Theoretical models of DNA topology simplification by type IIA DNA topoisomerases

Extensive Bioinformatics Analyses Reveal a Phylogenetically Conserved Winged Helix (WH) Domain (Zτ) of Topoisomerase IIα, Elucidating Its Very High Affinity for Left-Handed Z-DNA and Suggesting Novel Putative Functions

The dynamic processes operating on genomic DNA, such as gene expression and cellular division, lead inexorably to topological challenges in the form of entanglements, catenanes, knots, "bubbles", R-loops, and other outcomes of supercoiling and helical disruption. The resolution of toxic topological stress is the function attributed to DNA topoisomerases. A prominent example is the negative supercoiling (nsc) trailing processive enzymes such as DNA and RNA polymerases. The multiple equilibrium states that nscDNA can adopt by redistribution of helical twist and writhe include the left-handed double-helical conformation known as Z-DNA. Thirty years ago, one of our labs isolated a protein from Drosophila cells and embryos with a 100-fold greater affinity for Z-DNA than for B-DNA, and identified it as topoisomerase II (gene Top2, orthologous to the human UniProt proteins TOP2A and TOP2B). GTP increased the affinity and selectivity for Z-DNA even further and also led to inhibition of the isomerase enzymatic activity. An allosteric mechanism was proposed, in which topoII acts as a Z-DNA-binding protein (ZBP) to stabilize given states of topological (sub)domains and associated multiprotein complexes. We have now explored this possibility by comprehensive bioinformatic analyses of the available protein sequences of topoII representing organisms covering the whole tree of life. Multiple alignment of these sequences revealed an extremely high level of evolutionary conservation, including a winged-helix protein segment, here denoted as Zτ, constituting the putative structural homolog of Zα, the canonical Z-DNA/Z-RNA binding domain previously identified in the interferon-inducible RNA Adenosine-to-Inosine-editing deaminase, ADAR1p150. In contrast to Zα, which is separate from the protein segment responsible for catalysis, Zτ encompasses the active site tyrosine of topoII; a GTP-binding site and a GxxG sequence motif are in close proximity. Quantitative Zτ-Zα similarity comparisons and molecular docking with interaction scoring further supported the "B-Z-topoII hypothesis" and has led to an expanded mechanism for topoII function incorporating the recognition of Z-DNA segments ("Z-flipons") as an inherent and essential element. We further propose that the two Zτ domains of the topoII homodimer exhibit a single-turnover "conformase" activity on given G(ate) B-DNA segments ("Z-flipins"), inducing their transition to the left-handed Z-conformation. Inasmuch as the topoII-Z-DNA complexes are isomerase inactive, we infer that they fulfill important structural roles in key processes such as mitosis. Topoisomerases are preeminent targets of anti-cancer drug discovery, and we anticipate that detailed elucidation of their structural-functional interactions with Z-DNA and GTP will facilitate the design of novel, more potent and selective anti-cancer chemotherapeutic agents.

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.

Diversity and Functions of Type II Topoisomerases

The DNA double helix provides a simple and elegant way to store and copy genetic information. However, the processes requiring the DNA helix strands separation, such as transcription and replication, induce a topological side-effect - supercoiling of the molecule. Topoisomerases comprise a specific group of enzymes that disentangle the topological challenges associated with DNA supercoiling. They relax DNA supercoils and resolve catenanes and knots. Here, we review the catalytic cycles, evolution, diversity, and functional roles of type II topoisomerases in organisms from all domains of life, as well as viruses and other mobile genetic elements.

Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology

Grid diagrams with their relatively simple mathematical formalism provide a convenient way to generate and model projections of various knots. It has been an open question whether these 2D diagrams can be used to model a complex 3D process such as the topoisomerase-mediated preferential unknotting of DNA molecules. We model here topoisomerase-mediated passages of double-stranded DNA segments through each other using the formalism of grid diagrams. We show that this grid diagram-based modeling approach captures the essence of the preferential unknotting mechanism, based on topoisomerase selectivity of hooked DNA juxtapositions as the sites of intersegmental passages. We show that the grid diagram-based approach provides an important, new, and computationally convenient framework for investigating entanglement in biopolymers.

Promoter polymorphisms of TOP2A and ERCC1 genes as predictive factors for chemotherapy in non-small cell lung cancer patients

Background

Topoisomerase 2‐alpha (TOP2A) is an enzyme that controls topologic changes in DNA during transcription and replication. ERCC1 is an enzyme that takes part in DNA repair processes. The purpose of this study was to assess the predictive role of particular single nucleotide polymorphisms (SNPs) in the promoter regions of TOP2A and ERCC1 genes in non‐small cell lung cancer patients (NSCLC) treated with chemotherapy.

Materials and methods

We enrolled 113 NSCLC patients treated in the first line with platinum‐based chemotherapy. Effectiveness was available for 71 patients. DNA was isolated from whole blood using the Qiamp DNA Blood Mini kit (Qiagen). We examined five SNPs: rs11615 (ERCC1), rs3212986 (ERCC1), rs13695 (TOP2A), rs34300454 (TOP2A), rs11540720 (TOP2A). Quantitative PCR using the TaqMan probe (ThermoFisher) was performed on a Eco Illumina Real‐Time PCR system device (Illumina Inc).

Results

Patients with the A/A genotype in rs11615 of the ERCC1 gene had significantly longer median progression free survival (PFS) (8.5 months; P = .0088). Patients with the C/C genotype in rs3212986 of the ERCC1 gene had longer median PFS (7 months; P = .05). Patients with the C/C genotype in rs34300454 of TOP2A gene had significantly higher median PFS (7.5 months; P = .0029). Carriers of the C/C genotype in rs34300454 of the TOP2A gene had significantly longer median OS (15.5 months; P = .0017). Patients with the A/A genotype in rs11615 of the ERCC1 gene had significantly higher risk of neutropenia (P = .0133).

Conclusions

Polymorphisms of the TOP2A and ERCC1 genes may be a predictive factor of toxicities and survival for chemotherapy in NSCLC patients.

Kinetic pathways of topology simplification by Type-II topoisomerases in knotted supercoiled DNA

The topological state of covalently closed, double-stranded DNA is defined by the knot type $K$ and the linking-number difference $\Delta Lk$ relative to unknotted relaxed DNA. DNA topoisomerases are essential enzymes that control the topology of DNA in all cells. In particular, type-II topoisomerases change both $K$ and $\Delta Lk$ by a duplex-strand-passage mechanism and have been shown to simplify the topology of DNA to levels below thermal equilibrium at the expense of ATP hydrolysis. It remains a key question how small enzymes are able to preferentially select strand passages that result in topology simplification in much larger DNA molecules. Using numerical simulations, we consider the non-equilibrium dynamics of transitions between topological states $(K,\Delta Lk)$ in DNA induced by type-II topoisomerases. For a biological process that delivers DNA molecules in a given topological state $(K,\Delta Lk)$ at a constant rate we fully characterize the pathways of topology simplification by type-II topoisomerases in terms of stationary probability distributions and probability currents on the network of topological states $(K,\Delta Lk)$. In particular, we observe that type-II topoisomerase activity is significantly enhanced in DNA molecules that maintain a supercoiled state with constant torsional tension. This is relevant for bacterial cells in which torsional tension is maintained by enzyme-dependent homeostatic mechanisms such as DNA-gyrase activity.

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

Topological entanglements severely interfere with important biological processes. For this reason, genomes must be kept unknotted and unlinked during most of a cell cycle. Type II topoisomerase (TopoII) enzymes play an important role in this process but the precise mechanisms yielding systematic disentanglement of DNA in vivo are not clear. Here we report computational evidence that structural-maintenance-of-chromosomes (SMC) proteins-such as cohesins and condensins-can cooperate with TopoII to establish a synergistic mechanism to resolve topological entanglements. SMC-driven loop extrusion (or diffusion) induces the spatial localization of essential crossings, in turn catalyzing the simplification of knots and links by TopoII enzymes even in crowded and confined conditions. The mechanism we uncover is universal in that it does not qualitatively depend on the specific substrate, whether DNA or chromatin, or on SMC processivity; we thus argue that this synergy may be at work across organisms and throughout the cell cycle.

Role of special cross-links in structure formation of bacterial DNA polymer

Using data from contact maps of the DNA-polymer of Escherichia coli (E. Coli) (at kilobase pair resolution) as an input to our model, we introduce cross-links between monomers in a bead-spring model of a ring polymer at very specific points along the chain. Via suitable Monte Carlo simulations, we show that the presence of these cross-links leads to a particular organization of the chain at large (micron) length scales of the DNA. We also investigate the structure of a ring polymer with an equal number of cross-links at random positions along the chain. We find that though the polymer does get organized at the large length scales, the nature of the organization is quite different from the organization observed with cross-links at specific biologically determined positions. We used the contact map of E. Coli bacteria which has around 4.6 million base pairs in a single circular chromosome. In our coarse-grained flexible ring polymer model, we used 4642 monomer beads and observed that around 80 cross-links are enough to induce the large-scale organization of the molecule accounting for statistical fluctuations caused by thermal energy. The length of a DNA chain even of a simple bacterial cell such as E. Coli is much longer than typical proteins, hence we avoided methods used to tackle protein folding problems. We define new suitable quantities to identify the large scale structure of a polymer chain with a few cross-links.

Controlling gene expression by DNA mechanics: emerging insights and challenges

Transcription initiation is a major control point for the precise regulation of gene expression. Our knowledge of this process has been mainly derived from protein-centric studies wherein cis-regulatory DNA sequences play a passive role, mainly in arranging the protein machinery to coalesce at the transcription start sites of genes in a spatial and temporal-specific manner. However, this is a highly dynamic process in which molecular motors such as RNA polymerase II (RNAPII), helicases, and other transcription factors, alter the level of mechanical force in DNA, rather than simply a set of static DNA-protein interactions. The double helix is a fiber that responds to flexural and torsional stress, which if accumulated, can affect promoter output as well as change DNA and chromatin structure. The relationship between DNA mechanics and the control of early transcription initiation events has been under-investigated. Genomic techniques to display topological stress and conformational variation in DNA across the mammalian genome provide an exciting new insight on the role of DNA mechanics in the early stages of the transcription cycle. Without understanding how torsional and flexural stresses are generated, transmitted, and dissipated, no model of transcription will be complete and accurate.

The dynamic interplay between DNA topoisomerases and DNA topology

Topological properties of DNA influence its structure and biochemical interactions. Within the cell, DNA topology is constantly in flux. Transcription and other essential processes, including DNA replication and repair, not only alter the topology of the genome but also introduce additional complications associated with DNA knotting and catenation. These topological perturbations are counteracted by the action of topoisomerases, a specialized class of highly conserved and essential enzymes that actively regulate the topological state of the genome. This dynamic interplay among DNA topology, DNA processing enzymes, and DNA topoisomerases is a pervasive factor that influences DNA metabolism in vivo. Building on the extensive structural and biochemical characterization over the past four decades that has established the fundamental mechanistic basis of topoisomerase activity, scientists have begun to explore the unique roles played by DNA topology in modulating and influencing the activity of topoisomerases. In this review we survey established and emerging DNA topology-dependent protein-DNA interactions with a focus on in vitro measurements of the dynamic interplay between DNA topology and topoisomerase activity.

Controlling gene expression by DNA mechanics: emerging insights and challenges

Transcription initiation is a major control point for the precise regulation of gene expression. Our knowledge of this process has been mainly derived from protein-centric studies wherein cis-regulatory DNA sequences play a passive role, mainly in arranging the protein machinery to coalesce at the transcription start sites of genes in a spatial and temporal-specific manner. However, this is a highly dynamic process in which molecular motors such as RNA polymerase II (RNAPII), helicases, and other transcription factors, alter the level of mechanical force in DNA, rather than simply a set of static DNA-protein interactions. The double helix is a fiber that responds to flexural and torsional stress, which if accumulated, can affect promoter output as well as change DNA and chromatin structure. The relationship between DNA mechanics and the control of early transcription initiation events has been under-investigated. Genomic techniques to display topological stress and conformational variation in DNA across the mammalian genome provide an exciting new insight on the role of DNA mechanics in the early stages of the transcription cycle. Without understanding how torsional and flexural stresses are generated, transmitted, and dissipated, no model of transcription will be complete and accurate.

The Dynamic Interplay Between DNA Topoisomerases and DNA Topology

Topological properties of DNA influence its structure and biochemical interactions. Within the cell DNA topology is constantly in flux. Transcription and other essential processes including DNA replication and repair, alter the topology of the genome, while introducing additional complications associated with DNA knotting and catenation. These topological perturbations are counteracted by the action of topoisomerases, a specialized class of highly conserved and essential enzymes that actively regulate the topological state of the genome. This dynamic interplay among DNA topology, DNA processing enzymes, and DNA topoisomerases, is a pervasive factor that influences DNA metabolism in vivo. Building on the extensive structural and biochemical characterization over the past four decades that established the fundamental mechanistic basis of topoisomerase activity, the unique roles played by DNA topology in modulating and influencing the activity of topoisomerases have begun to be explored. In this review we survey established and emerging DNA topology dependent protein-DNA interactions with a focus on in vitro measurements of the dynamic interplay between DNA topology and topoisomerase activity.

Consistent rationalization of type-2 topoisomerases' unknotting, decatenating, supercoil-relaxing actions and their scaling relation

How type-2 topoisomerases discern global topology from local properties of DNA is not known precisely but the hypothesis that the enzymes selectively pass double-helix strands at hook-like juxtapositions is promising. Building upon an investigation of unknotting and decatenating using an improved wormlike DNA model, here we focus primarily on the enzymes' action in narrowing the distribution of linking number (Lk) in supercoiled DNA. Consistent with experiments, with selective passage at a hooked juxtaposition, the simulated narrowing factor RLk diminishes with decreasing DNA circle size but approaches an asymptotic RLk ≈ 1.7-1.8 for circle size ≳3.5 kb. For the larger DNA circles, we found that (RLk - 1) ≈ 0.42log10RK ≈ 0.68log10RL and thus RK ≈ (RL)(1.6) holds for the computed RLk and knot and catenane reduction factors RK and RL attained by selective passage at different juxtaposition geometries. Remarkably, this general scaling relation is essentially identical to that observed experimentally for several type-2 topoisomerases from a variety of organisms, indicating that the different disentangling powers of the topoisomerases likely arise from variations in the hooked geometries they select. Taken together, our results suggest strongly that type-2 topoisomerases recognize not only the curvature of the G-segment but also that of the T-segment.

Structural organization of human replication timing domains

Recent analysis of genome-wide epigenetic modification data, mean replication timing (MRT) profiles and chromosome conformation data in mammals have provided increasing evidence that flexibility in replication origin usage is regulated locally by the epigenetic landscape and over larger genomic distances by the 3D chromatin architecture. Here, we review the recent results establishing some link between replication domains and chromatin structural domains in pluripotent and various differentiated cell types in human. We reconcile the originally proposed dichotomic picture of early and late constant timing regions that replicate by multiple rather synchronous origins in separated nuclear compartments of open and closed chromatins, with the U-shaped MRT domains bordered by "master" replication origins specified by a localized (∼200-300 kb) zone of open and transcriptionally active chromatin from which a replication wave likely initiates and propagates toward the domain center via a cascade of origin firing. We discuss the relationships between these MRT domains, topologically associated domains and lamina-associated domains. This review sheds a new light on the epigenetically regulated global chromatin reorganization that underlies the loss of pluripotency and the determination of differentiation properties.

Extracting physics of life at the molecular level: A review of single-molecule data analyses

Studying individual biomolecules at the single-molecule level has proved very insightful recently. Single-molecule experiments allow us to probe both the equilibrium and nonequilibrium properties as well as make quantitative connections with ensemble experiments and equilibrium thermodynamics. However, it is important to be careful about the analysis of single-molecule data because of the noise present and the lack of theoretical framework for processes far away from equilibrium. Biomolecular motion, whether it is free in solution, on a substrate, or under force, involves thermal fluctuations in varying degrees, which makes the motion noisy. In addition, the noise from the experimental setup makes it even more complex. The details of biologically relevant interactions, conformational dynamics, and activities are hidden in the noisy single-molecule data. As such, extracting biological insights from noisy data is still an active area of research. In this review, we will focus on analyzing both fluorescence-based and force-based single-molecule experiments and gaining biological insights at the single-molecule level. Inherently nonequilibrium nature of biological processes will be highlighted. Simulated trajectories of biomolecular diffusion will be used to compare and validate various analysis techniques.

Extracting physical chemistry from mechanics: a new approach to investigate DNA interactions with drugs and proteins in single molecule experiments

In this review we focus on the idea of establishing connections between the mechanical properties of DNA–ligand complexes and the physical chemistry of DNA–ligand interactions.

Topoisomerase II minimizes DNA entanglements by proofreading DNA topology after DNA strand passage

By transporting one DNA double helix (T-segment) through a double-strand break in another (G-segment), topoisomerase II reduces fractions of DNA catenanes, knots and supercoils to below equilibrium values. How DNA segments are selected to simplify the equilibrium DNA topology is enigmatic, and the biological relevance of this activity is unclear. Here we examined the transit of the T-segment across the three gates of topoisomerase II (entry N-gate, DNA-gate and exit C-gate). Our experimental results uncovered that DNA transport probability is determined not only during the capture of a T-segment at the N-gate. When a captured T-segment has crossed the DNA-gate, it can backtrack to the N-gate instead of exiting by the C-gate. When such backtracking is precluded by locking the N-gate or by removing the C-gate, topoisomerase II no longer simplifies equilibrium DNA topology. Therefore, we conclude that the C-gate enables a post-DNA passage proofreading mechanism, which challenges the release of passed T-segments to either complete or cancel DNA transport. This proofreading activity not only clarifies how type-IIA topoisomerases simplify the equilibrium topology of DNA in free solution, but it may explain also why these enzymes are able to solve the topological constraints of intracellular DNA without randomly entangling adjacent chromosomal regions.

Crossing-sign discrimination and knot-reduction for a lattice model of strand passage

By performing strand-passages on DNA, type II topoisomerases are known to resolve topological constraints that impede normal cellular functions. The full details of this enzyme–DNA interaction mechanism are, however, not completely understood. To better understand this mechanism, researchers have proposed and studied a variety of random polygon models of enzyme-induced strand-passage. In the present article, we review results from one such model having the feature that it is amenable to combinatorial and asymptotic analysis (as polygon length goes to infinity). The polygons studied, called Θ-SAPs, are on the simple-cubic lattice and contain a specific strand-passage structure, called Θ, at a fixed site. Another feature of this model is the availability of Monte Carlo methods that facilitate the estimation of crossing-sign-dependent knot-transition probabilities. From such estimates, it has been possible to investigate how knot-reduction depends on the crossing-sign and the local juxtaposition geometry at the strand-passage site. A strong relationship between knot-reduction and a crossing-sign-dependent crossing-angle has been observed for this model. In the present article, we review these results and present heuristic geometrical arguments to explain this crossing-sign and angle-dependence. Finally, we discuss potential implications for other models of type II topoisomerase action on DNA.

Comparison of DNA decatenation by Escherichia coli topoisomerase IV and topoisomerase III: implications for non-equilibrium topology simplification

Type II topoisomerases are essential enzymes that regulate DNA topology through a strand-passage mechanism. Some type II topoisomerases relax supercoils, unknot and decatenate DNA to below thermodynamic equilibrium. Several models of this non-equilibrium topology simplification phenomenon have been proposed. The kinetic proofreading (KPR) model postulates that strand passage requires a DNA-bound topoisomerase to collide twice in rapid succession with a second DNA segment, implying a quadratic relationship between DNA collision frequency and relaxation rate. To test this model, we used a single-molecule assay to measure the unlinking rate as a function of DNA collision frequency for Escherichia coli topoisomerase IV (topo IV) that displays efficient non-equilibrium topology simplification activity, and for E. coli topoisomerase III (topo III), a type IA topoisomerase that unlinks and unknots DNA to equilibrium levels. Contrary to the predictions of the KPR model, topo IV and topo III unlinking rates were linearly related to the DNA collision frequency. Furthermore, topo III exhibited decatenation activity comparable with that of topo IV, supporting proposed roles for topo III in DNA segregation. This study enables us to rule out the KPR model for non-equilibrium topology simplification. More generally, we establish an experimental approach to systematically control DNA collision frequency.

Local sensing of global DNA topology: from crossover geometry to type II topoisomerase processivity

Type II topoisomerases are ubiquitous enzymes that control the topology and higher order structures of DNA. Type IIA enzymes have the remarkable property to sense locally the global DNA topology. Although many theoretical models have been proposed, the molecular mechanism of chiral discrimination is still unclear. While experimental studies have established that topoisomerases IIA discriminate topology on the basis of crossover geometry, a recent single-molecule experiment has shown that the enzyme has a different processivity on supercoiled DNA of opposite sign. Understanding how cross-over geometry influences enzyme processivity is, therefore, the key to elucidate the mechanism of chiral discrimination. Analysing this question from the DNA side reveals first, that the different stability of chiral DNA cross-overs provides a way to locally sense the global DNA topology. Second, it shows that these enzymes have evolved to recognize the G- and T-segments stably assembled into a right-handed cross-over. Third, it demonstrates how binding right-handed cross-overs across their large angle imposes a different topological link between the topoIIA rings and the plectonemes of opposite sign thus directly affecting the enzyme freedom of motion and processivity. In bridging geometry and kinetic data, this study brings a simple solution for type IIA topoisomerase chiral discrimination.

Direct measurement of DNA bending by type IIA topoisomerases: implications for non-equilibrium topology simplification

Type IIA topoisomerases modify DNA topology by passing one segment of duplex DNA (transfer or T-segment) through a transient double-strand break in a second segment of DNA (gate or G-segment) in an ATP-dependent reaction. Type IIA topoisomerases decatenate, unknot and relax supercoiled DNA to levels below equilibrium, resulting in global topology simplification. The mechanism underlying this non-equilibrium topology simplification remains speculative. The bend angle model postulates that non-equilibrium topology simplification scales with the bend angle imposed on the G-segment DNA by the binding of a type IIA topoisomerase. To test this bend angle model, we used atomic force microscopy and single-molecule Förster resonance energy transfer to measure the extent of bending imposed on DNA by three type IIA topoisomerases that span the range of topology simplification activity. We found that Escherichia coli topoisomerase IV, yeast topoisomerase II and human topoisomerase IIα each bend DNA to a similar degree. These data suggest that DNA bending is not the sole determinant of non-equilibrium topology simplification. Rather, they suggest a fundamental and conserved role for DNA bending in the enzymatic cycle of type IIA topoisomerases.

The fractal globule as a model of chromatin architecture in the cell

The fractal globule is a compact polymer state that emerges during polymer condensation as a result of topological constraints which prevent one region of the chain from passing across another one. This long-lived intermediate state was introduced in 1988 (Grosberg et al. 1988) and has not been observed in experiments or simulations until recently (Lieberman-Aiden et al. 2009). Recent characterization of human chromatin using a novel chromosome conformational capture technique brought the fractal globule into the spotlight as a structural model of human chromosome on the scale of up to 10 Mb (Lieberman-Aiden et al. 2009). Here, we present the concept of the fractal globule, comparing it to other states of a polymer and focusing on its properties relevant for the biophysics of chromatin. We then discuss properties of the fractal globule that make it an attractive model for chromatin organization inside a cell. Next, we connect the fractal globule to recent studies that emphasize topological constraints as a primary factor driving formation of chromosomal territories. We discuss how theoretical predictions, made on the basis of the fractal globule model, can be tested experimentally. Finally, we discuss whether fractal globule architecture can be relevant for chromatin packing in other organisms such as yeast and bacteria.

Action at hooked or twisted-hooked DNA juxtapositions rationalizes unlinking preference of type-2 topoisomerases

The mathematical basis of the hypothesis that type-2 topoisomerases recognize and act at specific DNA juxtapositions has been investigated by coarse-grained lattice polymer models, showing that selective segment passages at hooked juxtapositions can result in dramatic reductions in catenane and knot populations. The lattice modeling approach is here extended to account for the narrowing of variance of linking number (Lk) of DNA circles by type-2 topoisomerases. In general, the steady-state variance of Lk resulting from selective segment passages at a specific juxtaposition geometry j is inversely proportional to the average linking number, Lk(j), of circles with the given juxtaposition. Based on this formulation, we demonstrate that selective segment passages at hooked juxtapositions reduce the variance of Lk. The dependence of this effect on model DNA circle size is remarkably similar to that observed experimentally for type-2 topoisomerases, which appear to be less capable in narrowing Lk variance for small DNA circles than for larger DNA circles. This behavior is rationalized by a substantial cancellation of writhe in small circles with hook-like juxtapositions. During our simulations, we uncovered a twisted variation of the hooked juxtaposition that has an even more dramatic effect on Lk variance narrowing than the hooked juxtaposition. For an extended set of juxtapositions, we detected a significant correlation between the Lk narrowing potential and the logarithmic decatenating and unknotting potentials for a given juxtaposition, a trend reminiscent of scaling relations observed with experimental measurements on type-2 topoisomerases from a variety of organisms. The consistent agreement between theory and experiment argues for type-2 topoisomerase action at hooked or twisted-hooked DNA juxtapositions.

Biophysics of knotting

Knots appear in a wide variety of biophysical systems, ranging from biopolymers, such as DNA and proteins, to macroscopic objects, such as umbilical cords and catheters. Although significant advancements have been made in the mathematical theory of knots and some progress has been made in the statistical mechanics of knots in idealized chains, the mechanisms and dynamics of knotting in biophysical systems remain far from fully understood. We report on recent progress in the biophysics of knotting-the formation, characterization, and dynamics of knots in various biophysical contexts.

In front of and behind the replication fork: bacterial type IIA topoisomerases

Topoisomerases are vital enzymes specialized in controlling DNA topology, in particular supercoiling and decatenation, to properly handle nucleic acid packing and cell dynamics. The type IIA enzymes act by cleaving both strands of a double helix and having another strand from the same or another molecule cross the DNA gate before a re-sealing event completes the catalytic cycle. Here, we will consider the two types of IIA prokaryotic topoisomerases, DNA Gyrase and Topoisomerase IV, as crucial regulators of bacterial cell cycle progression. Their synergistic action allows control of chromosome packing and grants occurrence of functional transcription and replication processes. In addition to displaying a fascinating molecular mechanism of action, which transduces chemical energy into mechanical energy by means of large conformational changes, these enzymes represent attractive pharmacological targets for antibacterial chemotherapy.

DNA supercoiling and its role in DNA decatenation and unknotting

Chromosomal and plasmid DNA molecules in bacterial cells are maintained under torsional tension and are therefore supercoiled. With the exception of extreme thermophiles, supercoiling has a negative sign, which means that the torsional tension diminishes the DNA helicity and facilitates strand separation. In consequence, negative supercoiling aids such processes as DNA replication or transcription that require global- or local-strand separation. In extreme thermophiles, DNA is positively supercoiled which protects it from thermal denaturation. While the role of DNA supercoiling connected to the control of DNA stability, is thoroughly researched and subject of many reviews, a less known role of DNA supercoiling emerges and consists of aiding DNA topoisomerases in DNA decatenation and unknotting. Although DNA catenanes are natural intermediates in the process of DNA replication of circular DNA molecules, it is necessary that they become very efficiently decatenated, as otherwise the segregation of freshly replicated DNA molecules would be blocked. DNA knots arise as by-products of topoisomerase-mediated intramolecular passages that are needed to facilitate general DNA metabolism, including DNA replication, transcription or recombination. The formed knots are, however, very harmful for cells if not removed efficiently. Here, we overview the role of DNA supercoiling in DNA unknotting and decatenation.

DNA supercoiling helps to unlink sister duplexes after replication

DNA supercoiling is one of the mechanisms that can help unlinking of newly replicated DNA molecules. Although DNA topoisomerases, which catalyze the strand passing of DNA segments through one another, make the unlinking problem solvable in principle, it remains difficult to complete the process that enables the separation of the sister duplexes. A few different mechanisms were developed by nature to solve the problem. Some of the mechanisms are very intuitive while the others, like topology simplification by type II DNA topoisomerases and DNA supercoiling, are not so evident. A computer simulation and analysis of linked sister plasmids formed in Escherichia coli cells with suppressed topoisomerase IV suggests an insight into the latter mechanism.

Simulation of DNA catenanes

DNA catenanes are important objects in biology, foremost as they appear during replication of circular DNA molecules. In this review we analyze how conformational properties of DNA catenanes can be studied by computer simulation. We consider classification of catenanes, their topological invariants and the methods of calculation of these invariants. We briefly analyze the DNA model and the simulation procedure used to sample the equilibrium conformational ensemble of catenanes with a particular topology. We consider how to avoid direct simulation of many DNA molecules when we need to account for the linking-unlinking process. The simulation methods and their comparisons with experiments are illustrated by some examples. We also describe an approach that allows simulating the steady state fraction of DNA catenanes created by type II topoisomerases.