1
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Coshic K, Maffeo C, Winogradoff D, Aksimentiev A. The structure and physical properties of a packaged bacteriophage particle. Nature 2024; 627:905-914. [PMID: 38448589 DOI: 10.1038/s41586-024-07150-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 02/01/2024] [Indexed: 03/08/2024]
Abstract
A string of nucleotides confined within a protein capsid contains all the instructions necessary to make a functional virus particle, a virion. Although the structure of the protein capsid is known for many virus species1,2, the three-dimensional organization of viral genomes has mostly eluded experimental probes3,4. Here we report all-atom structural models of an HK97 virion5, including its entire 39,732 base pair genome, obtained through multiresolution simulations. Mimicking the action of a packaging motor6, the genome was gradually loaded into the capsid. The structure of the packaged capsid was then refined through simulations of increasing resolution, which produced a 26 million atom model of the complete virion, including water and ions confined within the capsid. DNA packaging occurs through a loop extrusion mechanism7 that produces globally different configurations of the packaged genome and gives each viral particle individual traits. Multiple microsecond-long all-atom simulations characterized the effect of the packaged genome on capsid structure, internal pressure, electrostatics and diffusion of water, ions and DNA, and revealed the structural imprints of the capsid onto the genome. Our approach can be generalized to obtain complete all-atom structural models of other virus species, thereby potentially revealing new drug targets at the genome-capsid interface.
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Affiliation(s)
- Kush Coshic
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Christopher Maffeo
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, USA
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - David Winogradoff
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Aleksei Aksimentiev
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, IL, USA.
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, USA.
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA.
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2
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Slongo F, Hauke P, Faccioli P, Micheletti C. Quantum-inspired encoding enhances stochastic sampling of soft matter systems. SCIENCE ADVANCES 2023; 9:eadi0204. [PMID: 37878707 PMCID: PMC10599611 DOI: 10.1126/sciadv.adi0204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Accepted: 09/21/2023] [Indexed: 10/27/2023]
Abstract
Quantum advantage in solving physical problems is still hard to assess due to hardware limitations. However, algorithms designed for quantum computers may engender transformative frameworks for modeling and simulating paradigmatically hard systems. Here, we show that the quadratic unconstrained binary optimization encoding enables tackling classical many-body systems that are challenging for conventional Monte Carlo. Specifically, in self-assembled melts of rigid lattice ring polymers, the combination of high density, chain stiffness, and topological constraints results in divergent autocorrelation times for real-space Monte Carlo. Our quantum-inspired encoding overcomes this problem and enables sampling melts of lattice rings with fixed curvature and compactness, unveiling counterintuitive topological effects. Tackling the same problems with the D-Wave quantum annealer leads to substantial performance improvements and advantageous scaling of sampling computational cost with the size of the self-assembled ring melts.
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Affiliation(s)
- Francesco Slongo
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, I-34136 Trieste, Italy
| | - Philipp Hauke
- Pitaevskii BEC Center, Department of Physics, University of Trento, Via Sommarive 14, I-38123 Povo, Trento, Italy
- INFN-TIFPA, Via Sommarive 14, I-38123 Povo, Trento, Italy
| | - Pietro Faccioli
- Department of Physics and BiQuTe Center, University of Milano-Bicocca, Piazza della Scienza 3, I-20126 Milan, Italy
- Department of Physics, University of Trento, Via Sommarive 14, I-38123 Povo, Trento, Italy
| | - Cristian Micheletti
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, I-34136 Trieste, Italy
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3
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Kolesnikov ES, Gushchin IY, Zhilyaev PA, Onufriev AV. Why Na+ has higher propensity than K+ to condense DNA in a crowded environment. J Chem Phys 2023; 159:145103. [PMID: 37815107 DOI: 10.1063/5.0159341] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 08/22/2023] [Indexed: 10/11/2023] Open
Abstract
Experimentally, in the presence of the crowding agent polyethylene glycol (PEG), sodium ions compact double-stranded DNA more readily than potassium ions. Here, we have used molecular dynamics simulations and the "ion binding shells model" of DNA condensation to provide an explanation for the observed variations in condensation of short DNA duplexes in solutions containing different monovalent cations and PEG; several predictions are made. According to the model we use, externally bound ions contribute the most to the ion-induced aggregation of DNA duplexes. The simulations reveal that for two adjacent DNA duplexes, the number of externally bound Na+ ions is larger than the number of K+ ions over a wide range of chloride concentrations in the presence of PEG, providing a qualitative explanation for the higher propensity of sodium ions to compact DNA under crowded conditions. The qualitative picture is confirmed by an estimate of the corresponding free energy of DNA aggregation that is at least 0.2kBT per base pair more favorable in solution with NaCl than with KCl at the same ion concentration. The estimated attraction free energy of DNA duplexes in the presence of Na+ depends noticeably on the DNA sequence; we predict that AT-rich DNA duplexes are more readily condensed than GC-rich ones in the presence of Na+. Counter-intuitively, the addition of a small amount of a crowding agent with high affinity for the specific condensing ion may lead to the weakening of the ion-mediated DNA-DNA attraction, shifting the equilibrium away from the DNA condensed phase.
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Affiliation(s)
- Egor S Kolesnikov
- Research Center for Molecular Mechanisms of Aging and Age-Related Diseases, Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Ivan Yu Gushchin
- Research Center for Molecular Mechanisms of Aging and Age-Related Diseases, Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia
| | - Petr A Zhilyaev
- The Center for Materials Technologies, Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, Moscow 121205, Russia
| | - Alexey V Onufriev
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
- Department of Computer Science, Virginia Tech, 2160C Torgersen Hall, Blacksburg, Virginia 24061, USA
- Center for Soft Matter and Biological Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
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4
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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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5
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Tortora MMC, Jost D. Orientational Wetting and Topological Transitions in Confined Solutions of Semiflexible Polymers. Macromolecules 2023. [DOI: 10.1021/acs.macromol.2c02350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023]
Affiliation(s)
- Maxime M. C. Tortora
- Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Biologie et Modélisation de la Cellule, 69364 Lyon CEDEX 07, France
| | - Daniel Jost
- Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Biologie et Modélisation de la Cellule, 69364 Lyon CEDEX 07, France
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6
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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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7
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Wettermann S, Datta R, Virnau P. Influence of ionic conditions on knotting in a coarse-grained model for DNA. Front Chem 2023; 10:1096014. [PMID: 36733610 PMCID: PMC9887150 DOI: 10.3389/fchem.2022.1096014] [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: 11/11/2022] [Accepted: 12/23/2022] [Indexed: 01/18/2023] Open
Abstract
We investigate knotting probabilities of long double-stranded DNA strands in a coarse-grained Kratky-Porod model for DNA with Monte Carlo simulations. Various ionic conditions are implemented by adjusting the effective diameter of monomers. We find that the occurrence of knots in DNA can be reinforced considerably by high salt conditions and confinement between plates. Likewise, knots can almost be dissolved completely in a low salt scenario. Comparisons with recent experiments confirm that the coarse-grained model is able to capture and quantitatively predict topological features of DNA and can be used for guiding future experiments on DNA knots.
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8
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Zeng S, Chinappi M, Cecconi F, Odijk T, Zhang Z. DNA compaction and dynamic observation in a nanopore gated sub-attoliter silicon nanocavity. NANOSCALE 2022; 14:12038-12047. [PMID: 35943364 DOI: 10.1039/d2nr02260e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Confinement of biopolymers inside volumes with micro- or nanoscale lateral dimensions is ubiquitous in nature. Investigating the behavior of biopolymers in a confined environment is essential to improve our basic understanding in life sciences. In this work, we present a nanopore gated sub-attoliter silicon nanocavity device, which allows DNA compaction similar to that in virus capsids. Single DNA molecules can be electrically driven into the nanocavity, and then get compacted inside the nanocavity under certain conditions. The dynamic fluctuations of the compacted DNA can be monitored via ionic current measurements. The mechanism for the DNA compaction is elucidated by varying the DNA length or concentration, voltage polarity, nanocavity dimensions and ionic strength. Furthermore, Brownian dynamics simulations reveal the dynamic fluctuations of the compacted DNA, which are reflected in the measured ionic current. Our nanocavity device is anticipated to provide a controlled environment in extremely small volumes for investigating the physics of confined biopolymers.
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Affiliation(s)
- Shuangshuang Zeng
- Division of Solid-State Electronics, Department of Electrical Engineering, Uppsala University, SE-751 03 Uppsala, Sweden.
| | - Mauro Chinappi
- Dipartimento di Ingegneria Industriale, Università di Roma Tor Vergata, Via del Politecnico 1, 00133 Roma, Italy
| | - Fabio Cecconi
- CNR-Istituto dei Sistemi Complessi, Via dei Taurini 19, 00185 Roma, Italy
- INFN, Unità di Roma 1, 00185, Roma, Italy
| | - Theo Odijk
- Lorentz Institute for Theoretical Physics, University of Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
| | - Zhen Zhang
- Division of Solid-State Electronics, Department of Electrical Engineering, Uppsala University, SE-751 03 Uppsala, Sweden.
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9
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Statistics and topology of fluctuating ribbons. Proc Natl Acad Sci U S A 2022; 119:e2122907119. [PMID: 35917354 PMCID: PMC9371672 DOI: 10.1073/pnas.2122907119] [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] [Indexed: 02/04/2023] Open
Abstract
Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases-a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase-that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a universal response curve of a topological quantity, the link, as a function of the applied torque that is similar to magnetization curves in second-order phase transitions.
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10
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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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11
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Sleiman JL, Burton RH, Caraglio M, Gutierrez Fosado YA, Michieletto D. Geometric Predictors of Knotted and Linked Arcs. ACS POLYMERS AU 2022; 2:341-350. [PMID: 36254317 PMCID: PMC9562465 DOI: 10.1021/acspolymersau.2c00021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
Inspired by how certain proteins “sense”
knots and
entanglements in DNA molecules, here, we ask if local geometric features
that may be used as a readout of the underlying topology of generic
polymers exist. We perform molecular simulations of knotted and linked
semiflexible polymers and study four geometric measures to predict
topological entanglements: local curvature, local density, local 1D
writhe, and nonlocal 3D writhe. We discover that local curvature is
a poor predictor of entanglements. In contrast, segments with maximum
local density or writhe correlate as much as 90% of the time with
the shortest knotted and linked arcs. We find that this accuracy is
preserved across different knot types and also under significant spherical
confinement, which is known to delocalize essential crossings in knotted
polymers. We further discover that nonlocal 3D writhe is the best
geometric readout of the knot location. Finally, we discuss how these
geometric features may be used to computationally analyze entanglements
in generic polymer melts and gels.
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Affiliation(s)
- Joseph L. Sleiman
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Robin H. Burton
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Michele Caraglio
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Yair Augusto Gutierrez Fosado
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
- MRC Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh, Edinburgh EH4 2XU, United Kingdom
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12
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Valov AF, Avetisov VA. Fluctuational Features of Diffusive Passage of Particles in Narrow Channels with Obstacles. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B 2022. [DOI: 10.1134/s1990793122030101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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13
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Spencer RKW, Ha BY, Saeidi N. Interplay between nematic and cholesteric interactions in self-consistent field theory. Phys Rev E 2022; 105:054501. [PMID: 35706232 DOI: 10.1103/physreve.105.054501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2021] [Accepted: 03/29/2022] [Indexed: 06/15/2023]
Abstract
Chirality is a design feature of a number of biomolecules (e.g., collagen). In these molecules, cholesteric (chiral-nematic) behavior emerges from a combination of the tendency for the biopolymers to align (nematic interactions) and for the alignment direction to change with position, rotating around an axis normal to the alignment direction. This paper presents self-consistent field theory (SCFT) of chiral-nematic polymers, which takes into account polymer flexibility and the orientational degrees of freedom of polymer segments. Using the resulting SCFT, we construct a phase diagram showing regions of stability for isotropic, nematic, and cholesteric phases. Furthermore, we find that nematic interactions can stabilize the cholesteric phase, pushing the isotropic-cholesteric phase transition to lower cholesteric interaction strength, until the isotropic-nematic-cholesteric triple point is reached.
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Affiliation(s)
- Russell K W Spencer
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - Bae-Yeun Ha
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - Nima Saeidi
- Department of Surgery, The Center for Engineering in Medicine, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114, USA
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14
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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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15
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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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16
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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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17
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Orlandini E, Micheletti C. Topological and physical links in soft matter systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:013002. [PMID: 34547745 DOI: 10.1088/1361-648x/ac28bf] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 09/21/2021] [Indexed: 06/13/2023]
Abstract
Linking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packedin vivoto interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges.
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Affiliation(s)
- Enzo Orlandini
- Department of Physics and Astronomy, University of Padova and Sezione INFN, Via Marzolo 8, Padova, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, Trieste, Italy
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18
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Panagiotou E, Kauffman LH. Vassiliev measures of complexity of open and closed curves in 3-space. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0440] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In this article, we define Vassiliev measures of complexity for open curves in 3-space. These are related to the coefficients of the enhanced Jones polynomial of open curves in 3-space. These Vassiliev measures are continuous functions of the curve coordinates; as the ends of the curve tend to coincide, they converge to the corresponding Vassiliev invariants of the resulting knot. We focus on the second Vassiliev measure from the enhanced Jones polynomial for closed and open curves in 3-space. For closed curves, this second Vassiliev measure can be computed by a Gauss code diagram and it has an integral formulation, the double alternating self-linking integral. The double alternating self-linking integral is a topological invariant of closed curves and a continuous function of the curve coordinates for open curves in 3-space. For polygonal curves, the double alternating self-linking integral obtains a simpler expression in terms of geometric probabilities.
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Affiliation(s)
- Eleni Panagiotou
- Department of Mathematics and SimCenter, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
| | - Louis H. Kauffman
- Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA
- Department of Mechanics and Mathematics, Novosibirsk State University, Novosibirsk, Russia
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19
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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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20
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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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21
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Liu P, Arsuaga J, Calderer MC, Golovaty D, Vazquez M, Walker S. Ion-dependent DNA configuration in bacteriophage capsids. Biophys J 2021; 120:3292-3302. [PMID: 34265262 DOI: 10.1016/j.bpj.2021.07.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Revised: 05/01/2021] [Accepted: 07/07/2021] [Indexed: 11/24/2022] Open
Abstract
Bacteriophages densely pack their long double-stranded DNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy that combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is possible using the existing molecular-level methods. In particular, we are able to estimate bending and repulsion between the DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and with molecular dynamics simulations for small capsids.
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Affiliation(s)
- Pei Liu
- School of Mathematics, University of Minnesota, Twin Cities, Minneapolis, Minnesota
| | - Javier Arsuaga
- Department of Mathematics, University of California Davis, Davis, California; Department of Molecular and Cellular Biology, University of California Davis, Davis, California.
| | - M Carme Calderer
- School of Mathematics, University of Minnesota, Twin Cities, Minneapolis, Minnesota
| | - Dmitry Golovaty
- Department of Mathematics, The University of Akron, Akron, Ohio.
| | - Mariel Vazquez
- Department of Mathematics, University of California Davis, Davis, California; Department of Microbiology and Molecular Genetics, University of California Davis, Davis, California
| | - Shawn Walker
- Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana
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22
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Hiltner L, Carme Calderer M, Arsuaga J, Vázquez M. Chromonic liquid crystals and packing configurations of bacteriophage viruses. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200111. [PMID: 34024128 DOI: 10.1098/rsta.2020.0111] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 12/01/2020] [Indexed: 06/12/2023]
Abstract
We study equilibrium configurations of hexagonal columnar liquid crystals in the context of characterizing packing structures of bacteriophage viruses in a protein capsid. These are viruses that infect bacteria and are currently the focus of intense research efforts, with the goal of finding new therapies for bacteria-resistant antibiotics. The energy that we propose consists of the Oseen-Frank free energy of nematic liquid crystals that penalizes bending of the columnar directions, in addition to the cross-sectional elastic energy accounting for distortions of the transverse hexagonal structure; we also consider the isotropic contribution of the core and the energy of the unknown interface between the outer ordered region of the capsid and the inner disordered core. The problem becomes of free boundary type, with constraints. We show that the concentric, azimuthal, spool-like configuration is the absolute minimizer. Moreover, we present examples of toroidal structures formed by DNA in free solution and compare them with the analogous ones occurring in experiments with other types of lyotropic liquid crystals, such as food dyes and additives. This article is part of the theme issue 'Topics in mathematical design of complex materials'.
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Affiliation(s)
- Lindsey Hiltner
- School of Mathematics, University of Minnesota, Minneapolis, MN 55442, USA
| | - M Carme Calderer
- School of Mathematics, University of Minnesota, Minneapolis, MN 55442, USA
| | - Javier Arsuaga
- Department of Cellular and Molecular Biology, Briggs Hall, Davis, CA 09
- Department of Mathematics, MSB, 2115, University of California Davis, One Shields Avenue, Davis, CA 95616, USA
| | - Mariel Vázquez
- Department of Mathematics, MSB, 2150, University of California Davis, One Shields Avenue, Davis, CA 95616, USA
- Department of Microbiology and Molecular Genetics, Briggs Hall, Davis, CA 09
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23
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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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24
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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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25
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Emanuel MD, Cherstvy AG, Metzler R, Gompper G. Buckling transitions and soft-phase invasion of two-component icosahedral shells. Phys Rev E 2021; 102:062104. [PMID: 33465945 DOI: 10.1103/physreve.102.062104] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2020] [Accepted: 11/11/2020] [Indexed: 12/18/2022]
Abstract
What is the optimal distribution of two types of crystalline phases on the surface of icosahedral shells, such as of many viral capsids? We here investigate the distribution of a thin layer of soft material on a crystalline convex icosahedral shell. We demonstrate how the shapes of spherical viruses can be understood from the perspective of elasticity theory of thin two-component shells. We develop a theory of shape transformations of an icosahedral shell upon addition of a softer, but still crystalline, material onto its surface. We show how the soft component "invades" the regions with the highest elastic energy and stress imposed by the 12 topological defects on the surface. We explore the phase diagram as a function of the surface fraction of the soft material, the shell size, and the incommensurability of the elastic moduli of the rigid and soft phases. We find that, as expected, progressive filling of the rigid shell by the soft phase starts from the most deformed regions of the icosahedron. With a progressively increasing soft-phase coverage, the spherical segments of domes are filled first (12 vertices of the shell), then the cylindrical segments connecting the domes (30 edges) are invaded, and, ultimately, the 20 flat faces of the icosahedral shell tend to be occupied by the soft material. We present a detailed theoretical investigation of the first two stages of this invasion process and develop a model of morphological changes of the cone structure that permits noncircular cross sections. In conclusion, we discuss the biological relevance of some structures predicted from our calculations, in particular for the shape of viral capsids.
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Affiliation(s)
- Marc D Emanuel
- Theoretical Physics of Living Matter, Institute of Biological Information Processing, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany.,Kavli Institute for Nanoscience, Technical University Delft, 2628 CJ Delft, Netherlands
| | - Andrey G Cherstvy
- Theoretical Physics of Living Matter, Institute of Biological Information Processing, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany.,Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Gerhard Gompper
- Theoretical Physics of Living Matter, Institute of Biological Information Processing, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
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26
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Lu L, Zhu H, Yuyuan Lu, An L, Dai L. Application of the Tube Model to Explain the Unexpected Decrease in Polymer Bending Energy Induced by Knot Formation. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01436] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Luwei Lu
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P.R. China
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P.R. China
- University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, P.R. China
| | - Haoqi Zhu
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P.R. China
- Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Yuyuan Lu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P.R. China
| | - Lijia An
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P.R. China
- University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, P.R. China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P.R. China
- Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
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27
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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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28
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Curk T, Brackley CA, Farrell JD, Xing Z, Joshi D, Direito S, Bren U, Angioletti-Uberti S, Dobnikar J, Eiser E, Frenkel D, Allen RJ. Computational design of probes to detect bacterial genomes by multivalent binding. Proc Natl Acad Sci U S A 2020; 117:8719-8726. [PMID: 32241887 PMCID: PMC7183166 DOI: 10.1073/pnas.1918274117] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Rapid methods for diagnosis of bacterial infections are urgently needed to reduce inappropriate use of antibiotics, which contributes to antimicrobial resistance. In many rapid diagnostic methods, DNA oligonucleotide probes, attached to a surface, bind to specific nucleotide sequences in the DNA of a target pathogen. Typically, each probe binds to a single target sequence; i.e., target-probe binding is monovalent. Here we show using computer simulations that the detection sensitivity and specificity can be improved by designing probes that bind multivalently to the entire length of the pathogen genomic DNA, such that a given probe binds to multiple sites along the target DNA. Our results suggest that multivalent targeting of long pieces of genomic DNA can allow highly sensitive and selective binding of the target DNA, even if competing DNA in the sample also contains binding sites for the same probe sequences. Our results are robust to mild fragmentation of the bacterial genome. Our conclusions may also be relevant for DNA detection in other fields, such as disease diagnostics more broadly, environmental management, and food safety.
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Affiliation(s)
- Tine Curk
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Faculty of Chemistry and Chemical Engineering, University of Maribor, Maribor 2000, Slovenia
- School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Chris A Brackley
- School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - James D Farrell
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhongyang Xing
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
| | - Darshana Joshi
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
| | - Susana Direito
- School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Urban Bren
- Faculty of Chemistry and Chemical Engineering, University of Maribor, Maribor 2000, Slovenia
| | | | - Jure Dobnikar
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Erika Eiser
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
| | - Daan Frenkel
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Rosalind J Allen
- School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom;
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29
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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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30
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Vandans O, Yang K, Wu Z, Dai L. Identifying knot types of polymer conformations by machine learning. Phys Rev E 2020; 101:022502. [PMID: 32168694 DOI: 10.1103/physreve.101.022502] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Accepted: 01/14/2020] [Indexed: 02/04/2023]
Abstract
We investigate the use of artificial neural networks (NNs) as an alternative tool to current analytical methods for recognizing knots in a given polymer conformation. The motivation is twofold. First, it is of interest to examine whether NNs are effective at learning the global and sequential properties that uniquely define a knot. Second, knot classification is an important and unsolved problem in mathematical and physical sciences, and NNs may provide insights into this problem. Motivated by these points, we generate millions of polymer conformations for five knot types: 0, 3_{1}, 4_{1}, 5_{1}, and 5_{2}, and we design various NN models for classification. Our best model achieves a five-class classification accuracy of above 99% on a polymer of 100 monomers. We find that the sequential modeling ability of recurrent NNs is crucial for this result, as it outperforms feed-forward NNs and successfully generalizes to differently sized conformations as well. We present our methods and suggest that deep learning may be used in specific applications of knot detection where some error is permissible. Hopefully, with further development, NNs can offer an alternative computational method for knot identification and facilitate knot research in mathematical and physical sciences.
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Affiliation(s)
- Olafs Vandans
- Department of Physics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China
| | - Kaiyuan Yang
- Department of Computer Science, School of Computing, National University of Singapore, Singapore 117417, Singapore
| | - Zhongtao Wu
- Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong, China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China.,Shenzhen Research Institute, City University of Hong Kong, Shenzhen, China
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31
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Walker S, Arsuaga J, Hiltner L, Calderer MC, Vázquez M. Fine structure of viral dsDNA encapsidation. Phys Rev E 2020; 101:022703. [PMID: 32168691 DOI: 10.1103/physreve.101.022703] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2019] [Accepted: 12/19/2019] [Indexed: 06/10/2023]
Abstract
Unraveling the mechanisms of packing of DNA inside viral capsids is of fundamental importance to understanding the spread of viruses. It could also help develop new applications to targeted drug delivery devices for a large range of therapies. In this article, we present a robust, predictive mathematical model and its numerical implementation to aid the study and design of bacteriophage viruses for application purposes. Exploiting the analogies between the columnar hexagonal chromonic phases of encapsidated viral DNA and chromonic aggregates formed by plank-shaped molecular compounds, we develop a first-principles effective mechanical model of DNA packing in a viral capsid. The proposed expression of the packing energy, which combines relevant aspects of the liquid crystal theory, is developed from the model of hexagonal columnar phases, together with that describing configurations of polymeric liquid crystals. The method also outlines a parameter selection strategy that uses available data for a collection of viruses, aimed at applications to viral design. The outcome of the work is a mathematical model and its numerical algorithm, based on the method of finite elements, and computer simulations to identify and label the ordered and disordered regions of the capsid and calculate the inner pressure. It also presents the tools for the local reconstruction of the DNA "scaffolding" and the center curve of the filament within the capsid.
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Affiliation(s)
- Shawn Walker
- Department of Mathematics, 303 Lockett Hall, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - Javier Arsuaga
- Department of Cellular and Molecular Biology, Briggs Hall 09, and Department of Mathematics, MSB 2115, University of California Davis, Davis, California 95616, USA
| | - Lindsey Hiltner
- School of Mathematics, 507 Vincent Hall, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - M Carme Calderer
- School of Mathematics, 507 Vincent Hall, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Mariel Vázquez
- Department of Microbiology and Molecular Genetics, Briggs Hall 09, and Department of Mathematics, MSB 2150, University of California Davis, Davis, California 95616, USA
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32
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Valov A, Avetisov V, Nechaev S, Oshanin G. Field-driven tracer diffusion through curved bottlenecks: fine structure of first passage events. Phys Chem Chem Phys 2020; 22:18414-18422. [DOI: 10.1039/d0cp03162c] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Using scaling arguments and extensive numerical simulations, we study the dynamics of a tracer particle in a corrugated channel represented by a periodic sequence of broad chambers and narrow funnel-like bottlenecks enclosed by a hard-wall boundary.
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Affiliation(s)
- A. Valov
- N. N. Semenov Institute of Chemical Physics RAS
- 119991 Moscow
- Russia
| | - V. Avetisov
- N. N. Semenov Institute of Chemical Physics RAS
- 119991 Moscow
- Russia
| | - S. Nechaev
- Interdisciplinary Scientific Center Poncelet (CNRS UMI 2615)
- 119002 Moscow
- Russia
- P. N. Lebedev Physical Institute RAS
- 119991 Moscow
| | - G. Oshanin
- Sorbonne Université
- CNRS
- Laboratoire de Physique Théorique de la Matière Condensée
- LPTMC (UMR CNRS 7600)
- 75252 Paris
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33
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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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34
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Perego C, Potestio R. Computational methods in the study of self-entangled proteins: a critical appraisal. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:443001. [PMID: 31269476 DOI: 10.1088/1361-648x/ab2f19] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The existence of self-entangled proteins, the native structure of which features a complex topology, unveils puzzling, and thus fascinating, aspects of protein biology and evolution. The discovery that a polypeptide chain can encode the capability to self-entangle in an efficient and reproducible way during folding, has raised many questions, regarding the possible function of these knots, their conservation along evolution, and their role in the folding paradigm. Understanding the function and origin of these entanglements would lead to deep implications in protein science, and this has stimulated the scientific community to investigate self-entangled proteins for decades by now. In this endeavour, advanced experimental techniques are more and more supported by computational approaches, that can provide theoretical guidelines for the interpretation of experimental results, and for the effective design of new experiments. In this review we provide an introduction to the computational study of self-entangled proteins, focusing in particular on the methodological developments related to this research field. A comprehensive collection of techniques is gathered, ranging from knot theory algorithms, that allow detection and classification of protein topology, to Monte Carlo or molecular dynamics strategies, that constitute crucial instruments for investigating thermodynamics and kinetics of this class of proteins.
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Affiliation(s)
- Claudio Perego
- Max Panck Institute for Polymer Research, Ackermannweg 10, Mainz 55128, Germany
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35
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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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36
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Curk T, Farrell JD, Dobnikar J, Podgornik R. Spontaneous Domain Formation in Spherically Confined Elastic Filaments. PHYSICAL REVIEW LETTERS 2019; 123:047801. [PMID: 31491267 DOI: 10.1103/physrevlett.123.047801] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2019] [Indexed: 06/10/2023]
Abstract
Although the free energy of a genome packing into a virus is dominated by DNA-DNA interactions, ordering of the DNA inside the capsid is elasticity driven, suggesting general solutions with DNA organized into spool-like domains. Using analytical calculations and computer simulations of a long elastic filament confined to a spherical container, we show that the ground state is not a single spool as assumed hitherto, but an ordering mosaic of multiple homogeneously ordered domains. At low densities, we observe concentric spools, while at higher densities, other morphologies emerge, which resemble topological links. We discuss our results in the context of metallic wires, viral DNA, and flexible polymers.
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Affiliation(s)
- Tine Curk
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Faculty of Chemistry and Chemical Engineering, University of Maribor, 2000 Maribor, Slovenia
| | | | - Jure Dobnikar
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Rudolf Podgornik
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
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37
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Suma A, Poppleton E, Matthies M, Šulc P, Romano F, Louis AA, Doye JPK, Micheletti C, Rovigatti L. TacoxDNA: A user-friendly web server for simulations of complex DNA structures, from single strands to origami. J Comput Chem 2019; 40:2586-2595. [PMID: 31301183 DOI: 10.1002/jcc.26029] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2019] [Revised: 06/20/2019] [Accepted: 06/22/2019] [Indexed: 12/11/2022]
Abstract
Simulations of nucleic acids at different levels of structural details are increasingly used to complement and interpret experiments in different fields, from biophysics to medicine and materials science. However, the various structural models currently available for DNA and RNA and their accompanying suites of computational tools can be very rarely used in a synergistic fashion. The tacoxDNA webserver and standalone software package presented here are a step toward a long-sought interoperability of nucleic acids models. The webserver offers a simple interface for converting various common input formats of DNA structures and setting up molecular dynamics (MD) simulations. Users can, for instance, design DNA rings with different topologies, such as knots, with and without supercoiling, by simply providing an XYZ coordinate file of the DNA centre-line. More complex DNA geometries, as designable in the cadnano, CanDo and Tiamat tools, can also be converted to all-atom or oxDNA representations, which can then be used to run MD simulations. Though the latter are currently geared toward the native and LAMMPS oxDNA representations, the open-source package is designed to be further expandable. TacoxDNA is available at http://tacoxdna.sissa.it. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Antonio Suma
- Institute for Computational Molecular Science, Temple University, Philadelphia, Pennsylvania, 19122.,SISSA-Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea, 265, 34136, Trieste, Italy
| | - Erik Poppleton
- Center for Molecular Design and Biomimetics, The Biodesign Institute, Arizona State University, 1001, South McAllister Avenue, Tempe, Arizona 85281
| | - Michael Matthies
- Center for Advancing Electronics Dresden (cfaed), Faculty of Chemistry and Food Chemistry, Technische Universität Dresden, 01062, Dresden, Germany
| | - Petr Šulc
- Center for Molecular Design and Biomimetics, The Biodesign Institute, Arizona State University, 1001, South McAllister Avenue, Tempe, Arizona 85281
| | - Flavio Romano
- Dipartimento di Scienze Molecolari e Nanosistemi, Universitá Ca Foscari di Venezia, Via Torino, 155, 30172, Venezia Mestre, Italy
| | - Ard A Louis
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, UK
| | - Jonathan P K Doye
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford, OX1 3QZ, UK
| | - Cristian Micheletti
- SISSA-Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea, 265, 34136, Trieste, Italy
| | - Lorenzo Rovigatti
- Dipartimento di Fisica, Sapienza Universitá di Roma, Piazzale A. Moro, 2, 00185, Rome, Italy.,CNR-ISC, Uos Sapienza, Piazzale A. Moro, 2, 00185, Rome, Italy
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38
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Soik SM, Sharp TA. Effects of spherical confinement and backbone stiffness on flexible polymer jamming. Phys Rev E 2019; 99:052505. [PMID: 31212486 DOI: 10.1103/physreve.99.052505] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2018] [Indexed: 11/07/2022]
Abstract
We use molecular simulations to study jamming of a crumpled bead-spring model polymer in a finite container and compare to jamming of repulsive spheres. After proper constraint counting, the onset of rigidity is seen to occur isostatically as in the case of repulsive spheres. Despite this commonality, the presence of the curved container wall and polymer backbone bonds introduce new mechanical properties. Notably, these include additional bands in the vibrational density of states that reflect the material structure as well as oscillations in local contact number and density near the wall but with lower amplitude for polymers. Polymers have fewer boundary contacts, and this low-density surface layer strongly reduces the global bulk modulus. We further show that bulk-modulus dependence on backbone stiffness can be described by a model of stiffnesses in series and discuss potential experimental and biological applications.
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Affiliation(s)
- Samuel M Soik
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Tristan A Sharp
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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39
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Caraglio M, Baldovin F, Marcone B, Orlandini E, Stella AL. Topological Disentanglement Dynamics of Torus Knots on Open Linear Polymers. ACS Macro Lett 2019; 8:576-581. [PMID: 35619367 DOI: 10.1021/acsmacrolett.9b00055] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We simulate and study the topological disentanglement occurring when torus knots reach the ends of a semiflexible open polymer (decay into simpler knots or unknotting). Through a rescaling procedure and the application of appropriate boundary conditions, we show that the full unknotting process can be understood in terms of point-like particles representing essential crossings, diffusing on the support [0, 1]. We address the bending and configurational free energy drives on the diffusion process, together with the scaling properties of the effective diffusion and friction coefficients. Agreement with simulations suggests universal features for these two model parameters.
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Affiliation(s)
- Michele Caraglio
- KU Leuven, Soft Matter and Biophysics Section, Celestijnenlaan 200D, 3001 Leuven, Belgium
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Fulvio Baldovin
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Boris Marcone
- Center of Excellence for Stability Police Units, via Medici 87, 36100 Vicenza, Italy
| | - Enzo Orlandini
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Attilio L. Stella
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
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40
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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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41
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Najafi S. Topological entanglement of interlocked knotted-unknotted polymer rings. SOFT MATTER 2019; 15:1916-1921. [PMID: 30734820 DOI: 10.1039/c8sm02530d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Topological entanglements in biopolymers could drive them to certain internal statics and dynamics with important implications for biological functions. In this study, by means of molecular dynamics simulations, we demonstrate that the minimal crossing pattern of a braid plays a major role in its structural and dynamical properties; the braid consists of a knotted ring and an interlocked entwined unknotted polymer ring. In particular, we show that depending on the bending rigidity of the chains, the conformational energy of the braid can be either lower or higher than the unlocked polymer rings. Additionally, we find that a non-identical crossing pattern in the braid could distinctly enforce concerted internal conformational fluctuations between the interlocked rings.
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Affiliation(s)
- Saeed Najafi
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA.
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42
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Malgaretti P, Oshanin G. Polymer Translocation Across a Corrugated Channel: Fick⁻Jacobs Approximation Extended Beyond the Mean First-Passage Time. Polymers (Basel) 2019; 11:E251. [PMID: 30960235 PMCID: PMC6419016 DOI: 10.3390/polym11020251] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2018] [Revised: 01/22/2019] [Accepted: 01/25/2019] [Indexed: 01/27/2023] Open
Abstract
Polymer translocation across a corrugated channel is a paradigmatic stochastic process encountered in diverse systems. The instance of time when a polymer first arrives to some prescribed location defines an important characteristic time-scale for various phenomena, which are triggered or controlled by such an event. Here we discuss the translocation dynamics of a Gaussian polymer in a periodically-corrugated channel using an appropriately generalized Fick⁻Jacobs approach. Our main aim is to probe an effective broadness of the first-passage time distribution (FPTD), by determining the so-called coefficient of variation γ of the FPTD, defined as the ratio of the standard deviation versus the mean first-passage time (MFPT). We present a systematic analysis of γ as a function of a variety of system's parameters. We show that γ never significantly drops below 1 and, in fact, can attain very large values, implying that the MFPT alone cannot characterize the first-passage statistics of the translocation process exhaustively well.
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Affiliation(s)
- Paolo Malgaretti
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany.
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.
| | - Gleb Oshanin
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC (UMR CNRS 7600), 4 Place Jussieu, CEDEX 05, 75252 Paris, France.
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43
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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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44
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Iubini S, Orlandini E, Michieletto D, Baiesi M. Topological Sieving of Rings According to Their Rigidity. ACS Macro Lett 2018; 7:1408-1412. [PMID: 35651235 DOI: 10.1021/acsmacrolett.8b00719] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
We present a novel mechanism for resolving the mechanical rigidity of nanoscopic circular polymers that flow in a complex environment. The emergence of a regime of negative differential mobility induced by topological interactions between the rings and the substrate is the key mechanism for selective sieving of circular polymers with distinct flexibilities. A simple model accurately describes the sieving process observed in molecular dynamics simulations and yields experimentally verifiable analytical predictions, which can be used as a reference guide for improving filtration procedures of circular filaments. The topological sieving mechanism we propose ought to be relevant also in probing the microscopic details of complex substrates.
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Affiliation(s)
- Stefano Iubini
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Enzo Orlandini
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, U.K
| | - Marco Baiesi
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
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45
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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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46
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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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47
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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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48
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Affiliation(s)
- Iurii Chubak
- Faculty of Physics, University of Vienna, Vienna, Austria
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49
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Beaton NR, Eng JW, Ishihara K, Shimokawa K, Soteros CE. Characterising knotting properties of polymers in nanochannels. SOFT MATTER 2018; 14:5775-5785. [PMID: 29987298 DOI: 10.1039/c8sm00734a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Using a lattice model of polymers in a tube, we define one way to characterise different configurations of a given knot as either "local" or "non-local", based on a standard approach for measuring the "size" of a knot within a knotted polymer chain. The method involves associating knot-types to subarcs of the chain, and then identifying a knotted subarc with minimal arclength; this arclength is then the knot-size. If the resulting knot-size is small relative to the whole length of the chain, then the knot is considered to be localised or "local"; otherwise, it is "non-local". Using this definition, we establish that all but exponentially few sufficiently long self-avoiding polygons (closed chains) in a tubular sublattice of the simple cubic lattice are "non-locally" knotted. This is shown to also hold for the case when the same polygons are subject to an external tensile force, as well as in the extreme case when they are as compact as possible (no empty lattice sites). We also provide numerical evidence for small tube sizes that at equilibrium non-local knotting is more likely than local knotting, regardless of the strength of the stretching or compressing force. The relevance of these results to other models and recent experiments involving DNA knots is also discussed.
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Affiliation(s)
- N R Beaton
- School of Mathematics and Statistics, The University of Melbourne, Australia.
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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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