RotoStep: A Chromosome Dynamics Simulator Reveals Mechanisms of Loop Extrusion

Polymer Modeling Reveals Interplay between Physical Properties of Chromosomal DNA and the Size and Distribution of Condensin-Based Chromatin Loops

Transient DNA loops occur throughout the genome due to thermal fluctuations of DNA and the function of SMC complex proteins such as condensin and cohesin. Transient crosslinking within and between chromosomes and loop extrusion by SMCs have profound effects on high-order chromatin organization and exhibit specificity in cell type, cell cycle stage, and cellular environment. SMC complexes anchor one end to DNA with the other extending some distance and retracting to form a loop. How cells regulate loop sizes and how loops distribute along chromatin are emerging questions. To understand loop size regulation, we employed bead-spring polymer chain models of chromatin and the activity of an SMC complex on chromatin. Our study shows that (1) the stiffness of the chromatin polymer chain, (2) the tensile stiffness of chromatin crosslinking complexes such as condensin, and (3) the strength of the internal or external tethering of chromatin chains cooperatively dictate the loop size distribution and compaction volume of induced chromatin domains. When strong DNA tethers are invoked, loop size distributions are tuned by condensin stiffness. When DNA tethers are released, loop size distributions are tuned by chromatin stiffness. In this three-way interaction, the presence and strength of tethering unexpectedly dictates chromatin conformation within a topological domain.

Single cohesin molecules generate force by two distinct mechanisms

Spatial organization of DNA is facilitated by cohesin protein complexes that move on DNA and extrude DNA loops. How cohesin works mechanistically as a molecular machine is poorly understood. Here, we measure mechanical forces generated by conformational changes in single cohesin molecules. We show that bending of SMC coiled coils is driven by random thermal fluctuations leading to a ~32 nm head-hinge displacement that resists forces up to 1 pN; ATPase head engagement occurs in a single step of ~10 nm and is driven by an ATP dependent head-head movement, resisting forces up to 15 pN. Our molecular dynamic simulations show that the energy of head engagement can be stored in a mechanically strained conformation of NIPBL and released during disengagement. These findings reveal how single cohesin molecules generate force by two distinct mechanisms. We present a model, which proposes how this ability may power different aspects of cohesin-DNA interaction.

It's all in the numbers: Cohesin stoichiometry

Cohesin, a structural maintenance of chromosome (SMC) complex, organizes chromatin into three-dimensional structures by threading chromatin into loops and stabilizing long-range chromatin interactions. Four subunits in a 1:1:1:1 ratio compose the cohesin core, which is regulated by auxiliary factors that interact with or modify the core subunits. An ongoing debate about cohesin's mechanism of action regards its stoichiometry. Namely, is cohesin activity mediated by a single complex or cooperation between several complexes that organize into dimers or oligomers? Several investigations that used various experimental approaches have tried to resolve this dispute. Some have convincingly demonstrated that the cohesin monomer is the active unit. However, others have revealed the formation of cohesin dimers and higher-order clusters on and off chromosomes. Elucidating the biological function of cohesin clusters and determining what regulates their formation are just two of the many new questions raised by these findings. We briefly review the history of the argument about cohesin stoichiometry and the central evidence for cohesin activity as a monomer vs. an oligomer. Finally, we discuss the possible biological significance of cohesin oligomerization and present open questions that remain to be answered.

Shaping centromeres to resist mitotic spindle forces

The centromere serves as the binding site for the kinetochore and is essential for the faithful segregation of chromosomes throughout cell division. The point centromere in yeast is encoded by a ∼115 bp specific DNA sequence, whereas regional centromeres range from 6-10 kbp in fission yeast to 5-10 Mbp in humans. Understanding the physical structure of centromere chromatin (pericentromere in yeast), defined as the chromatin between sister kinetochores, will provide fundamental insights into how centromere DNA is woven into a stiff spring that is able to resist microtubule pulling forces during mitosis. One hallmark of the pericentromere is the enrichment of the structural maintenance of chromosome (SMC) proteins cohesin and condensin. Based on studies from population approaches (ChIP-seq and Hi-C) and experimentally obtained images of fluorescent probes of pericentromeric structure, as well as quantitative comparisons between simulations and experimental results, we suggest a mechanism for building tension between sister kinetochores. We propose that the centromere is a chromatin bottlebrush that is organized by the loop-extruding proteins condensin and cohesin. The bottlebrush arrangement provides a biophysical means to transform pericentromeric chromatin into a spring due to the steric repulsion between radial loops. We argue that the bottlebrush is an organizing principle for chromosome organization that has emerged from multiple approaches in the field.

Mechanisms of DNA Mobilization and Sequestration

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

Theory and simulations of condensin mediated loop extrusion in DNA

Condensation of hundreds of mega-base-pair-long human chromosomes in a small nuclear volume is a spectacular biological phenomenon. This process is driven by the formation of chromosome loops. The ATP consuming motor, condensin, interacts with chromatin segments to actively extrude loops. Motivated by real-time imaging of loop extrusion (LE), we created an analytically solvable model, predicting the LE velocity and step size distribution as a function of external load. The theory fits the available experimental data quantitatively, and suggests that condensin must undergo a large conformational change, induced by ATP binding, bringing distant parts of the motor to proximity. Simulations using a simple model confirm that the motor transitions between an open and a closed state in order to extrude loops by a scrunching mechanism, similar to that proposed in DNA bubble formation during bacterial transcription. Changes in the orientation of the motor domains are transmitted over ~50 nm, connecting the motor head and the hinge, thus providing an allosteric basis for LE.

Statistical mechanics of chromosomes: in vivo and in silico approaches reveal high-level organization and structure arise exclusively through mechanical feedback between loop extruders and chromatin substrate properties

The revolution in understanding higher order chromosome dynamics and organization derives from treating the chromosome as a chain polymer and adapting appropriate polymer-based physical principles. Using basic principles, such as entropic fluctuations and timescales of relaxation of Rouse polymer chains, one can recapitulate the dominant features of chromatin motion observed in vivo. An emerging challenge is to relate the mechanical properties of chromatin to more nuanced organizational principles such as ubiquitous DNA loops. Toward this goal, we introduce a real-time numerical simulation model of a long chain polymer in the presence of histones and condensin, encoding physical principles of chromosome dynamics with coupled histone and condensin sources of transient loop generation. An exact experimental correlate of the model was obtained through analysis of a model-matching fluorescently labeled circular chromosome in live yeast cells. We show that experimentally observed chromosome compaction and variance in compaction are reproduced only with tandem interactions between histone and condensin, not from either individually. The hierarchical loop structures that emerge upon incorporation of histone and condensin activities significantly impact the dynamic and structural properties of chromatin. Moreover, simulations reveal that tandem condensin–histone activity is responsible for higher order chromosomal structures, including recently observed Z-loops.

Loop extrusion: theory meets single-molecule experiments

Chromosomes are organized as chromatin loops that promote segregation, enhancer-promoter interactions, and other genomic functions. Loops were hypothesized to form by 'loop extrusion,' by which structural maintenance of chromosomes (SMC) complexes, such as condensin and cohesin, bind to chromatin, reel it in, and extrude it as a loop. However, such exotic motor activity had never been observed. Following an explosion of indirect evidence, recent single-molecule experiments directly imaged DNA loop extrusion by condensin and cohesin in vitro. These experiments observe rapid (kb/s) extrusion that requires ATP hydrolysis and stalls under pN forces. Surprisingly, condensin extrudes loops asymmetrically, challenging previous models. Extrusion by cohesin is symmetric but requires the protein Nipbl. We discuss how SMC complexes may perform their functions on chromatin in vivo.

Organization of the Escherichia coli Chromosome by a MukBEF Axial Core

Structural maintenance of chromosomes (SMC) complexes organize chromosomes ubiquitously, thereby contributing to their faithful segregation. We demonstrate that under conditions of increased chromosome occupancy of the Escherichia coli SMC complex, MukBEF, the chromosome is organized as a series of loops around a thin (<130 nm) MukBEF axial core, whose length is ∼1,100 times shorter than the chromosomal DNA. The linear order of chromosomal loci is maintained in the axial cores, whose formation requires MukBEF ATP hydrolysis. Axial core structure in non-replicating chromosomes is predominantly linear (1 μm) but becomes circular (1.5 μm) in the absence of MatP because of its failure to displace MukBEF from the 800 kbp replication termination region (ter). Displacement of MukBEF from ter by MatP in wild-type cells directs MukBEF colocalization with the replication origin. We conclude that MukBEF individualizes and compacts the chromosome lengthwise, demonstrating a chromosome organization mechanism similar to condensin in mitotic chromosome formation.

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MukBEF forms a chromosome axial core dependent on ATP hydrolysis

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MukBEF compacts the chromosome lengthwise while avoiding links between replichores

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MatP determines the shape of the axial core by displacing MukBEF from ter

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The displacement by MatP directs MukBEF colocalization with the replication origin

Large-scale chromatin organisation in interphase, mitosis and meiosis

The spatial configuration of chromatin is fundamental to ensure any given cell can fulfil its functional duties, from gene expression to specialised cellular division. Significant technological innovations have facilitated further insights into the structure, function and regulation of three-dimensional chromatin organisation. To date, the vast majority of investigations into chromatin organisation have been conducted in interphase and mitotic cells leaving meiotic chromatin relatively unexplored. In combination, cytological and genome-wide contact frequency analyses in mammalian germ cells have recently demonstrated that large-scale chromatin structures in meiotic prophase I are reminiscent of the sequential loop arrays found in mitotic cells, although interphase-like segmentation of transcriptionally active and inactive regions are also evident along the length of chromosomes. Here, we discuss the similarities and differences of such large-scale chromatin architecture, between interphase, mitotic and meiotic cells, as well as their functional relevance and the proposed modulatory mechanisms which underlie them.

The regulation of chromosome segregation via centromere loops

Biophysical studies of the yeast centromere have shown that the organization of the centromeric chromatin plays a crucial role in maintaining proper tension between sister kinetochores during mitosis. While centromeric chromatin has traditionally been considered a simple spring, recent work reveals the centromere as a multifaceted, tunable shock absorber. Centromeres can differ from other regions of the genome in their heterochromatin state, supercoiling state, and enrichment of structural maintenance of chromosomes (SMC) protein complexes. Each of these differences can be utilized to alter the effective stiffness of centromeric chromatin. In budding yeast, the SMC protein complexes condensin and cohesin stiffen chromatin by forming and cross-linking chromatin loops, respectively, into a fibrous structure resembling a bottlebrush. The high density of the loops compacts chromatin while spatially isolating the tension from spindle pulling forces to a subset of the chromatin. Paradoxically, the molecular crowding of chromatin via cohesin and condensin also causes an outward/poleward force. The structure allows the centromere to act as a shock absorber that buffers the variable forces generated by dynamic spindle microtubules. Based on the distribution of SMCs from bacteria to human and the conserved distance between sister kinetochores in a wide variety of organisms (0.4 to 1 micron), we propose that the bottlebrush mechanism is the foundational principle for centromere function in eukaryotes.

Condensins and cohesins - one of these things is not like the other!

Condensins and cohesins are highly conserved complexes that tether together DNA loci within a single DNA molecule to produce DNA loops. Condensin and cohesin structures, however, are different, and the DNA loops produced by each underlie distinct cell processes. Condensin rods compact chromosomes during mitosis, with condensin I and II complexes producing spatially defined and nested looping in metazoan cells. Structurally adaptive cohesin rings produce loops, which organize the genome during interphase. Cohesin-mediated loops, termed topologically associating domains or TADs, antagonize the formation of epigenetically defined but untethered DNA volumes, termed compartments. While condensin complexes formed through cis-interactions must maintain chromatin compaction throughout mitosis, cohesins remain highly dynamic during interphase to allow for transcription-mediated responses to external cues and the execution of developmental programs. Here, I review differences in condensin and cohesin structures, and highlight recent advances regarding the intramolecular or cis-based tetherings through which condensins compact DNA during mitosis and cohesins organize the genome during interphase.

Three-Dimensional Thermodynamic Simulation of Condensin as a DNA-Based Translocase

Chromatin dynamics and organization can be altered by condensin complexes. In turn, the molecular behavior of a condensin complex changes based on the tension of the substrate to which condensin is bound. This interplay between chromatin organization and condensin behavior demonstrates the need for tools that allows condensin complexes to be observed on a variety of chromatin organizations. We provide a method for simulating condensin complexes on a dynamic polymer substrate using the polymer dynamics simulator ChromoShake and the condensin simulator RotoStep. These simulations can be converted into simulated fluorescent images that are able to be directly compared to experimental images of condensin and fluorescently labeled chromatin. Our pipeline enables users to explore how changes in condensin behavior alters chromatin dynamics and vice versa while providing simulated image datasets that can be directly compared to experimental observations.

Geometric partitioning of cohesin and condensin is a consequence of chromatin loops

SMC (structural maintenance of chromosomes) complexes condensin and cohesin are crucial for proper chromosome organization. Condensin has been reported to be a mechanochemical motor capable of forming chromatin loops, while cohesin passively diffuses along chromatin to tether sister chromatids. In budding yeast, the pericentric region is enriched in both condensin and cohesin. As in higher-eukaryotic chromosomes, condensin is localized to the axial chromatin of the pericentric region, while cohesin is enriched in the radial chromatin. Thus, the pericentric region serves as an ideal model for deducing the role of SMC complexes in chromosome organization. We find condensin-mediated chromatin loops establish a robust chromatin organization, while cohesin limits the area that chromatin loops can explore. Upon biorientation, extensional force from the mitotic spindle aggregates condensin-bound chromatin from its equilibrium position to the axial core of pericentric chromatin, resulting in amplified axial tension. The axial localization of condensin depends on condensin's ability to bind to chromatin to form loops, while the radial localization of cohesin depends on cohesin's ability to diffuse along chromatin. The different chromatin-tethering modalities of condensin and cohesin result in their geometric partitioning in the presence of an extensional force on chromatin.

In Vivo Evidence for ATPase-Dependent DNA Translocation by the Bacillus subtilis SMC Condensin Complex

Structural maintenance of chromosomes (SMC) complexes shape the genomes of virtually all organisms, but how they function remains incompletely understood. Recent studies in bacteria and eukaryotes have led to a unifying model in which these ring-shaped ATPases act along contiguous DNA segments, processively enlarging DNA loops. In support of this model, single-molecule imaging experiments indicate that Saccharomyces cerevisiae condensin complexes can extrude DNA loops in an ATP-hydrolysis-dependent manner in vitro. Here, using time-resolved high-throughput chromosome conformation capture (Hi-C), we investigate the interplay between ATPase activity of the Bacillus subtilis SMC complex and loop formation in vivo. We show that point mutants in the SMC nucleotide-binding domain that impair but do not eliminate ATPase activity not only exhibit delays in de novo loop formation but also have reduced rates of processive loop enlargement. These data provide in vivo evidence that SMC complexes function as loop extruders.

Condensin controls mitotic chromosome stiffness and stability without forming a structurally contiguous scaffold

During cell division, chromosomes must be folded into their compact mitotic form to ensure their segregation. This process is thought to be largely controlled by the action of condensin SMC protein complexes on chromatin fibers. However, how condensins organize metaphase chromosomes is not understood. We have combined micromanipulation of single human mitotic chromosomes, sub-nanonewton force measurement, siRNA interference of condensin subunit expression, and fluorescence microscopy, to analyze the role of condensin in large-scale chromosome organization. Condensin depletion leads to a dramatic (~ 10-fold) reduction in chromosome elastic stiffness relative to the native, non-depleted case. We also find that prolonged metaphase stalling of cells leads to overloading of chromosomes with condensin, with abnormally high chromosome stiffness. These results demonstrate that condensin is a main element controlling the stiffness of mitotic chromosomes. Isolated, slightly stretched chromosomes display a discontinuous condensing staining pattern, suggesting that condensins organize mitotic chromosomes by forming isolated compaction centers that do not form a continuous scaffold.

Real-time imaging of DNA loop extrusion by condensin

It has been hypothesized that SMC protein complexes such as condensin and cohesin spatially organize chromosomes by extruding DNA into large loops. We directly visualized the formation and processive extension of DNA loops by yeast condensin in real time. Our findings constitute unambiguous evidence for loop extrusion. We observed that a single condensin complex is able to extrude tens of kilobase pairs of DNA at a force-dependent speed of up to 1500 base pairs per second, using the energy of adenosine triphosphate hydrolysis. Condensin-induced loop extrusion was strictly asymmetric, which demonstrates that condensin anchors onto DNA and reels it in from only one side. Active DNA loop extrusion by SMC complexes may provide the universal unifying principle for genome organization.

Liberating cohesin from cohesion

Cohesin was identified through its major role in holding sister chromatids together. We are learning through analysis of cohesin and other members of the protein family (SMC [structural maintenance of chromosomes]) and their regulators that these ring complexes contribute to chromosome organization and dynamics throughout the cell cycle. We need to consider not only how ring complexes are regulated but how they interact with their fluctuating chromatin substrate.