Synergy of topoisomerase and structural-maintenance-of-chromosomes proteins creates a universal pathway to simplify genome topology

DNA fragility at topologically associated domain boundaries is promoted by alternative DNA secondary structure and topoisomerase II activity

CCCTC-binding factor (CTCF) binding sites are hotspots of genome instability. Although many factors have been associated with CTCF binding site fragility, no study has integrated all fragility-related factors to understand the mechanism(s) of how they work together. Using an unbiased, genome-wide approach, we found that DNA double-strand breaks (DSBs) are enriched at strong, but not weak, CTCF binding sites in five human cell types. Energetically favorable alternative DNA secondary structures underlie strong CTCF binding sites. These structures coincided with the location of topoisomerase II (TOP2) cleavage complex, suggesting that DNA secondary structure acts as a recognition sequence for TOP2 binding and cleavage at CTCF binding sites. Furthermore, CTCF knockdown significantly increased DSBs at strong CTCF binding sites and at CTCF sites that are located at topologically associated domain (TAD) boundaries. TAD boundary-associated CTCF sites that lost CTCF upon knockdown displayed increased DSBs when compared to the gained sites, and those lost sites are overrepresented with G-quadruplexes, suggesting that the structures act as boundary insulators in the absence of CTCF, and contribute to increased DSBs. These results model how alternative DNA secondary structures facilitate recruitment of TOP2 to CTCF binding sites, providing mechanistic insight into DNA fragility at CTCF binding sites.

Stromal Rigidity Stress Accelerates Pancreatic Intraepithelial Neoplasia Progression and Chromosomal Instability via Nuclear Protein Tyrosine Kinase 2 Localization

Because the mechanotransduction by stromal stiffness stimulates the rupture and repair of the nuclear envelope in pancreatic progenitor cells, accumulated genomic aberrations are under selection in the tumor microenvironment. Analysis of cell growth, micronuclei, and γH2AX foci links to mechanotransduction pressure in vivo during serial orthotopic passages of mouse KrasLSL-G12D/+;Trp53flox/flox;Pdx1-Cre (KPC) cancer cells in the tumor and in migrating through the size-restricted 3-μm micropores. To search for pancreatic cancer cell of origin, analysis of single-cell data sets revealed that the extracellular matrix shapes an alternate route of acinar-ductal transdifferentiation of acinar cells into a central hub of elegantly restrained topoisomerase II α (TOP2A)-overexpressing cancer cells that spread out as unique cancer clusters with copy number amplifications in MYC-PTK2 (protein tyrosine kinase 2) locus and PIK3CA. High-PTK2 expression is associated with 171 differentially methylated CpG loci, 319 differentially expressed genes, and poor overall survival in patients with The Cancer Genome Atlas-PAAD. Abolished RGD-integrin signaling by disintegrin KG blocked the PTK2 phosphorylation, increased cancer apoptosis, decreased VAV1 expression, and prolonged overall survival in the KPC mice. Decreases of α-smooth muscle actin deposition in the CD248 knockout KPC mice remodel the tissue stroma and down-regulated TOP2A expression in the epithelium. In summary, stromal stiffness induces the onset of cells of origin of cancer by ectopic TOP2A expression, and the genomic amplification of MYC-PTK2 locus via alternative transdifferentiation of pancreatic progenitor cells is the vulnerability useful for disintegrin KG treatment against cells-of-origin cancer.

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.

Topoisomerases I and II facilitate condensin DC translocation to organize and repress X chromosomes in C. elegans

Condensins are evolutionarily conserved molecular motors that translocate along DNA and form loops. To address how DNA topology affects condensin translocation, we applied auxin-inducible degradation of topoisomerases I and II and analyzed the binding and function of an interphase condensin that mediates X chromosome dosage compensation in C. elegans. TOP-2 depletion reduced long-range spreading of condensin-DC (dosage compensation) from its recruitment sites and shortened 3D DNA contacts measured by Hi-C. TOP-1 depletion did not affect long-range spreading but resulted in condensin-DC accumulation within expressed gene bodies. Both TOP-1 and TOP-2 depletion resulted in X chromosome derepression, indicating that condensin-DC translocation at both scales is required for its function. Together, the distinct effects of TOP-1 and TOP-2 suggest two distinct modes of condensin-DC association with chromatin: long-range DNA loop extrusion that requires decatenation/unknotting of DNA and short-range translocation across genes that requires resolution of transcription-induced supercoiling.

Topological gelation of reconnecting polymers

Shuffling of genetic material via reconnection of proximal DNA segments is seen in meiosis and some cancers. In contrast with textbook pictures, reconnections are performed within an entangled environment and can result in knotting or linking, detrimental for cells. By performing Brownian dynamics simulations of reconnecting polymers under confinement, modeling the genome in vivo, we find a topological transition between a gas or liquid of unlinked rings and a gel-like structure with a large number of polydisperse linked rings. This transition can be triggered by increasing polymer stiffness or confinement. Our results suggest ways to design future topological materials, such as DNA-based gels involving recombinase proteins.

DNA recombination is a ubiquitous process that ensures genetic diversity. Contrary to textbook pictures, DNA recombination, as well as generic DNA translocations, occurs in a confined and highly entangled environment. Inspired by this observation, here, we investigate a solution of semiflexible polymer rings undergoing generic cutting and reconnection operations under spherical confinement. Our setup may be realized using engineered DNA in the presence of recombinase proteins or by considering micelle-like components able to form living (or reversibly breakable) polymer rings. We find that in such systems, there is a topological gelation transition, which can be triggered by increasing either the stiffness or the concentration of the rings. Flexible or dilute polymers break into an ensemble of short, unlinked, and segregated rings, whereas sufficiently stiff or dense polymers self-assemble into a network of long, linked, and mixed loops, many of which are knotted. We predict that the two phases should behave qualitatively differently in elution experiments monitoring the escape dynamics from a permeabilized container. Besides shedding some light on the biophysics and topology of genomes undergoing DNA reconnection in vivo, our findings could be leveraged in vitro to design polymeric complex fluids—e.g., DNA-based complex fluids or living polymer networks—with desired topologies.

Regulation of the mitotic chromosome folding machines

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

Dynamic and facilitated binding of topoisomerase accelerates topological relaxation

How type 2 Topoisomerase (TopoII) proteins relax and simplify the topology of DNA molecules is one of the most intriguing open questions in genome and DNA biophysics. Most of the existing models neglect the dynamics of TopoII which is expected of proteins searching their targets via facilitated diffusion. Here, we show that dynamic binding of TopoII speeds up the topological relaxation of knotted substrates by enhancing the search of the knotted arc. Intriguingly, this in turn implies that the timescale of topological relaxation is virtually independent of the substrate length. We then discover that considering binding biases due to facilitated diffusion on looped substrates steers the sampling of the topological space closer to the boundaries between different topoisomers yielding an optimally fast topological relaxation. We discuss our findings in the context of topological simplification in vitro and in vivo.

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

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

Circuit topology analysis of cellular genome reveals signature motifs, conformational heterogeneity, and scaling

Reciprocal regulation of genome topology and function is a fundamental and enduring puzzle in biology. The wealth of data provided by Hi-C libraries offers the opportunity to unravel this relationship. However, there is a need for a comprehensive theoretical framework in order to extract topological information for genome characterization and comparison. Here, we develop a toolbox for topological analysis based on Circuit Topology, allowing for the quantification of inter- and intracellular genomic heterogeneity, at various levels of fold complexity: pairwise contact arrangement, higher-order contact arrangement, and topological fractal dimension. Single-cell Hi-C data were analyzed and characterized based on topological content, revealing not only a strong multiscale heterogeneity but also highly conserved features such as a characteristic topological length scale and topological signature motifs in the genome. We propose that these motifs inform on the topological state of the nucleus and indicate the presence of active loop extrusion.

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Circuit topology quantifies heterogeneity in genomic arrangement

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Scale analysis reveals a characteristic length scale of 10 Mb in genome topology

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We identify highly conserved topological structures related to loop extrusion

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We suggest a topological model of chromatin arrangement for loop extrusion, the L-loop

Conformation and dynamic interactions of the multipartite genome in Agrobacterium tumefaciens

How bacteria with multipartite genomes organize and segregate their DNA is poorly understood. Here, we investigate a prototypical multipartite genome in the plant pathogen Agrobacterium tumefaciens. We identify previously unappreciated interreplicon interactions: the four replicons cluster through interactions at their centromeres, and the two chromosomes, one circular and one linear, interact along their replication arms. Our data suggest that these interreplicon contacts play critical roles in the organization and maintenance of multipartite genomes.

Bacterial species from diverse phyla contain multiple replicons, yet how these multipartite genomes are organized and segregated during the cell cycle remains poorly understood. Agrobacterium tumefaciens has a 2.8-Mb circular chromosome (Ch1), a 2.1-Mb linear chromosome (Ch2), and two large plasmids (pAt and pTi). We used this alpha proteobacterium as a model to investigate the global organization and temporal segregation of a multipartite genome. Using chromosome conformation capture assays, we demonstrate that both the circular and the linear chromosomes, but neither of the plasmids, have their left and right arms juxtaposed from their origins to their termini, generating interarm interactions that require the broadly conserved structural maintenance of chromosomes complex. Moreover, our study revealed two types of interreplicon interactions: “ori-ori clustering” in which the replication origins of all four replicons interact, and “Ch1-Ch2 alignment” in which the arms of Ch1 and Ch2 interact linearly along their lengths. We show that the centromeric proteins (ParB1 for Ch1 and RepB^Ch2 for Ch2) are required for both types of interreplicon contacts. Finally, using fluorescence microscopy, we validated the clustering of the origins and observed their frequent colocalization during segregation. Altogether, our findings provide a high-resolution view of the conformation of a multipartite genome. We hypothesize that intercentromeric contacts promote the organization and maintenance of diverse replicons.

Keeping intracellular DNA untangled: A new role for condensin?

The DNA-passage activity of topoisomerase II accidentally produces DNA knots and interlinks within and between chromatin fibers. Fortunately, these unwanted DNA entanglements are actively removed by some mechanism. Here we present an outline on DNA knot formation and discuss recent studies that have investigated how intracellular DNA knots are removed. First, although topoisomerase II is able to minimize DNA entanglements in vitro to below equilibrium values, it is unclear whether such capacity performs equally in vivo in chromatinized DNA. Second, DNA supercoiling could bias topoisomerase II to untangle the DNA. However, experimental evidence indicates that transcriptional supercoiling of intracellular DNA boosts knot formation. Last, cohesin and condensin could tighten DNA entanglements via DNA loop extrusion (LE) and force their dissolution by topoisomerase II. Recent observations indicate that condensin activity promotes the removal of DNA knots during interphase and mitosis. This activity might facilitate the spatial organization and dynamics of chromatin.

Permanent deformation of triangle weaver silk enables ultrafast tangle-free release of spider webs

Entanglements are common in both natural and artificial systems and can result in both beneficial and harmful effects. Most spider webs are static structures held under constant tension and do not tangle. However, many spiders actively load tension into their webs by coiling silk threads that are released to "fire" webs at prey. Here we test whether or not tangling occurs during the rapid release of webs built by the triangle spider Hyptiotes cavatus. We use high-speed videography to examine the release of the spider's web, looking for signs of tangling both visually on the videos and on acceleration graphs. The spider tenses the web by pulling on a silken anchor line using a leg-over-leg movement, deforming the silk into permanent coils and storing excess slack in a loose bundle between the spider's legs. This 1-3cm long bundle of coils straightens during the web's release in as few as 4ms. Though the messy silk coils are pressed closely together, the web's release is never impeded by catastrophic tangling. This lack of serious tangling is perhaps due to the permanent coils preventing random movement of the silk. The coils also compact the loose silk, preventing interference with the spider's movement. The ability to coil its anchor line allows H. cavatus to permanently restructure its silk, facilitating its active web-hunting behavior. Our findings broaden our knowledge of silk manipulation by spiders and may give insights into creating tangle-free systems through structural changes.

Channels with Helical Modulation Display Stereospecific Sensitivity for Chiral Superstructures

By means of coarse-grained molecular dynamics simulations, we explore chiral sensitivity of confining spaces modelled as helical channels to chiral superstructures represented by polymer knots. The simulations show that helical channels exhibit stereosensitivity to chiral knots localized on linear chains by effect of external pulling force and also to knots embedded on circular chains. The magnitude of the stereoselective effect is stronger for torus knots, the effect is weaker in the case of twist knots, and amphichiral knots do exhibit no chiral effects. The magnitude of the effect can be tuned by the so-far investigated radius of the helix, the pitch of the helix and the strength of the pulling force. The model is aimed to simulate and address a range of practical situations that may occur in experimental settings such as designing of nanotechnological devices for the detection of topological state of molecules, preparation of new gels with tailor made stereoselective properties, or diffusion of knotted DNA in biological conditions.

Transcription-mediated supercoiling regulates genome folding and loop formation

The chromatin fiber folds into loops, but the mechanisms controlling loop extrusion are still poorly understood. Using super-resolution microscopy, we visualize that loops in intact nuclei are formed by a scaffold of cohesin complexes from which the DNA protrudes. RNA polymerase II decorates the top of the loops and is physically segregated from cohesin. Augmented looping upon increased loading of cohesin on chromosomes causes disruption of Lamin at the nuclear rim and chromatin blending, a homogeneous distribution of chromatin within the nucleus. Altering supercoiling via either transcription or topoisomerase inhibition counteracts chromatin blending, increases chromatin condensation, disrupts loop formation, and leads to altered cohesin distribution and mobility on chromatin. Overall, negative supercoiling generated by transcription is an important regulator of loop formation in vivo.

A low Smc flux avoids collisions and facilitates chromosome organization in Bacillus subtilis

SMC complexes are widely conserved ATP-powered DNA-loop-extrusion motors indispensable for organizing and faithfully segregating chromosomes. How SMC complexes translocate along DNA for loop extrusion and what happens when two complexes meet on the same DNA molecule is largely unknown. Revealing the origins and the consequences of SMC encounters is crucial for understanding the folding process not only of bacterial, but also of eukaryotic chromosomes. Here, we uncover several factors that influence bacterial chromosome organization by modulating the probability of such clashes. These factors include the number, the strength, and the distribution of Smc loading sites, the residency time on the chromosome, the translocation rate, and the cellular abundance of Smc complexes. By studying various mutants, we show that these parameters are fine-tuned to reduce the frequency of encounters between Smc complexes, presumably as a risk mitigation strategy. Mild perturbations hamper chromosome organization by causing Smc collisions, implying that the cellular capacity to resolve them is limited. Altogether, we identify mechanisms that help to avoid Smc collisions and their resolution by Smc traversal or other potentially risky molecular transactions.

Mechanisms for Chromosome Segregation in Bacteria

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

DNA-Topology Simplification by Topoisomerases

The topological properties of DNA molecules, supercoiling, knotting, and catenation, are intimately connected with essential biological processes, such as gene expression, replication, recombination, and chromosome segregation. Non-trivial DNA topologies present challenges to the molecular machines that process and maintain genomic information, for example, by creating unwanted DNA entanglements. At the same time, topological distortion can facilitate DNA-sequence recognition through localized duplex unwinding and longer-range loop-mediated interactions between the DNA sequences. Topoisomerases are a special class of essential enzymes that homeostatically manage DNA topology through the passage of DNA strands. The activities of these enzymes are generally investigated using circular DNA as a model system, in which case it is possible to directly assay the formation and relaxation of DNA supercoils and the formation/resolution of knots and catenanes. Some topoisomerases use ATP as an energy cofactor, whereas others act in an ATP-independent manner. The free energy of ATP hydrolysis can be used to drive negative and positive supercoiling or to specifically relax DNA topologies to levels below those that are expected at thermodynamic equilibrium. The latter activity, which is known as topology simplification, is thus far exclusively associated with type-II topoisomerases and it can be understood through insight into the detailed non-equilibrium behavior of type-II enzymes. We use a non-equilibrium topological-network approach, which stands in contrast to the equilibrium models that are conventionally used in the DNA-topology field, to gain insights into the rates that govern individual transitions between topological states. We anticipate that our quantitative approach will stimulate experimental work and the theoretical/computational modeling of topoisomerases and similar enzyme systems.

Mitotic chromosomes

Our understanding of the structure and function of mitotic chromosomes has come a long way since these iconic objects were first recognized more than 140 years ago, though many details remain to be elucidated. In this chapter, we start with the early history of chromosome studies and then describe the path that led to our current understanding of the formation and structure of mitotic chromosomes. We also discuss some of the remaining questions. It is now well established that each mitotic chromatid consists of a central organizing region containing a so-called "chromosome scaffold" from which loops of DNA project radially. Only a few key non-histone proteins and protein complexes are required to form the chromosome: topoisomerase IIα, cohesin, condensin I and condensin II, and the chromokinesin KIF4A. These proteins are concentrated along the axis of the chromatid. Condensins I and II are primarily responsible for shaping the chromosome and the scaffold, and they produce the loops of DNA by an ATP-dependent process known as loop extrusion. Modelling of Hi-C data suggests that condensin II adopts a spiral staircase arrangement with an extruded loop extending out from each step in a roughly helical pattern. Condensin I then forms loops nested within these larger condensin II loops, thereby giving rise to the final compaction of the mitotic chromosome in a process that requires Topo IIα.

Gradual opening of Smc arms in prokaryotic condensin

Multi-subunit SMC ATPases control chromosome superstructure apparently by catalyzing a DNA-loop-extrusion reaction. SMC proteins harbor an ABC-type ATPase "head" and a "hinge" dimerization domain connected by a coiled coil "arm." Two arms in a SMC dimer can co-align, thereby forming a rod-shaped particle. Upon ATP binding, SMC heads engage, and arms are thought to separate. Here, we study the shape of Bacillus subtilis Smc-ScpAB by electron-spin resonance spectroscopy. Arm separation is readily detected proximal to the heads in the absence of ligands, and separation near the hinge largely depends on ATP and DNA. Artificial blockage of arm opening eliminates DNA stimulation of ATP hydrolysis but does not prevent basal ATPase activity. We report an arm contact as being important for controlling the transformations. Point mutations at this arm interface eliminated Smc function. We propose that partially open, intermediary conformations provide directionality to SMC DNA translocation by (un)binding suitable DNA substrates.

Condensin minimizes topoisomerase II-mediated entanglements of DNA in vivo

The juxtaposition of intracellular DNA segments, together with the DNA-passage activity of topoisomerase II, leads to the formation of DNA knots and interlinks, which jeopardize chromatin structure and gene expression. Recent studies in budding yeast have shown that some mechanism minimizes the knotting probability of intracellular DNA. Here, we tested whether this is achieved via the intrinsic capacity of topoisomerase II for simplifying the equilibrium topology of DNA; or whether it is mediated by SMC (structural maintenance of chromosomes) protein complexes like condensin or cohesin, whose capacity to extrude DNA loops could enforce dissolution of DNA knots by topoisomerase II. We show that the low knotting probability of DNA does not depend on the simplification capacity of topoisomerase II nor on the activities of cohesin or Smc5/6 complexes. However, inactivation of condensin increases the occurrence of DNA knots throughout the cell cycle. These results suggest an in vivo role for the DNA loop extrusion activity of condensin and may explain why condensin disruption produces a variety of alterations in interphase chromatin, in addition to persistent sister chromatid interlinks in mitotic chromatin.

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

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

Non-Equilibrium Living Polymers

Systems of "living" polymers are ubiquitous in industry and are traditionally realised using surfactants. Here I first review the theoretical state-of-the-art of living polymers and then discuss non-equilibrium extensions that may be realised with advanced synthetic chemistry or DNA functionalised by proteins. These systems are not only interesting in order to realise novel "living" soft matter but can also shed insight into how genomes are (topologically) regulated in vivo.

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

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

Separation of Geometrical and Topological Entanglement in Confined Polymers Driven out of Equilibrium

We use Brownian dynamics simulations and advanced topological profiling methods to characterize the out-of-equilibrium evolution of self-entanglement in linear polymers confined into nanochannels and under periodic compression. By introducing suitable observables, we can distinguish two main forms of entanglement that we term geometrical and topological. The latter is measured by the number of (essential) crossings of the physical knot detected after a suitable bridging of the chain termini. The former is instead measured as the average number of times a linear chain appears to cross itself when viewed under all projections and is irrespective of the physical knotted state. The key discovery of our work is that these two forms of entanglement are uncoupled and evolve with distinct dynamics. While geometrical entanglement is typically in phase with the compression-elongation cycles and it is primarily sensitive to its force f, the topological measure is mildly sensitive to cyclic modulation but strongly depends on both compression force f and duration k. The findings could assist the interpretation of experiments using fluorescence molecular tracers to track physical knots in polymers. Furthermore, we identify optimal regions in the experimentally controllable parameter space in which to obtain more/less topological and geometrical entanglement; this may help designing polymers with targeted topology.

Chromatin Architectural Factors as Safeguards against Excessive Supercoiling during DNA Replication

Key DNA transactions, such as genome replication and transcription, rely on the speedy translocation of specialized protein complexes along a double-stranded, right-handed helical template. Physical tethering of these molecular machines during translocation, in conjunction with their internal architectural features, generates DNA topological strain in the form of template supercoiling. It is known that the build-up of transient excessive supercoiling poses severe threats to genome function and stability and that highly specialized enzymes—the topoisomerases (TOP)—have evolved to mitigate these threats. Furthermore, due to their intracellular abundance and fast supercoil relaxation rates, it is generally assumed that these enzymes are sufficient in coping with genome-wide bursts of excessive supercoiling. However, the recent discoveries of chromatin architectural factors that play important accessory functions have cast reasonable doubts on this concept. Here, we reviewed the background of these new findings and described emerging models of how these accessory factors contribute to supercoil homeostasis. We focused on DNA replication and the generation of positive (+) supercoiling in front of replisomes, where two accessory factors—GapR and HMGA2—from pro- and eukaryotic cells, respectively, appear to play important roles as sinks for excessive (+) supercoiling by employing a combination of supercoil constrainment and activation of topoisomerases. Looking forward, we expect that additional factors will be identified in the future as part of an expanding cellular repertoire to cope with bursts of topological strain. Furthermore, identifying antagonists that target these accessory factors and work synergistically with clinically relevant topoisomerase inhibitors could become an interesting novel strategy, leading to improved treatment outcomes.

A topological analysis of difference topology experiments of condensin with topoisomerase II

An experimental technique called difference topology combined with the mathematics of tangle analysis has been used to unveil the structure of DNA bound by the Mu transpososome. However, difference topology experiments can be difficult and time consuming. We discuss a modification that greatly simplifies this experimental technique. This simple experiment involves using a topoisomerase to trap DNA crossings bound by a protein complex and then running a gel to determine the crossing number of the knotted product(s). We develop the mathematics needed to analyze the results and apply these results to model the topology of DNA bound by 13S condensin and by the condensin MukB.

Genome organization via loop extrusion, insights from polymer physics models

Understanding how genomes fold and organize is one of the main challenges in modern biology. Recent high-throughput techniques like Hi-C, in combination with cutting-edge polymer physics models, have provided access to precise information on 3D chromosome folding to decipher the mechanisms driving such multi-scale organization. In particular, structural maintenance of chromosome (SMC) proteins play an important role in the local structuration of chromatin, putatively via a loop extrusion process. Here, we review the different polymer physics models that investigate the role of SMCs in the formation of topologically associated domains (TADs) during interphase via the formation of dynamic loops. We describe the main physical ingredients, compare them and discuss their relevance against experimental observations.

Chromosome compaction and chromatin stiffness enhance diffusive loop extrusion by slip-link proteins

We use Brownian dynamics simulations to study the formation of chromatin loops through diffusive sliding of slip-link-like proteins, mimicking the behaviour of cohesin molecules. We recently proposed that diffusive sliding is sufficient to explain the extrusion of chromatin loops of hundreds of kilo-base-pairs (kbp), which may then be stabilised by interactions between cohesin and CTCF proteins. Here we show that the flexibility of the chromatin fibre strongly affects this dynamical process, and find that diffusive loop extrusion is more efficient on stiffer chromatin regions. We also show that the dynamics of loop formation are faster in confined and collapsed chromatin conformations but that this enhancement is counteracted by the increased crowding. We provide a simple theoretical argument explaining why stiffness and collapsed conformations favour diffusive extrusion. In light of the heterogeneous physical and conformational properties of eukaryotic chromatin, we suggest that our results are relevant to understand the looping and organisation of interphase chromosomes in vivo.

Integrating transposable elements in the 3D genome

Chromosome organisation is increasingly recognised as an essential component of genome regulation, cell fate and cell health. Within the realm of transposable elements (TEs) however, the spatial information of how genomes are folded is still only rarely integrated in experimental studies or accounted for in modelling. Whilst polymer physics is recognised as an important tool to understand the mechanisms of genome folding, in this commentary we discuss its potential applicability to aspects of TE biology. Based on recent works on the relationship between genome organisation and TE integration, we argue that existing polymer models may be extended to create a predictive framework for the study of TE integration patterns. We suggest that these models may offer orthogonal and generic insights into the integration profiles (or "topography") of TEs across organisms. In addition, we provide simple polymer physics arguments and preliminary molecular dynamics simulations of TEs inserting into heterogeneously flexible polymers. By considering this simple model, we show how polymer folding and local flexibility may generically affect TE integration patterns. The preliminary discussion reported in this commentary is aimed to lay the foundations for a large-scale analysis of TE integration dynamics and topography as a function of the three-dimensional host genome.

Mitotic chromosome organization: General rules meet species-specific variability

Research on the formation of mitotic chromosomes from interphase chromatin domains, ongoing for several decades, made significant progress in recent years. It was stimulated by the development of advanced microscopic techniques and implementation of chromatin conformation capture methods that provide new insights into chromosome ultrastructure. This review aims to summarize and compare several models of chromatin fiber folding to form mitotic chromosomes and discusses them in the light of the novel findings. Functional genomics studies in several organisms confirmed condensins and cohesins as the major players in chromosome condensation. Here we compare available data on the role of these proteins across lower and higher eukaryotes and point to differences indicating evolutionary different pathways to shape mitotic chromosomes. Moreover, we discuss a controversial phenomenon of the mitotic chromosome ultrastructure - chromosome cavities - and using our super-resolution microscopy data, we contribute to its elucidation.

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

Eukaryote cell division features a chromosome compaction-decompaction cycle that is synchronized with their physical and topological segregation. It has been proposed that lengthwise compaction of chromatin into mitotic chromosomes via loop extrusion underlies the compaction-segregation/resolution process. We analyze this disentanglement scheme via considering the chromosome to be a succession of DNA/chromatin loops-a polymer "brush"-where active extrusion of loops controls the brush structure. Given type-II DNA topoisomerase (Topo II)-catalyzed topology fluctuations, we find that interchromosome entanglements are minimized for a certain "optimal" loop that scales with the chromosome size. The optimal loop organization is in accord with experimental data across species, suggesting an important structural role of genomic loops in maintaining a less entangled genome. Application of the model to the interphase genome indicates that active loop extrusion can maintain a level of chromosome compaction with suppressed entanglements; the transition to the metaphase state requires higher lengthwise compaction and drives complete topological segregation. Optimized genomic loops may provide a means for evolutionary propagation of gene-expression patterns while simultaneously maintaining a disentangled genome. We also find that compact metaphase chromosomes have a densely packed core along their cylindrical axes that explains their observed mechanical stiffness. Our model connects chromosome structural reorganization to topological resolution through the cell cycle and highlights a mechanism of directing Topo II-mediated strand passage via loop extrusion-driven lengthwise compaction.

Chromatin Is Frequently Unknotted at the Megabase Scale

Knots in the human genome would greatly impact diverse cellular processes ranging from transcription to gene regulation. To date, it has not been possible to directly examine the genome in vivo for the presence of knots. Recently, methods for serial fluorescent in situ hybridization have made it possible to measure the three-dimensional position of dozens of consecutive genomic loci in vivo. However, the determination of whether genomic trajectories are knotted remains challenging because small errors in the localization of a single locus can transform an unknotted trajectory into a highly knotted trajectory and vice versa. Here, we use stochastic closure analysis to determine if a genomic trajectory is knotted in the setting of experimental noise. We analyze 4727 deposited genomic trajectories of a 2-Mb-long chromatin interval from human chromosome 21. For 243 of these trajectories, their knottedness could be reliably determined despite the possibility of localization errors. Strikingly, in each of these 243 cases, the trajectory was unknotted. We note a potential source of bias insofar as knotted contours may be more difficult to reliably resolve. Nevertheless, our data are consistent with a model in which, at the scales probed, the human genome is often free of knots.

Magnetic polymer models for epigenetics-driven chromosome folding

Epigenetics is a driving force of important and ubiquitous phenomena in nature such as cell differentiation or even metamorphosis. Opposite to its widespread role, understanding the biophysical principles that allow epigenetics to control and rewire gene regulatory networks remains an open challenge. In this work we study the effects of epigenetic modifications on the spatial folding of chromosomes-and hence on the expression of the underlying genes-by mapping the problem to a class of models known as magnetic polymers. In this work we show that a first order phase transition underlies the simultaneous spreading of certain epigenetic marks and the conformational collapse of a chromosome. Further, we describe Brownian dynamics simulations of the model in which the topology of the polymer and thermal fluctuations are fully taken into account and that confirm our mean field predictions. Extending our models to allow for nonequilibrium terms yields new stable phases which qualitatively agrees with observations in vivo. Our results show that statistical mechanics techniques applied to models of magnetic polymers can be successfully exploited to rationalize the outcomes of experiments designed to probe the interplay between a dynamic epigenetic landscape and chromatin organization.

Merging 1D and 3D genomic information: Challenges in modelling and validation

Genome organization in eukaryotes during interphase stems from the delicate balance between non-random correlations present in the DNA polynucleotide linear sequence and the physico/chemical reactions which shape continuously the form and structure of DNA and chromatin inside the nucleus of the cell. It is now clear that these mechanisms have a key role in important processes like gene regulation, yet the detailed ways they act simultaneously and, eventually, come to influence each other even across very different length-scales remain largely unexplored. In this paper, we recapitulate some of the main results concerning gene regulatory and physical mechanisms, in relation to the information encoded in the 1D sequence and the 3D folding structure of DNA. In particular, we stress how reciprocal crossfeeding between 1D and 3D models may provide original insight into how these complex processes work and influence each other. This article is part of a Special Issue entitled: Transcriptional Profiles and Regulatory Gene Networks edited by Dr. Dr. Federico Manuel Giorgi and Dr. Shaun Mahony.