1
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Fizari M, Keller N, Jardine PJ, Smith DE. Role of DNA-DNA sliding friction and nonequilibrium dynamics in viral genome ejection and packaging. Nucleic Acids Res 2023; 51:8060-8069. [PMID: 37449417 PMCID: PMC10450192 DOI: 10.1093/nar/gkad582] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2023] [Revised: 06/17/2023] [Accepted: 06/27/2023] [Indexed: 07/18/2023] Open
Abstract
Many viruses eject their DNA via a nanochannel in the viral shell, driven by internal forces arising from the high-density genome packing. The speed of DNA exit is controlled by friction forces that limit the molecular mobility, but the nature of this friction is unknown. We introduce a method to probe the mobility of the tightly confined DNA by measuring DNA exit from phage phi29 capsids with optical tweezers. We measure extremely low initial exit velocity, a regime of exponentially increasing velocity, stochastic pausing that dominates the kinetics and large dynamic heterogeneity. Measurements with variable applied force provide evidence that the initial velocity is controlled by DNA-DNA sliding friction, consistent with a Frenkel-Kontorova model for nanoscale friction. We confirm several aspects of the ejection dynamics predicted by theoretical models. Features of the pausing suggest that it is connected to the phenomenon of 'clogging' in soft matter systems. Our results provide evidence that DNA-DNA friction and clogging control the DNA exit dynamics, but that this friction does not significantly affect DNA packaging.
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Affiliation(s)
- Mounir Fizari
- Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA
| | - Nicholas Keller
- Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA
| | - Paul J Jardine
- Department of Diagnostic and Biological Sciences and Institute for Molecular Virology, University of Minnesota, Minneapolis, MN 55455, USA
| | - Douglas E Smith
- Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA
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2
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Panagiotou E. Following the entangled state of filaments. Science 2023; 380:340-341. [PMID: 37104575 DOI: 10.1126/science.adh4055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/29/2023]
Abstract
California blackworms serve as a template for the topological design of active matter.
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Affiliation(s)
- Eleni Panagiotou
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA
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3
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Nguyen NTT, Ngo AT, Hoang TX. Energetic preference and topological constraint effects on the formation of DNA twisted toroidal bundles. J Chem Phys 2023; 158:114904. [PMID: 36948817 DOI: 10.1063/5.0134710] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/06/2023] Open
Abstract
DNA toroids are compact torus-shaped bundles formed by one or multiple DNA molecules being condensed from the solution due to various condensing agents. It has been shown that the DNA toroidal bundles are twisted. However, the global conformations of DNA inside these bundles are still not well understood. In this study, we investigate this issue by solving different models for the toroidal bundles and performing replica-exchange molecular dynamics (REMD) simulations for self-attractive stiff polymers of various chain lengths. We find that a moderate degree of twisting is energetically favorable for toroidal bundles, yielding optimal configurations of lower energies than for other bundles corresponding to spool-like and constant radius of curvature arrangements. The REMD simulations show that the ground states of the stiff polymers are twisted toroidal bundles with the average twist degrees close to those predicted by the theoretical model. Constant-temperature simulations show that twisted toroidal bundles can be formed through successive processes of nucleation, growth, quick tightening, and slow tightening of the toroid, with the two last processes facilitating the polymer threading through the toroid's hole. A relatively long chain of 512 beads has an increased dynamical difficulty to access the twisted bundle states due to the polymer's topological constraint. Interestingly, we also observed significantly twisted toroidal bundles with a sharp U-shaped region in the polymer conformation. It is suggested that this U-shaped region makes the formation of twisted bundles easier by effectively reducing the polymer length. This effect can be equivalent to having multiple chains in the toroid.
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Affiliation(s)
- Nhung T T Nguyen
- Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi 11108, Vietnam
| | - Anh T Ngo
- Chemical Engineering Department, University of Illinois at Chicago, Chicago, Illinois 60608, USA
| | - Trinh X Hoang
- Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi 11108, Vietnam
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4
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Zhao Y, Rothörl J, Besenius P, Virnau P, Daoulas KC. Can Polymer Helicity Affect Topological Chirality of Polymer Knots? ACS Macro Lett 2023; 12:234-240. [PMID: 36706453 PMCID: PMC9948535 DOI: 10.1021/acsmacrolett.2c00600] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
We investigate the effect of helicity in isolated polymers on the topological chirality of their knots with computer simulations. Polymers are described by generic worm-like chains (WLC), where helical conformations are promoted by chiral coupling between segments that are neighbors along the chain contour. The sign and magnitude of the coupling coefficient u determine the sense and strength of helicity. The corrugation of the helix is adjusted via the radius R of a spherical, hard excluded volume around each WLC segment. Open and compact helices are, respectively, obtained for R that is either zero or smaller than the length of the WLC bond, and R that is a few times larger than the bond length. We use a Monte Carlo algorithm to sample polymer conformations for different values of u, spanning the range from achiral polymers to chains with well-developed helices. Monitoring the average helix torsion and fluctuations of chiral order as a function of u, for two very different chain lengths, demonstrates that the coil-helix transition in this model is not a phase transition but a crossover. Statistical analysis of conformations forming the simplest chiral knots, 31, 51, and 52, demonstrates that topological mirror symmetry is broken─knots formed by helices with a given sense prefer one handedness over the other. For the 31 and 51 knots, positive helical sense favors positive handedness. Intriguingly, an opposite trend is observed for 52 knots, where positive helical sense promotes negative handedness. We argue that this special coupling between helicity and topological chirality stems from a generic mechanism: conformations where some of the knot crossings are found in "braids" formed by two tightly interwoven sections of the polymer.
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Affiliation(s)
- Yani Zhao
- Max
Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Jan Rothörl
- Department
of Physics, Johannes Gutenberg University
Mainz, Staudingerweg 9, 55128 Mainz, Germany
| | - Pol Besenius
- Department
of Chemistry, Johannes Gutenberg University
Mainz, Duesbergweg 10-14, 55128 Mainz, Germany
| | - Peter Virnau
- Department
of Physics, Johannes Gutenberg University
Mainz, Staudingerweg 9, 55128 Mainz, Germany,E-mail:
| | - Kostas Ch. Daoulas
- Max
Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany,E-mail: . Phone: +49
(0)6131 379218
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5
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Expansion of Single Chains Released from a Spherical Cavity. Polymers (Basel) 2022; 15:polym15010198. [PMID: 36616547 PMCID: PMC9824584 DOI: 10.3390/polym15010198] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2022] [Revised: 12/18/2022] [Accepted: 12/23/2022] [Indexed: 01/03/2023] Open
Abstract
A two-stage model is developed to explain the phenomena of chain expansion, released from a confining cavity. In the first stage, the chain is assumed to expand as a sphere, while in the second stage it expands like a coil. The kinetic equations for the variation of chain size are derived in the two stages by balancing the rate of the free energy change with the rate of the energy dissipation. Langevin dynamics simulations are then performed to examine the theory. We find that the expansion process is dominated by the second stage and the evolution of chain size follows, mainly, the predicted curve for coil expansion, which depends on the chain length and is not sensitive to the confining volume fraction. It permits to define the expansion time for the process. Further study reveals that the chain does undergo a spherical expansion in the first stage with the characteristic time much shorter than the one for the second stage. As a consequence, the first-stage variation of chain size can be regarded as an add-on to the principal curve of expansion designated by the second stage. The scaling behaviors and the associated scaling exponents are analyzed in details. The simulation results well support the theory.
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6
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Tagliabue A, Micheletti C, Mella M. Tuning Knotted Copolyelectrolyte Conformations via Solution Properties. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01933] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Affiliation(s)
- Andrea Tagliabue
- Dipartimento di Scienza ed Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio 11, 22100Como, Italy
- SISSA (Scuola Internazionale Superiore di Studi Avanzati), via Bonomea 265, 34136Trieste, Italy
| | - Cristian Micheletti
- SISSA (Scuola Internazionale Superiore di Studi Avanzati), via Bonomea 265, 34136Trieste, Italy
| | - Massimo Mella
- Dipartimento di Scienza ed Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio 11, 22100Como, Italy
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7
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Liu J, Xia KL, Wu J, Yau SST, Wei GW. Biomolecular Topology: Modelling and Analysis. ACTA MATHEMATICA SINICA, ENGLISH SERIES 2022; 38:1901-1938. [PMID: 36407804 PMCID: PMC9640850 DOI: 10.1007/s10114-022-2326-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2022] [Accepted: 07/12/2022] [Indexed: 05/25/2023]
Abstract
With the great advancement of experimental tools, a tremendous amount of biomolecular data has been generated and accumulated in various databases. The high dimensionality, structural complexity, the nonlinearity, and entanglements of biomolecular data, ranging from DNA knots, RNA secondary structures, protein folding configurations, chromosomes, DNA origami, molecular assembly, to others at the macromolecular level, pose a severe challenge in their analysis and characterization. In the past few decades, mathematical concepts, models, algorithms, and tools from algebraic topology, combinatorial topology, computational topology, and topological data analysis, have demonstrated great power and begun to play an essential role in tackling the biomolecular data challenge. In this work, we introduce biomolecular topology, which concerns the topological problems and models originated from the biomolecular systems. More specifically, the biomolecular topology encompasses topological structures, properties and relations that are emerged from biomolecular structures, dynamics, interactions, and functions. We discuss the various types of biomolecular topology from structures (of proteins, DNAs, and RNAs), protein folding, and protein assembly. A brief discussion of databanks (and databases), theoretical models, and computational algorithms, is presented. Further, we systematically review related topological models, including graphs, simplicial complexes, persistent homology, persistent Laplacians, de Rham-Hodge theory, Yau-Hausdorff distance, and the topology-based machine learning models.
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Affiliation(s)
- Jian Liu
- School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024 P. R. China
- Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, 101408 P. R. China
| | - Ke-Lin Xia
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 639798 Singapore
| | - Jie Wu
- Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, 101408 P. R. China
- Department of Mathematical Sciences, Tsinghua University, Beijing, 100084 P. R. China
| | - Stephen Shing-Toung Yau
- Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, 101408 P. R. China
- Department of Mathematical Sciences, Tsinghua University, Beijing, 100084 P. R. China
| | - Guo-Wei Wei
- Department of Mathematics & Department of Biochemistry and Molecular Biology & Department of Electrical and Computer Engineering, Michigan State University, Wells Hall 619 Red Cedar Road, East Lansing, MI 48824-1027 USA
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8
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On the Classification of Polyhedral Links. Symmetry (Basel) 2022. [DOI: 10.3390/sym14081712] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Knots and links are ubiquitous in chemical systems. Their structure can be responsible for a variety of physical and chemical properties, making them very important in materials development. In this article, we analyze the topological structures of interlocking molecules composed of metal-peptide rings using the concept of polyhedral links. To that end, we discuss the topological classification of alternating polyhedral links.
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9
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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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10
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Celoria D, Mahler BI. A statistical approach to knot confinement via persistent homology. Proc Math Phys Eng Sci 2022; 478:20210709. [PMID: 35645602 PMCID: PMC9116441 DOI: 10.1098/rspa.2021.0709] [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: 09/06/2021] [Accepted: 04/08/2022] [Indexed: 11/12/2022] Open
Abstract
In this paper, we study how randomly generated knots occupy a volume of space using topological methods. To this end, we consider the evolution of the first homology of an immersed metric neighbourhood of a knot's embedding for growing radii. Specifically, we extract features from the persistent homology (PH) of the Vietoris-Rips complexes built from point clouds associated with knots. Statistical analysis of our data shows the existence of increasing correlations between geometric quantities associated with the embedding and PH-based features, as a function of the knots' lengths. We further study the variation of these correlations for different knot types. Finally, this framework also allows us to define a simple notion of deviation from ideal configurations of knots.
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Affiliation(s)
- Daniele Celoria
- Mathematical Institute, University of Oxford, Radcliffe Observatory, Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG, UK
| | - Barbara I Mahler
- Mathematical Institute, University of Oxford, Radcliffe Observatory, Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG, UK
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11
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Rothörl J, Wettermann S, Virnau P, Bhattacharya A. Knot formation of dsDNA pushed inside a nanochannel. Sci Rep 2022; 12:5342. [PMID: 35351953 PMCID: PMC8964721 DOI: 10.1038/s41598-022-09242-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 03/17/2022] [Indexed: 12/23/2022] Open
Abstract
Recent experiments demonstrated that knots in single molecule dsDNA can be formed by compression in a nanochannel. In this manuscript, we further elucidate the underlying molecular mechanisms by carrying out a compression experiment in silico, where an equilibrated coarse-grained double-stranded DNA confined in a square channel is pushed by a piston. The probability of forming knots is a non-monotonic function of the persistence length and can be enhanced significantly by increasing the piston speed. Under compression knots are abundant and delocalized due to a backfolding mechanism from which chain-spanning loops emerge, while knots are less frequent and only weakly localized in equilibrium. Our in silico study thus provides insights into the formation, origin and control of DNA knots in nanopores.
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12
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Zhu Y, Zhu H, Tian F, Qiu Q, Dai L. Quantifying the effects of slit confinement on polymer knots using the tube model. Phys Rev E 2022; 105:024501. [PMID: 35291068 DOI: 10.1103/physreve.105.024501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 01/27/2022] [Indexed: 06/14/2023]
Abstract
Knots can spontaneously form in DNA, proteins, and other polymers and affect their properties. These knots often experience spatial confinement in biological systems and experiments. While confinement dramatically affects the knot behavior, the physical mechanisms underlying the confinement effects are not fully understood. In this work, we provide a simple physical picture of the polymer knots in slit confinement using the tube model. In the tube model, the polymer segments in the knot core are assumed to be confined in a virtual tube due to the topological restriction. We first perform Monte Carlo simulation of a flexible knotted chain confined in a slit. We find that with the decrease of the slit height from H=+∞ (the 3D case) to H=2a (the 2D case), the most probable knot size L_{knot}^{*} dramatically shrinks from (L_{knot}^{*})_{3D}≈140a to (L_{knot}^{*})_{2D}≈26a, where a is the monomer diameter of the flexible chain. Then we quantitatively explain the confinement-induced knot shrinking and knot deformation using the tube model. Our results for H=2a can be applied to a polymer knot on a surface, which resembles DNA knots measured by atomic force microscopy under the conditions that DNA molecules are weakly absorbed on the surface and reach equilibrium 2D conformations. This work demonstrates the effectiveness of the tube model in understanding polymer knots.
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Affiliation(s)
- Yongjian Zhu
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Haoqi Zhu
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Fujia Tian
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Qiyuan Qiu
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
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13
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Chen W, Wei S. Compressive deformations of ring polymers in a confining channel. POLYMER 2021. [DOI: 10.1016/j.polymer.2021.124340] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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14
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Roca J, Dyson S, Segura J, Valdés A, Martínez-García B. Keeping intracellular DNA untangled: A new role for condensin? Bioessays 2021; 44:e2100187. [PMID: 34761394 DOI: 10.1002/bies.202100187] [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: 08/06/2021] [Revised: 10/25/2021] [Accepted: 10/26/2021] [Indexed: 12/25/2022]
Abstract
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.
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Affiliation(s)
- Joaquim Roca
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona, Spain
| | - Silvia Dyson
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona, Spain
| | - Joana Segura
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona, Spain
| | - Antonio Valdés
- Julius Maximilian University of Würzburg, Würzburg, Germany
| | - Belén Martínez-García
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona, Spain
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15
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Affiliation(s)
- Liang Dai
- Department of Physics, City University of Hong Kong, Hong Kong 999077, China
- Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
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16
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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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17
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Park CB, Sung BJ. Effects of Packaging History on the Ejection of a Polymer Chain from a Small Confinement. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00857] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Affiliation(s)
- Chung Bin Park
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 04107, Republic of Korea
| | - Bong June Sung
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 04107, Republic of Korea
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18
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Sharma RK, Agrawal I, Dai L, Doyle P, Garaj S. DNA Knot Malleability in Single-Digit Nanopores. NANO LETTERS 2021; 21:3772-3779. [PMID: 33661654 DOI: 10.1021/acs.nanolett.0c05142] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Knots in long DNA molecules are prevalent in biological systems and serve as a model system for investigating static and dynamic properties of biopolymers. We explore the dynamics of knots in double-stranded DNA in a new regime of nanometer-scale confinement, large forces, and short time scales, using solid-state nanopores. We show that DNA knots undergo isomorphic translocation through a nanopore, retaining their equilibrium morphology by swiftly compressing in a lateral direction to fit the constriction. We observe no evidence of knot tightening or jamming, even for single-digit nanopores. We explain the observations as the malleability of DNA, characterized by sharp buckling of the DNA in nanopores, driven by the transient disruption of base pairing. Our molecular dynamics simulations support the model. These results are relevant not only for the understanding of DNA packing and manipulation in living cells but also for the polymer physics of DNA and the development of nanopore-based sequencing technologies.
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Affiliation(s)
- Rajesh Kumar Sharma
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
- Singapore-MIT Alliance for Research and Technology Centre, Singapore 138602, Singapore
- Centre for Advanced 2D Materials, National University of Singapore, Singapore 117546, Singapore
| | - Ishita Agrawal
- Department of Biomedical Engineering, National University of Singapore, Singapore 117583, Singapore
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, P. R. China
| | - Patrick Doyle
- Singapore-MIT Alliance for Research and Technology Centre, Singapore 138602, Singapore
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142, United States
| | - Slaven Garaj
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
- Centre for Advanced 2D Materials, National University of Singapore, Singapore 117546, Singapore
- Department of Biomedical Engineering, National University of Singapore, Singapore 117583, Singapore
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19
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Tubiana L, Kobayashi H, Potestio R, Dünweg B, Kremer K, Virnau P, Daoulas K. Comparing equilibration schemes of high-molecular-weight polymer melts with topological indicators. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:204003. [PMID: 33765663 DOI: 10.1088/1361-648x/abf20c] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Accepted: 03/25/2021] [Indexed: 06/12/2023]
Abstract
Recent theoretical studies have demonstrated that the behaviour of molecular knots is a sensitive indicator of polymer structure. Here, we use knots to verify the ability of two state-of-the-art algorithms-configuration assembly and hierarchical backmapping-to equilibrate high-molecular-weight (MW) polymer melts. Specifically, we consider melts with MWs equivalent to several tens of entanglement lengths and various chain flexibilities, generated with both strategies. We compare their unknotting probability, unknotting length, knot spectra, and knot length distributions. The excellent agreement between the two independent methods with respect to knotting properties provides an additional strong validation of their ability to equilibrate dense high-MW polymeric liquids. By demonstrating this consistency of knotting behaviour, our study opens the way for studying topological properties of polymer melts beyond time and length scales accessible to brute-force molecular dynamics simulations.
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Affiliation(s)
- Luca Tubiana
- Physics Department, University of Trento, via Sommarive, 14 I-38123 Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Hideki Kobayashi
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Raffaello Potestio
- Physics Department, University of Trento, via Sommarive, 14 I-38123 Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy
| | - Burkhard Dünweg
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
- Department of Chemical Engineering, Monash University, Clayton, Victoria 3800, Australia
| | - Kurt Kremer
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Peter Virnau
- Institute of Physics, Johannes Gutenberg University, Staudingerweg 9, 55128 Mainz, Germany
| | - Kostas Daoulas
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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20
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Gendron I, Savard K, Capaldi X, Liu Z, Zeng L, Reisner W, Capaldi L. Time-dependent knotting of agitated chains. Phys Rev E 2021; 103:032501. [PMID: 33862677 DOI: 10.1103/physreve.103.032501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 02/19/2021] [Indexed: 11/07/2022]
Abstract
Agitated strings serve as macroscale models of spontaneous knotting, providing valuable insight into knotting dynamics at the microscale while allowing explicit analysis of the resulting knot topologies. We present an experimental setup for confined macroscale knot formation via tumbling along with a software interface to process complex knot data. Our setup allows characterization of knotting probability, knot complexity, and knot formation dynamics for knots with as many as 50 crossings. We find that the probability of knotting saturates below 80% within 100 s of the initiation of tumbling and that this saturation probability does not increase for chains above a critical length, an indication of nonequilibrium knot-formation conditions in our experiment. Despite the saturation in knot formation, we show that longer chains, while being more confined, will always tend to form knots of higher complexity since the free end can access a greater number of loops during tumbling.
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Affiliation(s)
- Ingrid Gendron
- Physics Department, McGill University, 3600 rue University, Montreal, Canada
| | - Katherine Savard
- Physics Department, McGill University, 3600 rue University, Montreal, Canada
| | - Xavier Capaldi
- Physics Department, McGill University, 3600 rue University, Montreal, Canada
| | - Zezhou Liu
- Physics Department, McGill University, 3600 rue University, Montreal, Canada
| | - Lili Zeng
- Physics Department, McGill University, 3600 rue University, Montreal, Canada
| | - Walter Reisner
- Physics Department, McGill University, 3600 rue University, Montreal, Canada
| | - Luc Capaldi
- Department of Mechanical Engineering, University of Vermont, Burlington, Vermont 05405, USA
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21
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Zhu H, Tian F, Sun L, Wang S, Dai L. Revisiting the Non-monotonic Dependence of Polymer Knotting Probability on the Bending Stiffness. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02640] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Haoqi Zhu
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
| | - Fujia Tian
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
| | - Liang Sun
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
| | - Simin Wang
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
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22
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Halun J, Karbowniczek P, Kuterba P, Danel Z. Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations. ENTROPY 2021; 23:e23020242. [PMID: 33669820 PMCID: PMC7922339 DOI: 10.3390/e23020242] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Revised: 02/06/2021] [Accepted: 02/08/2021] [Indexed: 12/03/2022]
Abstract
The calculations of the dimensionless layer monomer density profiles for a dilute solution of phantom ideal ring polymer chains and star polymers with f=4 arms in a Θ-solvent confined in a slit geometry of two parallel walls with repulsive surfaces and for the mixed case of one repulsive and the other inert surface were performed. Furthermore, taking into account the Derjaguin approximation, the dimensionless layer monomer density profiles for phantom ideal ring polymer chains and star polymers immersed in a solution of big colloidal particles with different adsorbing or repelling properties with respect to polymers were calculated. The density-force relation for the above-mentioned cases was analyzed, and the universal amplitude ratio B was obtained. Taking into account the small sphere expansion allowed obtaining the monomer density profiles for a dilute solution of phantom ideal ring polymers immersed in a solution of small spherical particles, or nano-particles of finite size, which are much smaller than the polymer size and the other characteristic mesoscopic length of the system. We performed molecular dynamics simulations of a dilute solution of linear, ring, and star-shaped polymers with N=300, 300 (360), and 1201 (4 × 300 + 1-star polymer with four arms) beads accordingly. The obtained analytical and numerical results for phantom ring and star polymers are compared with the results for linear polymer chains in confined geometries.
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Affiliation(s)
- Joanna Halun
- Institute of Nuclear Physics, Polish Academy of Sciences, 31-342 Cracow, Poland
- Correspondence:
| | - Pawel Karbowniczek
- Institute of Physics, Cracow University of Technology, 30-084 Cracow, Poland; (P.K.); (Z.D.)
| | - Piotr Kuterba
- Faculty of Physics, Astronomy and Applied Computer Sciences, Jagiellonian University in Cracow, 30-348 Cracow, Poland;
| | - Zoriana Danel
- Institute of Physics, Cracow University of Technology, 30-084 Cracow, Poland; (P.K.); (Z.D.)
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23
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Dyson S, Segura J, Martínez‐García B, Valdés A, Roca J. Condensin minimizes topoisomerase II-mediated entanglements of DNA in vivo. EMBO J 2021; 40:e105393. [PMID: 33155682 PMCID: PMC7780148 DOI: 10.15252/embj.2020105393] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2020] [Revised: 09/10/2020] [Accepted: 10/07/2020] [Indexed: 12/24/2022] Open
Abstract
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.
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Grants
- BFU2015-67007-P Ministerio de Economía, Industria y Competitividad, Gobierno de España (MINECO)
- PID2019-109482GB-I00 Ministerio de Economía, Industria y Competitividad, Gobierno de España (MINECO)
- BES-2016-077806 Ministerio de Economía, Industria y Competitividad, Gobierno de España (MINECO)
- BES-2012-061167 Ministerio de Economía, Industria y Competitividad, Gobierno de España (MINECO)
- BES-2015-071597 Ministerio de Economía, Industria y Competitividad, Gobierno de España (MINECO)
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Affiliation(s)
- Sílvia Dyson
- Molecular Biology Institute of Barcelona (IBMB)Spanish National Research Council (CSIC)BarcelonaSpain
| | - Joana Segura
- Molecular Biology Institute of Barcelona (IBMB)Spanish National Research Council (CSIC)BarcelonaSpain
| | - Belén Martínez‐García
- Molecular Biology Institute of Barcelona (IBMB)Spanish National Research Council (CSIC)BarcelonaSpain
| | - Antonio Valdés
- Molecular Biology Institute of Barcelona (IBMB)Spanish National Research Council (CSIC)BarcelonaSpain
| | - Joaquim Roca
- Molecular Biology Institute of Barcelona (IBMB)Spanish National Research Council (CSIC)BarcelonaSpain
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24
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Caraglio M, Marcone B, Baldovin F, Orlandini E, Stella AL. Topological Disentanglement of Linear Polymers under Tension. Polymers (Basel) 2020; 12:E2580. [PMID: 33153057 PMCID: PMC7692779 DOI: 10.3390/polym12112580] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2020] [Revised: 10/30/2020] [Accepted: 10/30/2020] [Indexed: 01/01/2023] Open
Abstract
We develop a theoretical description of the topological disentanglement occurring when torus knots reach the ends of a semiflexible polymer under tension. These include decays into simpler knots and total unknotting. The minimal number of crossings and the minimal knot contour length are the topological invariants playing a key role in the model. The crossings behave as particles diffusing along the chain and the application of appropriate boundary conditions at the ends of the chain accounts for the knot disentanglement. Starting from the number of particles and their positions, suitable rules allow reconstructing the type and location of the knot moving on the chain Our theory is extensively benchmarked with corresponding molecular dynamics simulations and the results show a remarkable agreement between the simulations and the theoretical predictions of the model.
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Affiliation(s)
- Michele Caraglio
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Boris Marcone
- Istituto Tecnico Economico Tecnologico Statale ‘L. Einaudi’, via Tommaso D’Aquino 8, I-36061 Bassano del Grappa, Italy;
| | - Fulvio Baldovin
- Dipartimento di Fisica e Astronomia and Sezione INFN Università di Padova, Via Marzolo 8, I-35131 Padova, Italy; (F.B.); (E.O.); (A.L.S.)
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia and Sezione INFN Università di Padova, Via Marzolo 8, I-35131 Padova, Italy; (F.B.); (E.O.); (A.L.S.)
| | - Attilio L. Stella
- Dipartimento di Fisica e Astronomia and Sezione INFN Università di Padova, Via Marzolo 8, I-35131 Padova, Italy; (F.B.); (E.O.); (A.L.S.)
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25
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Zhou X, Wu J, Zhang L. Ordered aggregation of semiflexible ring-linear blends in ellipsoidal confinement. POLYMER 2020. [DOI: 10.1016/j.polymer.2020.122494] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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26
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Cruz B, Zhu Z, Calderer C, Arsuaga J, Vazquez M. Quantitative Study of the Chiral Organization of the Phage Genome Induced by the Packaging Motor. Biophys J 2020; 118:2103-2116. [PMID: 32353255 PMCID: PMC7203069 DOI: 10.1016/j.bpj.2020.03.030] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2019] [Revised: 11/04/2019] [Accepted: 03/16/2020] [Indexed: 12/11/2022] Open
Abstract
Molecular motors that translocate DNA are ubiquitous in nature. During morphogenesis of double-stranded DNA bacteriophages, a molecular motor drives the viral genome inside a protein capsid. Several models have been proposed for the three-dimensional geometry of the packaged genome, but very little is known of the signature of the molecular packaging motor. For instance, biophysical experiments show that in some systems, DNA rotates during the packaging reaction, but most current biophysical models fail to incorporate this property. Furthermore, studies including rotation mechanisms have reached contradictory conclusions. In this study, we compare the geometrical signatures imposed by different possible mechanisms for the packaging motors: rotation, revolution, and rotation with revolution. We used a previously proposed kinetic Monte Carlo model of the motor, combined with Brownian dynamics simulations of DNA to simulate deterministic and stochastic motor models. We find that rotation is necessary for the accumulation of DNA writhe and for the chiral organization of the genome. We observe that although in the initial steps of the packaging reaction, the torsional strain of the genome is released by rotation of the molecule, in the later stages, it is released by the accumulation of writhe. We suggest that the molecular motor plays a key role in determining the final structure of the encapsidated genome in bacteriophages.
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Affiliation(s)
- Brian Cruz
- Department of Mathematics, University of California, Berkeley, California
| | - Zihao Zhu
- Department of Microbiology and Molecular Genetics, University of California at Davis, Davis, California
| | - Carme Calderer
- School of Mathematics, University of Minnesota, Minneapolis, Minnesota
| | - Javier Arsuaga
- Department of Mathematics, University of California at Davis, Davis, California; Department of Molecular and Cellular Biology, University of California at Davis, Davis, California.
| | - Mariel Vazquez
- Department of Microbiology and Molecular Genetics, University of California at Davis, Davis, California; Department of Mathematics, University of California at Davis, Davis, California.
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27
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Valdés A, Coronel L, Martínez-García B, Segura J, Dyson S, Díaz-Ingelmo O, Micheletti C, Roca J. Transcriptional supercoiling boosts topoisomerase II-mediated knotting of intracellular DNA. Nucleic Acids Res 2020; 47:6946-6955. [PMID: 31165864 PMCID: PMC6649788 DOI: 10.1093/nar/gkz491] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2019] [Revised: 05/09/2019] [Accepted: 05/22/2019] [Indexed: 12/04/2022] Open
Abstract
Recent studies have revealed that the DNA cross-inversion mechanism of topoisomerase II (topo II) not only removes DNA supercoils and DNA replication intertwines, but also produces small amounts of DNA knots within the clusters of nucleosomes that conform to eukaryotic chromatin. Here, we examine how transcriptional supercoiling of intracellular DNA affects the occurrence of these knots. We show that although (−) supercoiling does not change the basal DNA knotting probability, (+) supercoiling of DNA generated in front of the transcribing complexes increases DNA knot formation over 25-fold. The increase of topo II-mediated DNA knotting occurs both upon accumulation of (+) supercoiling in topoisomerase-deficient cells and during normal transcriptional supercoiling of DNA in TOP1 TOP2 cells. We also show that the high knotting probability (Pkn ≥ 0.5) of (+) supercoiled DNA reflects a 5-fold volume compaction of the nucleosomal fibers in vivo. Our findings indicate that topo II-mediated DNA knotting could be inherent to transcriptional supercoiling of DNA and other chromatin condensation processes and establish, therefore, a new crucial role of topoisomerase II in resetting the knotting–unknotting homeostasis of DNA during chromatin dynamics.
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Affiliation(s)
- Antonio Valdés
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona 08028, Spain
| | - Lucia Coronel
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), 34136 Trieste, Italy
| | - Belén Martínez-García
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona 08028, Spain
| | - Joana Segura
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona 08028, Spain
| | - Sílvia Dyson
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona 08028, Spain
| | - Ofelia Díaz-Ingelmo
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona 08028, Spain
| | - Cristian Micheletti
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), 34136 Trieste, Italy
| | - Joaquim Roca
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona 08028, Spain
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28
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Rosa A, Di Stefano M, Micheletti C. Topological Constraints in Eukaryotic Genomes and How They Can Be Exploited to Improve Spatial Models of Chromosomes. Front Mol Biosci 2019; 6:127. [PMID: 31803755 PMCID: PMC6873889 DOI: 10.3389/fmolb.2019.00127] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2019] [Accepted: 10/28/2019] [Indexed: 11/13/2022] Open
Affiliation(s)
- Angelo Rosa
- Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy
| | - Marco Di Stefano
- Centre Nacional d'Anàlisi Genòmica-Centre de Regulació Genòmica, Barcelona, Spain
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29
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Valdés A, Martínez-García B, Segura J, Dyson S, Díaz-Ingelmo O, Roca J. Quantitative disclosure of DNA knot chirality by high-resolution 2D-gel electrophoresis. Nucleic Acids Res 2019; 47:e29. [PMID: 30649468 PMCID: PMC6412111 DOI: 10.1093/nar/gkz015] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2018] [Revised: 11/24/2018] [Accepted: 01/07/2019] [Indexed: 11/13/2022] Open
Abstract
The characterization of knots formed in duplex DNA has proved useful to infer biophysical properties and the spatial trajectory of DNA, both in free solution and across its macromolecular interactions. Since knotting, like supercoiling, makes DNA molecules more compact, DNA knot probability and knot complexity can be assessed by the electrophoretic velocity of nicked DNA circles. However, the chirality of the DNA knots has to be determined by visualizing the sign of their DNA crossings by means of electron microscopy. This procedure, which requires purifying the knotted DNA molecules and coating them with protein, is semi-quantitative and it is impracticable in biological samples that contain little amount of knotted DNA forms. Here, we took advantage of an earlier observation that the two chiral forms of a trefoil knot acquire slightly different electrophoretic velocity when the DNA is supercoiled. We introduced a second gel dimension to reveal these chiral forms in DNA mixtures that are largely unknotted. The result is a high-resolution 2D-gel electrophoresis procedure that quantitatively discerns the fractions of positive- and negative-noded trefoil knots formed in vitro and in vivo systems. This development in DNA knot analysis may uncover valuable information toward disclosing the architecture of DNA ensembles.
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Affiliation(s)
- Antonio Valdés
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona 08028, Spain
| | - Belén Martínez-García
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona 08028, Spain
| | - Joana Segura
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona 08028, Spain
| | - Sílvia Dyson
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona 08028, Spain
| | - Ofelia Díaz-Ingelmo
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona 08028, Spain
| | - Joaquim Roca
- Molecular Biology Institute of Barcelona (IBMB), Spanish National Research Council (CSIC), Barcelona 08028, Spain
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30
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Weiss LB, Likos CN, Nikoubashman A. Spatial Demixing of Ring and Chain Polymers in Pressure-Driven Flow. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b01629] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Lisa B. Weiss
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Christos N. Likos
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
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31
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Kumar Sharma R, Agrawal I, Dai L, Doyle PS, Garaj S. Complex DNA knots detected with a nanopore sensor. Nat Commun 2019; 10:4473. [PMID: 31578328 PMCID: PMC6775256 DOI: 10.1038/s41467-019-12358-4] [Citation(s) in RCA: 63] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2019] [Accepted: 08/27/2019] [Indexed: 01/15/2023] Open
Abstract
Equilibrium knots are common in biological polymers-their prevalence, size distribution, structure, and dynamics have been extensively studied, with implications to fundamental biological processes and DNA sequencing technologies. Nanopore microscopy is a high-throughput single-molecule technique capable of detecting the shape of biopolymers, including DNA knots. Here we demonstrate nanopore sensors that map the equilibrium structure of DNA knots, without spurious knot tightening and sliding. We show the occurrence of both tight and loose knots, reconciling previous contradictory results from different experimental techniques. We evidence the occurrence of two quantitatively different modes of knot translocation through the nanopores, involving very different tension forces. With large statistics, we explore the complex knots and, for the first time, reveal the existence of rare composite knots. We use parametrized complexity, in concert with simulations, to test the theoretical assumptions of the models, further asserting the relevance of nanopores in future investigation of knots.
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Affiliation(s)
- Rajesh Kumar Sharma
- Department of Biomedical Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore, 117583, Singapore
- Singapore-MIT Alliance for Research and Technology Centre, 1 CREATE Way, Singapore, 138602, Singapore
- Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, Singapore, 117546, Singapore
| | - Ishita Agrawal
- Department of Biomedical Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore, 117583, Singapore
| | - Liang Dai
- Department of Physics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China
| | - Patrick S Doyle
- Singapore-MIT Alliance for Research and Technology Centre, 1 CREATE Way, Singapore, 138602, Singapore.
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02142, USA.
| | - Slaven Garaj
- Department of Biomedical Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore, 117583, Singapore.
- Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, Singapore, 117546, Singapore.
- Department of Physics, National University of Singapore, Singapore, Science Drive 3, Singapore, 117551, Singapore.
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32
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Affiliation(s)
- Liang Dai
- Department of Physics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China
| | - Beatrice W. Soh
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Patrick S. Doyle
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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33
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Soh BW, Klotz AR, Dai L, Doyle PS. Conformational State Hopping of Knots in Tensioned Polymer Chains. ACS Macro Lett 2019; 8:905-911. [PMID: 35619478 DOI: 10.1021/acsmacrolett.9b00462] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We use Brownian dynamics simulations to study the conformational states of knots on tensioned chains. Focusing specifically on the 81 knot, we observe knot conformational state hopping and show that the process can be described by a two-state kinetic model in the presence of an external force. The distribution of knot conformational states depends on the applied chain tension, which leads to a force-dependent distribution of knot untying pathways. We generalize our findings by considering the untying pathways of other knots and find that the way knots untie is generally governed by the force applied to the chain. From a broader perspective, being able to influence how a knot unties via external force can potentially be useful for applications of single-molecule techniques in which knots are unwanted.
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Affiliation(s)
- Beatrice W Soh
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Alexander R Klotz
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Liang Dai
- Department of Physics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China
| | - Patrick S Doyle
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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34
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Park CB, Kwon S, Sung BJ. The effects of a knot and its conformational relaxation on the ejection of a single polymer chain from confinement. J Chem Phys 2019. [DOI: 10.1063/1.5110428] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chung Bin Park
- Department of Chemistry, Sogang University, Seoul 04107, South Korea
| | - Seulki Kwon
- Department of Chemistry, Sogang University, Seoul 04107, South Korea
| | - Bong June Sung
- Department of Chemistry, Sogang University, Seoul 04107, South Korea
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35
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Cooper RG, Mesgarnezhad M, Baggaley AW, Barenghi CF. Knot spectrum of turbulence. Sci Rep 2019; 9:10545. [PMID: 31332254 PMCID: PMC6646329 DOI: 10.1038/s41598-019-47103-w] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2018] [Accepted: 07/05/2019] [Indexed: 11/09/2022] Open
Abstract
Streamlines, vortex lines and magnetic flux tubes in turbulent fluids and plasmas display a great amount of coiling, twisting and linking, raising the question as to whether their topological complexity (continually created and destroyed by reconnections) can be quantified. In superfluid helium, the discrete (quantized) nature of vorticity can be exploited to associate to each vortex loop a knot invariant called the Alexander polynomial whose degree characterizes the topology of that vortex loop. By numerically simulating the dynamics of a tangle of quantum vortex lines, we find that this quantum turbulence always contains vortex knots of very large degree which keep forming, vanishing and reforming, creating a distribution of topologies which we quantify in terms of a knot spectrum and its scaling law. We also find results analogous to those in the wider literature, demonstrating that the knotting probability of the vortex tangle grows with the vortex length, as for macromolecules, and saturates above a characteristic length, as found for tumbled strings.
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Affiliation(s)
- R G Cooper
- School of Mathematics, Statistics and Physics Newcastle University, Newcastle upon Tyne, NE1 7RU, UK
| | - M Mesgarnezhad
- School of Mathematics, Statistics and Physics Newcastle University, Newcastle upon Tyne, NE1 7RU, UK
| | - A W Baggaley
- School of Mathematics, Statistics and Physics Newcastle University, Newcastle upon Tyne, NE1 7RU, UK.,JQC (Joint Quantum Centre), Durham-Newcastle, UK
| | - C F Barenghi
- School of Mathematics, Statistics and Physics Newcastle University, Newcastle upon Tyne, NE1 7RU, UK. .,JQC (Joint Quantum Centre), Durham-Newcastle, UK.
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36
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Valdés A, Segura J, Dyson S, Martínez-García B, Roca J. DNA knots occur in intracellular chromatin. Nucleic Acids Res 2019; 46:650-660. [PMID: 29149297 PMCID: PMC5778459 DOI: 10.1093/nar/gkx1137] [Citation(s) in RCA: 40] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2017] [Accepted: 10/28/2017] [Indexed: 01/12/2023] Open
Abstract
In vivo DNA molecules are narrowly folded within chromatin fibers and self-interacting chromatin domains. Therefore, intra-molecular DNA entanglements (knots) might occur via DNA strand passage activity of topoisomerase II. Here, we assessed the presence of such DNA knots in a variety of yeast circular minichromosomes. We found that small steady state fractions of DNA knots are common in intracellular chromatin. These knots occur irrespective of DNA replication and cell proliferation, though their abundance is reduced during DNA transcription. We found also that in vivo DNA knotting probability does not scale proportionately with chromatin length: it reaches a value of ∼0.025 in domains of ∼20 nucleosomes but tends to level off in longer chromatin fibers. These figures suggest that, while high flexibility of nucleosomal fibers and clustering of nearby nucleosomes facilitate DNA knotting locally, some mechanism minimizes the scaling of DNA knot formation throughout intracellular chromatin. We postulate that regulation of topoisomerase II activity and the fractal architecture of chromatin might be crucial to prevent a potentially massive and harmful self-entanglement of DNA molecules in vivo.
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Affiliation(s)
- Antonio Valdés
- Molecular Biology Institute of Barcelona (IBMB); Spanish National Research Council (CSIC); Barcelona 08028; Spain
| | - Joana Segura
- Molecular Biology Institute of Barcelona (IBMB); Spanish National Research Council (CSIC); Barcelona 08028; Spain
| | - Sílvia Dyson
- Molecular Biology Institute of Barcelona (IBMB); Spanish National Research Council (CSIC); Barcelona 08028; Spain
| | - Belén Martínez-García
- Molecular Biology Institute of Barcelona (IBMB); Spanish National Research Council (CSIC); Barcelona 08028; Spain
| | - Joaquim Roca
- Molecular Biology Institute of Barcelona (IBMB); Spanish National Research Council (CSIC); Barcelona 08028; Spain
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37
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The Rabl configuration limits topological entanglement of chromosomes in budding yeast. Sci Rep 2019; 9:6795. [PMID: 31043625 PMCID: PMC6494875 DOI: 10.1038/s41598-019-42967-4] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2018] [Accepted: 03/27/2019] [Indexed: 11/25/2022] Open
Abstract
The three dimensional organization of genomes remains mostly unknown due to their high degree of condensation. Biophysical studies predict that condensation promotes the topological entanglement of chromatin fibers and the inhibition of function. How organisms balance between functionally active genomes and a high degree of condensation remains to be determined. Here we hypothesize that the Rabl configuration, characterized by the attachment of centromeres and telomeres to the nuclear envelope, helps to reduce the topological entanglement of chromosomes. To test this hypothesis we developed a novel method to quantify chromosome entanglement complexity in 3D reconstructions obtained from Chromosome Conformation Capture (CCC) data. Applying this method to published data of the yeast genome, we show that computational models implementing the attachment of telomeres or centromeres alone are not sufficient to obtain the reduced entanglement complexity observed in 3D reconstructions. It is only when the centromeres and telomeres are attached to the nuclear envelope (i.e. the Rabl configuration) that the complexity of entanglement of the genome is comparable to that of the 3D reconstructions. We therefore suggest that the Rabl configuration is an essential player in the simplification of the entanglement of chromatin fibers.
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38
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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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39
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Calculation of π and Classification of Self-avoiding Lattices via DNA Configuration. Sci Rep 2019; 9:2252. [PMID: 30783171 PMCID: PMC6381155 DOI: 10.1038/s41598-019-38699-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2018] [Accepted: 01/08/2019] [Indexed: 11/09/2022] Open
Abstract
Numerical simulation (e.g. Monte Carlo simulation) is an efficient computational algorithm establishing an integral part in science to understand complex physical and biological phenomena related with stochastic problems. Aside from the typical numerical simulation applications, studies calculating numerical constants in mathematics, and estimation of growth behavior via a non-conventional self-assembly in connection with DNA nanotechnology, open a novel perspective to DNA related to computational physics. Here, a method to calculate the numerical value of π, and way to evaluate possible paths of self-avoiding walk with the aid of Monte Carlo simulation, are addressed. Additionally, experimentally obtained variation of the π as functions of DNA concentration and the total number of trials, and the behaviour of self-avoiding random DNA lattice growth evaluated through number of growth steps, are discussed. From observing experimental calculations of π (πexp) obtained by double crossover DNA lattices and DNA rings, fluctuation of πexp tends to decrease as either DNA concentration or the number of trials increases. Based upon experimental data of self-avoiding random lattices grown by the three-point star DNA motifs, various lattice configurations are examined and analyzed. This new kind of study inculcates a novel perspective for DNA nanostructures related to computational physics and provides clues to solve analytically intractable problems.
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40
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Bimodality in the knotting probability of semiflexible rings suggested by mapping with self-avoiding polygons. REACT FUNCT POLYM 2019. [DOI: 10.1016/j.reactfunctpolym.2018.11.008] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
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41
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Soh BW, Klotz AR, Doyle PS. Untying of Complex Knots on Stretched Polymers in Elongational Fields. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01879] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Affiliation(s)
- Beatrice W. Soh
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Alexander R. Klotz
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Patrick S. Doyle
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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42
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Zhou X, Liu L, Chen J, Zhang L. Unusual conformations of semiflexible ring polymers confined in two parallel surfaces. POLYMER 2018. [DOI: 10.1016/j.polymer.2018.10.039] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
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43
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Jarmolinska AI, Perlinska AP, Runkel R, Trefz B, Ginn HM, Virnau P, Sulkowska JI. Proteins' Knotty Problems. J Mol Biol 2018; 431:244-257. [PMID: 30391297 DOI: 10.1016/j.jmb.2018.10.012] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2018] [Revised: 10/17/2018] [Accepted: 10/17/2018] [Indexed: 12/20/2022]
Abstract
Knots in proteins are increasingly being recognized as an important structural concept, and the folding of these peculiar structures still poses considerable challenges. From a functional point of view, most protein knots discovered so far are either enzymes or DNA-binding proteins. Our comprehensive topological analysis of the Protein Data Bank reveals several novel structures including knotted mitochondrial proteins and the most deeply embedded protein knot discovered so far. For the latter, we propose a novel folding pathway based on the idea that a loose knot forms at a terminus and slides to its native position. For the mitochondrial proteins, we discuss the folding problem from the perspective of transport and suggest that they fold inside the mitochondria. We also discuss the evolutionary origin of a novel class of knotted membrane proteins and argue that a novel knotted DNA-binding protein constitutes a new fold. Finally, we have also discovered a knot in an artificially designed protein structure.
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Affiliation(s)
- Aleksandra I Jarmolinska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland; College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, Banacha 2c, 02-097 Warsaw, Poland
| | - Agata P Perlinska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland; College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, Banacha 2c, 02-097 Warsaw, Poland
| | - Robert Runkel
- Department of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Benjamin Trefz
- Department of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany; Graduate School Material Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany
| | - Helen M Ginn
- Division of Structural Biology, Wellcome Trust Centre for Human Genetics, University of Oxford, Oxford, UK
| | - Peter Virnau
- Department of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Joanna I Sulkowska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland.
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44
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Cardelli C, Tubiana L, Bianco V, Nerattini F, Dellago C, Coluzza I. Heteropolymer Design and Folding of Arbitrary Topologies Reveals an Unexpected Role of Alphabet Size on the Knot Population. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01359] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Chiara Cardelli
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Luca Tubiana
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Valentino Bianco
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Francesca Nerattini
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Christoph Dellago
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Ivan Coluzza
- CIC biomaGUNE, Paseo Miramon 182, 20014 San Sebastian, Spain
- IKERBASQUE,
Basque
Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
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45
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Coarse-grained models of double-stranded DNA based on experimentally determined knotting probabilities. REACT FUNCT POLYM 2018. [DOI: 10.1016/j.reactfunctpolym.2018.08.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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46
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Si D, Xu Z, Nan N, Hu G. DNA Confined in a Nanodroplet: A Molecular Dynamics Study. J Phys Chem B 2018; 122:8812-8818. [PMID: 30180585 DOI: 10.1021/acs.jpcb.8b05056] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
As a major genetic material, the configuration and the mechanical properties of a double-stranded DNA (dsDNA) molecule in confinement are crucial for the application of nanotechnology and biological engineering. In the present paper, molecular dynamics simulation is utilized to study the configuration of dsDNA in a nanodroplet on a graphene substrate. The results show that the semiflexible dsDNA molecule changes its configuration with radius of gyration ( Rg) of a few nanometers because of the confined space, that is, the Rg of the dsDNA molecule decreases with the reduction of the nanodroplet size. In comparison, the dsDNA in the bulk usually has a persistent length of tens of nanometers. Especially, if the nanodroplet is small enough, the dsDNA molecule might form a loop structure inside. The dsDNA molecule affects the wetting properties of the graphene substrate. It is found that the graphene becomes more hydrophilic in smaller systems containing the dsDNA molecule, whereas for larger droplets, the changes of the contact angles are not significant with the presence of dsDNA. Moreover, the results indicate that for larger droplets, the line tension of the droplet containing DNA is positive and greater than that without DNA; for smaller droplets, the line tension becomes negative because the dsDNA is compressed and bent in the confinement, and has the potential to expand outwards. The worm-like chain model is used to study the bending energy of a dsDNA molecule in a droplet. The results address that the bending energy of the non-loop-structured dsDNA decreases as the droplet becomes larger, and it is larger than that of loop-structured dsDNA, as the loop structure efficiently prevents the DNA from bending in the vertical direction.
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Affiliation(s)
- Dongqing Si
- Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering , Shanghai University , Shanghai 200072 , China
| | - Zhen Xu
- School of Mechanical Engineering , Shanghai University of Engineering Science , Shanghai 201620 , China
| | - Nan Nan
- Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering , Shanghai University , Shanghai 200072 , China
| | - Guohui Hu
- Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering , Shanghai University , Shanghai 200072 , China
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47
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Coronel L, Suma A, Micheletti C. Dynamics of supercoiled DNA with complex knots: large-scale rearrangements and persistent multi-strand interlocking. Nucleic Acids Res 2018; 46:7533-7541. [PMID: 29931074 PMCID: PMC6125635 DOI: 10.1093/nar/gky523] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2018] [Revised: 05/22/2018] [Accepted: 05/24/2018] [Indexed: 02/04/2023] Open
Abstract
Knots and supercoiling are both introduced in bacterial plasmids by catalytic processes involving DNA strand passages. While the effects on plasmid organization has been extensively studied for knotting and supercoiling taken separately, much less is known about their concurrent action. Here, we use molecular dynamics simulations and oxDNA, an accurate mesoscopic DNA model, to study the kinetic and metric changes introduced by complex (five-crossing) knots and supercoiling in 2 kbp-long DNA rings. We find several unexpected results. First, the conformational ensemble is dominated by two distinct states, differing in branchedness and knot size. Secondly, fluctuations between these states are as fast as the metric relaxation of unknotted rings. In spite of this, certain boundaries of knotted and plectonemically-wound regions can persist over much longer timescales. These pinned regions involve multiple strands that are interlocked by the cooperative action of topological and supercoiling constraints. Their long-lived character may be relevant for the simplifying action of topoisomerases.
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Affiliation(s)
- Lucia Coronel
- SISSA - Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
| | - Antonio Suma
- SISSA - Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
- Institute for Computational Molecular Science, College of Science and Technology, Temple University, Philadelphia, PA 19122, USA
| | - Cristian Micheletti
- SISSA - Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
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48
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543
| | - Patrick S. Doyle
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543
- Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139, United States
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49
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Meyer H, Horwath E, Virnau P. Mapping onto Ideal Chains Overestimates Self-Entanglements in Polymer Melts. ACS Macro Lett 2018; 7:757-761. [PMID: 35632960 DOI: 10.1021/acsmacrolett.8b00210] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We analyze the occurrence of knots, their spectrum, and sizes in polymer melts. Surprisingly, the number of knots in melt conformations is much lower than expected from a mapping to a random walk with the same Kuhn segment length. The effective random walk severely overrates the occurrence of knots and their complexity, particularly when compared to melts of flexible chains, indicating that nontrivial effects due to remnants of self-avoidance play a role for the chain lengths considered in this numerical study. For melt chains with higher persistence length, the effect is less pronounced. In addition, we find that chains in a melt have a knot structure very similar to dilute single chains close to the collapse transition. We finally show that typical equilibration procedures are well-suited to relax the topology in melts.
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Affiliation(s)
- Hendrik Meyer
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR 22, 23 rue du Loess-BP 84047, 67034 Strasbourg, France
| | - Eric Horwath
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, 55099 Mainz, Germany
| | - Peter Virnau
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, 55099 Mainz, Germany
- Graduate School of Excellence Materials Science in Mainz, 55099 Mainz, Germany
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50
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Tubiana L, Polles G, Orlandini E, Micheletti C. KymoKnot: A web server and software package to identify and locate knots in trajectories of linear or circular polymers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:72. [PMID: 29884956 DOI: 10.1140/epje/i2018-11681-0] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Accepted: 05/18/2018] [Indexed: 06/08/2023]
Abstract
The KymoKnot software package and web server identifies and locates physical knots or proper knots in a series of polymer conformations. It is mainly intended as an analysis tool for trajectories of linear or circular polymers, but it can be used on single instances too, e.g. protein structures in PDB format. A key element of the software package is the so-called minimally interfering chain closure algorithm that is used to detect physical knots in open chains and to locate the knotted region in both open and closed chains. The web server offers a user-friendly graphical interface that identifies the knot type and highlights the knotted region on each frame of the trajectory, which the user can visualize interactively from various viewpoints. The dynamical evolution of the knotted region along the chain contour is presented as a kymograph. All data can be downloaded in text format. The KymoKnot package is licensed under the BSD 3-Clause licence. The server is publicly available at http://kymoknot.sissa.it/kymoknot/interactive.php .
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Affiliation(s)
- Luca Tubiana
- Computational Physics Department, University of Vienna, Sensengasse 8/10, 1090, Vienna, Austria.
| | - Guido Polles
- Molecular and Computational Biology, Department of Biological Sciences, University of Southern California, 90089, Los Angeles, CA, USA
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia and Sezione INFN, Università di Padova, Via Marzolo 8, 35131, Padova, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, Via Bonomea 265, I-34136, Trieste, Italy
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