Three-dimensional loop extrusion

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.

Multicontact statistics distinguish models of chromosome organization

Chromosome organization can be modeled using various approaches, ranging from mechanistic bottom-up models to models inferred directly from experimental data. Many such models can recapitulate experimental Hi-C data for pairwise contact probabilities, meaning that these data cannot always be used to distinguish different models. Here, we consider two illustrative example models for bacterial chromosome organization: one a bottom-up model for loop extrusion, the other a data-driven maximum entropy model inferred from Hi-C data. We find that despite predicting similar pairwise contact frequencies, the models predict qualitatively different features on three-point contact maps. We explain these differences by constructing analytical approximations for three-point contact probabilities in each model. Finally, we apply our analytical approximations to previously published experimental multicontact data from human chromosomes, and find that these data are well described by the loop extruder approximation. Our work illustrates how multicontact statistics can be used to compare and test models for chromosome organization.

Motor domain of condensin and step formation in extruding loop of DNA

During the asymmetric loop extrusion of DNA by a condensin complex, one domain of the complex stably anchors to the DNA molecule, and another domain reels in the DNA strand into a loop. The DNA strand in the loop is fully relaxed, or there is no tension in the loop. Just outside of the loop, there is a tension that resists the extrusion of DNA. To maintain the extrusion of the DNA loop, the condensin complex must have a domain capable of generating a force to overcome the tension outside of the loop. This study proposes that the groove-shaped HEAT repeat domain Ycg1 plays the role of a molecular motor. A DNA molecule may bind to the groove electrostatically, and the weak binding force facilitates the random thermal motion of DNA molecules. A mechanical model that random collisions between DNA and the nonparallel inner surfaces of the groove may generate a directional force which is required for the loop extrusion to sustain. The hinge domain binds to the DNA molecule and acts as an anchor during asymmetric DNA loop extrusion. When the effects of ATP hydrolysis and the viscous drag of the fluid environment are considered, the motor-anchor model for the condensin complex and the mechanical model might explain the asymmetric loop extrusion, the formation of steps, the step size distribution in the loop extrusion, the tension-dependent extrusion speed, the interaction between coexisting loops on the DNA strand, and untying the knots during extrusion. This model can also explain the observed formation of the Z-loop.

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.

Anisotropic scrunching of SMC with a baton-pass mechanism

DNA-loop extrusion is considered to be a universal principle of structural maintenance of chromosome (SMC) proteins with regard to chromosome organization. Despite recent advancements in structural dynamics studies that involve the use of cryogenic-electron microscopy (Cryo-EM), atomic force microscopy (AFM), etc., the precise molecular mechanism underlying DNA-loop extrusion by SMC proteins remains the subject of ongoing discussions. In this context, we propose a scrunching model that incorporates the anisotropic motion of SMC folding with a baton-pass mechanism, offering a potential explanation of how a "DNA baton" is transferred from the hinge domain to a DNA pocket via an anisotropic hinge motion. This proposed model provides insights into how SMC proteins unidirectionally extrude DNA loops in the direction of loop elongation while also maintaining the stability of a DNA loop throughout the dynamic process of DNA-loop extrusion.

Nonequilibrium switching of segmental states can influence compaction of chromatin

Knowledge about the dynamic nature of chromatin organization is essential to understand the regulation of processes like DNA transcription and repair. The existing models of chromatin assume that protein organization and chemical states along chromatin are static and the 3D organization is purely a result of protein-mediated intra-chromatin interactions. Here we present a new hypothesis that certain nonequilibrium processes, such as switching of chemical and physical states due to nucleosome assembly/disassembly or gene repression/activation, can also simultaneously influence chromatin configurations. To understand the implications of this inherent nonequilibrium switching, we present a block copolymer model of chromatin, with switching of its segmental states between two states, mimicking active/repressed or protein unbound/bound states. We show that competition between switching timescale Tt, polymer relaxation timescale τp, and segmental relaxation timescale τs can lead to non-trivial changes in chromatin organization, leading to changes in local compaction and contact probabilities. As a function of the switching timescale, the radius of gyration of chromatin shows a non-monotonic behavior with a prominent minimum when Tt ≈ τp and a maximum when Tt ≈ τs. We find that polymers with a small segment length exhibit a more compact structure than those with larger segment lengths. We also find that the switching can lead to higher contact probability and better mixing of far-away segments. Our study also shows that the nature of the distribution of chromatin clusters varies widely as we change the switching rate.

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.

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.

Mesoscale, long-time mixing of chromosomes and its connection to polymer dynamics

Chromosomes are arranged in distinct territories within the nucleus of animal cells. Recent experiments have shown that these territories overlap at their edges, suggesting partial mixing during interphase. Experiments that knock-down of condensin II proteins during interphase indicate increased chromosome mixing, which demonstrates control of the mixing. In this study, we use a generic polymer simulation to quantify the dynamics of chromosome mixing over time. We introduce the chromosome mixing index, which quantifies the mixing of distinct chromosomes in the nucleus. We find that the chromosome mixing index in a small confinement volume (as a model of the nucleus), increases as a power-law of the time, with the scaling exponent varying non-monotonically with self-interaction and volume fraction. By comparing the chromosome mixing index with both monomer subdiffusion due to (non-topological) intermingling of chromosomes as well as even slower reptation, we show that for relatively large volume fractions, the scaling exponent of the chromosome mixing index is related to Rouse dynamics for relatively weak chromosome attractions and to reptation for strong attractions. In addition, we extend our model to more realistically account for the situation of the Drosophila chromosome by including the heterogeneity of the polymers and their lengths to account for microphase separation of euchromatin and heterochromatin and their interactions with the nuclear lamina. We find that the interaction with the lamina further impedes chromosome mixing.

DNA tension-modulated translocation and loop extrusion by SMC complexes revealed by molecular dynamics simulations

Structural Maintenance of Chromosomes (SMC) complexes play essential roles in genome organization across all domains of life. To determine how the activities of these large (≈50 nm) complexes are controlled by ATP binding and hydrolysis, we developed a molecular dynamics model that accounts for conformational motions of the SMC and DNA. The model combines DNA loop capture with an ATP-induced 'power stroke' to translocate the SMC complex along DNA. This process is sensitive to DNA tension: at low tension (0.1 pN), the model makes loop-capture steps of average 60 nm and up to 200 nm along DNA (larger than the complex itself), while at higher tension, a distinct inchworm-like translocation mode appears. By tethering DNA to an experimentally-observed additional binding site ('safety belt'), the model SMC complex can perform loop extrusion (LE). The dependence of LE on DNA tension is distinct for fixed DNA tension vs. fixed DNA end points: LE reversal occurs above 0.5 pN for fixed tension, while LE stalling without reversal occurs at about 2 pN for fixed end points. Our model matches recent experimental results for condensin and cohesin, and makes testable predictions for how specific structural variations affect SMC function.