatin spatial organization. These features, termed topologically associating domains (TADs), have led to the loop extrusion factor (LEF) model. Currently, our ability to model TADs relies on the observation that in vertebrates TAD boundaries are correlated with DNA sequences that bind CTCF, which therefore is inferred to block loop extrusion. However, although TADs feature prominently in their Hi-C maps, non-vertebrate eukaryotes either do not express CTCF or show few TAD boundaries that correlate with CTCF sites. In all of these organisms, the counterparts of CTCF remain unknown, frustrating comparisons between Hi-C data and simulations.

RESULTS

To extend the LEF model across the tree of life, here, we propose the conserved-current loop extrusion (CCLE) model that interprets loop-extruding cohesin as a nearly conserved probability current. From cohesin ChIP-seq data alone, we derive a position-dependent loop extrusion rate, allowing for a modified paradigm for loop extrusion, that goes beyond solely localized barriers to also include loop extrusion rates that vary continuously. We show that CCLE accurately predicts the TAD-scale Hi-C maps of interphase Schizosaccharomyces pombe, as well as those of meiotic and mitotic Saccharomyces cerevisiae, demonstrating its utility in organisms lacking CTCF.

CONCLUSIONS

The success of CCLE in yeasts suggests that loop extrusion by cohesin is indeed the primary mechanism underlying TADs in these systems. CCLE allows us to obtain loop extrusion parameters such as the LEF density and processivity, which compare well to independent estimates.

The chromosome folding problem and how cells solve it

Every cell must solve the problem of how to fold its genome. We describe how the folded state of chromosomes is the result of the combined activity of multiple conserved mechanisms. Homotypic affinity-driven interactions lead to spatial partitioning of active and inactive loci. Molecular motors fold chromosomes through loop extrusion. Topological features such as supercoiling and entanglements contribute to chromosome folding and its dynamics, and tethering loci to sub-nuclear structures adds additional constraints. Dramatically diverse chromosome conformations observed throughout the cell cycle and across the tree of life can be explained through differential regulation and implementation of these basic mechanisms. We propose that the first functions of chromosome folding are to mediate genome replication, compaction, and segregation and that mechanisms of folding have subsequently been co-opted for other roles, including long-range gene regulation, in different conditions, cell types, and species.

DNA packaging by molecular motors: from bacteriophage to human chromosomes

Dense packaging of genomic DNA is crucial for organismal survival, as DNA length always far exceeds the dimensions of the cells that contain it. Organisms, therefore, use sophisticated machineries to package their genomes. These systems range across kingdoms from a single ultra-powerful rotary motor that spools the DNA into a bacteriophage head, to hundreds of thousands of relatively weak molecular motors that coordinate the compaction of mitotic chromosomes in eukaryotic cells. Recent technological advances, such as DNA proximity-based sequencing approaches, polymer modelling and in vitro reconstitution of DNA loop extrusion, have shed light on the biological mechanisms driving DNA organization in different systems. Here, we discuss DNA packaging in bacteriophage, bacteria and eukaryotic cells, which, despite their extreme variation in size, structure and genomic content, all rely on the action of molecular motors to package their genomes.

Nature of barriers determines first passage times in heterogeneous media

Intuition suggests that passage times across a region increase with the number of barriers along the path. Can this fail depending on the nature of the barrier? To probe this fundamental question, we exactly solve for the first passage time in general d-dimensions for diffusive transport through a spatially patterned array of obstacles - either entropic or energetic, depending on the nature of the obstacles. For energetic barriers, we show that first passage times vary non-monotonically with the number of barriers, while for entropic barriers it increases monotonically. This non-monotonicity for energetic barriers is further reflected in the behaviour of effective diffusivity as well. We then design a simple experiment where a robotic bug navigates in a heterogeneous environment through a spatially patterned array of obstacles to validate our predictions. Finally, using numerical simulations, we show that this non-monotonic behaviour for energetic barriers is general and extends to even super-diffusive transport.

Nanoscale 3D DNA tracing reveals the mechanism of self-organization of mitotic chromosomes

How genomic DNA is folded during cell division to form the characteristic rod-shaped mitotic chromosomes essential for faithful genome inheritance is a long-standing open question in biology. Here, we use nanoscale DNA-tracing in single dividing cells to directly visualize how the 3D fold of genomic DNA changes during mitosis, at scales from single loops to entire chromosomes. Our structural analysis reveals a characteristic genome scaling minimum at 6-8 Mbp in mitosis. Combined with data-driven modeling and molecular perturbations, we can show that very large and strongly overlapping loops formed by Condensins are the fundamental structuring principle of mitotic chromosomes. These loops compact chromosomes locally and globally to the limit set by chromatin self-repulsion. The characteristic length, density and increasingly overlapping structure of mitotic loops we observe in 3D, fully explain how the rod-shaped mitotic chromosome structure emerges by self-organization during cell division.

Prediction and functional interpretation of inter-chromosomal genome architecture from DNA sequence with TwinC

Three-dimensional nuclear DNA architecture comprises well-studied intra-chromosomal (cis) folding and less characterized inter-chromosomal (trans) interfaces. Current predictive models of 3D genome folding can effectively infer pairwise cis-chromatin interactions from the primary DNA sequence but generally ignore trans contacts. There is an unmet need for robust models of trans-genome organization that provide insights into their underlying principles and functional relevance. We present TwinC, an interpretable convolutional neural network model that reliably predicts trans contacts measurable through genome-wide chromatin conformation capture (Hi-C). TwinC uses a paired sequence design from replicate Hi-C experiments to learn single base pair relevance in trans interactions across two stretches of DNA. The method achieves high predictive accuracy (AUROC=0.80) on a cross-chromosomal test set from Hi-C experiments in heart tissue. Mechanistically, the neural network learns the importance of compartments, chromatin accessibility, clustered transcription factor binding and G-quadruplexes in forming trans contacts. In summary, TwinC models and interprets trans genome architecture, shedding light on this poorly understood aspect of gene regulation.

Symmetry of loop extrusion by dimeric SMC complexes is DNA-tension-dependent

Structural maintenance of chromosome (SMC) complexes organize and regulate genomes via DNA loop extrusion. During this process, the complexes increase the loop size by reeling in DNA from one or both sides of the loop. The factors governing this symmetry remain unclear. Here, we combine single-molecule analysis and molecular dynamic simulations to investigate the symmetry of loop extrusion of various SMC complexes. We find that whereas monomeric condensin and cohesin are one-sided extruders, the symmetry of dimeric SMCs, such as Smc5/6 and Wadjet, is DNA tension dependent. At low DNA tension (< 0.1pN), Smc5/6 and Wadjet extrude DNA from both sides of the loop. At higher tension, however, they transition to a behavior akin to one-sided extruders, yet still capable of extruding from one or the other side thereby switching the direction of extrusion. Our simulations further reveal that thermal fluctuations significantly influence loop extrusion symmetry, causing variations in DNA reeling rates between the two motors in the dimeric complexes and their direction switching at stalling tensions. Our findings challenge the previous view of loop extrusion symmetry as a fixed characteristic, revealing its dynamic nature and regulation by both intrinsic protein properties and extrinsic factors.

The physical chemistry of interphase loop extrusion

Loop extrusion constitutes a universal mechanism of genome organization, whereby structural maintenance of chromosomes (SMC) protein complexes load onto the chromatin fiber and generate DNA loops of increasingly-larger sizes until their eventual release. In mammalian interphase cells, loop extrusion is mediated by the cohesin complex, which is dynamically regulated by the interchange of multiple accessory proteins. Although these regulators bind the core cohesin complex only transiently, their disruption can dramatically alter cohesin dynamics, gene expression, chromosome morphology and contact patterns. Still, a theory of how cohesin regulators and their molecular interplay with the core complex modulate genome folding remains at large. Here we derive a model of cohesin loop extrusion from first principles, based on in vivo measurements of the abundance and dynamics of cohesin regulators. We systematically evaluate potential chemical reaction networks that describe the association of cohesin with its regulators and with the chromatin fiber. Remarkably, experimental observations are consistent with only a single biochemical reaction cycle, which results in a unique minimal model that may be fully parameterized by quantitative protein measurements. We demonstrate how distinct roles for cohesin regulators emerge simply from the structure of the reaction network, and how their dynamic exchange can regulate loop extrusion kinetics over time-scales that far exceed their own chromatin residence times. By embedding our cohesin biochemical reaction network within biophysical chromatin simulations, we evidence how variations in regulatory protein abundance can alter chromatin architecture across multiple length- and time-scales. Predictions from our model are corroborated by biophysical and biochemical assays, optical microscopy observations, and Hi-C conformation capture techniques. More broadly, our theoretical and numerical framework bridges the gap between in vitro observations of extrusion motor dynamics at the molecular scale and their structural consequences at the genome-wide level.

Unique territorial and compartmental organization of chromosomes in the holocentric silkmoth

The hallmarks of chromosome organization in multicellular eukaryotes are chromosome territories (CT), chromatin compartments, and insulated domains, including topologically associated domains (TADs). Yet, most of these elements of chromosome organization are derived from analyses of a limited set of model organisms, while large eukaryotic groups, including insects, remain mostly unexplored. Here we combine Hi-C, biophysical modeling, and microscopy to characterize the 3D genome architecture of the silkworm, Bombyx mori. In contrast to other eukaryotes, B. mori chromosomes form highly separated territories. Similar to other eukaryotes, B. mori chromosomes segregate into active A and inactive B compartments, yet unlike in vertebrate systems, contacts between euchromatic A regions appear to be a strong driver of compartmentalization. Remarkably, we also identify a third compartment, called secluded S, with a unique contact pattern. Each S region shows prominent short-range self-contacts and is remarkably devoid of contacts with the rest of the chromosome, including other S regions. Compartment S hosts a unique combination of genetic and epigenetic features, localizes towards the periphery of CTs, and shows developmental plasticity. Biophysical modeling reveals that the formation of such secluded domains requires highly localized loop extrusion within them, along with a low level of extrusion in A and B. Our Hi-C data supports predicted genome-wide and localized extrusion. Such a broad, non-uniform distribution of extruders has not been seen in other organisms. Overall, our analyses support loop extrusion in insects and highlight the evolutionary plasticity of 3D genome organization, driven by a new combination of known processes.

Heterogeneous flexibility can contribute to chromatin segregation in the cell nucleus

The highly and slightly condensed forms of chromatin, heterochromatin and euchromatin, respectively, segregate in the cell nucleus. Heterochromatin is more abundant in the nucleus periphery. Here we study the mechanism of heterochromatin segregation by modeling interphase chromosomes as diblock ring copolymers confined in a rigid spherical shell using molecular dynamics simulations. In our model, heterochromatin and euchromatin are distinguished by their bending stiffnesses only, while an interaction potential between the spherical shell and chromatin is used to model lamin-associated proteins. Our simulations indicate that in the absence of attractive interactions between the nuclear shell and the chromatin, most heterochromatin segregates towards the nuclear interior due to the depletion of less flexible heterochromatin segments from the nuclear periphery. This inverted chromatin distribution,which is opposite to the conventional case with heterochromatin dominating at the periphery, is in accord with experimental observations in rod cells. This "inversion" is also found to be independent of the heterochromatin concentration and chromosome number. The chromatin distribution at the periphery found in vivo can be recovered by further increasing the bending stiffness of heterochromatin segments or by turning on attractive interactions between the nuclear shell and heterochromatin. Our results indicate that the bending stiffness of chromatin could be a contributor to chromosome organization along with differential effects of HP1α-driven phase segregation and of loop extruders and interactions with the nuclear envelope and topological constraints.

Different relative scalings between transient forces and thermal fluctuations tune regimes of chromatin organization

Within the nucleus, structural maintenance of chromosome protein complexes, namely condensin and cohesin, create an architecture to facilitate the organization and proper function of the genome. Condensin, in addition to performing loop extrusion, creates localized clusters of chromatin in the nucleolus through transient crosslinks. Large-scale simulations revealed three different dynamic behaviors as a function of timescale: slow crosslinking leads to no clusters, fast crosslinking produces rigid slowly changing clusters, while intermediate timescales produce flexible clusters that mediate gene interaction. By mathematically analyzing different relative scalings of the two sources of stochasticity, thermal fluctuations and the force induced by the transient crosslinks, we predict these three distinct regimes of cluster behavior. Standard time-averaging that takes the fluctuations of the transient crosslink force to zero predicts the existence of rigid clusters. Accounting for the interaction of both fluctuations from the crosslinks and thermal noise with an effective energy landscape predicts the timescale-dependent lifetimes of flexible clusters. No clusters are predicted when the fluctuations of the transient crosslink force are taken to be large relative to thermal fluctuations. This mathematical perturbation analysis illuminates the importance of accounting for stochasticity in local incoherent transient forces to predict emergent complex biological behavior.

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.

Loop-extruders alter bacterial chromosome topology to direct entropic forces for segregation

Entropic forces have been argued to drive bacterial chromosome segregation during replication. In many bacterial species, however, specifically evolved mechanisms, such as loop-extruding SMC complexes and the ParABS origin segregation system, contribute to or are even required for chromosome segregation, suggesting that entropic forces alone may be insufficient. The interplay between and the relative contributions of these segregation mechanisms remain unclear. Here, we develop a biophysical model showing that purely entropic forces actually inhibit bacterial chromosome segregation until late replication stages. By contrast, our model reveals that loop-extruders loaded at the origins of replication, as observed in many bacterial species, alter the effective topology of the chromosome, thereby redirecting and enhancing entropic forces to enable accurate chromosome segregation during replication. We confirm our model predictions with polymer simulations: purely entropic forces do not allow for concurrent replication and segregation, whereas entropic forces steered by specifically loaded loop-extruders lead to robust, global chromosome segregation during replication. Finally, we show how loop-extruders can complement locally acting origin separation mechanisms, such as the ParABS system. Together, our results illustrate how changes in the geometry and topology of the polymer, induced by DNA-replication and loop-extrusion, impact the organization and segregation of bacterial chromosomes.

Compaction and Segregation of DNA in Escherichia coli

Theoretical and experimental approaches have been applied to study the polymer physics underlying the compaction of DNA in the bacterial nucleoid. Knowledge of the compaction mechanism is necessary to obtain a mechanistic understanding of the segregation process of replicating chromosome arms (replichores) during the cell cycle. The first part of this review discusses light microscope observations demonstrating that the nucleoid has a lower refractive index and thus, a lower density than the cytoplasm. A polymer physics explanation for this phenomenon was given by a theory discussed at length in this review. By assuming a phase separation between the nucleoid and the cytoplasm and by imposing equal osmotic pressure and chemical potential between the two phases, a minimal energy situation is obtained, in which soluble proteins are depleted from the nucleoid, thus explaining its lower density. This theory is compared to recent views on DNA compaction that are based on the exclusion of polyribosomes from the nucleoid or on the transcriptional activity of the cell. These new views prompt the question of whether they can still explain the lower refractive index or density of the nucleoid. In the second part of this review, we discuss the question of how DNA segregation occurs in Escherichia coli in the absence of the so-called active ParABS system, which is present in the majority of bacteria. How is the entanglement of nascent chromosome arms generated at the origin in the parental DNA network of the E. coli nucleoid prevented? Microscopic observations of the position of fluorescently-labeled genetic loci have indicated that the four nascent chromosome arms synthesized in the initial replication bubble segregate to opposite halves of the sister nucleoids. This implies that extensive intermingling of daughter strands does not occur. Based on the hypothesis that leading and lagging replichores synthesized in the replication bubble fold into microdomains that do not intermingle, a passive four-excluding-arms model for segregation is proposed. This model suggests that the key for segregation already exists in the structure of the replication bubble at the very start of DNA replication; it explains the different patterns of chromosome arms as well as the segregation distances between replicated loci, as experimentally observed.

Rules of engagement for condensins and cohesins guide mitotic chromosome formation

During mitosis, interphase chromatin is rapidly converted into rod-shaped mitotic chromosomes. Using Hi-C, imaging, proteomics and polymer modeling, we determine how the activity and interplay between loop-extruding SMC motors accomplishes this dramatic transition. Our work reveals rules of engagement for SMC complexes that are critical for allowing cells to refold interphase chromatin into mitotic chromosomes. We find that condensin disassembles interphase chromatin loop organization by evicting or displacing extrusive cohesin. In contrast, condensin bypasses cohesive cohesins, thereby maintaining sister chromatid cohesion while separating the sisters. Studies of mitotic chromosomes formed by cohesin, condensin II and condensin I alone or in combination allow us to develop new models of mitotic chromosome conformation. In these models, loops are consecutive and not overlapping, implying that condensins do not freely pass one another but stall upon encountering each other. The dynamics of Hi-C interactions and chromosome morphology reveal that during prophase loops are extruded in vivo at ~1-3 kb/sec by condensins as they form a disordered discontinuous helical scaffold within individual chromatids.

Ipsilateral restriction of chromosome movement along a centrosome, and apical-basal axis during the cell cycle

Little is known about how distance between homologous chromosomes are controlled during the cell cycle. Here, we show that the distribution of centromere components display two discrete clusters placed to either side of the centrosome and apical/basal axis from prophase to G1 interphase. 4-Dimensional live cell imaging analysis of centromere and centrosome tracking reveals that centromeres oscillate largely within one cluster, but do not cross over to the other cluster. We propose a model of an axis-dependent ipsilateral restriction of chromosome oscillations throughout mitosis.

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.

Footprints of loop extrusion in statistics of intra-chromosomal distances: An analytically solvable model

Active loop extrusion-the process of formation of dynamically growing chromatin loops due to the motor activity of DNA-binding protein complexes-is a firmly established mechanism responsible for chromatin spatial organization at different stages of a cell cycle in eukaryotes and bacteria. The theoretical insight into the effect of loop extrusion on the experimentally measured statistics of chromatin conformation can be gained with an appropriately chosen polymer model. Here, we consider the simplest analytically solvable model of an interphase chromosome, which is treated as an ideal chain with disorder of sufficiently sparse random loops whose conformations are sampled from the equilibrium ensemble. This framework allows us to arrive at the closed-form analytical expression for the mean-squared distance between pairs of genomic loci, which is valid beyond the one-loop approximation in diagrammatic representation. In addition, we analyze the loop-induced deviation of chain conformations from the Gaussian statistics by calculating kurtosis of probability density of the pairwise separation vector. The presented results suggest the possible ways of estimating the characteristics of the loop extrusion process based on the experimental data on the scale-dependent statistics of intra-chromosomal pair-wise distances.

Human Coronavirus Infection Reorganizes Spatial Genomic Architecture in Permissive Lung Cells

Chromatin conformation capture followed by next-generation sequencing in combination with large-scale polymer simulations (4DHiC) produces detailed information on genomic loci interactions, allowing for the interrogation of 3D spatial genomic structures. Here, Hi-C data was acquired from the infection of fetal lung fibroblast (MRC5) cells with α-coronavirus 229E (CoV229E). Experimental Hi-C contact maps were used to determine viral-induced changes in genomic architecture over a 48-hour time period following viral infection, revealing substantial alterations in contacts within chromosomes and in contacts between different chromosomes. To gain further structural insight and quantify the underlying changes, we applied the 4DHiC polymer simulation method to reconstruct the 3D genomic structures and dynamics corresponding to the Hi-C maps. The models successfully reproduced experimental Hi-C data, including the changes in contacts induced by viral infection. Our 3D spatial simulations uncovered widespread chromatin restructuring, including increased chromosome compactness and A-B compartment mixing arising from infection. Our model also suggests increased spatial accessibility to regions containing interferon-stimulated genes upon infection with CoV229E, followed by chromatin restructuring at later time points, potentially inducing the migration of chromatin into more compact regions. This is consistent with previously observed suppression of gene expression. Our spatial genomics study provides a mechanistic structural basis for changes in chromosome architecture induced by coronavirus infection in lung cells.

Effect of local active fluctuations on structure and dynamics of flexible biopolymers

Active fluctuations play a significant role in the structure and dynamics of biopolymers (e.g. chromatin and cytoskeletal proteins) that are instrumental in the functioning of living cells. For a large range of experimentally accessible length and time scales, these polymers can be represented as flexible chains that are subjected to spatially and temporally varying fluctuating forces. In this work, we introduce a mathematical framework that correlates the spatial and temporal patterns of the fluctuations to different observables that describe the dynamics and conformations of the polymer. We demonstrate the power of this approach by analyzing the case of a point fluctuation on the polymer with an exponential decay of correlation in time with a finite time constant. Specifically, we identify the length and time scale over which the behavior of the polymer exhibits a significant departure from the behavior of a Rouse chain and the range of impact of the fluctuation along the chain. Furthermore, we show that the conformation of the polymer retains the memory of the active fluctuation from earlier times. Altogether, this work sets the basis for understanding and interpreting the role of spatio-temporal patterns of fluctuations in the dynamics, conformation, and functionality of biopolymers in living cells.

Computational methods for analysing multiscale 3D genome organization

Recent progress in whole-genome mapping and imaging technologies has enabled the characterization of the spatial organization and folding of the genome in the nucleus. In parallel, advanced computational methods have been developed to leverage these mapping data to reveal multiscale three-dimensional (3D) genome features and to provide a more complete view of genome structure and its connections to genome functions such as transcription. Here, we discuss how recently developed computational tools, including machine-learning-based methods and integrative structure-modelling frameworks, have led to a systematic, multiscale delineation of the connections among different scales of 3D genome organization, genomic and epigenomic features, functional nuclear components and genome function. However, approaches that more comprehensively integrate a wide variety of genomic and imaging datasets are still needed to uncover the functional role of 3D genome structure in defining cellular phenotypes in health and disease.

Replicating Chromosomes in Whole-Cell Models of Bacteria

Computational models of cells cannot be considered complete unless they include the most fundamental process of life, the replication of genetic material. In a recent study, we presented a computational framework to model systems of replicating bacterial chromosomes as polymers at 10 bp resolution with Brownian dynamics. This approach was used to 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 modeled the chromosome as a self-avoiding homopolymer with bending and torsional stiffnesses that capture the essential mechanical properties of dsDNA in Syn3A. Additionally, the polymer interacts with ribosomes distributed according to cryo-electron tomograms of Syn3A. The polymer model was further augmented by computational models of loop extrusion by structural maintenance of chromosomes (SMC) protein complexes and topoisomerase action, and the modeling and analysis of multi-fork replication states.

Bridging condensins mediate compaction of mitotic chromosomes

Eukaryotic chromosomes compact during mitosis into elongated cylinders-and not the spherical globules expected of self-attracting long flexible polymers. This process is mainly driven by condensin-like proteins. Here, we present Brownian-dynamic simulations involving two types of such proteins with different activities. One, which we refer to as looping condensins, anchors long-lived chromatin loops to create bottlebrush structures. The second, referred to as bridging condensins, forms multivalent bridges between distant parts of these loops. We show that binding of bridging condensins leads to the formation of shorter and stiffer mitotic-like cylinders without requiring any additional energy input. These cylinders have several features matching experimental observations. For instance, the axial condensin backbone breaks up into clusters as found by microscopy, and cylinder elasticity qualitatively matches that seen in chromosome pulling experiments. Additionally, simulating global condensin depletion or local faulty condensin loading gives phenotypes seen experimentally and points to a mechanistic basis for the structure of common fragile sites in mitotic chromosomes.

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.

Establishment of dsDNA-dsDNA interactions by the condensin complex

Condensin is a structural maintenance of chromosomes (SMC) complex family member thought to build mitotic chromosomes by DNA loop extrusion. However, condensin variants unable to extrude loops, yet proficient in chromosome formation, were recently described. Here, we explore how condensin might alternatively build chromosomes. Using bulk biochemical and single-molecule experiments with purified fission yeast condensin, we observe that individual condensins sequentially and topologically entrap two double-stranded DNAs (dsDNAs). Condensin loading transitions through a state requiring DNA bending, as proposed for the related cohesin complex. While cohesin then favors the capture of a second single-stranded DNA (ssDNA), second dsDNA capture emerges as a defining feature of condensin. We provide complementary in vivo evidence for DNA-DNA capture in the form of condensin-dependent chromatin contacts within, as well as between, chromosomes. Our results support a "diffusion capture" model in which condensin acts in mitotic chromosome formation by sequential dsDNA-dsDNA capture.

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.

Leveraging polymer modeling to reconstruct chromatin connectivity from live images

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

Genome control by SMC complexes

Many cellular processes require large-scale rearrangements of chromatin structure. Structural maintenance of chromosomes (SMC) protein complexes are molecular machines that can provide structure to chromatin. These complexes can connect DNA elements in cis, walk along DNA, build and processively enlarge DNA loops and connect DNA molecules in trans to hold together the sister chromatids. These DNA-shaping abilities place SMC complexes at the heart of many DNA-based processes, including chromosome segregation in mitosis, transcription control and DNA replication, repair and recombination. In this Review, we discuss the latest insights into how SMC complexes such as cohesin, condensin and the SMC5-SMC6 complex shape DNA to direct these fundamental chromosomal processes. We also consider how SMC complexes, by building chromatin loops, can counteract the natural tendency of alike chromatin regions to cluster. SMC complexes thus control nuclear organization by participating in a molecular tug of war that determines the architecture of our genome.