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Baldwin Q, Sumpter B, Panagiotou E. The Local Topological Free Energy of the SARS-CoV-2 Spike Protein. Polymers (Basel) 2022; 14:polym14153014. [PMID: 35893978 PMCID: PMC9332627 DOI: 10.3390/polym14153014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Revised: 07/15/2022] [Accepted: 07/19/2022] [Indexed: 02/04/2023] Open
Abstract
The novel coronavirus SARS-CoV-2 infects human cells using a mechanism that involves binding and structural rearrangement of its Spike protein. Understanding protein rearrangement and identifying specific amino acids where mutations affect protein rearrangement has attracted much attention for drug development. In this manuscript, we use a mathematical method to characterize the local topology/geometry of the SARS-CoV-2 Spike protein backbone. Our results show that local conformational changes in the FP, HR1, and CH domains are associated with global conformational changes in the RBD domain. The SARS-CoV-2 variants analyzed in this manuscript (alpha, beta, gamma, delta Mink, G614, N501) show differences in the local conformations of the FP, HR1, and CH domains as well. Finally, most mutations of concern are either in or in the vicinity of high local topological free energy conformations, suggesting that high local topological free energy conformations could be targets for mutations with significant impact of protein function. Namely, the residues 484, 570, 614, 796, and 969, which are present in variants of concern and are targeted as important in protein function, are predicted as such from our model.
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Affiliation(s)
- Quenisha Baldwin
- Department of Biology, Tuskegee University, Tuskegee, AL 36088, USA;
| | - Bobby Sumpter
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA;
| | - Eleni Panagiotou
- Department of Mathematics and SimCenter, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
- Correspondence: or
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2
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Baldwin Q, Panagiotou E. The local topological free energy of proteins. J Theor Biol 2021; 529:110854. [PMID: 34358536 DOI: 10.1016/j.jtbi.2021.110854] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Revised: 07/27/2021] [Accepted: 07/29/2021] [Indexed: 11/16/2022]
Abstract
Protein folding, the process by which proteins attain a 3-dimensional conformation necessary for their function, remains an important unsolved problem in biology. A major gap in our understanding is how local properties of proteins relate to their global properties. In this manuscript, we use the Writhe and Torsion to introduce a new local topological/geometrical free energy that can be associated to 4 consecutive amino acids along the protein backbone. By analyzing a culled protein dataset from the PDB, our results show that high local topological free energy conformations are independent of sequence and may be involved in the rate limiting step in protein folding. By analyzing a set of 2-state single domain proteins, we find that the total local topological free energy of these proteins correlates with the experimentally observed folding rates reported in Plaxco et al. (2000).
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Affiliation(s)
- Quenisha Baldwin
- Department of Biology, Tuskegee University, 1200 W Montgomery Rd, Tuskegee, AL 36088, USA
| | - Eleni Panagiotou
- Department of Mathematics and SimCenter, University of Tennessee at Chattanooga, 615 McCallie Ave, Chattanooga, TN 37403, USA.
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3
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Barbensi A, Celoria D, Harrington HA, Stasiak A, Buck D. Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology. SCIENCE ADVANCES 2020; 6:eaay1458. [PMID: 32133398 PMCID: PMC7043919 DOI: 10.1126/sciadv.aay1458] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Accepted: 12/06/2019] [Indexed: 06/10/2023]
Abstract
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.
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Affiliation(s)
| | | | | | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne, Lausanne, Switzerland
- SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | - Dorothy Buck
- Department of Mathematical Sciences, University of Bath, Bath, UK
- Department of Mathematics/Biology, Trinity College of Arts and Sciences, Duke University, Durham, NC, USA
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4
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Orlandini E, Marenduzzo D, Michieletto D. Synergy of topoisomerase and structural-maintenance-of-chromosomes proteins creates a universal pathway to simplify genome topology. Proc Natl Acad Sci U S A 2019; 116:8149-8154. [PMID: 30962387 PMCID: PMC6486742 DOI: 10.1073/pnas.1815394116] [Citation(s) in RCA: 45] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
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.
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Affiliation(s)
- Enzo Orlandini
- Dipartimento di Fisica e Astronomia "Galileo Galilei," Sezione Istituto Nazionale di Fisica Nucleare, Università degli Studi di Padova, I-35131 Padova, Italy
| | - Davide Marenduzzo
- School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
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Pathways of DNA unlinking: A story of stepwise simplification. Sci Rep 2017; 7:12420. [PMID: 28963549 PMCID: PMC5622096 DOI: 10.1038/s41598-017-12172-2] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Accepted: 09/01/2017] [Indexed: 11/23/2022] Open
Abstract
In Escherichia coli DNA replication yields interlinked chromosomes. Controlling topological changes associated with replication and returning the newly replicated chromosomes to an unlinked monomeric state is essential to cell survival. In the absence of the topoisomerase topoIV, the site-specific recombination complex XerCD- dif-FtsK can remove replication links by local reconnection. We previously showed mathematically that there is a unique minimal pathway of unlinking replication links by reconnection while stepwise reducing the topological complexity. However, the possibility that reconnection preserves or increases topological complexity is biologically plausible. In this case, are there other unlinking pathways? Which is the most probable? We consider these questions in an analytical and numerical study of minimal unlinking pathways. We use a Markov Chain Monte Carlo algorithm with Multiple Markov Chain sampling to model local reconnection on 491 different substrate topologies, 166 knots and 325 links, and distinguish between pathways connecting a total of 881 different topologies. We conclude that the minimal pathway of unlinking replication links that was found under more stringent assumptions is the most probable. We also present exact results on unlinking a 6-crossing replication link. These results point to a general process of topology simplification by local reconnection, with applications going beyond DNA.
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Micheletti C, Orland H. Efficient Sampling of Knotting-Unknotting Pathways for Semiflexible Gaussian Chains. Polymers (Basel) 2017; 9:polym9060196. [PMID: 30970873 PMCID: PMC6432015 DOI: 10.3390/polym9060196] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2017] [Revised: 05/17/2017] [Accepted: 05/19/2017] [Indexed: 11/16/2022] Open
Abstract
We propose a stochastic method to generate exactly the overdamped Langevin dynamics of semi-flexible Gaussian chains, conditioned to evolve between given initial and final conformations in a preassigned time. The initial and final conformations have no restrictions, and hence can be in any knotted state. Our method allows the generation of statistically independent paths in a computationally efficient manner. We show that these conditioned paths can be exactly generated by a set of local stochastic differential equations. The method is used to analyze the transition routes between various knots in crossable filamentous structures, thus mimicking topological reconnections occurring in soft matter systems or those introduced in DNA by topoisomerase enzymes. We find that the average number of crossings, writhe and unknotting number are not necessarily monotonic in time and that more complex topologies than the initial and final ones can be visited along the route.
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Affiliation(s)
- Cristian Micheletti
- International School for Advanced Studies (SISSA), Physics Area via Bonomea 265, I-34136 Trieste, Italy.
| | - Henri Orland
- Institut de Physique Théorique, CEA, CNRS, UMR3681, F-91191 Gif-sur-Yvette, France.
- Beijing Computational Science Research Center, No.10 East Xibeiwang Road, 100193 Beijing, China.
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Liu Z, Chan HS. Consistent rationalization of type-2 topoisomerases' unknotting, decatenating, supercoil-relaxing actions and their scaling relation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:354103. [PMID: 26291958 DOI: 10.1088/0953-8984/27/35/354103] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
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.
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Affiliation(s)
- Zhirong Liu
- College of Chemistry and Molecular Engineering, Center for Quantitative Biology, and Beijing National Laboratory for Molecular Sciences, Peking University, Beijing 100871, People's Republic of China
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9
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Crossing-sign discrimination and knot-reduction for a lattice model of strand passage. Biochem Soc Trans 2013; 41:576-81. [DOI: 10.1042/bst20120333] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
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.
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Portillo J, Diao Y, Scharein R, Arsuaga J, Vazquez M. On the mean and variance of the writhe of random polygons. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL 2011; 44:275004. [PMID: 25685182 PMCID: PMC4324762 DOI: 10.1088/1751-8113/44/27/275004] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We here address two problems concerning the writhe of random polygons. First, we study the behavior of the mean writhe as a function length. Second, we study the variance of the writhe. Suppose that we are dealing with a set of random polygons with the same length and knot type, which could be the model of some circular DNA with the same topological property. In general, a simple way of detecting chirality of this knot type is to compute the mean writhe of the polygons; if the mean writhe is non-zero then the knot is chiral. How accurate is this method? For example, if for a specific knot type K the mean writhe decreased to zero as the length of the polygons increased, then this method would be limited in the case of long polygons. Furthermore, we conjecture that the sign of the mean writhe is a topological invariant of chiral knots. This sign appears to be the same as that of an "ideal" conformation of the knot. We provide numerical evidence to support these claims, and we propose a new nomenclature of knots based on the sign of their expected writhes. This nomenclature can be of particular interest to applied scientists. The second part of our study focuses on the variance of the writhe, a problem that has not received much attention in the past. In this case, we focused on the equilateral random polygons. We give numerical as well as analytical evidence to show that the variance of the writhe of equilateral random polygons (of length n) behaves as a linear function of the length of the equilateral random polygon.
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Affiliation(s)
- J Portillo
- Department of Mathematics, San Francisco State University, 1600 Holloway Ave, San Francisco, CA 94132
| | - Y Diao
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
| | - R Scharein
- Department of Mathematics, San Francisco State University, 1600 Holloway Ave, San Francisco, CA 94132
| | - J Arsuaga
- Department of Mathematics, San Francisco State University, 1600 Holloway Ave, San Francisco, CA 94132
| | - M Vazquez
- Department of Mathematics, San Francisco State University, 1600 Holloway Ave, San Francisco, CA 94132
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11
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Liu Z, Zechiedrich L, Chan HS. Action at hooked or twisted-hooked DNA juxtapositions rationalizes unlinking preference of type-2 topoisomerases. J Mol Biol 2010; 400:963-82. [PMID: 20460130 PMCID: PMC6794154 DOI: 10.1016/j.jmb.2010.05.007] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2010] [Accepted: 05/03/2010] [Indexed: 01/30/2023]
Abstract
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.
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Affiliation(s)
- Zhirong Liu
- College of Chemistry and Molecular Engineering, Center for Theoretical Biology, and Beijing National Laboratory for Molecular Sciences, Peking University, Beijing 100871, China
- Departments of Biochemistry and of Molecular Genetics, University of Toronto, Toronto, Ontario, Canada M5S 1A8
| | - Lynn Zechiedrich
- Department of Molecular Virology and Microbiology, Verna and Marrs McLean Department of Biochemistry and Molecular Biology, and Department of Pharmacology, Baylor College of Medicine, Houston, TX 77030, USA
| | - Hue Sun Chan
- Departments of Biochemistry and of Molecular Genetics, University of Toronto, Toronto, Ontario, Canada M5S 1A8
- Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7
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Swigon D. The Mathematics of DNA Structure, Mechanics, and Dynamics. MATHEMATICS OF DNA STRUCTURE, FUNCTION AND INTERACTIONS 2009. [DOI: 10.1007/978-1-4419-0670-0_14] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
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13
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Liu Z, Chan HS. Efficient chain moves for Monte Carlo simulations of a wormlike DNA model: excluded volume, supercoils, site juxtapositions, knots, and comparisons with random-flight and lattice models. J Chem Phys 2008; 128:145104. [PMID: 18412482 DOI: 10.1063/1.2899022] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
We develop two classes of Monte Carlo moves for efficient sampling of wormlike DNA chains that can have significant degrees of supercoiling, a conformational feature that is key to many aspects of biological function including replication, transcription, and recombination. One class of moves entails reversing the coordinates of a segment of the chain along one, two, or three axes of an appropriately chosen local frame of reference. These transformations may be viewed as a generalization, to the continuum, of the Madras-Orlitsky-Shepp algorithm for cubic lattices. Another class of moves, termed T+/-2, allows for interconversions between chains with different lengths by adding or subtracting two beads (monomer units) to or from the chain. Length-changing moves are generally useful for conformational sampling with a given site juxtaposition, as has been shown in previous lattice studies. Here, the continuum T+/-2 moves are designed to enhance their acceptance rate in supercoiled conformations. We apply these moves to a wormlike model in which excluded volume is accounted for by a bond-bond repulsion term. The computed autocorrelation functions for the relaxation of bond length, bond angle, writhe, and branch number indicate that the new moves lead to significantly more efficient sampling than conventional bead displacements and crankshaft rotations. A close correspondence is found in the equilibrium ensemble between the map of writhe computed for pair of chain segments and the map of site juxtapositions or self-contacts. To evaluate the more coarse-grained freely jointed chain (random-flight) and cubic lattice models that are commonly used in DNA investigations, twisting (torsional) potentials are introduced into these models. Conformational properties for a given superhelical density sigma may then be sampled by computing the writhe and using White's formula to relate the degree of twisting to writhe and sigma. Extensive comparisons of contact patterns and knot probabilities of the more coarse-grained models with the wormlike model show that the behaviors of the random-flight model are similar to that of DNA molecules in a solution environment with high ionic strengths, whereas the behaviors of the cubic lattice model with excluded volume are akin to that of DNA molecules under low ionic strengths.
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Affiliation(s)
- Zhirong Liu
- Department of Biochemistry and Department of Molecular Genetics, Faculty of Medicine, University of Toronto, Toronto, Ontario M5S 1A8, Canada
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Darcy IK, Scharein RG, Stasiak A. 3D visualization software to analyze topological outcomes of topoisomerase reactions. Nucleic Acids Res 2008; 36:3515-21. [PMID: 18440983 PMCID: PMC2441796 DOI: 10.1093/nar/gkn192] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The action of various DNA topoisomerases frequently results in characteristic changes in DNA topology. Important information for understanding mechanistic details of action of these topoisomerases can be provided by investigating the knot types resulting from topoisomerase action on circular DNA forming a particular knot type. Depending on the topological bias of a given topoisomerase reaction, one observes different subsets of knotted products. To establish the character of topological bias, one needs to be aware of all possible topological outcomes of intersegmental passages occurring within a given knot type. However, it is not trivial to systematically enumerate topological outcomes of strand passage from a given knot type. We present here a 3D visualization software (TopoICE-X in KnotPlot) that incorporates topological analysis methods in order to visualize, for example, knots that can be obtained from a given knot by one intersegmental passage. The software has several other options for the topological analysis of mechanisms of action of various topoisomerases.
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Affiliation(s)
- I K Darcy
- Department of Mathematics, University of Iowa, Iowa City, IA 52245, USA.
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15
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Burnier Y, Weber C, Flammini A, Stasiak A. Local selection rules that can determine specific pathways of DNA unknotting by type II DNA topoisomerases. Nucleic Acids Res 2007; 35:5223-31. [PMID: 17670794 PMCID: PMC1976442 DOI: 10.1093/nar/gkm532] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2007] [Revised: 06/26/2007] [Accepted: 06/26/2007] [Indexed: 11/24/2022] Open
Abstract
We performed numerical simulations of DNA chains to understand how local geometry of juxtaposed segments in knotted DNA molecules can guide type II DNA topoisomerases to perform very efficient relaxation of DNA knots. We investigated how the various parameters defining the geometry of inter-segmental juxtapositions at sites of inter-segmental passage reactions mediated by type II DNA topoisomerases can affect the topological consequences of these reactions. We confirmed the hypothesis that by recognizing specific geometry of juxtaposed DNA segments in knotted DNA molecules, type II DNA topoisomerases can maintain the steady-state knotting level below the topological equilibrium. In addition, we revealed that a preference for a particular geometry of juxtaposed segments as sites of strand-passage reaction enables type II DNA topoisomerases to select the most efficient pathway of relaxation of complex DNA knots. The analysis of the best selection criteria for efficient relaxation of complex knots revealed that local structures in random configurations of a given knot type statistically behave as analogous local structures in ideal geometric configurations of the corresponding knot type.
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Affiliation(s)
- Yannis Burnier
- Laboratoire d’Analyse Ultrastructurale, Faculté de Biologie et de Médecine, Université de Lausanne, 1015 Lausanne-Dorigny, Switzerland and School of Informatics, Indiana University, 901 E, 10th St., Bloomington, IN 47408, USA
| | - Cedric Weber
- Laboratoire d’Analyse Ultrastructurale, Faculté de Biologie et de Médecine, Université de Lausanne, 1015 Lausanne-Dorigny, Switzerland and School of Informatics, Indiana University, 901 E, 10th St., Bloomington, IN 47408, USA
| | - Alessandro Flammini
- Laboratoire d’Analyse Ultrastructurale, Faculté de Biologie et de Médecine, Université de Lausanne, 1015 Lausanne-Dorigny, Switzerland and School of Informatics, Indiana University, 901 E, 10th St., Bloomington, IN 47408, USA
| | - Andrzej Stasiak
- Laboratoire d’Analyse Ultrastructurale, Faculté de Biologie et de Médecine, Université de Lausanne, 1015 Lausanne-Dorigny, Switzerland and School of Informatics, Indiana University, 901 E, 10th St., Bloomington, IN 47408, USA
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