Theory and simulations of condensin mediated loop extrusion in DNA

Polymer model integrates imaging and sequencing to reveal how nanoscale heterochromatin domains influence gene expression

Chromatin organization regulates gene expression, with nanoscale heterochromatin domains playing a fundamental role. Their size varies with microenvironmental stiffness and epigenetic interventions, but how these factors regulate their formation and influence transcription remains unclear. To address this, we developed a sequencing-informed copolymer model that simulates chromatin evolution through diffusion and active epigenetic reactions. Our model predicts the formation of nanoscale heterochromatin domains and quantifies how domain size scales with epigenetic reaction rates, showing that epigenetic and compaction changes primarily occur at domain boundaries. We validated these predictions via Hi-C and super-resolution imaging of hyperacetylated melanoma cells and identified differential expression of metastasis-related genes through RNA-seq. We validated our findings in hMSCs, where epigenetic reaction rates respond to microenvironmental stiffness. Conclusively, our simulations reveal that heterochromatin domain boundaries regulate gene expression and epigenetic memory. These findings demonstrate how external cues drive chromatin organization and transcriptional memory in development and disease.

Organization and Dynamics of Chromosomes

How long thread-like eukaryotic chromosomes fit tidily in the small volume of the nucleus without significant entanglement is just beginning to be understood, thanks to major advances in experimental techniques. Several polymer models, which reproduce contact maps that measure the probabilities that two loci are in spatial contact, have predicted the 3D structures of interphase chromosomes. Data-driven approaches, using contact maps as input, predict that mitotic helical chromosomes are characterized by a switch in handedness, referred to as perversion. By using experimentally derived effective interactions between chromatin loci in simulations, structures of conventional and inverted nuclei have been accurately predicted. Polymer theory and simulations show that the dynamics of individual loci in chromatin exhibit subdiffusive behavior but the diffusion exponents are broadly distributed, which accords well with experiments. Although coarse-grained models are successful, many challenging problems remain, which require the creation of new experimental and computational tools to understand genome biology.

Insulation between adjacent TADs is controlled by the width of their boundaries through distinct mechanisms

Topologically associating domains (TADs) are sub-Megabase regions in vertebrate genomes with enriched intradomain interactions that restrict enhancer-promoter contacts across their boundaries. However, the mechanisms that separate TADs remain incompletely understood. Most boundaries between TADs contain CTCF binding sites (CBSs), which individually contribute to the blocking of Cohesin-mediated loop extrusion. Using genome-wide classification, here we show that the width of TAD boundaries forms a continuum from narrow to highly extended and correlates with CBSs distribution, chromatin features, and gene regulatory elements. To investigate how these boundary widths emerge, we modified the random crosslinker polymer model to incorporate specific boundary configurations, enabling us to evaluate the differential impact of boundary composition on TAD insulation. Our analysis, using three generic boundary categories, identifies differential influence on TAD insulation, with varying local and distal effects on neighboring domains. Notably, we find that increasing boundary width reduces long-range inter-TAD contacts, as confirmed by Hi-C data. While blocking loop extrusion at boundaries indirectly promotes spurious intermingling of neighboring TADs, extended boundaries counteract this effect, emphasizing their role in establishing genome organization. In conclusion, TAD boundary width not only enhances the efficiency of loop extrusion blocking but may also modulate enhancer-promoter contacts over long distances across TAD boundaries, providing a further mechanism for transcriptional regulation.

NCAPD3 promotes diffuse large B-cell lymphoma progression through modulating SIRT1 expression in an H3K9 monomethylation-dependent manner

INTRODUCTION

Condensin, a family of structural maintenance of chromosome complexes, has been shown to regulate chromosome compaction and segregation during mitosis. NCAPD3, a HEAT-repeat subunit of condensin II, plays a dominant role in condensin-mediated chromosome dynamics but remains unexplored in lymphoma.

OBJECTIVES

The study aims to unravel the molecular function and mechanism of NCAPD3 in diffuse large B-cell lymphoma (DLBCL).

METHODS

The expression and clinical significance of NCAPD3 were assessed in public database and clinical specimens. Chromosome spreads, co-immunoprecipitation (co-IP), mass spectrometry (MS), and chromatin immunoprecipitation (ChIP) assays were conducted to untangle the role and mechanism of NCAPD3 in DLBCL.

RESULTS

NCAPD3 was highly expressed in DLBCL, correlated with poor prognosis. NCAPD3 deficiency impeded cell proliferation, induced apoptosis and increased the chemosensitivity. Instead, NCAPD3 overexpression facilitated cell proliferation. In vivo experiments further indicated targeting NCAPD3 suppressed tumor growth. Noteworthily, NCAPD3 deficiency disturbed the mitosis, triggering the formation of aneuploids. To reveal the function of NCAPD3 in DLBCL, chromosome spreads were conducted, presenting that chromosomes became compact upon NCAPD3 overexpression, instead, loose, twisted and lacking axial rigidity upon NCAPD3 absence. Meanwhile, the classical transcription-activated marker, H3K4 trimethylation, was found globally upregulated after NCAPD3 knockout, suggesting that NCAPD3 might participate in chromatin remodeling and transcription regulation. MS revealed NCAPD3 could interact with transcription factor, TFII I. Further co-IP and ChIP assays verified NCAPD3 could be anchored at the promoter of SIRT1 by TFII I and then supported the transcription of SIRT1 via recognizing H3K9 monomethylation (H3K9me1) on SIRT1 promoter. Function reversion assay verified the oncogenic role of NCAPD3 in DLBCL was partially mediated by SIRT1.

CONCLUSION

This study demonstrated that dysregulation of NCAPD3 could disturb chromosome compaction and segregation and regulate the transcription activity of SIRT1 in an H3K9me1-dependent manner, which provided novel insights into targeted strategy for DLBCL.

Global hinge sites of proteins as target sites for drug binding

Hinge sites of proteins play a key role in mediating conformational mechanics. Among them, those involved in the most collective modes of motion, also called global hinges, are of particular interest, as they support cooperative rearrangements that are often functional. Yet, the utility of targeting global hinges for modulating function remains to be established. We present here a systematic study of a series of proteins resolved in drug-bound forms to examine the probabilistic occurrence of spatial overlaps between hinge sites and drug-binding pockets. Our analysis reveals a high propensity of drug binding to hinge sites compared to random. Notably, one-third of currently approved drugs are colocalized with hinge sites. These mechanosensitive sites are predictable by simple models such as the Gaussian Network Model. Their targeting thus emerges as a viable strategy for developing a new class of drugs that would exploit and modulate the target proteins' intrinsic dynamics, and potentially alleviate drug-resistance when used in combination with orthosteric or allosteric drugs.

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.

Escape of an active ring from an attractive surface: Behaving like a self-propelled Brownian particle

Escape of active agents from metastable states is of great interest in statistical and biological physics. In this paper, we investigate the escape of a flexible active ring, composed of active Brownian particles, from a flat attractive surface using Brownian dynamics simulations. To systematically explore the effects of activity, persistence time, and the shape of attractive potentials, we calculate escape time τ_{e} and effective temperature T_{eff}. We observe two distinct escape mechanisms: Kramers-like thermal activation at small persistence times, where ln(τ_{e})∼1/(k_{B}T_{eff}), and the maximal force problem at large persistence time, where τ_{e} is determined by persistence time. The escape time explicitly depends on the shape of the potential barrier at high activity and large persistence time. Moreover, when the propulsion force is biased along the ring's contour, escape becomes more difficult and is primarily driven by thermal noise. Our findings highlight that, despite its intricate configuration, the active ring can be effectively modeled as a self-propelled Brownian particle when studying its escape from a smooth surface.

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.

Activity-induced stiffness, entanglement network and dynamic slowdown in unentangled semidilute polymer solutions

Active polymers possess numerous unique properties that are quite different from those observed in the system of small active molecules due to the intricate interplay between their activity and topological constraints. This study focuses on the conformational changes induced by activity, impacting effective stiffness and crucially influencing entanglement and dynamics. When the two terminals of a linear chain undergo active modification through coupling to a high-temperature thermal bath, there is a substantial increase in chain size, indicating a notable enhancement in effective stiffness. Unlike in passive semiflexible chains where stiffness predominantly affects local bond angles, activity-induced stiffness manifests at the scale of tens of monomers. While activity raises the ambient temperature, it significantly decreases diffusion by over an order of magnitude. The slowdown of the dynamics observed can be attributed to increased entanglement due to chain elongation.

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.

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.

Theory of chromatin organization maintained by active loop extrusion

The active loop extrusion hypothesis proposes that chromatin threads through the cohesin protein complex into progressively larger loops until reaching specific boundary elements. We build upon this hypothesis and develop an analytical theory for active loop extrusion which predicts that loop formation probability is a nonmonotonic function of loop length and describes chromatin contact probabilities. We validate our model with Monte Carlo and hybrid Molecular Dynamics-Monte Carlo simulations and demonstrate that our theory recapitulates experimental chromatin conformation capture data. Our results support active loop extrusion as a mechanism for chromatin organization and provide an analytical description of chromatin organization that may be used to specifically modify chromatin contact probabilities.

Structural changes in chromosomes driven by multiple condensin motors during mitosis

We create a computational framework that utilizes loop extrusion (LE) by multiple condensin I/II motors to predict changes in chromosome organization during mitosis. The theory accurately reproduces the experimental contact probability profiles for the mitotic chromosomes in HeLa and DT40 cells. The LE rate is smaller at the start of mitosis and increases as the cells approach metaphase. Condensin II-mediated mean loop size is about six times larger than loops because of condensin I. The loops, which overlap each other, are stapled to a central dynamically changing helical scaffold formed by the motors during the LE process. A polymer physics-based data-driven method that uses the Hi-C contact map as the only input shows that the helix is characterized as random helix perversions (RHPs) in which the handedness changes randomly along the scaffold. The theoretical predictions, which are testable using imaging experiments, do not contain any parameters.

Single-molecule experiments reveal the elbow as an essential folding guide in SMC coiled-coil arms

Structural maintenance of chromosome (SMC) complexes form ring-like structures through exceptional elongated coiled-coils (CCs). Recent studies found that variable CC conformations, including open and collapsed forms, which might result from discontinuities in the CC, facilitate the diverse functions of SMCs in DNA organization. However, a detailed description of the SMC CC architecture is still missing. Here, we study the structural composition and mechanical properties of SMC proteins with optical tweezers unfolding experiments using the isolated Psm3 CC as a model system. We find a comparatively unstable protein with three unzipping intermediates, which we could directly assign to CC features by crosslinking experiments and state-of-the-art prediction software. Particularly, the CC elbow is shown to be a flexible, potentially non-structured feature, which divides the CC into sections, induces a pairing shift from one CC strand to the other and could facilitate large-scale conformational changes, most likely via thermal fluctuations of the flanking CC sections. A replacement of the elbow amino acids hinders folding of the consecutive CC region and frequently leads to non-native misalignments, revealing the elbow as a guide for proper folding. Additional in vivo manipulation of the elbow flexibility resulted in impaired cohesin complexes, which directly link the sensitive CC architecture to the biological function of cohesin.

Molecular dynamics simulations for the study of chromatin biology

The organization of Eukaryotic DNA into chromatin has profound implications for the processing of genetic information. In the past years, molecular dynamics (MD) simulations proved to be a powerful tool to investigate the mechanistic basis of chromatin biology. We review recent all-atom and coarse-grained MD studies revealing how the structure and dynamics of chromatin underlie its biological functions. We describe the latest method developments; the structural fluctuations of nucleosomes and the various factors affecting them; the organization of chromatin fibers, with particular emphasis on its liquid-like character; the interactions and dynamics of transcription factors on chromatin; and how chromatin organization is modulated by molecular motors acting on DNA.

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.

Meiotic chromosome organization and crossover patterns

Meiosis is the foundation of sexual reproduction, and crossover recombination is one hallmark of meiosis. Crossovers establish the physical connections between homolog chromosomes (homologs) for their proper segregation and exchange DNA between homologs to promote genetic diversity in gametes and thus progenies. Aberrant crossover patterns, e.g. absence of the obligatory crossover, are the leading cause of infertility, miscarriage, and congenital disease. Therefore, crossover patterns have to be tightly controlled. During meiosis, loop/axis organized chromosomes provide the structural basis and regulatory machinery for crossover patterning. Accumulating evidence shows that chromosome axis length regulates not only the numbers but also the positions of crossovers. In addition, recent studies suggest that alterations in axis length and the resultant alterations in crossover frequency may contribute to evolutionary adaptation. Here, current advances regarding these issues are reviewed, the possible mechanisms for axis length regulating crossover frequency are discussed, and important issues that need further investigations are suggested.

Transcriptional Regulation and Implications for Controlling Hox Gene Expression

Hox genes play key roles in axial patterning and regulating the regional identity of cells and tissues in a wide variety of animals from invertebrates to vertebrates. Nested domains of Hox expression generate a combinatorial code that provides a molecular framework for specifying the properties of tissues along the A–P axis. Hence, it is important to understand the regulatory mechanisms that coordinately control the precise patterns of the transcription of clustered Hox genes required for their roles in development. New insights are emerging about the dynamics and molecular mechanisms governing transcriptional regulation, and there is interest in understanding how these may play a role in contributing to the regulation of the expression of the clustered Hox genes. In this review, we summarize some of the recent findings, ideas and emerging mechanisms underlying the regulation of transcription in general and consider how they may be relevant to understanding the transcriptional regulation of Hox genes.

Condensin extrudes DNA loops in steps up to hundreds of base pairs that are generated by ATP binding events

The condensin SMC protein complex organizes chromosomal structure by extruding loops of DNA. Its ATP-dependent motor mechanism remains unclear but likely involves steps associated with large conformational changes within the ∼50 nm protein complex. Here, using high-resolution magnetic tweezers, we resolve single steps in the loop extrusion process by individual yeast condensins. The measured median step sizes range between 20–40 nm at forces of 1.0–0.2 pN, respectively, comparable with the holocomplex size. These large steps show that, strikingly, condensin typically reels in DNA in very sizeable amounts with ∼200 bp on average per single extrusion step at low force, and occasionally even much larger, exceeding 500 bp per step. Using Molecular Dynamics simulations, we demonstrate that this is due to the structural flexibility of the DNA polymer at these low forces. Using ATP-binding-impaired and ATP-hydrolysis-deficient mutants, we find that ATP binding is the primary step-generating stage underlying DNA loop extrusion. We discuss our findings in terms of a scrunching model where a stepwise DNA loop extrusion is generated by an ATP-binding-induced engagement of the hinge and the globular domain of the SMC complex.

Three-dimensional loop extrusion

Loop extrusion convincingly describes how certain structural maintenance of chromosome (SMC) proteins mediate the formation of large DNA loops. Yet most of the existing computational models cannot reconcile recent in vitro observations showing that condensins can traverse each other, bypass large roadblocks, and perform steps longer than their own size. To fill this gap, we propose a three-dimensional (3D) "trans-grabbing" model for loop extrusion, which not only reproduces the experimental features of loop extrusion by one SMC complex but also predicts the formation of so-called Z-loops via the interaction of two or more SMCs extruding along the same DNA substrate. By performing molecular dynamics simulations of this model, we discover that the experimentally observed asymmetry in the different types of Z-loops is a natural consequence of the DNA tethering in vitro. Intriguingly, our model predicts this bias to disappear in the absence of tethering and a third type of Z-loop, which has not yet been identified in experiments, to appear. Our model naturally explains roadblock bypassing and the appearance of steps larger than the SMC size as a consequence of non-contiguous DNA grabbing. Finally, this study is the first, to our knowledge, to address how Z-loops and bypassing might occur in a way that is broadly consistent with existing cis-only 1D loop extrusion models.