1
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Goto S, Kim K, Matubayasi N. Unraveling the Glass-like Dynamic Heterogeneity in Ring Polymer Melts: From Semiflexible to Stiff Chain. ACS POLYMERS AU 2023; 3:437-446. [PMID: 38107414 PMCID: PMC10722566 DOI: 10.1021/acspolymersau.3c00013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Revised: 08/08/2023] [Accepted: 08/08/2023] [Indexed: 12/19/2023]
Abstract
Ring polymers are an intriguing class of polymers with unique physical properties, and understanding their behavior is important for developing accurate theoretical models. In this study, we investigate the effect of chain stiffness and monomer density on the static and dynamic behaviors of ring polymer melts using molecular dynamics simulations. Our first focus is on the non-Gaussian parameter of center-of-mass displacement as a measure of dynamic heterogeneity, which is commonly observed in glass-forming liquids. We find that the non-Gaussianity in the displacement distribution increases with the monomer density and stiffness of the polymer chains, suggesting that excluded volume interactions between centers of mass have a strong effect on the dynamics of ring polymers. We then analyze the relationship between the radius of gyration and monomer density for semiflexible and stiff ring polymers. Our results indicate that the relationship between the two varies with chain stiffness, which can be attributed to the competition between repulsive forces inside the ring and from adjacent rings. Finally, we study the dynamics of bond-breakage virtually connected between the centers of mass of rings to analyze the exchanges of intermolecular networks of bonds. Our results demonstrate that the dynamic heterogeneity of bond-breakage is coupled with the non-Gaussianity in ring polymer melts, highlighting the importance of the bond-breaking method in determining the intermolecular dynamics of ring polymer melts. Overall, our study sheds light on the factors that govern the dynamic behaviors of ring polymers.
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Affiliation(s)
- Shota Goto
- Division of Chemical Engineering, Department
of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Kang Kim
- Division of Chemical Engineering, Department
of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Department
of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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2
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Galata AA, Kröger M. Globular Proteins and Where to Find Them within a Polymer Brush-A Case Study. Polymers (Basel) 2023; 15:polym15102407. [PMID: 37242983 DOI: 10.3390/polym15102407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Revised: 05/15/2023] [Accepted: 05/19/2023] [Indexed: 05/28/2023] Open
Abstract
Protein adsorption by polymerized surfaces is an interdisciplinary topic that has been approached in many ways, leading to a plethora of theoretical, numerical and experimental insight. There is a wide variety of models trying to accurately capture the essence of adsorption and its effect on the conformations of proteins and polymers. However, atomistic simulations are case-specific and computationally demanding. Here, we explore universal aspects of the dynamics of protein adsorption through a coarse-grained (CG) model, that allows us to explore the effects of various design parameters. To this end, we adopt the hydrophobic-polar (HP) model for proteins, place them uniformly at the upper bound of a CG polymer brush whose multibead-spring chains are tethered to a solid implicit wall. We find that the most crucial factor affecting the adsorption efficiency appears to be the polymer grafting density, while the size of the protein and its hydrophobicity ratio come also into play. We discuss the roles of ligands and attractive tethering surfaces to the primary adsorption as well as secondary and ternary adsorption in the presence of attractive (towards the hydrophilic part of the protein) beads along varying spots of the backbone of the polymer chains. The percentage and rate of adsorption, density profiles and the shapes of the proteins, alongside with the respective potential of mean force are recorded to compare the various scenarios during protein adsorption.
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Affiliation(s)
- Aikaterini A Galata
- Magnetism and Interface Physics, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Martin Kröger
- Magnetism and Interface Physics, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland
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3
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Conformational Behavior of Single Circular Semiflexible Polyelectrolyte in Presence of Multivalent Counterions. CHINESE JOURNAL OF POLYMER SCIENCE 2022. [DOI: 10.1007/s10118-022-2842-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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4
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Conformation and structure of ring polymers in semidilute solutions: A molecular dynamics simulation study. POLYMER 2022. [DOI: 10.1016/j.polymer.2022.124953] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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5
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Chiarantoni P, Micheletti C. Effect of Ring Rigidity on the Statics and Dynamics of Linear Catenanes. Macromolecules 2022. [DOI: 10.1021/acs.macromol.1c02542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Pietro Chiarantoni
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Cristian Micheletti
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
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6
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Mao DJ, Qin CR, Tian WD. Kick effect of enzymes causes filament compression. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:284003. [PMID: 35477158 DOI: 10.1088/1361-648x/ac6b09] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2021] [Accepted: 04/27/2022] [Indexed: 06/14/2023]
Abstract
We investigate the influence of enzymes on the structure and dynamics of a filament by dissipative particle dynamics simulations. Enzyme exerts a kick force on the filament monomer. We pay particular attention to two factors: the magnitude of kick force and enzyme concentration. Large kick force as well as high enzyme concentration prefers a remarkable compression of the filament reminiscent of the effective depletion interaction owing to an effective increase in enzyme size and the reduction of solvent quality. Additionally, the kick effect gives rise to an increase of enzyme density from the center-of-mass of the filament to its periphery. Moreover, the increase of enzyme concentration and kick force also causes a decrease in relaxation time. Our finding is helpful to understand the role of catalytic force in chemo-mechano-biological function and the filament behavior under chemical reaction via kick-induced change of solvent quality.
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Affiliation(s)
- Dan-Jian Mao
- Center for Soft Condensed Matter Physics & Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, People's Republic of China
| | - Chao-Ran Qin
- Center for Soft Condensed Matter Physics & Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, People's Republic of China
| | - Wen-de Tian
- Center for Soft Condensed Matter Physics & Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, People's Republic of China
- Department of Chemical Engineering, Macromolecular Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States of America
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7
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Abou‐Jaoude A, Goedde CG, Lichter S. Ring Homopolymers Prefer Crumpling into Odd‐Length Segments. MACROMOL THEOR SIMUL 2022. [DOI: 10.1002/mats.202200013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Alexander Abou‐Jaoude
- Energy Futures Lab Imperial College London London SW7 2BU UK
- Department of Mechanical Engineering Northwestern University Evanston Illinois 60208 USA
| | | | - Seth Lichter
- Energy Futures Lab Imperial College London London SW7 2BU UK
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8
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Chen W, Wei S. Compressive deformations of ring polymers in a confining channel. POLYMER 2021. [DOI: 10.1016/j.polymer.2021.124340] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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9
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Stochastic chromatin packing of 3D mitotic chromosomes revealed by coherent X-rays. Proc Natl Acad Sci U S A 2021; 118:2109921118. [PMID: 34750262 DOI: 10.1073/pnas.2109921118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/01/2021] [Indexed: 11/18/2022] Open
Abstract
DNA molecules are atomic-scale information storage molecules that promote reliable information transfer via fault-free repetitions of replications and transcriptions. Remarkable accuracy of compacting a few-meters-long DNA into a micrometer-scale object, and the reverse, makes the chromosome one of the most intriguing structures from both physical and biological viewpoints. However, its three-dimensional (3D) structure remains elusive with challenges in observing native structures of specimens at tens-of-nanometers resolution. Here, using cryogenic coherent X-ray diffraction imaging, we succeeded in obtaining nanoscale 3D structures of metaphase chromosomes that exhibited a random distribution of electron density without characteristics of high-order folding structures. Scaling analysis of the chromosomes, compared with a model structure having the same density profile as the experimental results, has discovered the fractal nature of density distributions. Quantitative 3D density maps, corroborated by molecular dynamics simulations, reveal that internal structures of chromosomes conform to diffusion-limited aggregation behavior, which indicates that 3D chromatin packing occurs via stochastic processes.
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10
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Zhu Y, Kumar PBS, Laradji M. Conformational behavior and self-assembly of disjoint semi-flexible ring polymers adsorbed on solid substrates. SOFT MATTER 2021; 17:5427-5435. [PMID: 33969850 DOI: 10.1039/d1sm00500f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The conformational behavior and spatial organization of self-avoiding semi-flexible ring polymers, that are fully adsorbed on solid substrates, are investigated via systematic coarse-grained molecular dynamics simulations. Our results show that both conformations and spatial organization of the polymers depend strongly on their bending stiffness, κ, and on their areal number density, ρ. For ρ < ρ*, where ρ* is the overlap density, and for low values of κ, thermal fluctuations lead to weakly anisotropic instantaneous conformations of the polymers. The interplay between thermal fluctuations and polymer stiffness leads to a non-monotonic dependence of the polymers elongation on κ with a maximum elongation at some intermediate κ. Regardless of κ, the polymers elongation is almost independent of ρ for ρ ⪅ ρ*, then increases with ρ. At ρ ≈ ρ* and high κ, the almost circularly-shaped polymers self-assemble into a triangular lattice with quasi-long range order. For ρ above ρ* and high κ, crowding of the polymers leads to their self-assembly into liquid-crystalline phases. In particular, for ρ moderately above ρ* and high κ, the polymer conformations are obround and self-assemble into domains with smectic-A-like order. At higher densities, the polymer have a biconcave geometry and self-assemble into domains with smectic-C-like order.
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Affiliation(s)
- Yu Zhu
- Department of Physics and Materials Science, The University of Memphis, Memphis, TN 38152, USA.
| | - P B Sunil Kumar
- Department of Physics, Indian Institute of Technology Palakkad, Palakkad-668557, Kerala, India
| | - Mohamed Laradji
- Department of Physics and Materials Science, The University of Memphis, Memphis, TN 38152, USA.
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11
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Hagita K, Murashima T. Effect of chain-penetration on ring shape for mixtures of rings and linear polymers. POLYMER 2021. [DOI: 10.1016/j.polymer.2021.123493] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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12
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Halun J, Karbowniczek P, Kuterba P, Danel Z. Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations. ENTROPY 2021; 23:e23020242. [PMID: 33669820 PMCID: PMC7922339 DOI: 10.3390/e23020242] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Revised: 02/06/2021] [Accepted: 02/08/2021] [Indexed: 12/03/2022]
Abstract
The calculations of the dimensionless layer monomer density profiles for a dilute solution of phantom ideal ring polymer chains and star polymers with f=4 arms in a Θ-solvent confined in a slit geometry of two parallel walls with repulsive surfaces and for the mixed case of one repulsive and the other inert surface were performed. Furthermore, taking into account the Derjaguin approximation, the dimensionless layer monomer density profiles for phantom ideal ring polymer chains and star polymers immersed in a solution of big colloidal particles with different adsorbing or repelling properties with respect to polymers were calculated. The density-force relation for the above-mentioned cases was analyzed, and the universal amplitude ratio B was obtained. Taking into account the small sphere expansion allowed obtaining the monomer density profiles for a dilute solution of phantom ideal ring polymers immersed in a solution of small spherical particles, or nano-particles of finite size, which are much smaller than the polymer size and the other characteristic mesoscopic length of the system. We performed molecular dynamics simulations of a dilute solution of linear, ring, and star-shaped polymers with N=300, 300 (360), and 1201 (4 × 300 + 1-star polymer with four arms) beads accordingly. The obtained analytical and numerical results for phantom ring and star polymers are compared with the results for linear polymer chains in confined geometries.
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Affiliation(s)
- Joanna Halun
- Institute of Nuclear Physics, Polish Academy of Sciences, 31-342 Cracow, Poland
- Correspondence:
| | - Pawel Karbowniczek
- Institute of Physics, Cracow University of Technology, 30-084 Cracow, Poland; (P.K.); (Z.D.)
| | - Piotr Kuterba
- Faculty of Physics, Astronomy and Applied Computer Sciences, Jagiellonian University in Cracow, 30-348 Cracow, Poland;
| | - Zoriana Danel
- Institute of Physics, Cracow University of Technology, 30-084 Cracow, Poland; (P.K.); (Z.D.)
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13
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14
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Zhang G, Zhang J. Topological catenation induced swelling of ring polymers revealed by molecular dynamics simulation. POLYMER 2020. [DOI: 10.1016/j.polymer.2020.122475] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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15
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Chen A, Zhang B, Zhao N. A comparative study of semi-flexible linear and ring polymer conformational change in an anisotropic environment. Phys Chem Chem Phys 2020; 22:9137-9147. [PMID: 32301953 DOI: 10.1039/c9cp07018d] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
We adopt a Langevin-dynamics based simulation to systematically study the conformational change of a semi-flexible probed polymer in a rod crowding environment. Two topologically different probed polymer types, linear and ring polymers, are specifically considered. Our results unravel the significance of the interplay of probed polymer's semi-flexibility and crowding anisotropy. Firstly, both ring and linear polymers show a non-trivial dimensional change including nonmonotonicity and collapse-swelling crossover as their stiffness increases. Secondly, we modulate rod crowder length to investigate the anisotropic effect. We reveal that the formation of an ordered parallel arrangement of the environment can effectively lead to a remarkable stretching effect on the probed polymer. The coupling between the crowding anisotropy-induced stretching and the polymer stiffness can account for the unusual swelling behavior. Lastly, nonmonotonic swelling and shape change of the ring polymer are analyzed. We find out that the ring polymer is subject to most pronounced swelling at robust stiffness. Moreover, the maximum prolate shape is also observed at the same robust location.
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Affiliation(s)
- Anpu Chen
- College of Chemistry, Sichuan University, Chengdu 610064, China.
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16
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Abstract
Unraveling the packing structure of dense assemblies of semiflexible rings is not only fundamental for the dynamical description of polymer rings, but also key to understand biopackaging, such as observed in circular DNA of viruses or genome folding. Here we use X-ray tomography to study the geometrical and topological features of disordered packings of rubber bands in a cylindrical container. Assemblies of short bands assume a liquid-like disordered structure, with short-range orientational order, and reveal only minor influence of the container. In the case of longer bands, the confinement causes folded configurations and the bands interpenetrate and entangle. Most of the systems are found to display a threading network which percolates the system. Surprisingly, for long bands whose diameter is more than twice the diameter of the container, we found that all bands interpenetrate each other, in a complex fully entangled structure.
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Affiliation(s)
- Leopoldo R Gómez
- Department of Physics, Universidad Nacional del Sur-IFISUR-CONICET, 8000 Bahía Blanca, Argentina;
| | | | - Thorsten Pöschel
- Institut für Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91052 Erlangen, Germany
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17
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Zhou X, Guo F, Li K, He L, Zhang L. Entropy-induced Separation of Binary Semiflexible Ring Polymer Mixtures in Spherical Confinement. Polymers (Basel) 2019; 11:E1992. [PMID: 31810347 PMCID: PMC6960585 DOI: 10.3390/polym11121992] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Revised: 11/24/2019] [Accepted: 11/27/2019] [Indexed: 11/25/2022] Open
Abstract
Coarse-grained molecular dynamics simulations are used to investigate the conformations of binary semiflexible ring polymers (SRPs) of two different lengths confined in a hard sphere. Segregated structures of SRPs in binary mixtures are strongly dependent upon the number density of system (ρ), the bending energy of long SRPs (Kb, long), and the chain length ratio of long to short SRPs (α). With a low ρ or a weak Kb, long at a small ratio α, long SRPs are immersed randomly in the matrix of short SRPs. As ρ and bending energy of long SRPs (Kb, long) are increased up to a certain value for a large ratio α, a nearly complete segregation between long and short SRPs is observed, which can be further characterized by the ratio of tangential and radial components of long SRPs velocity. These explicit segregated structures of the two components in spherical confinement are induced by a delicate competition between the entropic excluded volume (depletion) effects and bending contributions.
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Affiliation(s)
- Xiaolin Zhou
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China; (X.Z.); (F.G.); (K.L.)
| | - Fuchen Guo
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China; (X.Z.); (F.G.); (K.L.)
| | - Ke Li
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China; (X.Z.); (F.G.); (K.L.)
| | - Linli He
- Department of Physics, Wenzhou University, Wenzhou 325035, Zhejiang, China
| | - Linxi Zhang
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China; (X.Z.); (F.G.); (K.L.)
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18
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Walsh DJ, Dutta S, Sing CE, Guironnet D. Engineering of Molecular Geometry in Bottlebrush Polymers. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b00845] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
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19
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Zhou X, Li K, Guo F, Zhang L. Ordered aggregation structures of semiflexible ring polymers in ring-linear blends. POLYMER 2019. [DOI: 10.1016/j.polymer.2019.05.005] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
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20
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Dabrowski-Tumanski P, Gren B, Sulkowska JI. Statistical Properties of Lasso-Shape Polymers and Their Implications for Complex Lasso Proteins Function. Polymers (Basel) 2019; 11:E707. [PMID: 30999683 PMCID: PMC6523798 DOI: 10.3390/polym11040707] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Revised: 04/11/2019] [Accepted: 04/12/2019] [Indexed: 12/19/2022] Open
Abstract
The shape and properties of closed loops depend on various topological factors. One of them is loop-threading, which is present in complex lasso proteins. In this work, we analyze the probability of loop-threading by the tail and its influence on the shape of the loop measured by the radius of gyration, distention, asphericity, and prolateness. In particular, we show that the probability of a trivial lasso for phantom polymer is non-zero even for an infinite structure, as well as that the threading flattens the loop by restricting its motion in one dimension. These results are further used to show that there are fewer non-trivial protein lassos than expected and select potentially functional complex lasso proteins.
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Affiliation(s)
- Pawel Dabrowski-Tumanski
- Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland.
- Faculty of Chemistry, University of Warsaw, 02-093 Warsaw, Poland.
| | - Bartosz Gren
- Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland.
- Faculty of Physics, University of Warsaw, 02-093 Warsaw, Poland.
| | - Joanna I Sulkowska
- Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland.
- Faculty of Chemistry, University of Warsaw, 02-093 Warsaw, Poland.
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21
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Huang W, Zaburdaev V. The shape of pinned forced polymer loops. SOFT MATTER 2019; 15:1785-1792. [PMID: 30746544 DOI: 10.1039/c8sm02357c] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Loop geometry is a frequent encounter in synthetic and biological polymers. Here we provide an analytical theory to characterize the shapes of polymer loops subjected to an external force field. We show how to calculate the polymer density, gyration radius and its distribution. Interestingly, the distribution of the gyration radius shows a non-monotonic behavior as a function of the external force. Furthermore, we analyzed the gyration tensor of the polymer loop characterizing its overall shape. Two parameters called asphericity and the nature of asphericity derived from the gyration tensor, along with the gyration radius, can be used to quantify the shape of polymer loops in theory and experiments.
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Affiliation(s)
- Wenwen Huang
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany.
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22
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Zhou X, Liu L, Chen J, Zhang L. Unusual conformations of semiflexible ring polymers confined in two parallel surfaces. POLYMER 2018. [DOI: 10.1016/j.polymer.2018.10.039] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
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23
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Liu L, Chen J, An L. Individual circular polyelectrolytes under shear flow. J Chem Phys 2018; 149:163316. [PMID: 30384673 DOI: 10.1063/1.5028406] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Individual circular polyelectrolytes in simple shear flow are studied by means of mesoscale hydrodynamic simulations, revealing the complex coupling effects of shear rate, electrostatic interaction, and circular architecture on their conformational and dynamical properties. Shear flow deforms the polyelectrolyte and strips condensed counterions from its backbone. A decrease in condensed counterions alters electrostatic interactions among charged particles, affecting shear-induced polymer deformation and orientation. Circular architecture determines the features of deformation and orientation. At weak electrostatic interaction strengths, the polyelectrolyte changes its shape from an oblate ring at small shear rates to a prolate ring at large shear rates, whereas strong electrostatic interaction strengths are associated with a transition from a prolate coil to a prolate ring. Circular polyelectrolytes exhibit tumbling and tank-treading motions in the range of large shear rates. Further study reveals a similarity between the roles of intramolecular electrostatic repulsion and chain rigidity in shear-induced dynamics.
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Affiliation(s)
- Lijun Liu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People's Republic of China
| | - Jizhong Chen
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People's Republic of China
| | - Lijia An
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People's Republic of China
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24
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Liu L, Chen W, Chen J. Shape and Diffusion of Circular Polyelectrolytes in Salt-Free Dilute Solutions and Comparison with Linear Polyelectrolytes. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b00189] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Lijun Liu
- State Key Laboratory
of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, China
| | - Wenduo Chen
- State Key Laboratory
of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, China
| | - Jizhong Chen
- State Key Laboratory
of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, China
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25
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Sassi AS, Assenza S, De Los Rios P. Shape of a Stretched Polymer. PHYSICAL REVIEW LETTERS 2017; 119:037801. [PMID: 28777625 DOI: 10.1103/physrevlett.119.037801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2015] [Indexed: 06/07/2023]
Abstract
The shape of a polymer plays an important role in its interactions with surrounding molecules. We characterize the shape and the orientational properties of a polymer chain under tension in a good solvent, a physical condition that is often realized both in single-molecule experiments and in vivo. Our findings reveal the existence of hitherto unobserved universal laws encompassing polymers with different rigidities and including the possible presence of excluded-volume effects, showing that both shape and orientation are solely determined by the force contribution to the free energy. In doing so, they also provide a simple way to retrieve these quantities from the knowledge of the force-versus-extension curve.
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Affiliation(s)
- Alberto S Sassi
- Laboratoire de Biophysique Statistique, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Salvatore Assenza
- Laboratoire de Biophysique Statistique, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Paolo De Los Rios
- Laboratoire de Biophysique Statistique, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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26
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Chen W, Zhang K, Liu L, Chen J, Li Y, An L. Conformation and Dynamics of Individual Star in Shear Flow and Comparison with Linear and Ring Polymers. Macromolecules 2017. [DOI: 10.1021/acs.macromol.6b02636] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
| | - Kexin Zhang
- School
of Environmental Science, Northeast Normal University, 5268 Renmin
Street, Changchun, P. R. China 130024
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27
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Coil-helix-globule transition for self-attractive semiflexible ring chains. POLYMER 2017. [DOI: 10.1016/j.polymer.2016.12.075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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28
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Deng Z, Jiang Y, He L, Zhang L. Aggregation–Dispersion Transition for Nanoparticles in Semiflexible Ring Polymer Nanocomposite Melts. J Phys Chem B 2016; 120:11574-11581. [DOI: 10.1021/acs.jpcb.6b07292] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Zhenyu Deng
- Department
of Physics, Zhejiang University, Hangzhou 310027, China
| | - Yangwei Jiang
- Department
of Physics, Zhejiang University, Hangzhou 310027, China
| | - Linli He
- Department
of Physics, Wenzhou University, Wenzhou 325027, China
| | - Linxi Zhang
- Department
of Physics, Zhejiang University, Hangzhou 310027, China
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29
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Benková Z, Námer P, Cifra P. Comparison of a stripe and slab confinement for ring and linear macromolecules in nanochannel. SOFT MATTER 2016; 12:8425-8439. [PMID: 27722460 DOI: 10.1039/c6sm01507g] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The combined effects of the channel asymmetry and the closed chain topology on the chain extension, structure factor, and the orientation correlations were studied using coarse-grained molecular dynamics simulations for moderate chain lengths. These effects are related to applications in linearization experiments with a DNA molecule in nanofluidic devices. According to the aspect ratio, the channels are classified as a stripe or slabs. The chain segments do not have any freedom to move in the direction of the narrowest stripe size, being approximately the same size as the segment size. The chains of both ring and linear topologies are extended more in a stripe than in a slab; this effect is strengthened for a ring. For a ring in a stripe, the extension-confinement strength dependence leads to effective Flory exponents even larger than 3/4, which is characteristic for a self-avoiding two-dimensional chain. While the chain extension-confinement strength dependence for both topologies conforms to the de Gennes regime in a stripe, a linear chain undergoes gradual transition to the pseudoideal regime as the slab height increases in the slab-like confinement. For a confined circle, the onset of the pseudoideal regime is shifted to larger slab heights. The structure factor confirms the absence of the pseudoideal and extended de Gennes regime in a stripe and the transition from the extended to the pseudoideal regime of a circular and linear chain upon increasing the slab heights.
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Affiliation(s)
- Zuzana Benková
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia. and LAQV@REQUIMTE, Department of Chemistry and Biochemistry, Faculty of Sciences, University of Porto, Rua do Campo Alegre 687, 4168-007 Porto, Portugal
| | - Pavol Námer
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia.
| | - Peter Cifra
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia.
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30
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Abstract
We present an exact solution for the distribution of sample averaged monomer to monomer distance of ring polymers. For non-interacting and local-interaction models these distributions correspond to the distribution of the area under the reflected Bessel bridge and the Bessel excursion respectively, and are shown to be identical in dimension d ≥ 2, albeit with pronounced finite size effects at the critical dimension, d = 2. A symmetry of the problem reveals that dimension d and 4 - d are equivalent, thus the celebrated Airy distribution describing the areal distribution of the d = 1 Brownian excursion describes also a polymer in three dimensions. For a self-avoiding polymer in dimension d we find numerically that the fluctuations of the scaled averaged distance are nearly identical in dimension d = 2, 3 and are well described to a first approximation by the non-interacting excursion model in dimension 5.
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31
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Horner KE, Miller MA, Steed JW, Sutcliffe PM. Knot theory in modern chemistry. Chem Soc Rev 2016; 45:6432-6448. [DOI: 10.1039/c6cs00448b] [Citation(s) in RCA: 61] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
This tutorial review provides an introduction to the mathematics of knots and topological concepts in the context of the chemical sciences.
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Affiliation(s)
- Kate E. Horner
- SPOCK Group
- Department of Mathematical Sciences
- Durham University
- Durham
- UK
| | | | | | - Paul M. Sutcliffe
- SPOCK Group
- Department of Mathematical Sciences
- Durham University
- Durham
- UK
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32
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Haydukivska K, Blavatska V. Ring polymers in crowded environment: conformational properties. J Chem Phys 2014; 141:094906. [PMID: 25194393 DOI: 10.1063/1.4894278] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
We analyze the universal size characteristics of flexible ring polymers in solutions in presence of structural obstacles (impurities) in d dimensions. One encounters such situations when considering polymers in gels, colloidal solutions, intra- and extracellular environments. A special case of extended impurities correlated on large distances r according to a power law ~r(-a) is considered. Applying the direct polymer renormalization scheme, we evaluate the estimates for averaged gyration radius ⟨R(g ring)⟩ and spanning radius ⟨R(1/2 ring)⟩ of typical ring polymer conformation up to the first order of double ɛ = 4 - d, δ = 4 - a expansion. Our results quantitatively reveal an extent of the effective size and anisotropy of closed ring macromolecules in disordered environment. In particular, the size ratio of ring and open (linear) polymers of the same molecular weight grows when increasing the strength of disorder according to ⟨R(g ring)(2)⟩/⟨R(g chain)(2)⟩=½(1+(13/48)δ).
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Affiliation(s)
- K Haydukivska
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine
| | - V Blavatska
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine
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33
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Polanowski P, Jeszka JK, Sikorski A. Dynamic Properties of Linear and Cyclic Chains in Two Dimensions. Computer Simulation Studies. Macromolecules 2014. [DOI: 10.1021/ma500460b] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | | | - Andrzej Sikorski
- Department
of Chemistry, University of Warsaw, Pasteura 1, 02-093, Warsaw, Poland
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34
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Dolgushev M, Guérin T, Blumen A, Bénichou O, Voituriez R. Gaussian semiflexible rings under angular and dihedral restrictions. J Chem Phys 2014; 141:014901. [PMID: 25005305 DOI: 10.1063/1.4885445] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
Semiflexible polymer rings whose bonds obey both angular and dihedral restrictions [M. Dolgushev and A. Blumen, J. Chem. Phys. 138, 204902 (2013)], are treated under exact closure constraints. This allows us to obtain semianalytic results for their dynamics, based on sets of Langevin equations. The dihedral restrictions clearly manifest themselves in the behavior of the mean-square monomer displacement. The determination of the equilibrium ring conformations shows that the dihedral constraints influence the ring curvature, leading to compact folded structures. The method for imposing such constraints in Gaussian systems is very general and it allows to account for heterogeneous (site-dependent) restrictions. We show it by considering rings in which one site differs from the others.
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Affiliation(s)
- Maxim Dolgushev
- Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Thomas Guérin
- Laboratoire de Physique Théorique de la Matière Condensée, Centre National de la Recherche Scientifique, Université Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France
| | - Alexander Blumen
- Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Olivier Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, Centre National de la Recherche Scientifique, Université Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France
| | - Raphaël Voituriez
- Laboratoire de Physique Théorique de la Matière Condensée, Centre National de la Recherche Scientifique, Université Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France
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35
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Lang PS, Obermayer B, Frey E. Dynamics of a semiflexible polymer or polymer ring in shear flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022606. [PMID: 25353501 DOI: 10.1103/physreve.89.022606] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2013] [Indexed: 06/04/2023]
Abstract
Polymers exposed to shear flow exhibit a remarkably rich tumbling dynamics. While rigid rods rotate on Jeffery orbits, a flexible polymer stretches and coils up during tumbling. Theoretical results show that in both of these asymptotic regimes the corresponding tumbling frequency f(c) in a linear shear flow of strength γ scales as a power law Wi(2/3) in the Weissenberg number Wi = γτ, where τ is a characteristic time of the polymer's relaxational dynamics. For a flexible polymer these theoretical results are well confirmed by a large body of experimental single molecule studies. However, for the intermediate semiflexible regime, especially relevant for cytoskeletal filaments like F-actin and microtubules, the situation is less clear. While recent experiments on single F-actin filaments are still interpreted within the classical Wi(2/3) scaling law, theoretical results indicated deviations from it. Here we perform extensive Brownian dynamics simulations to explore the tumbling dynamics of semiflexible polymers over a broad range of shear strength and the polymer's persistence length l(p). We find that the Weissenberg number alone does not suffice to fully characterize the tumbling dynamics, and the classical scaling law breaks down. Instead, both the polymer's stiffness and the shear rate are relevant control parameters. Based on our Brownian dynamics simulations we postulate that in the parameter range most relevant for cytoskeletal filaments there is a distinct scaling behavior with f(c) τ* = Wi(3/4)f(c)(x) with Wi = γτ* and the scaling variable x = (l(p)/L)(Wi)(-1/3); here τ* is the time the polymer's center of mass requires to diffuse its own contour length L. Comparing these results with experimental data on F-actin we find that the Wi(3/4) scaling law agrees quantitatively significantly better with the data than the classical Wi(2/3) law. Finally, we extend our results to single ring polymers in shear flow, and find similar results as for linear polymers with slightly different power laws.
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Affiliation(s)
- Philipp S Lang
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany and Nanosystems Initiative Munich (NIM), Ludwig-Maximilians-Universität München, Schellingstraße 4, D-80333 Munich, Germany
| | - Benedikt Obermayer
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany
| | - Erwin Frey
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany and Nanosystems Initiative Munich (NIM), Ludwig-Maximilians-Universität München, Schellingstraße 4, D-80333 Munich, Germany
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36
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Santalla SN, Rodríguez-Laguna J, Cuerno R. Circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:010401. [PMID: 24580156 DOI: 10.1103/physreve.89.010401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2013] [Indexed: 06/03/2023]
Abstract
We consider the Kardar-Parisi-Zhang equation for a circular interface in two dimensions, unconstrained by the standard small-slope and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate the complete time evolution as a crossover between a short-time regime with the interface fluctuations of a self-avoiding ring or two-dimensional vesicle, and a long-time regime governed by the Tracy-Widom distribution expected for this geometry. For small-noise amplitudes, scaling behavior is only of the latter type. Large noise is also seen to renormalize the bare physical parameters of the ring, akin to analogous parameter renormalization for equilibrium three-dimensional membranes. Our results bear particular importance on the relation between relevant universality classes of scale-invariant systems in two dimensions.
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Affiliation(s)
- Silvia N Santalla
- Departamento de Física and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Carlos III de Madrid, Leganés, Spain
| | - Javier Rodríguez-Laguna
- ICFO-Institut de Ciències Fotòniques, Castelldefels, Spain and Departamento de Matemáticas and GISC, Universidad Carlos III de Madrid, Leganés, Spain
| | - Rodolfo Cuerno
- Departamento de Matemáticas and GISC, Universidad Carlos III de Madrid, Leganés, Spain
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37
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Bohr J, Olsen KW. Total positive curvature of circular DNA. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052714. [PMID: 24329303 DOI: 10.1103/physreve.88.052714] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2013] [Revised: 08/15/2013] [Indexed: 06/03/2023]
Abstract
The properties of double-stranded DNA and other chiral molecules depend on the local geometry, i.e., on curvature and torsion, yet the paths of closed chain molecules are globally restricted by topology. When both of these characteristics are to be incorporated in the description of circular chain molecules, e.g., plasmids, it is shown to have implications for the total positive curvature integral. For small circular micro-DNAs it follows as a consequence of Fenchel's inequality that there must exist a minimum length for the circular plasmids to be double stranded. It also follows that all circular micro-DNAs longer than the minimum length must be concave, a result that is consistent with typical atomic force microscopy images of plasmids. Predictions for the total positive curvature of circular micro-DNAs are given as a function of length, and comparisons with circular DNAs from the literature are presented.
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Affiliation(s)
- Jakob Bohr
- DTU Nanotech, Building 345Ø, Ørsteds Plads, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
| | - Kasper W Olsen
- DTU Nanotech, Building 345Ø, Ørsteds Plads, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
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38
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Chen W, Chen J, Liu L, Xu X, An L. Effects of Chain Stiffness on Conformational and Dynamical Properties of Individual Ring Polymers in Shear Flow. Macromolecules 2013. [DOI: 10.1021/ma401137c] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Wenduo Chen
- State Key Laboratory of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Jizhong Chen
- State Key Laboratory of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Lijun Liu
- State Key Laboratory of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Xiaolei Xu
- State Key Laboratory of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Lijia An
- State Key Laboratory of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
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39
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The collapse of polyethylene rings on an attractive surface. CHINESE JOURNAL OF POLYMER SCIENCE 2013. [DOI: 10.1007/s10118-013-1307-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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40
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Reiss P, Fritsche M, Heermann DW. Looped star polymers show conformational transition from spherical to flat toroidal shapes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:051910. [PMID: 22181447 DOI: 10.1103/physreve.84.051910] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2011] [Revised: 11/02/2011] [Indexed: 05/31/2023]
Abstract
Inspired by the topological organization of the circular Escherichia coli chromosome, which is compacted by separate domains, we study a polymer architecture consisting of a central ring to which either looped or linear side chains are grafted. A shape change from a spherical to a toroidal organization takes place as soon as the inner ring becomes large enough for the attached arms to fit within its circumference. Building up a torus, the system flattens, depending on the effective bending rigidity of the chain induced by entropic repulsion of the attached loops and, to a lesser extent, linear arms. Our results suggest that the natural formation of a toroidal structure with a decreased amount of writhe induced by a specific underlying topology could be one driving force, among others, that nature exploits to ensure proper packaging of the genetic material within a rod-shaped, bacterial envelope.
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Affiliation(s)
- Pascal Reiss
- Institute for Theoretical Physics, University of Heidelberg, Heidelberg, Germany
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41
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Tubiana L, Orlandini E, Micheletti C. Multiscale entanglement in ring polymers under spherical confinement. PHYSICAL REVIEW LETTERS 2011; 107:188302. [PMID: 22107680 DOI: 10.1103/physrevlett.107.188302] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2011] [Revised: 08/23/2011] [Indexed: 05/31/2023]
Abstract
The interplay of geometrical and topological entanglement in semiflexible knotted polymer rings confined inside a spherical cavity is investigated by using advanced numerical methods. By using stringent and robust algorithms for locating knots, we characterize how the knot length l(k) depends on the ring contour length L(c) and the radius of the confining sphere R(c). In the no- and strong-confinement cases, we observe weak knot localization and complete knot delocalization, respectively. We show that the complex interplay of l(k), L(c), and R(c) that seamlessly bridges these two limits can be encompassed by a simple scaling argument based on deflection theory. The same argument is used to rationalize the multiscale character of the entanglement that emerges with increasing confinement.
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42
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Rosa A, Orlandini E, Tubiana L, Micheletti C. Structure and Dynamics of Ring Polymers: Entanglement Effects Because of Solution Density and Ring Topology. Macromolecules 2011. [DOI: 10.1021/ma201827f] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Affiliation(s)
- Angelo Rosa
- SISSA, Scuola Internazionale Superiore di Studi Avanzati and IIT, Italian Institute of Technology (SISSA unit), Via Bonomea 265, 34136 Trieste, Italy
| | - Enzo Orlandini
- Dipartimento di Fisica and Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - Luca Tubiana
- SISSA, Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
| | - Cristian Micheletti
- SISSA, Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
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43
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Dolgushev M, Berezovska G, Blumen A. Maximum entropy principle applied to semiflexible ring polymers. J Chem Phys 2011; 135:094901. [PMID: 21913779 DOI: 10.1063/1.3631943] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on the success of the maximum entropy principle (MEP) in the study of semiflexible treelike polymers [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)], it is of much interest to establish MEP's potential for general semiflexible polymers which contain loops. Here, we embark on this endeavor by considering discrete semiflexible polymer rings in a Rouse-type scheme. Now, for treelike polymers a beads-and-bonds (i.e., a discrete) picture is essential for an easy inclusion of branching points. Moreover, one may envisage (similar to our former work [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)]) to impose for each angle between two bonds a distinct stiffness condition. Working in this way leads already for a polymer ring to a complicated problem. Hence, we follow a reduced variational approach as applied earlier to polymer chains, in which a single Lagrange multiplier is used for each set of identical conditions imposed on topologically equivalent bonds and bonds' orientations. In this way, we obtain for the discrete ring an analytically closed form which involves Chebyshev polynomials. This expression turns out to lead to a series of solutions: Apart from the regular solution, several other solutions appear. One may be tempted to discard the other solutions, since for them the potential energy matrix is not positive definite. A more careful analysis based on topological features suggests, however, that such solutions can be assigned to rings displaying knots. Monte Carlo simulations which take excluded volume interactions into account agree with our interpretation.
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Affiliation(s)
- Maxim Dolgushev
- Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany.
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44
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Hadizadeh S, Linhananta A, Plotkin SS. Improved Measures for the Shape of a Disordered Polymer To Test a Mean-Field Theory of Collapse. Macromolecules 2011. [DOI: 10.1021/ma200454e] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Shirin Hadizadeh
- Department of Physics and Astronomy, University of British Columbia, Vancouver, Canada
| | | | - Steven S. Plotkin
- Department of Physics and Astronomy, University of British Columbia, Vancouver, Canada
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45
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Witz G, Rechendorff K, Adamcik J, Dietler G. Conformation of ring polymers in 2D constrained environments. PHYSICAL REVIEW LETTERS 2011; 106:248301. [PMID: 21770605 DOI: 10.1103/physrevlett.106.248301] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2010] [Indexed: 05/31/2023]
Abstract
The combination of ring closure and spatial constraints has a fundamental effect on the statistics of semiflexible polymers such as DNA. However, studies of the interplay between circularity and constraints are scarce and single-molecule experimental data concerning polymer conformations are missing. By means of atomic force microscopy we probe the conformation of circular DNA molecules in two dimensions and in the concentrated regime (above the overlap concentration c*). Molecules in this regime experience a collapse, and their statistical properties agree very well with those of simulated vesicles under pressure. Some circular molecules also create confining regions in which other molecules are trapped. Thus we show further that spatially confined molecules fold into specific conformations close to those found for linear chains, and strongly dependent on the size of the confining box.
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Affiliation(s)
- G Witz
- Laboratoire de Physique de la Matière Vivante, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
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46
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Benková Z, Cifra P. Stiffening Transition in Semiflexible Cyclic Macromolecules. MACROMOL THEOR SIMUL 2010. [DOI: 10.1002/mats.201000047] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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47
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Ostermeir K, Alim K, Frey E. Buckling of stiff polymer rings in weak spherical confinement. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010. [PMID: 20866431 DOI: 10.1039/c0sm00290a] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nanobiomaterials. We investigate the conformations of a semiflexible polymer ring in weak spherical confinement imposed by an impenetrable shell. We develop an analytic argument for the dominating polymer trajectory depending on polymer flexibility considering elastic and entropic contributions. Monte Carlo simulations are performed to assess polymer ring conformations in probability densities and by the shape measures asphericity and nature of asphericity. Comparison of the analytic argument with the mean asphericity and the mean nature of asphericity confirm our reasoning to explain polymer ring conformations in the stiff regime, where elastic response prevails.
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Affiliation(s)
- Katja Ostermeir
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
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48
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Ostermeir K, Alim K, Frey E. Buckling of stiff polymer rings in weak spherical confinement. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:061802. [PMID: 20866431 DOI: 10.1103/physreve.81.061802] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2010] [Indexed: 05/29/2023]
Abstract
Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nanobiomaterials. We investigate the conformations of a semiflexible polymer ring in weak spherical confinement imposed by an impenetrable shell. We develop an analytic argument for the dominating polymer trajectory depending on polymer flexibility considering elastic and entropic contributions. Monte Carlo simulations are performed to assess polymer ring conformations in probability densities and by the shape measures asphericity and nature of asphericity. Comparison of the analytic argument with the mean asphericity and the mean nature of asphericity confirm our reasoning to explain polymer ring conformations in the stiff regime, where elastic response prevails.
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Affiliation(s)
- Katja Ostermeir
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
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49
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Drube F, Alim K, Witz G, Dietler G, Frey E. Excluded volume effects on semiflexible ring polymers. NANO LETTERS 2010; 10:1445-1449. [PMID: 20235507 DOI: 10.1021/nl1003575] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Two-dimensional semiflexible polymer rings are studied both by imaging circular DNA adsorbed on a mica surface and by Monte Carlo simulations of phantom polymers as well as of polymers with finite thickness. Comparison of size and shape of the different models over the full range of flexibilities shows that excluded volume caused by finite thickness induces an anisotropic increase of the main axes of the conformations, a change of shape, accomplished by an enhanced correlation along the contour.
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Affiliation(s)
- Fabian Drube
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, München, Germany
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Sanchez T, Kulic IM, Dogic Z. Circularization, photomechanical switching, and a supercoiling transition of actin filaments. PHYSICAL REVIEW LETTERS 2010; 104:098103. [PMID: 20367015 DOI: 10.1103/physrevlett.104.098103] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2009] [Indexed: 05/29/2023]
Abstract
We confine actin filaments onto a 2D surface using depletion interactions and show that this significantly increases the probability of intramolecular circularization. Quantitative analysis reveals that the resulting semiflexible rings fluctuate significantly less then their linear counterparts with equal stiffness-an effect induced by the constraint of circular geometry. When exposed to fluorescence excitation light, rhodamine-phalloidin-labeled filaments undergo a change in their natural twist. This photomechanical transition induces a localized small-wavelength supercoiling transition of absorbed actin rings. Upon completion of the photoinduced reaction, the twist of neighboring monomers in an actin filament changes by approximately 0.26 degrees .
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Affiliation(s)
- T Sanchez
- Department of Physics, Brandeis University, Waltham, Massachusetts 02454, USA
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