1
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Andersen NT, Chen JZY. Forced extension of a wormlike chain in the Gibbs and Helmholtz ensembles. J Chem Phys 2024; 160:084903. [PMID: 38385518 DOI: 10.1063/5.0191727] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2023] [Accepted: 01/29/2024] [Indexed: 02/23/2024] Open
Abstract
A semiflexible polymer can be stretched by either applying a force to it or by fixing the positions of its endpoints. The two approaches generally yield different results and correspond to experiments performed in either the Gibbs or Helmholtz statistical ensembles. Here, we derive the Helmholtz force-extension relationship for the commonly used wormlike-chain model in the strongly stretched regime. By analyzing it in comparison with the Gibbs ensemble result, we show that equivalence between the two relationships is achieved only in the long-chain thermodynamic limit.
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Affiliation(s)
- Nigel T Andersen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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2
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Morrison G, Thirumalai D. Scaling regimes for wormlike chains confined to cylindrical surfaces under tension. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2024; 47:6. [PMID: 38252375 DOI: 10.1140/epje/s10189-023-00384-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2023] [Accepted: 11/20/2023] [Indexed: 01/23/2024]
Abstract
We compute the free energy of confinement [Formula: see text] for a wormlike chain (WLC), with persistence length [Formula: see text], that is confined to the surface of a cylinder of radius R under an external tension f using a mean field variational approach. For long chains, we analytically determine the behavior of the chain in a variety of regimes, which are demarcated by the interplay of [Formula: see text], the Odijk deflection length ([Formula: see text]), and the Pincus length ([Formula: see text], with [Formula: see text] being the thermal energy). The theory accurately reproduces the Odijk scaling for strongly confined chains at [Formula: see text], with [Formula: see text]. For moderate values of f, the Odijk scaling is discernible only when [Formula: see text] for strongly confined chains. Confinement does not significantly alter the scaling of the mean extension for sufficiently high tension. The theory is used to estimate unwrapping forces for DNA from nucleosomes.
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Affiliation(s)
- Greg Morrison
- Department of Physics, University of Houston, Houston, TX, 77204, USA
- Center for Theoretical Biological Physics, Rice University, Houston, TX, 77005, USA
| | - D Thirumalai
- Departments of Chemistry, The University of Texas at Austin, Austin, TX, 78712, USA.
- Department of Physics, The University of Texas at Austin, Austin, TX, 78712, USA.
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3
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Sanganna Gari RR, Tagiltsev G, Pumroy RA, Jiang Y, Blackledge M, Moiseenkova-Bell VY, Scheuring S. Intrinsically disordered regions in TRPV2 mediate protein-protein interactions. Commun Biol 2023; 6:966. [PMID: 37736816 PMCID: PMC10516966 DOI: 10.1038/s42003-023-05343-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2023] [Accepted: 09/11/2023] [Indexed: 09/23/2023] Open
Abstract
Transient receptor potential (TRP) ion channels are gated by diverse intra- and extracellular stimuli leading to cation inflow (Na+, Ca2+) regulating many cellular processes and initiating organismic somatosensation. Structures of most TRP channels have been solved. However, structural and sequence analysis showed that ~30% of the TRP channel sequences, mainly the N- and C-termini, are intrinsically disordered regions (IDRs). Unfortunately, very little is known about IDR 'structure', dynamics and function, though it has been shown that they are essential for native channel function. Here, we imaged TRPV2 channels in membranes using high-speed atomic force microscopy (HS-AFM). The dynamic single molecule imaging capability of HS-AFM allowed us to visualize IDRs and revealed that N-terminal IDRs were involved in intermolecular interactions. Our work provides evidence about the 'structure' of the TRPV2 IDRs, and that the IDRs may mediate protein-protein interactions.
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Affiliation(s)
| | - Grigory Tagiltsev
- Department of Anesthesiology, Weill Cornell Medicine, 1300 York Avenue, New York, NY, 10065, USA
| | - Ruth A Pumroy
- Department of Systems Pharmacology and Translational Therapeutics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, 19104, USA
- Institute of Structural Biology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, 19104, USA
| | - Yining Jiang
- Department of Anesthesiology, Weill Cornell Medicine, 1300 York Avenue, New York, NY, 10065, USA
- Biochemistry & Structural Biology, Cell & Developmental Biology, and Molecular Biology (BCMB) Program, Weill Cornell Graduate School of Biomedical Sciences, New York, USA
| | - Martin Blackledge
- Université Grenoble Alpes, Centre National de la Recherche Scientifique (CNRS), Commissariat à l'Énergie Atomique et aux Énergies Alternatives (CEA), Institut de Biologie Structurale (IBS), 38000, Grenoble, France
| | - Vera Y Moiseenkova-Bell
- Department of Systems Pharmacology and Translational Therapeutics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, 19104, USA
- Institute of Structural Biology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, 19104, USA
| | - Simon Scheuring
- Department of Anesthesiology, Weill Cornell Medicine, 1300 York Avenue, New York, NY, 10065, USA.
- Department of Physiology and Biophysics, Weill Cornell Medicine, 1300 York Avenue, New York, NY, 10065, USA.
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4
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Gómez LR, García NA, Pöschel T. Macroscopic analogue to entangled polymers. SOFT MATTER 2023; 19:3538-3542. [PMID: 37114347 DOI: 10.1039/d3sm00148b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
The entangled structure of polymeric materials is often described as resembling a bowl of spaghetti, swarms of earthworms, or snakes. These analogies not only illustrate the concept, but form the foundation of polymer physics. However, the similarity between these macroscopic, athermal systems and polymers in terms of topology remains uncertain. To better understand this relationship, we conducted an experiment using X-ray tomography to study the structure of arrays of linear rubber bands. We found that, similar to linear polymers, the average number of entanglements increases linearly with the length of the ribbons. Additionally, we observed that entanglements are less frequent near the surface of the container, where there are also more ends, similar to what has been seen in trapped polymers. These findings provide the first experimental evidence supporting the visualization of polymer structures using macroscopic, athermal analogues, confirming the initial intuitive insights of the pioneers of polymer physics.
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Affiliation(s)
- Leopoldo R Gómez
- Institut für Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91052, Erlangen, Germany.
- Department of Physics, Universidad Nacional del Sur - IFISUR - CONICET, Bahía Blanca 8000, Argentina
| | - Nicolás A García
- Department of Physics, Universidad Nacional del Sur - IFISUR - CONICET, Bahía Blanca 8000, Argentina
- Institut Laue-Langevin, 71 Avenue des Martyrs, Grenoble 38042, France
| | - Thorsten Pöschel
- Institut für Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91052, Erlangen, Germany.
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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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Chen M, Chen Y, Zhu Y, Jiang Y, Andelman D, Man X. Chain Flexibility Effects on the Self-Assembly of Diblock Copolymer in Thin Films. Macromolecules 2023. [DOI: 10.1021/acs.macromol.2c02292] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
Affiliation(s)
- Mingyang Chen
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
- School of Physics, Beihang University, Beijing 100191, China
| | - Yuguo Chen
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
- School of Chemistry, Beihang University, Beijing 100191, China
| | - Yanyan Zhu
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
- School of Physics, Beihang University, Beijing 100191, China
| | - Ying Jiang
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
- School of Chemistry, Beihang University, Beijing 100191, China
| | - David Andelman
- School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel
| | - Xingkun Man
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
- School of Physics, Beihang University, Beijing 100191, China
- Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China
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7
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Martens CM, Tuinier R, Vis M. Depletion interaction mediated by semiflexible polymers. J Chem Phys 2022; 157:154102. [PMID: 36272806 DOI: 10.1063/5.0112015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present a simple mean-field theory to describe the polymer-mediated depletion attraction between colloidal particles that accounts for the polymer's chain stiffness. We find that for fixed polymer radius of gyration and volume fraction, the strength of this attraction increases with increasing chain stiffness in both dilute and semidilute concentration regimes. In contrast, the range of attraction monotonically decreases with chain stiffness in the dilute regime, while it attains a maximum in the semidilute regime. The obtained analytical expressions for the depletion interaction were compared with numerical self-consistent field lattice computations and shown to be in quantitative agreement. From the interaction potential between two spheres, we calculated the second osmotic virial coefficient B2, which appears to be a convex function of chain stiffness. A minimum of B2 as a function of chain stiffness was observed both in the numerical self-consistent field computations and the analytical theory. These findings help explain the general observation that semiflexible polymers are more effective depletants than flexible polymers and give insight into the phase behavior of mixtures containing spherical colloids and semiflexible polymers.
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Affiliation(s)
- C M Martens
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - R Tuinier
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - M Vis
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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8
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Taylor MP. Confinement free energy for a polymer chain: Corrections to scaling. J Chem Phys 2022; 157:094902. [PMID: 36075705 DOI: 10.1063/5.0105142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Spatial confinement of a polymer chain results in a reduction of conformational entropy. For confinement of a flexible N-mer chain in a planar slit or cylindrical pore (confining dimension D), a blob model analysis predicts the asymptotic scaling behavior ΔF/N ∼ D-γ with γ ≈ 1.70, where ΔF is the free energy increase due to confinement. Here, we extend this scaling analysis to include the variation of local monomer density upon confinement giving ΔF/N ∼ D-γ(1 - h(N, D)), where the correction-to-scaling term has the form h ∼ Dy/NΔ with exponents y = 3 - γ ≈ 1.30 and Δ = 3/γ - 1 ≈ 0.76. To test these scaling predictions, we carry out Wang-Landau simulations of confined and unconfined tangent-hard-sphere chains (bead diameter σ) in the presence of a square-well trapping potential. The fully trapped chain provides a common reference state, allowing for an absolute determination of the confinement free energy. Our simulation results for 32 ≤ N ≤ 1024 and 3 ≤ D/σ ≤ 14 are well-described by the extended scaling relation giving exponents of γ = 1.69(1), y = 1.25(2), and Δ = 0.75(6).
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Affiliation(s)
- Mark P Taylor
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
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9
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Milchev A, Binder K. Surface enrichment and interdiffusion in blends of semiflexible polymers of different stiffness. SOFT MATTER 2022; 18:3781-3792. [PMID: 35514321 DOI: 10.1039/d2sm00036a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
A model for a mixture of two kinds of semiflexible polymers (A and B) with the same chain length (NA = NB = 32), but different persistence lengths, confined between parallel planar repulsive walls in a common good solvent is studied by molecular dynamics simulations. In the isotropic phase at low polymer concentrations, both polymers are repelled by the walls, and the system is anisotropic near the walls over a range controlled by the polymer linear dimensions. Close to the concentrations where in the bulk nematic order sets in, precursors of thick nematic layers at the walls are observed, strongly enriched by a stiffer component, which hence is depleted in the center of the slit pore. At larger concentrations, where in the bulk a uniformly mixed nematic phase occurs, the enrichment of B-chains at the walls is rather minor, extending over the scale of the transverse correlation length of concentration fluctuations, which is of the order of a few monomeric diameters only for the present model. In this ordered phase, both self-diffusion and interdiffusion of chains (in the direction perpendicular to the director) are found to be significantly slowed down in comparison to dilute solutions. Since equilibration times scale with the square of the slit thickness, incomplete equilibration is predicted when polymeric coatings on substrate containing polymers differing in stiffness are produced.
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Affiliation(s)
- Andrey Milchev
- Institute for Physical Chemistry, Bulgarian Academia of Sciences, 1113, Sofia, Bulgaria.
| | - Kurt Binder
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
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10
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Yao X, Zhang L, Chen JZY. Defect patterns of two-dimensional nematic liquid crystals in confinement. Phys Rev E 2022; 105:044704. [PMID: 35590543 DOI: 10.1103/physreve.105.044704] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2021] [Accepted: 03/23/2022] [Indexed: 06/15/2023]
Abstract
A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface-confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form a deformed texture that may display defect points or defect lines, for which winding numbers can be clearly defined. Here, a particular attention is paid to the case when the liquid crystal molecules prefer to form a boundary nematic texture in parallel to the wall surface (i.e., following the homogeneous boundary condition). A general theory, based on geometric argument, is presented for the relationship between the sum of all winding numbers in the system (the total winding number) and the type of confinement angles and curved segments. The conclusion is validated by comparing the theoretical defect rule with existing nematic textures observed experimentally and theoretically in recent years.
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Affiliation(s)
- Xiaomei Yao
- Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
| | - Lei Zhang
- Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
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11
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Chen J, Sun L, Wang S, Tian F, Zhu H, Zhang R, Dai L. Crowding-induced polymer trapping in a channel. Phys Rev E 2021; 104:054502. [PMID: 34942690 DOI: 10.1103/physreve.104.054502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2021] [Accepted: 10/20/2021] [Indexed: 11/07/2022]
Abstract
In this work, we report an intriguing phenomenon: crowding-induced polymer trapping in a channel. Using Langevin dynamics simulations and analytical calculations, we find that for a polymer confined in a channel, crowding particles can push a polymer into the channel corner through inducing an effective polymer-corner attraction due to the depletion effect. This phenomenon is referred to as polymer trapping. The occurrence of polymer trapping requires a minimum volume fraction of crowders, ϕ^{*}, which scales as ϕ^{*}∼(a_{c}/L_{p})^{1/3} for a_{c}≫a_{m} and ϕ^{*}∼(a_{c}/L_{p})^{1/3}(a_{c}/a_{m})^{1/2} for a_{c}≪a_{m}, where a_{c} is the crowder diameter, a_{m} is the monomer diameter, and L_{p} is the polymer persistence length. For DNA, ϕ^{*} is estimated to be around 0.25 for crowders with a_{c}=2nm. We find that ϕ^{*} also strongly depends on the shape of the channel cross section, and ϕ^{*} is much smaller for a triangle channel than a square channel. The polymer trapping leads to a nearly fully stretched polymer conformation along a channel corner, which may have practical applications, such as full stretching of DNA for the nanochannel-based genome mapping technology.
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Affiliation(s)
- Jialu Chen
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Liang Sun
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Simin Wang
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Fujia Tian
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Haoqi Zhu
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Ruiqin Zhang
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Hong Kong, China
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12
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Affiliation(s)
- Nigel T. Andersen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
| | - Yue Teng
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
| | - Jeff Z. Y. Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
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13
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Chen W, Wei S. Compressive deformations of ring polymers in a confining channel. POLYMER 2021. [DOI: 10.1016/j.polymer.2021.124340] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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14
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Chen G, Zhang H, Lu T, Jiang Y. The stress deformation response influenced by the chain rigidity for mesostructures in diblock copolymers. Phys Chem Chem Phys 2021; 23:22992-23004. [PMID: 34611676 DOI: 10.1039/d1cp03159g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A self-consistent field theory formalism based on the wormlike chain model is developed to investigate the stress-strain relation for mesostructures in diblock copolymers under the influence of chain rigidity, involving the adjustable simulation cell in the non-orthogonal coordinates by means of optimization of free energy. We elucidate the effect of the chain persistency broadly spanning from the Gaussian chain to the rigid rodlike chain on the elastic response of mesophases that deviate from the initial equilibrium structures. We analytically and numerically demonstrate that our current approach in the long chain limit recovers to the Gaussian-chain-based theory. Being ascribed to the distinct conformational behaviors for flexible chains and rigid rodlike chains, the tensile and compressive stresses applied to lamellae exhibit asymmetric deformation behaviors and the shear stress applied to the initial equilibrium hexagonal cylinders results in noticeable deviations in the shape and spatial arrangement of cylindroids for various chain rigidity values. For the zero stress, in addition, our approach can be straightforwardly utilized to explore the optimal size and shape of the simulation cell in order to achieve a stress free configuration of systems.
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Affiliation(s)
- Gaohang Chen
- School of Chemistry and Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education and Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China. .,School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
| | - Hui Zhang
- School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
| | - Teng Lu
- Computer Network Information Center of the Chinese Academy of Sciences, Beijing 100190, China
| | - Ying Jiang
- School of Chemistry and Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education and Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China. .,Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing 100191, China
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15
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Milchev A, Binder K. Adsorption of Semiflexible Polymers in Cylindrical Tubes. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:11759-11770. [PMID: 34581575 DOI: 10.1021/acs.langmuir.1c01715] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Conformations of wormlike chains in cylindrical pores with attractive walls are explored for varying pore radius and strength of the attractive wall potential by molecular dynamics simulations of a coarse-grained model. Local quantities such as the fraction of monomeric units bound to the surface and the bond-orientational order parameter as well as the radial density distribution are studied, as well as the global chain extensions parallel to the cylinder axis and perpendicular to the cylinder surface. A nonmonotonic convergence of these properties to their counterparts for adsorption on a planar substrate is observed due to the conflict between pore surface curvature and chain stiffness. Also the interpretation of partially adsorbed chains in terms of trains, loops, and tails is discussed.
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Affiliation(s)
- A Milchev
- Institute of Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
| | - K Binder
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany
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16
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Ding M, Li L. Flow-Induced Translocation and Conformational Transition of Polymer Chains through Nanochannels: Recent Advances and Future Perspectives. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00909] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Mingming Ding
- School of Chemical Engineering and Light Industry, Guangdong University of Technology, Guangzhou 510006, China
| | - Lianwei Li
- Food Science and Processing Research Center, College of Chemistry and Environmental Engineering, Shenzhen University, Shenzhen 518060, China
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17
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Teng Y, Andersen NT, Chen JZY. Statistical Properties of a Slit-Confined Wormlike Chain of Finite Length. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00759] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Affiliation(s)
- Yue Teng
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Nigel T. Andersen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Jeff Z. Y. Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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18
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Milchev A, Binder K. Cylindrical confinement of solutions containing semiflexible macromolecules: surface-induced nematic order versus phase separation. SOFT MATTER 2021; 17:3443-3454. [PMID: 33646224 DOI: 10.1039/d1sm00172h] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Solutions of semiflexible polymers confined in cylindrical pores with repulsive walls are studied by Molecular Dynamics simulations for a wide range of polymer concentrations. Both the case where both lengths are of the same order and the case when the persistence length by far exceeds the contour length are considered, and the enhancement of nematic order along the cylinder axis is characterized. With increasing density the character of the surface effect changes from depletion to the formation of a layered structure. For binary 50 : 50 mixtures of the two types of polymers an interplay between surface enrichment of the stiffer component and the isotropic-nematic transition is found, and a phase separated structure with cylindrical symmetry occurs, with the isotropic phase located around the cylinder axis. For melt densities the mixed nematic phase forms at the wall a layer with a screw-like structure of a tilted smectic phase. The observed behavior is tentatively interpreted in terms of the competition of the chain orientational entropy with entropy of mixing and excluded volume due to the wall.
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Affiliation(s)
- Andrey Milchev
- Institute for Physical Chemistry, Bulgarian Academia of Sciences, 1113, Sofia, Bulgaria.
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19
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Nikoubashman A. Ordering, phase behavior, and correlations of semiflexible polymers in confinement. J Chem Phys 2021; 154:090901. [DOI: 10.1063/5.0038052] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
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20
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Razbin M, Mashaghi A. Elasticity of connected semiflexible quadrilaterals. SOFT MATTER 2021; 17:102-112. [PMID: 33150925 DOI: 10.1039/d0sm01719a] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Using the positional-orientational propagator of a semiflexible filament in the weakly bending regime, we analytically calculate the probability densities associated with the fluctuating tip and the corners of a grafted system of connected quadrilaterals. We calculate closed analytic expressions for the probability densities within the framework of the worm-like chain model, which are valid in the weakly bending regime. The probability densities give the physical quantities related to the elasticity of the system such as the force-extension relation in the fixed extension ensemble, the Poisson's ratio and the average of the force exerted to a confining stiff planar wall by the fluctuating tip of the system. Our analysis reveals that the force-extension relations depend on the contour length of the system (material content), the bending stiffness (chemical nature), the geometrical angle and the number of the quadrilaterals, while the Poisson's ratio depends only on the geometrical angle and the number of the quadrilaterals, and is thus a purely geometric property of the system.
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Affiliation(s)
- Mohammadhosein Razbin
- Department of Energy Engineering and Physics, Amirkabir University of Technology, 14588 Tehran, Iran.
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21
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Chen Y, Zhang X, Jiang Y. The influence of side-chain conformations on the phase behavior of bottlebrush block polymers. SOFT MATTER 2020; 16:8047-8056. [PMID: 32785406 DOI: 10.1039/d0sm00918k] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
A self-consistent field theory based on the wormlike chain model is implemented in the investigation of the self-assembly behavior of bottlebrush block polymers in the formation of a lamellar phase. We utilize the model in which the semi-flexible side chains of two types A and B are grafted at the semi-flexible backbone of type C to mimic the bottlebrush molecule, particularly allowing for the extended chain conformation due to the high grafting density. We examine the positional and orientational probability distribution for the segments along the backbone and side chains as a function of the grafting density and chain flexibility for all blocks, covering a broad regime spanning from the flexible chain to rigid rod chain. This reveals that the persistence length of side chains λSC which intrinsically tunes the chain conformation of bottlebrush polymers plays a pivotal role in determining the manner of the local monomer packing in microphase segregation. As an important adjustable factor, λSC has a remarkable impact on the backbone extension and then realizes the effective manipulation of the characteristic structural size of self-assembled microstructures, such as the domain spacing and the interfacial width.
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Affiliation(s)
- Yuguo Chen
- School of Chemistry & Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education & Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China.
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22
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Kloza PA, Elliott JA. Freely Suspended Semiflexible Chains in a Strong Aligning Field: Simple Closed‐Form Solutions for the Small‐Angle Approximation. MACROMOL THEOR SIMUL 2020. [DOI: 10.1002/mats.202000049] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Philipp A. Kloza
- Department of Materials Science & Metallurgy University of Cambridge 27 Charles Babbage Road Cambridge CB3 0FS UK
| | - James A. Elliott
- Department of Materials Science & Metallurgy University of Cambridge 27 Charles Babbage Road Cambridge CB3 0FS UK
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23
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Yao X, Chen JZY. Rodlike molecules in extreme confinement. Phys Rev E 2020; 101:062706. [PMID: 32688519 DOI: 10.1103/physreve.101.062706] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 06/15/2020] [Indexed: 11/07/2022]
Abstract
A unique feature of colloid particles and biopolymers is the molecule's intrinsic rigidity characterized by a molecular-level length scale. Under extreme confinement conditions at cellular scales or in nanodevices, these molecules can display orientational ordering accompanied by severe density depletion. Conventional liquid-crystal theories, such as the Oseen-Frank or Landau-de Gennes theories, cannot capture the essential molecular-level properties: the boundary effects, which extend to a distance of the rigidity length scale, and the drastic variations of the inhomogeneous molecular density. Here we show, based on a simple interpretation of the Onsager model, that rodlike molecules in extreme annular confinement produce unusual liquid-crystal defect structures that are independent phases from the patterns usually seen in a weaker confinement environment.
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Affiliation(s)
- Xiaomei Yao
- School of Chemistry, Beihang University, Beijing 100191, People's Republic of China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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24
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Spencer RKW, Saeidi N, Ha BY. Nematic ordering of worm-like polymers near an interface. J Chem Phys 2020; 152:204907. [PMID: 32486695 PMCID: PMC7261236 DOI: 10.1063/1.5132928] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Accepted: 05/03/2020] [Indexed: 11/14/2022] Open
Abstract
The phase behavior of semi-flexible polymers is integral to various contexts, from materials science to biophysics, many of which utilize or require specific confinement geometries as well as the orientational behavior of the polymers. Inspired by collagen assembly, we study the orientational ordering of semi-flexible polymers, modeled as Maier-Saupe worm-like chains, using self-consistent field theory. We first examine the bulk behavior of these polymers, locating the isotropic-nematic transition and delineating the limit of stability of the isotropic and nematic phases. This effort explains how nematic ordering emerges from the isotropic phase and offers insight into how different (e.g., mono-domain vs multi-domain) nematic phases form. We then clarify the influence of planar confinement on the nematic ordering of the polymers. We find that while the presence of a single confining wall does not shift the location of nematic transition, it aligns the polymers in parallel to the wall; above the onset of nematic transition, this preference tends to propagate into the bulk phase. Introducing a second, perpendicular, wall leads to a nematic phase that is parallel to both walls, allowing the ordering direction to be uniquely set by the geometry of the experimental setup. The advantage of wall-confinement is that it can be used to propagate mono-domain nematic phases into the bulk phase.
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Affiliation(s)
- Russell K. W. Spencer
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Nima Saeidi
- Department of Surgery, The Center for Engineering in Medicine (CEM), Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114, USA
| | - Bae-Yeun Ha
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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25
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Dutta S, Benetatos P. Statistical ensemble inequivalence for flexible polymers under confinement in various geometries. SOFT MATTER 2020; 16:2114-2127. [PMID: 32016271 DOI: 10.1039/c9sm02246e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The problem of statistical ensemble inequivalence for single polymers has been the subject of intense research. In a recent publication, we show that even though the force-extension relation of a free Gaussian chain exhibits ensemble equivalence, confinement to half-space due to tethering to a planar substrate induces significant inequivalence [S. Dutta and P. Benetatos, Soft Matter, 2018, 14, 6857-6866]. In the present article, we extend that work to the conformational response to confining forces distributed over surfaces. We analyze in both the Helmholtz and the Gibbs ensemble the pressure-volume equation of state of a chain in rectangular, spherical, and cylindrical confinement. We especially consider the case of a directed polymer in a cylinder. We also analyze the case of a tethered chain inside a rectangular box, a sphere, and outside a sphere. In general, confinement causes significant ensemble inequivalence. Remarkably, we recover ensemble equivalence in the limit of squashing confinement. We trace the ensemble inequivalence to the persistence of strong fluctuations. Our work may be useful in the interpretation of single molecule experiments and caging phenomena.
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Affiliation(s)
- Sandipan Dutta
- Center for Soft and Living Matter, Institute for Basic Science, Ulsan 44919, Korea
| | - Panayotis Benetatos
- Department of Physics, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Korea.
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26
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Milchev A, Binder K. How does stiffness of polymer chains affect their adsorption transition? J Chem Phys 2020; 152:064901. [DOI: 10.1063/1.5139940] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Affiliation(s)
- A. Milchev
- Institute of Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
| | - K. Binder
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany
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27
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Semiflexible Polymers Interacting With Planar Surfaces: Weak versus Strong Adsorption. Polymers (Basel) 2020; 12:polym12020255. [PMID: 31978981 PMCID: PMC7077214 DOI: 10.3390/polym12020255] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2019] [Revised: 01/13/2020] [Accepted: 01/15/2020] [Indexed: 12/12/2022] Open
Abstract
Semiflexible polymers bound to planar substrates by a short-range surface potential are studied by Molecular Dynamics simulations to clarify the extent to which these chain molecules can be considered as strictly two-dimensional. Applying a coarse-grained bead-spring model, the chain length N and stiffness κ as well as the strength of the adsorption potential ϵwall are varied over a wide range. The excluded-volume (EV) interactions inherent in this model can also be “switched off” to provide a discretized version of the Kratky–Porod wormlike chain model. We study both local order parameters (fraction f of monomers within the range of the potential, bond-orientational order parameter η) and the mean square gyration radius parallel, 〈Rg2〉||, and perpendicular, 〈Rg2〉⊥, to the wall. While for strongly adsorbed chains EV has negligible effect on f and η, we find that 〈Rg2〉|| is strongly affected when the chain contour length exceeds the persistence length. Monomer coordinates in perpendicular (⊥) direction are correlated over the scale of the deflection length which is estimated. It is found that f,η, and 〈Rg2〉⊥ converge to their asymptotic values with 1/N corrections. For both weakly and strongly adsorbed chains, the distribution functions of “loops”, “trains”, and “tails” are analyzed. Some consequences pertaining to the analysis of experiments on adsorbed semiflexible polymers are pointed out.
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28
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Fu Y, Wu F, Huang JH, Chen YC, Luo MB. Simulation Study on the Extension of Semi-flexible Polymer Chains in Cylindrical Channel. CHINESE JOURNAL OF POLYMER SCIENCE 2019. [DOI: 10.1007/s10118-019-2291-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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29
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Chuang HM, Reifenberger JG, Bhandari AB, Dorfman KD. Extension distribution for DNA confined in a nanochannel near the Odijk regime. J Chem Phys 2019; 151:114903. [PMID: 31542006 DOI: 10.1063/1.5121305] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
DNA confinement in a nanochannel typically is understood via mapping to the confinement of an equivalent neutral polymer by hard walls. This model has proven to be effective for confinement in relatively large channels where hairpin formation is frequent. An analysis of existing experimental data for Escherichia coli DNA extension in channels smaller than the persistence length, combined with an additional dataset for λ-DNA confined in a 34 nm wide channel, reveals a breakdown in this approach as the channel size approaches the Odijk regime of strong confinement. In particular, the predicted extension distribution obtained from the asymptotic solution to the weakly correlated telegraph model for a confined wormlike chain deviates significantly from the experimental distribution obtained for DNA confinement in the 34 nm channel, and the discrepancy cannot be resolved by treating the alignment fluctuations or the effective channel size as fitting parameters. We posit that the DNA-wall electrostatic interactions, which are sensible throughout a significant fraction of the channel cross section in the Odijk regime, are the source of the disagreement between theory and experiment. Dimensional analysis of the wormlike chain propagator in channel confinement reveals the importance of a dimensionless parameter, reflecting the magnitude of the DNA-wall electrostatic interactions relative to thermal energy, which has not been considered explicitly in the prevailing theories for DNA confinement in a nanochannel.
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Affiliation(s)
- Hui-Min Chuang
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Jeffrey G Reifenberger
- Bionano Genomics, Inc., 9640 Towne Centre Drive, Suite 100, San Diego, California 92121, USA
| | - Aditya Bikram Bhandari
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
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30
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Numerical Simulation of the Distribution Function and Free Energy of a Single Wormlike Polymer Confined between Hard Walls. CHINESE JOURNAL OF POLYMER SCIENCE 2019. [DOI: 10.1007/s10118-019-2322-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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31
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Castro-Villarreal P, Ramírez JE. Stochastic curvature of enclosed semiflexible polymers. Phys Rev E 2019; 100:012503. [PMID: 31499867 DOI: 10.1103/physreve.100.012503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2018] [Indexed: 11/07/2022]
Abstract
The conformational states of a semiflexible polymer enclosed in a compact domain of typical size a are studied as stochastic realizations of paths defined by the Frenet equations under the assumption that stochastic "curvature" satisfies a white noise fluctuation theorem. This approach allows us to derive the Hermans-Ullman equation, where we exploit a multipolar decomposition that allows us to show that the positional probability density function is well described by a telegrapher's equation whenever 2a/ℓ_{p}>1, where ℓ_{p} is the persistence length. We also develop a Monte Carlo algorithm for use in computer simulations in order to study the conformational states in a compact domain. In addition, the case of a semiflexible polymer enclosed in a square domain of side a is presented as an explicit example of the formulated theory and algorithm. In this case, we show the existence of a polymer shape transition similar to the one found by Spakowitz and Wang [Phys. Rev. Lett. 91, 166102 (2003)PRLTAO0031-900710.1103/PhysRevLett.91.166102] where in this case the critical persistence length is ℓ_{p}^{*}≃a/8 such that the mean-square end-to-end distance exhibits an oscillating behavior for values ℓ_{p}>ℓ_{p}^{*}, whereas for ℓ_{p}<ℓ_{p}^{*} it behaves monotonically increasing.
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Affiliation(s)
- Pavel Castro-Villarreal
- Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas, Carretera Emiliano Zapata, Km. 8, Rancho San Francisco, 29050 Tuxtla Gutiérrez, Chiapas, Mexico
| | - J E Ramírez
- Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 165, 72000 Puebla, Puebla, Mexico.,Departamento de Física de Partículas, Universidad de Santiago de Compostela, E-15782 Santiago de Compostela, Spain
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32
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Liang Q, Jiang Y, Chen JZY. Orientationally ordered states of a wormlike chain in spherical confinement. Phys Rev E 2019; 100:032502. [PMID: 31640076 DOI: 10.1103/physreve.100.032502] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2019] [Indexed: 06/10/2023]
Abstract
One of the basic characteristics of a linear dsDNA molecule is its persistence length, typically of order 50 nm. The DNA chain inflicts a large energy penalty if it is bent sharply at that length scale. Viruses of bacteria, known as bacteriophages, typically have a dimension of a few tens of nanometers. Yet, it is known that a bacteriophage actively packages viral DNA inside the capsid and ejects it afterwards. Here, adopting a commonly used polymer model known as the wormlike chain, we answer an idealized question: Placing a linear DNA molecule inside a spherical cavity, what ordered states can we derive from known tools in statistical physics? Solving the model in a rigorous field-theory framework, we report a universal phase diagram for four orientationally ordered and disordered states, in terms of two relevant physical parameters.
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Affiliation(s)
- Qin Liang
- Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China
- School of Chemistry, Beihang University, Beijing 100191, China
| | - Ying Jiang
- School of Chemistry, Beihang University, Beijing 100191, China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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33
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Wang J, Li K. Statistical Behaviors of Semiflexible Polymer Chains Stretched in Rectangular Tubes. Polymers (Basel) 2019; 11:E260. [PMID: 30960244 PMCID: PMC6419070 DOI: 10.3390/polym11020260] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2018] [Revised: 01/27/2019] [Accepted: 01/31/2019] [Indexed: 11/23/2022] Open
Abstract
We investigated the statistical behaviors of semiflexible polymer chains, which were simultaneously subjected to force stretching and rectangular tube confinement. Based on the wormlike chain model and Odijk deflection theory, we derived a new deflection length, by using which new compact formulas were obtained for the confinement free energy and force⁻confinement⁻extension relations. These newly derived formulas were justified by numerical solutions of the eigenvalue problem associated with the Fokker⁻Planck governing equation and extensive Brownian dynamics simulations based on the so-called generalized bead-rod (GBR) model. We found that, compared to classical deflection theory, these new formulas were valid for a much more extended range of the confinement size/persistence length ratio and had no adjustable fitting parameters for sufficiently long semiflexible chains in the whole deflection regime.
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Affiliation(s)
- Jizeng Wang
- Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, Gansu, China.
| | - Kai Li
- Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, Gansu, China.
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34
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Keul ND, Oruganty K, Schaper Bergman ET, Beattie NR, McDonald WE, Kadirvelraj R, Gross ML, Phillips RS, Harvey SC, Wood ZA. The entropic force generated by intrinsically disordered segments tunes protein function. Nature 2018; 563:584-588. [PMID: 30420606 PMCID: PMC6415545 DOI: 10.1038/s41586-018-0699-5] [Citation(s) in RCA: 88] [Impact Index Per Article: 14.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2017] [Accepted: 09/10/2018] [Indexed: 11/09/2022]
Abstract
Protein structures are dynamic and can explore a large conformational landscape1,2. Only some of these structural substates are important for protein function (such as ligand binding, catalysis and regulation)3-5. How evolution shapes the structural ensemble to optimize a specific function is poorly understood3,4. One of the constraints on the evolution of proteins is the stability of the folded 'native' state. Despite this, 44% of the human proteome contains intrinsically disordered peptide segments greater than 30 residues in length6, the majority of which have no known function7-9. Here we show that the entropic force produced by an intrinsically disordered carboxy terminus (ID-tail) shifts the conformational ensemble of human UDP-α-D-glucose-6-dehydrogenase (UGDH) towards a substate with a high affinity for an allosteric inhibitor. The function of the ID-tail does not depend on its sequence or chemical composition. Instead, the affinity enhancement can be accurately predicted based on the length of the intrinsically disordered segment, and is consistent with the entropic force generated by an unstructured peptide attached to the protein surface10-13. Our data show that the unfolded state of the ID-tail rectifies the dynamics and structure of UGDH to favour inhibitor binding. Because this entropic rectifier does not have any sequence or structural constraints, it is an easily acquired adaptation. This model implies that evolution selects for disordered segments to tune the energy landscape of proteins, which may explain the persistence of intrinsic disorder in the proteome.
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Affiliation(s)
- Nicholas D Keul
- Department of Biochemistry and Molecular Biology, University of Georgia, Athens, GA, USA
| | - Krishnadev Oruganty
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
| | | | - Nathaniel R Beattie
- Department of Biochemistry and Molecular Biology, University of Georgia, Athens, GA, USA
| | - Weston E McDonald
- Department of Biochemistry and Molecular Biology, University of Georgia, Athens, GA, USA
| | - Renuka Kadirvelraj
- Department of Biochemistry and Molecular Biology, University of Georgia, Athens, GA, USA
| | - Michael L Gross
- Department of Chemistry, Washington University in St. Louis, St. Louis, MO, USA
| | | | - Stephen C Harvey
- Department of Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, PA, USA
| | - Zachary A Wood
- Department of Biochemistry and Molecular Biology, University of Georgia, Athens, GA, USA.
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35
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Barde C, Destainville N, Manghi M. Energy required to pinch a DNA plectoneme. Phys Rev E 2018; 97:032412. [PMID: 29776038 DOI: 10.1103/physreve.97.032412] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2017] [Indexed: 11/07/2022]
Abstract
DNA supercoiling plays an important role from a biological point of view. One of its consequences at the supramolecular level is the formation of DNA superhelices named plectonemes. Normally separated by a distance on the order of 10 nm, the two opposite double strands of a DNA plectoneme must be brought closer if a protein or protein complex implicated in genetic regulation is to be bound simultaneously to both strands, as if the plectoneme was locally pinched. We propose an analytic calculation of the energetic barrier, of elastic nature, required to bring closer the two loci situated on the opposed double strands. We examine how this energy barrier scales with the DNA supercoiling. For physically relevant values of elastic parameters and of supercoiling density, we show that the energy barrier is in the k_{B}T range under physiological conditions, thus demonstrating that the limiting step to loci encounter is more likely the preceding plectoneme slithering bringing the two loci side by side.
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Affiliation(s)
- Céline Barde
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS 118 route de Narbonne, F-31062 Toulouse, France, EU
| | - Nicolas Destainville
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS 118 route de Narbonne, F-31062 Toulouse, France, EU
| | - Manoel Manghi
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS 118 route de Narbonne, F-31062 Toulouse, France, EU
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36
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Chen JZY. Self-Avoiding Wormlike Chain Confined in a Cylindrical Tube: Scaling Behavior. PHYSICAL REVIEW LETTERS 2018; 121:037801. [PMID: 30085819 DOI: 10.1103/physrevlett.121.037801] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2018] [Revised: 04/27/2018] [Indexed: 05/27/2023]
Abstract
Within a confining tube section, the multithreads of a strongly confined, backfolding polymer exert the excluded-volume repulsions on each other and produce physical properties that are very different from those of a confined ideal chain. The conformational properties of a such confined wormlike chain are of fundamental interest and are also practically useful in understanding the DNA confinement problems. Here, the excluded-volume effects are added to the standard wormlike-chain model by a self-consistent field theory. The numerical solutions are examined in light of their scaling properties.
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Affiliation(s)
- Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3GI, Canada
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37
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Klop KE, Dullens RPA, Lettinga MP, Egorov SA, Aarts DGAL. Capillary nematisation of colloidal rods in confinement. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1497210] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Kira E. Klop
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK
| | - Roel P. A. Dullens
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK
| | - M. Paul Lettinga
- ICS-3, Forschungszentrum Jülich, D-52425 Jülich, Germany
- Laboratory for Soft Matter and Biophysics, KU Leuven, Leuven, Belgium
| | - Sergei A. Egorov
- Department of Chemistry, University of Virginia, Charlottesville, VA, USA
| | - Dirk G. A. L. Aarts
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK
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38
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Burke CJ, Grason GM. Intradomain phase transitions in flexible block copolymers with self-aligning segments. J Chem Phys 2018; 148:174905. [PMID: 29739210 DOI: 10.1063/1.5025809] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study a model of flexible block copolymers (BCPs) in which there is an enlthalpic preference for orientational order, or local alignment, among like-block segments. We describe a generalization of the self-consistent field theory of flexible BCPs to include inter-segment orientational interactions via a Landau-de Gennes free energy associated with a polar or nematic order parameter for segments of one component of a diblock copolymer. We study the equilibrium states of this model numerically, using a pseudo-spectral approach to solve for chain conformation statistics in the presence of a self-consistent torque generated by inter-segment alignment forces. Applying this theory to the structure of lamellar domains composed of symmetric diblocks possessing a single block of "self-aligning" polar segments, we show the emergence of spatially complex segment order parameters (segment director fields) within a given lamellar domain. Because BCP phase separation gives rise to spatially inhomogeneous orientation order of segments even in the absence of explicit intra-segment aligning forces, the director fields of BCPs, as well as thermodynamics of lamellar domain formation, exhibit a highly non-linear dependence on both the inter-block segregation (χN) and the enthalpy of alignment (ε). Specifically, we predict the stability of new phases of lamellar order in which distinct regions of alignment coexist within the single mesodomain and spontaneously break the symmetries of the lamella (or smectic) pattern of composition in the melt via in-plane tilt of the director in the centers of the like-composition domains. We further show that, in analogy to Freedericksz transition confined nematics, the elastic costs to reorient segments within the domain, as described by the Frank elasticity of the director, increase the threshold value ε needed to induce this intra-domain phase transition.
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Affiliation(s)
- Christopher J Burke
- Department of Polymer Science, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Gregory M Grason
- Department of Polymer Science, University of Massachusetts, Amherst, Massachusetts 01003, USA
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39
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Yao X, Zhang H, Chen JZY. Topological defects in two-dimensional liquid crystals confined by a box. Phys Rev E 2018; 97:052707. [PMID: 29906923 DOI: 10.1103/physreve.97.052707] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2018] [Indexed: 06/08/2023]
Abstract
When a spatially uniform system that displays a liquid-crystal ordering on a two-dimensional surface is confined inside a rectangular box, the liquid crystal direction field develops inhomogeneous textures accompanied by topological defects because of the geometric frustrations. We show that the rich variety of nematic textures and defect patterns found in recent experimental and theoretical studies can be classified by the solutions of the rather fundamental, extended Onsager model. This is critically examined based on the determined free energies of different defect states, as functions of a few relevant, dimensionless geometric parameters.
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Affiliation(s)
- Xiaomei Yao
- School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People's Republic of China
- School of Chemistry, Beihang University, Beijing 100191, People's Republic of China
| | - Hui Zhang
- School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
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40
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Frydel D, Podgornik R. Mean-field theory of active electrolytes: Dynamic adsorption and overscreening. Phys Rev E 2018; 97:052609. [PMID: 29906940 DOI: 10.1103/physreve.97.052609] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2018] [Indexed: 06/08/2023]
Abstract
We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of constituting ions. One feature of active dynamics is that particles adhere to hard surfaces, regardless of chemical properties of a surface and specifically in complete absence of any chemisorption or physisorption. To carry out the mean-field analysis of the system that is out of equilibrium, we develop the "mean-field simulation" technique, where the simulated system consists of charged parallel sheets moving on a line and obeying active dynamics, with the interaction strength rescaled by the number of sheets. The mean-field limit becomes exact in the limit of an infinite number of movable sheets.
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Affiliation(s)
- Derek Frydel
- Department of Chemistry, Federico Santa Maria Technical University, Campus San Joaquín, Santiago, Chile
| | - Rudolf Podgornik
- School of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China; CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia; and Department of Theoretical Physics, J. Stefan Institute, 1000 Ljubljana, Slovenia
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41
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Milchev A, Egorov SA, Vega DA, Binder K, Nikoubashman A. Densely Packed Semiflexible Macromolecules in a Rigid Spherical Capsule. Macromolecules 2018. [DOI: 10.1021/acs.macromol.7b02643] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Andrey Milchev
- Institute for Physical Chemistry, Bulgarian Academia of Sciences, 1113 Sofia, Bulgaria
| | - Sergei A. Egorov
- Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901, United States
| | - Daniel A. Vega
- Department of Physics, Universidad Nacional del Sur-IFISUR-CONICET, 8000 Bahía Blanca, Argentina
| | - Kurt Binder
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
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42
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Affiliation(s)
- Zhen-Gang Wang
- Division of Chemistry and
Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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43
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Sonnet AM, Virga EG. Bistable curvature potential at hyperbolic points of nematic shells. SOFT MATTER 2017; 13:6792-6802. [PMID: 28828443 DOI: 10.1039/c7sm01216k] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Nematic shells are colloidal particles coated with nematic liquid crystal molecules which may freely glide and rotate on the colloid's surface while keeping their long axis on the local tangent plane. We describe the nematic order on a shell by a unit director field on an orientable surface. Equilibrium fields can then be found by minimising the elastic energy, which in general is a function of the surface gradient of the director field. We learn how to extract systematically out of this energy a fossil component, related only to the surface and its curvatures, which expresses a curvature potential for the molecular torque. At hyperbolic points on the colloid's surface, and only there, the alignment preferred by the curvature potential may fail to be a direction of principal curvature. There the fossil energy becomes bistable.
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Affiliation(s)
- André M Sonnet
- Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, Scotland, UK.
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44
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Chen JZY. Conformational Properties of a Back-Folding Wormlike Chain Confined in a Cylindrical Tube. PHYSICAL REVIEW LETTERS 2017; 118:247802. [PMID: 28665664 DOI: 10.1103/physrevlett.118.247802] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2017] [Indexed: 06/07/2023]
Abstract
When a semiflexible chain is confined in a narrow cylindrical tube, the formation of a polymer hairpin is a geometrical conformation that accompanies an exponentially large local free energy and, hence, is a relatively rare event. Numerical solutions of the hairpin distribution functions for persistence-length-to-tube-radius ratios over a wide range are obtained in high precision, by using the Green's function approach for the wormlike-chain model. The crossover region between the narrow and moderately narrow tubes is critically investigated in terms of the hairpin free energy, global persistence length, mean hairpin-tip distance from the tube axis, and hairpin-plane orientational properties. Accurate representations of the solutions by simple interpolation formulae are suggested.
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Affiliation(s)
- Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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45
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Sheats J, Sclavi B, Cosentino Lagomarsino M, Cicuta P, Dorfman KD. Role of growth rate on the orientational alignment of Escherichia coli in a slit. ROYAL SOCIETY OPEN SCIENCE 2017; 4:170463. [PMID: 28680690 PMCID: PMC5493932 DOI: 10.1098/rsos.170463] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2017] [Accepted: 05/19/2017] [Indexed: 05/08/2023]
Abstract
We present experimental data on the nematic alignment of Escherichia coli bacteria confined in a slit, with an emphasis on the effect of growth rate and corresponding changes in cell aspect ratio. Global alignment with the channel walls arises from the combination of local nematic ordering of nearby cells, induced by cell division and the elongated shape of the cells, and the preferential orientation of cells proximate to the side walls of the slit. Decreasing the growth rate leads to a decrease in alignment with the walls, which is attributed primarily to effects of changing cell aspect ratio rather than changes in the variance in cell area. Decreasing confinement also reduces the degree of alignment by a similar amount as a decrease in the growth rate, but the distribution of the degree of alignment differs. The onset of alignment with the channel walls is coincident with the slits reaching their steady-state occupancy and connected to the re-orientation of locally aligned regions with respect to the walls during density fluctuations.
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Affiliation(s)
- Julian Sheats
- Department of Chemical Engineering and Materials Science, University of Minnesota—Twin Cities, 421 Washington Avenue SE, Minneapolis, MN 55455, USA
| | - Bianca Sclavi
- LBPA, UMR 8113 du CNRS, École Normale Supérieure de Cachan, Cachan, France
| | - Marco Cosentino Lagomarsino
- Sorbonne Universités, Université Pierre et Marie Curie, 4 Place Jussieu, Paris, France
- CNRS, UMR7238 Computational and Quantitative Biology, Paris, France
- IFOM Institute for Molecular Oncology, Milan, Italy
| | - Pietro Cicuta
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota—Twin Cities, 421 Washington Avenue SE, Minneapolis, MN 55455, USA
- Author for correspondence: Kevin D. Dorfman e-mail:
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46
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Joo H, Kim JS. Confinement-driven organization of a histone-complexed DNA molecule in a dense array of nanoposts. NANOSCALE 2017; 9:6391-6398. [PMID: 28453018 DOI: 10.1039/c7nr00859g] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The first step in the controlled storage of lengthy DNA molecules is to keep DNA molecules separated while integrated in micrometer-sized space. Herein, we present hybrid Monte Carlo simulations of a histone-complexed DNA (hcDNA) molecule confined in a dense array of nanoposts. Depending on the nanopost dimension, a single, 8.7 kilobase pair hcDNA molecule was either localized and elongated in a single inter-post space surrounded by four nanoposts or spread over several inter-post spaces through passages between two neighboring nanoposts. The conformational change of a hcDNA molecule is interpreted in terms of competitive effects of confinements in the inter-post and passage spaces. We propose that, by elaborately designing nanopost arrays, the competitive confinement effects can be adjusted such that each hcDNA molecule is localized in a single inter-post space, and thereby multiple hcDNA molecules can be physically separated from each other while stored together in the nanopost array.
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Affiliation(s)
- Heesun Joo
- Department of Chemistry and Nanoscience, Ewha Womans University, Seoul 03760, Republic of Korea.
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47
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Fu J, Zhang X, Miao B, Yan D. Light-responsive expansion-contraction of spherical nanoparticle grafted with azopolymers. J Chem Phys 2017; 146:164901. [PMID: 28456201 DOI: 10.1063/1.4981914] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Jie Fu
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Xinghua Zhang
- School of Science, Beijing Jiaotong University, Beijing 100044, China
| | - Bing Miao
- College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Dadong Yan
- Department of Physics, Beijing Normal University, Beijing 100875, China
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48
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Meng F, Terentjev EM. Theory of Semiflexible Filaments and Networks. Polymers (Basel) 2017; 9:E52. [PMID: 30970730 PMCID: PMC6432424 DOI: 10.3390/polym9020052] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2016] [Revised: 01/25/2017] [Accepted: 01/26/2017] [Indexed: 01/07/2023] Open
Abstract
We briefly review the recent developments in the theory of individual semiflexible filaments, and of a crosslinked network of such filaments, both permanent and transient. Starting from the free energy of an individual semiflexible chain, models on its force-extension relation and other mechanical properties such as Euler buckling are discussed. For a permanently crosslinked network of filaments, theories on how the network responds to deformation are provided, with a focus on continuum approaches. Characteristic features of filament networks, such as nonlinear stress-strain relation, negative normal stress, tensegrity, and marginal stability are discussed. In the new area of transient filament network, where the crosslinks can be dynamically broken and re-formed, we show some recent attempts for understanding the dynamics of the crosslinks, and the related rheological properties, such as stress relaxation, yield stress and plasticity.
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Affiliation(s)
- Fanlong Meng
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK.
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK.
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49
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Thermodynamics of a Compressible Maier-Saupe Model Based on the Self-Consistent Field Theory of Wormlike Polymer. Polymers (Basel) 2017; 9:polym9020048. [PMID: 30970727 PMCID: PMC6431982 DOI: 10.3390/polym9020048] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2016] [Revised: 01/27/2017] [Accepted: 01/30/2017] [Indexed: 11/17/2022] Open
Abstract
This paper presents a theoretical formalism for describing systems of semiflexible polymers, which can have density variations due to finite compressibility and exhibit an isotropic-nematic transition. The molecular architecture of the semiflexible polymers is described by a continuum wormlike-chain model. The non-bonded interactions are described through a functional of two collective variables, the local density and local segmental orientation tensor. In particular, the functional depends quadratically on local density-variations and includes a Maier–Saupe-type term to deal with the orientational ordering. The specified density-dependence stems from a free energy expansion, where the free energy of an isotropic and homogeneous homopolymer melt at some fixed density serves as a reference state. Using this framework, a self-consistent field theory is developed, which produces a Helmholtz free energy that can be used for the calculation of the thermodynamics of the system. The thermodynamic properties are analysed as functions of the compressibility of the model, for values of the compressibility realizable in mesoscopic simulations with soft interactions and in actual polymeric materials.
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50
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Greco C, Jiang Y, Chen JZY, Kremer K, Daoulas KC. Maier-Saupe model of polymer nematics: Comparing free energies calculated with Self Consistent Field theory and Monte Carlo simulations. J Chem Phys 2016; 145:184901. [PMID: 27846703 DOI: 10.1063/1.4966919] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Self Consistent Field (SCF) theory serves as an efficient tool for studying mesoscale structure and thermodynamics of polymeric liquid crystals (LC). We investigate how some of the intrinsic approximations of SCF affect the description of the thermodynamics of polymeric LC, using a coarse-grained model. Polymer nematics are represented as discrete worm-like chains (WLC) where non-bonded interactions are defined combining an isotropic repulsive and an anisotropic attractive Maier-Saupe (MS) potential. The range of the potentials, σ, controls the strength of correlations due to non-bonded interactions. Increasing σ (which can be seen as an increase of coarse-graining) while preserving the integrated strength of the potentials reduces correlations. The model is studied with particle-based Monte Carlo (MC) simulations and SCF theory which uses partial enumeration to describe discrete WLC. In MC simulations the Helmholtz free energy is calculated as a function of strength of MS interactions to obtain reference thermodynamic data. To calculate the free energy of the nematic branch with respect to the disordered melt, we employ a special thermodynamic integration (TI) scheme invoking an external field to bypass the first-order isotropic-nematic transition. Methodological aspects which have not been discussed in earlier implementations of the TI to LC are considered. Special attention is given to the rotational Goldstone mode. The free-energy landscape in MC and SCF is directly compared. For moderate σ the differences highlight the importance of local non-bonded orientation correlations between segments, which SCF neglects. Simple renormalization of parameters in SCF cannot compensate the missing correlations. Increasing σ reduces correlations and SCF reproduces well the free energy in MC simulations.
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Affiliation(s)
- Cristina Greco
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Ying Jiang
- School of Chemistry and Environment, Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L4K1, Canada
| | - Kurt Kremer
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Kostas Ch Daoulas
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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