1
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Topological Catenation Enhances Elastic Modulus of Single Linear Polycatenane. CHINESE JOURNAL OF POLYMER SCIENCE 2023. [DOI: 10.1007/s10118-023-2902-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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2
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Rothörl J, Wettermann S, Virnau P, Bhattacharya A. Knot formation of dsDNA pushed inside a nanochannel. Sci Rep 2022; 12:5342. [PMID: 35351953 PMCID: PMC8964721 DOI: 10.1038/s41598-022-09242-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 03/17/2022] [Indexed: 12/23/2022] Open
Abstract
Recent experiments demonstrated that knots in single molecule dsDNA can be formed by compression in a nanochannel. In this manuscript, we further elucidate the underlying molecular mechanisms by carrying out a compression experiment in silico, where an equilibrated coarse-grained double-stranded DNA confined in a square channel is pushed by a piston. The probability of forming knots is a non-monotonic function of the persistence length and can be enhanced significantly by increasing the piston speed. Under compression knots are abundant and delocalized due to a backfolding mechanism from which chain-spanning loops emerge, while knots are less frequent and only weakly localized in equilibrium. Our in silico study thus provides insights into the formation, origin and control of DNA knots in nanopores.
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3
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Pan X, Ding M, Li L. Experimental Validation on Average Conformation of a Comblike Polystyrene Library in Dilute Solutions: Universal Scaling Laws and Abnormal SEC Elution Behavior. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01029] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Xuejun Pan
- Food Science and Processing Research Center, College of Chemistry and Environmental Engineering, Shenzhen University, Shenzhen 518060, China
- Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China
| | - 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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4
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Baral S, Liu C, Chakraborty UK, Kubo K, Mao X, Coates GW, Chen P. Single-chain polymerization dynamics and conformational mechanics of conjugated polymers. Chem 2021. [DOI: 10.1016/j.chempr.2021.05.007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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5
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Gilbert BR, Thornburg ZR, Lam V, Rashid FZM, Glass JI, Villa E, Dame RT, Luthey-Schulten Z. Generating Chromosome Geometries in a Minimal Cell From Cryo-Electron Tomograms and Chromosome Conformation Capture Maps. Front Mol Biosci 2021; 8:644133. [PMID: 34368224 PMCID: PMC8339304 DOI: 10.3389/fmolb.2021.644133] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2020] [Accepted: 05/14/2021] [Indexed: 12/31/2022] Open
Abstract
JCVI-syn3A is a genetically minimal bacterial cell, consisting of 493 genes and only a single 543 kbp circular chromosome. Syn3A’s genome and physical size are approximately one-tenth those of the model bacterial organism Escherichia coli’s, and the corresponding reduction in complexity and scale provides a unique opportunity for whole-cell modeling. Previous work established genome-scale gene essentiality and proteomics data along with its essential metabolic network and a kinetic model of genetic information processing. In addition to that information, whole-cell, spatially-resolved kinetic models require cellular architecture, including spatial distributions of ribosomes and the circular chromosome’s configuration. We reconstruct cellular architectures of Syn3A cells at the single-cell level directly from cryo-electron tomograms, including the ribosome distributions. We present a method of generating self-avoiding circular chromosome configurations in a lattice model with a resolution of 11.8 bp per monomer on a 4 nm cubic lattice. Realizations of the chromosome configurations are constrained by the ribosomes and geometry reconstructed from the tomograms and include DNA loops suggested by experimental chromosome conformation capture (3C) maps. Using ensembles of simulated chromosome configurations we predict chromosome contact maps for Syn3A cells at resolutions of 250 bp and greater and compare them to the experimental maps. Additionally, the spatial distributions of ribosomes and the DNA-crowding resulting from the individual chromosome configurations can be used to identify macromolecular structures formed from ribosomes and DNA, such as polysomes and expressomes.
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Affiliation(s)
- Benjamin R Gilbert
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, United States
| | - Zane R Thornburg
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, United States
| | - Vinson Lam
- Division of Biological Sciences, University of California San Diego, San Diego, CA, United States
| | - Fatema-Zahra M Rashid
- Leiden Institute of Chemistry, Leiden University, Leiden, Netherlands.,Center for Microbial Cell Biology, Leiden University, Leiden, Netherlands
| | - John I Glass
- Synthetic Biology Group, J. Craig Venter Institute, La Jolla, CA, United States
| | - Elizabeth Villa
- Division of Biological Sciences, University of California San Diego, San Diego, CA, United States
| | - Remus T Dame
- Leiden Institute of Chemistry, Leiden University, Leiden, Netherlands.,Center for Microbial Cell Biology, Leiden University, Leiden, Netherlands
| | - Zaida Luthey-Schulten
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, United States
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6
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Majumdar D. Elasticity of a DNA chain dotted with bubbles under force. Phys Rev E 2021; 103:052412. [PMID: 34134228 DOI: 10.1103/physreve.103.052412] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2020] [Accepted: 05/04/2021] [Indexed: 11/07/2022]
Abstract
The flexibility and the extension along the direction of the force are shown to be related to the bubble number fluctuation and the average number of bubbles, respectively, when the strands of the DNA are subjected to a force along the same direction, here called a stretching force. The force-temperature phase diagram shows the existence of a tricritical point, where the first-order force-induced zipping transition becomes continuous. On the other hand, when the forces are being applied in opposite directions, here called an unzipping force, the transition remains first order, with the possibility of vanishing of the low-temperature reentrant phase for a semiflexible DNA. Moreover, we found that the bulk elasticity changes only if an external force penetrates the bound phase and affects the bubble states.
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Affiliation(s)
- Debjyoti Majumdar
- Institute of Physics, Bhubaneswar, Odisha 751005, India and Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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7
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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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8
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Sherck N, Webber T, Brown DR, Keller T, Barry M, DeStefano A, Jiao S, Segalman RA, Fredrickson GH, Shell MS, Han S. End-to-End Distance Probability Distributions of Dilute Poly(ethylene oxide) in Aqueous Solution. J Am Chem Soc 2020; 142:19631-19641. [DOI: 10.1021/jacs.0c08709] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Nicholas Sherck
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Thomas Webber
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Dennis Robinson Brown
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Timothy Keller
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
| | - Mikayla Barry
- Department of Materials, University of California, Santa Barbara, California 93106, United States
| | - Audra DeStefano
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Sally Jiao
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Rachel A. Segalman
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Department of Materials, University of California, Santa Barbara, California 93106, United States
| | - Glenn H. Fredrickson
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Department of Materials, University of California, Santa Barbara, California 93106, United States
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - M. Scott Shell
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Songi Han
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
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9
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Affiliation(s)
- Sarit Dutta
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Charles E. Sing
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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10
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Jia J, Li K, Hofmann A, Heermann DW. The Effect of Bending Rigidity on Polymers. MACROMOL THEOR SIMUL 2019. [DOI: 10.1002/mats.201800071] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Jiying Jia
- Institute for Theoretical Physics Philosophenweg 12 69120 Heidelberg Germany
| | - Kunhe Li
- Institute for Theoretical Physics Philosophenweg 12 69120 Heidelberg Germany
| | - Andreas Hofmann
- Institute for Theoretical Physics Philosophenweg 12 69120 Heidelberg Germany
| | - Dieter W. Heermann
- Institute for Theoretical Physics Philosophenweg 19 69120 Heidelberg Germany
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11
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Zhang JZ, Peng XY, Liu S, Jiang BP, Ji SC, Shen XC. The Persistence Length of Semiflexible Polymers in Lattice Monte Carlo Simulations. Polymers (Basel) 2019; 11:E295. [PMID: 30960279 PMCID: PMC6419224 DOI: 10.3390/polym11020295] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2019] [Revised: 02/01/2019] [Accepted: 02/05/2019] [Indexed: 01/10/2023] Open
Abstract
While applying computer simulations to study semiflexible polymers, it is a primary task to determine the persistence length that characterizes the chain stiffness. One frequently asked question concerns the relationship between persistence length and the bending constant of applied bending potential. In this paper, theoretical persistence lengths of polymers with two different bending potentials were analyzed and examined by using lattice Monte Carlo simulations. We found that the persistence length was consistent with theoretical predictions only in bond fluctuation model with cosine squared angle potential. The reason for this is that the theoretical persistence length is calculated according to a continuous bond angle, which is discrete in lattice simulations. In lattice simulations, the theoretical persistence length is larger than that in continuous simulations.
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Affiliation(s)
- Jing-Zi Zhang
- State Key Laboratory for Chemistry and Molecular Engineering of Medical Resources, School of Chemistry and Pharmaceutical Sciences, Guangxi Normal University, Guilin 541004, China.
| | - Xiang-Yao Peng
- State Key Laboratory for Chemistry and Molecular Engineering of Medical Resources, School of Chemistry and Pharmaceutical Sciences, Guangxi Normal University, Guilin 541004, China.
| | - Shan Liu
- State Key Laboratory for Chemistry and Molecular Engineering of Medical Resources, School of Chemistry and Pharmaceutical Sciences, Guangxi Normal University, Guilin 541004, China.
| | - Bang-Ping Jiang
- State Key Laboratory for Chemistry and Molecular Engineering of Medical Resources, School of Chemistry and Pharmaceutical Sciences, Guangxi Normal University, Guilin 541004, China.
| | - Shi-Chen Ji
- State Key Laboratory for Chemistry and Molecular Engineering of Medical Resources, School of Chemistry and Pharmaceutical Sciences, Guangxi Normal University, Guilin 541004, China.
| | - Xing-Can Shen
- State Key Laboratory for Chemistry and Molecular Engineering of Medical Resources, School of Chemistry and Pharmaceutical Sciences, Guangxi Normal University, Guilin 541004, China.
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12
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Linna RP, Suhonen PM, Piili J. Rigidity-induced scale invariance in polymer ejection from capsid. Phys Rev E 2017; 96:052402. [PMID: 29347730 DOI: 10.1103/physreve.96.052402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2017] [Indexed: 06/07/2023]
Abstract
While the dynamics of a fully flexible polymer ejecting a capsid through a nanopore has been extensively studied, the ejection dynamics of semiflexible polymers has not been properly characterized. Here we report results from simulations of ejection dynamics of semiflexible polymers ejecting from spherical capsids. Ejections start from strongly confined polymer conformations of constant initial monomer density. We find that, unlike for fully flexible polymers, for semiflexible polymers the force measured at the pore does not show a direct relation to the instantaneous ejection velocity. The cumulative waiting time t(s), that is, the time at which a monomer s exits the capsid the last time, shows a clear change when increasing the polymer rigidity κ. The major part of an ejecting polymer is driven out of the capsid by internal pressure. At the final stage the polymer escapes the capsid by diffusion. For the driven part there is a crossover from essentially exponential growth of t with s of the fully flexible polymers to a scale-invariant form. In addition, a clear dependence of t on polymer length N_{0} was found. These findings combined give the dependence t(s)∝N_{0}^{0.55}s^{1.33} for the strongly rigid polymers. This crossover in dynamics where κ acts as a control parameter is reminiscent of a phase transition. This analogy is further enhanced by our finding a perfect data collapse of t for polymers of different N_{0} and any constant κ.
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Affiliation(s)
- R P Linna
- Department of Computer Science, Aalto University, P.O. Box 15400, FI-00076 Aalto, Finland
| | - P M Suhonen
- Department of Computer Science, Aalto University, P.O. Box 15400, FI-00076 Aalto, Finland
| | - J Piili
- Department of Computer Science, Aalto University, P.O. Box 15400, FI-00076 Aalto, Finland
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13
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Xu G, Huang Z, Chen P, Cui T, Zhang X, Miao B, Yan LT. Optimal Reactivity and Improved Self-Healing Capability of Structurally Dynamic Polymers Grafted on Janus Nanoparticles Governed by Chain Stiffness and Spatial Organization. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2017; 13:1603155. [PMID: 28092430 DOI: 10.1002/smll.201603155] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2016] [Revised: 11/04/2016] [Indexed: 06/06/2023]
Abstract
Structurally dynamic polymers are recognized as a key potential to revolutionize technologies ranging from design of self-healing materials to numerous biomedical applications. Despite intense research in this area, optimizing reactivity and thereby improving self-healing ability at the most fundamental level pose urgent issue for wider applications of such emerging materials. Here, the authors report the first mechanistic investigation of the fundamental principle for the dependence of reactivity and self-healing capabilities on the properties inherent to dynamic polymers by combining large-scale computer simulation, theoretical analysis, and experimental discussion. The results allow to reveal how chain stiffness and spatial organization regulate reactivity of dynamic polymers grafted on Janus nanoparticles and mechanically mediated reaction in their reverse chemistry, and, particularly, identify that semiflexible dynamic polymers possess the optimal reactivity and self-healing ability. The authors also develop an analytical model of blob theory of polymer chains to complement the simulation results and reveal essential scaling laws for optimal reactivity. The findings offer new insights into the physical mechanism in various systems involving reverse/dynamic chemistry. These studies highlight molecular engineering of polymer architecture and intrinsic property as a versatile strategy in control over the structural responses and functionalities of emerging materials with optimized self-healing capabilities.
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Affiliation(s)
- Guoxi Xu
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, P. R. China
| | - Zihan Huang
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, P. R. China
| | - Pengyu Chen
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, P. R. China
| | - Tianqi Cui
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, P. R. 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
| | - Li-Tang Yan
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, P. R. China
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14
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Milchev A, Egorov SA, Binder K. Semiflexible polymers confined in a slit pore with attractive walls: two-dimensional liquid crystalline order versus capillary nematization. SOFT MATTER 2017; 13:1888-1903. [PMID: 28180230 DOI: 10.1039/c7sm00105c] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Semiflexible polymers under good solvent conditions interacting with attractive planar surfaces are investigated by Molecular Dynamics (MD) simulations and classical Density Functional Theory (DFT). A bead-spring type potential complemented by a bending potential is used, allowing variation of chain stiffness from completely flexible coils to rod-like polymers whose persistence length by far exceeds their contour length. Solvent is only implicitly included, monomer-monomer interactions being purely repulsive, while two types of attractive wall-monomer interactions are considered: (i) a strongly attractive Mie-type potential, appropriate for a strictly structureless wall, and (ii) a corrugated wall formed by Lennard-Jones particles arranged on a square lattice. It is found that in dilute solutions the former case leads to the formation of a strongly adsorbed surface layer, and the profile of density and orientational order in the z-direction perpendicular to the wall is predicted by DFT in nice agreement with MD. While for very low bulk densities a Kosterlitz-Thouless type transition from the isotropic phase to a phase with power-law decay of nematic correlations is suggested to occur in the strongly adsorbed layer, for larger densities a smectic-C phase in the surface layer is detected. No "capillary nematization" effect at higher bulk densities is found in this system, unlike systems with repulsive walls. This finding is attributed to the reduction of the bulk density (in the center of the slit pore) due to polymer adsorption on the attractive wall, for a system studied in the canonical ensemble. Consequently in a system with two attractive walls nematic order in the slit pore can occur only at a higher density than for a bulk system.
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Affiliation(s)
- Andrey Milchev
- Institute for Physical Chemistry, Bulgarian Academia of Sciences, 1113 Sofia, Bulgaria. and Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany
| | - Sergei A Egorov
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany and Department of Chemistry, University of Virginia, Charlottesville, VA 22901, USA
| | - Kurt Binder
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany
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15
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Salari H, Eslami-Mossallam B, Ranjbar HF, Ejtehadi MR. Stiffer double-stranded DNA in two-dimensional confinement due to bending anisotropy. Phys Rev E 2017; 94:062407. [PMID: 28085439 DOI: 10.1103/physreve.94.062407] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2016] [Indexed: 11/07/2022]
Abstract
Using analytical approach and Monte Carlo (MC) simulations, we study the elastic behavior of the intrinsically twisted elastic ribbons with bending anisotropy, such as double-stranded DNA (dsDNA), in two-dimensional (2D) confinement. We show that, due to the bending anisotropy, the persistence length of dsDNA in 2D conformations is always greater than three-dimensional (3D) conformations. This result is in consistence with the measured values for DNA persistence length in 2D and 3D in equal biological conditions. We also show that in two dimensions, an anisotropic, intrinsically twisted polymer exhibits an implicit twist-bend coupling, which leads to the transient curvature increasing with a half helical turn periodicity along the bent polymer.
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Affiliation(s)
- H Salari
- Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran
| | - B Eslami-Mossallam
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, the Netherlands
| | - H F Ranjbar
- Institute of Complex Systems (ICS-2), Forschungszentrum Jülich, Wilhelm-Johnen-Straße, 52425 Jülich, Germany
| | - M R Ejtehadi
- Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran and School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
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16
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Nikoubashman A, Milchev A, Binder K. Dynamics of single semiflexible polymers in dilute solution. J Chem Phys 2016; 145:234903. [DOI: 10.1063/1.4971861] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Andrey Milchev
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
- 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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17
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Chatterjee D, Vilgis TA. Scaling Laws of Bottle-Brush Polymers in Dilute Solutions. MACROMOL THEOR SIMUL 2016. [DOI: 10.1002/mats.201600074] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Debarati Chatterjee
- Max-Planck Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Thomas A. Vilgis
- Max-Planck Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
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18
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Huang A, Hsu HP, Bhattacharya A, Binder K. Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles. J Chem Phys 2016; 143:243102. [PMID: 26723587 DOI: 10.1063/1.4929600] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
The conformations of semiflexible polymers in two dimensions confined in a strip of width D are studied by computer simulations, investigating two different models for the mechanism by which chain stiffness is realized. One model (studied by molecular dynamics) is a bead-spring model in the continuum, where stiffness is controlled by a bond angle potential allowing for arbitrary bond angles. The other model (studied by Monte Carlo) is a self-avoiding walk chain on the square lattice, where only discrete bond angles (0° and ±90°) are possible, and the bond angle potential then controls the density of kinks along the chain contour. The first model is a crude description of DNA-like biopolymers, while the second model (roughly) describes synthetic polymers like alkane chains. It is first demonstrated that in the bulk the crossover from rods to self-avoiding walks for both models is very similar, when one studies average chain linear dimensions, transverse fluctuations, etc., despite their differences in local conformations. However, in quasi-one-dimensional confinement two significant differences between both models occur: (i) The persistence length (extracted from the average cosine of the bond angle) gets renormalized for the lattice model when D gets less than the bulk persistence length, while in the continuum model it stays unchanged. (ii) The monomer density near the repulsive walls for semiflexible polymers is compatible with a power law predicted for the Kratky-Porod model in the case of the bead-spring model, while for the lattice case it tends to a nonzero constant across the strip. However, for the density of chain ends, such a constant behavior seems to occur for both models, unlike the power law observed for flexible polymers. In the regime where the bulk persistence length ℓp is comparable to D, hairpin conformations are detected, and the chain linear dimensions are discussed in terms of a crossover from the Daoud/De Gennes "string of blobs"-picture to the flexible rod picture when D decreases and/or the chain stiffness increases. Introducing a suitable further coarse-graining of the chain contours of the continuum model, direct estimates for the deflection length and its distribution could be obtained.
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Affiliation(s)
- Aiqun Huang
- Department of Physics, University of Central Florida, Orlando, Florida 32816-2385, USA
| | - Hsiao-Ping Hsu
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany
| | - Aniket Bhattacharya
- Department of Physics, University of Central Florida, Orlando, Florida 32816-2385, USA
| | - Kurt Binder
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany
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19
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Bu X, Zhang X. Scattering and Gaussian Fluctuation Theory for Semiflexible Polymers. Polymers (Basel) 2016; 8:E301. [PMID: 30974614 PMCID: PMC6432401 DOI: 10.3390/polym8090301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2016] [Revised: 08/05/2016] [Accepted: 08/08/2016] [Indexed: 11/16/2022] Open
Abstract
The worm-like chain is one of the best theoretical models of the semiflexible polymer. The structure factor, which can be obtained by scattering experiment, characterizes the density correlation in different length scales. In the present review, the numerical method to compute the static structure factor of the worm-like chain model and its general properties are demonstrated. Especially, the chain length and persistence length involved multi-scale nature of the worm-like chain model are well discussed. Using the numerical structure factor, Gaussian fluctuation theory of the worm-like chain model can be developed, which is a powerful tool to analyze the structure stability and to predict the spinodal line of the system. The microphase separation of the worm-like diblock copolymer is considered as an example to demonstrate the usage of Gaussian fluctuation theory.
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Affiliation(s)
- Xiangyu Bu
- School of Science, Beijing Jiaotong University, Beijing 100044, China.
| | - Xinghua Zhang
- School of Science, Beijing Jiaotong University, Beijing 100044, China.
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20
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Eisenstecken T, Gompper G, Winkler RG. Conformational Properties of Active Semiflexible Polymers. Polymers (Basel) 2016; 8:E304. [PMID: 30974577 PMCID: PMC6431937 DOI: 10.3390/polym8080304] [Citation(s) in RCA: 63] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2016] [Revised: 08/03/2016] [Accepted: 08/04/2016] [Indexed: 01/21/2023] Open
Abstract
The conformational properties of flexible and semiflexible polymers exposed to active noise are studied theoretically. The noise may originate from the interaction of the polymer with surrounding active (Brownian) particles or from the inherent motion of the polymer itself, which may be composed of active Brownian particles. In the latter case, the respective monomers are independently propelled in directions changing diffusively. For the description of the polymer, we adopt the continuous Gaussian semiflexible polymer model. Specifically, the finite polymer extensibility is taken into account, which turns out to be essential for the polymer conformations. Our analytical calculations predict a strong dependence of the relaxation times on the activity. In particular, semiflexible polymers exhibit a crossover from a bending elasticity-dominated dynamics to the flexible polymer dynamics with increasing activity. This leads to a significant activity-induced polymer shrinkage over a large range of self-propulsion velocities. For large activities, the polymers swell and their extension becomes comparable to the contour length. The scaling properties of the mean square end-to-end distance with respect to the polymer length and monomer activity are discussed.
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Affiliation(s)
- Thomas Eisenstecken
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany.
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany.
| | - Roland G Winkler
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany.
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21
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Luzhbin DA, Chen YL. Shifting the Isotropic–Nematic Transition in Very Strongly Confined Semiflexible Polymer Solutions. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b00986] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Dmytro A. Luzhbin
- Institute of Physics, Academia Sinica, Taipei, Taiwan, R.O.C
- Department of Chemical Engineering, National Tsing-Hua University, Hsinchu, Taiwan, R.O.C
- Department of Physics, National Taiwan University, Taipei, Taiwan, R.O.C
| | - Yeng-Long Chen
- Institute of Physics, Academia Sinica, Taipei, Taiwan, R.O.C
- Department of Chemical Engineering, National Tsing-Hua University, Hsinchu, Taiwan, R.O.C
- Department of Physics, National Taiwan University, Taipei, Taiwan, R.O.C
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22
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Egorov SA, Milchev A, Virnau P, Binder K. Semiflexible polymers under good solvent conditions interacting with repulsive walls. J Chem Phys 2016; 144:174902. [DOI: 10.1063/1.4947254] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sergei A. Egorov
- Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901, USA
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany
- Leibniz-Institut für Polymerforschung, Institut Theorie der Polymere, Hohe St. 6, 01069 Dresden, Germany
| | - Andrey Milchev
- Institute for Physical Chemistry, Bulgarian Academia of Sciences, 1113 Sofia, Bulgaria
| | - Peter Virnau
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany
| | - Kurt Binder
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany
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23
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Kumar S, Pattanayek SK, Pereira GG, Mohanty S. Effect of Uniformly Applied Force and Molecular Characteristics of a Polymer Chain on Its Adhesion to Graphene Substrates. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2016; 32:2750-2760. [PMID: 26919125 DOI: 10.1021/acs.langmuir.5b04028] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The force-induced desorption of a polymer chain from a graphene substrate is studied with molecular dynamics (MD). A critical force needs to be exceeded before detachment of the polymer from the substrate. It is found that for a chain to exhibit good adhesive properties the chain configuration should consist of fibrils-elongated, aligned sections of polymers and cavities which dissipate the applied energy. A fibrillation index is defined to quantify the quality of fibrils. We focus on the molecular properties of the polymer chain, which can lead to large amounts of fibrillation, and find that both strong attraction between the polymer and substrate and good solvency conditions are important conditions for this. We also vary the stiffness of the chain and find that for less stiff chains a plateau in the stress-strain curve gives rise to good adhesion however for very stiff chains there is limited elongation of the chain but the chain can still exhibit good fibrillation by a lamella-like rearrangement. Finally, it is found that the detachment time, t, of a polymer from the adsorbed substrate is inversely proportional to force, F (i.e., t ∝ F(-γ)), where exponent γ depends on the solvent quality, polymer-substrate attraction, and chain stiffness.
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Affiliation(s)
- Sunil Kumar
- Department of Chemical Engineering, Indian Institute of Technology , New Delhi, 110016 India
| | - Sudip K Pattanayek
- Department of Chemical Engineering, Indian Institute of Technology , New Delhi, 110016 India
| | - Gerald G Pereira
- CSIRO Mathematics, Informatics & Statistics, Private Bag 10, Clayton South, 3169 Australia
| | - Sanat Mohanty
- Department of Chemical Engineering, Indian Institute of Technology , New Delhi, 110016 India
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24
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Li X, Dorfman KD. Effect of excluded volume on the force-extension of wormlike chains in slit confinement. J Chem Phys 2016; 144:104902. [PMID: 26979704 DOI: 10.1063/1.4943195] [Citation(s) in RCA: 4] [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 use pruned-enriched Rosenbluth method simulations to develop a quantitative phase diagram for the stretching of a real wormlike chain confined in a slit. Our simulations confirm the existence of a "confined Pincus" regime in slit confinement, analogous to the Pincus regime in free solution, where excluded volume effects are sensible. The lower bound for the confined Pincus regime in the force-molecular weight plane, as well as the scaling of the extension with force and slit size, agree with an existing scaling theory for this regime. The upper bound of the confined Pincus regime depends on the strength of the confinement. For strong confinement, the confined Pincus regime ends when the contour length in the Pincus blob is too short to have intrablob excluded volume. As a result, the chain statistics become ideal and the confined Pincus regime at low forces is connected directly to ideal chain stretching at large forces. In contrast, for weak confinement, the confined Pincus regime ends when the Pincus blobs no longer fit inside the slit, even though there is sufficient contour length to have excluded volume inside the Pincus blob. As a result, weak confinement leads to a free-solution Pincus regime intervening between the confined Pincus regime for weak forces and ideal chain stretching at strong forces. Our results highlight shortcomings in existing models for the stretching of wormlike chains in slits.
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Affiliation(s)
- Xiaolan Li
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
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25
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Huang Z, Lu C, Dong B, Xu G, Ji C, Zhao K, Yan LT. Chain stiffness regulates entropy-templated perfect mixing at single-nanoparticle level. NANOSCALE 2016; 8:1024-1032. [PMID: 26660086 DOI: 10.1039/c5nr06134b] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The mixing on a single-particle level of chemically incompatible nanoparticles is an outstanding challenge for many applications. Burgeoning research activity suggests that entropic templating is a potential strategy to address this issue. Herein, using systematic computer simulations of model nanoparticle systems, we show that the entropy-templated interfacial organization of nanoparticles significantly depends on the stiffness of tethered chains. Unexpectedly, the optimal chain stiffness can be identified wherein a system exhibits the most perfect mixing for a certain compression ratio. Our simulations demonstrate that entropic templating regulated by chain stiffness precisely reflects various entropic repulsion states that arise from typical conformation regimes of semiflexible chains. The physical mechanism of the chain stiffness effect is revealed by analyzing the entropic repulsion states of tethered chains and quantitatively estimating the resulting entropy penalties, which provides direct evidence that supports the key role of entropic transition in the entropic templating strategy, as suggested in experiments. Moreover, the model nanoparticle systems are found to evolve into binary nanoparticle superlattices by remixing at extremely high stiffness. The findings facilitate the wide application of the entropic templating strategy in creating interfacially reactive nanomaterials with ordered structures on the single-nanoparticle level as well as mechanomutable responses.
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Affiliation(s)
- Zihan Huang
- Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China.
| | - Ce Lu
- Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China.
| | - Bojun Dong
- Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China.
| | - Guoxi Xu
- Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China.
| | - Chengcheng Ji
- Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China.
| | - Kongyin Zhao
- State Key Laboratory of Separation Membranes and Membrane Processes, Tianjin Polytechnic University, Tianjin 300387, China.
| | - Li-Tang Yan
- Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China.
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26
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Malekzadeh Moghani M, Khomami B. Flexible polyelectrolyte chain in a strong electrolyte solution: Insight into equilibrium properties and force-extension behavior from mesoscale simulation. J Chem Phys 2016; 144:024903. [PMID: 26772586 DOI: 10.1063/1.4939720] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Macromolecules with ionizable groups are ubiquitous in biological and synthetic systems. Due to the complex interaction between chain and electrostatic decorrelation lengths, both equilibrium properties and micro-mechanical response of dilute solutions of polyelectrolytes (PEs) are more complex than their neutral counterparts. In this work, the bead-rod micromechanical description of a chain is used to perform hi-fidelity Brownian dynamics simulation of dilute PE solutions to ascertain the self-similar equilibrium behavior of PE chains with various linear charge densities, scaling of the Kuhn step length (lE) with salt concentration cs and the force-extension behavior of the PE chain. In accord with earlier theoretical predictions, our results indicate that for a chain with n Kuhn segments, lE ∼ cs (-0.5) as linear charge density approaches 1/n. Moreover, the constant force ensemble simulation results accurately predict the initial non-linear force-extension region of PE chain recently measured via single chain experiments. Finally, inspired by Cohen's extraction of Warner's force law from the inverse Langevin force law, a novel numerical scheme is developed to extract a new elastic force law for real chains from our discrete set of force-extension data similar to Padè expansion, which accurately depicts the initial non-linear region where the total Kuhn length is less than the thermal screening length.
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Affiliation(s)
- Mahdy Malekzadeh Moghani
- Materials Research and Innovation Laboratory, Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Bamin Khomami
- Materials Research and Innovation Laboratory, Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
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27
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Klepinger AC, Greenier MK, Levy SL. Stretching DNA Molecules in Strongly Confining Nanofluidic Slits. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b01712] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | - Madeline K. Greenier
- Department
of Physics, Binghamton University, Binghamton, New York 13902, United States
| | - Stephen L. Levy
- Department
of Physics, Binghamton University, Binghamton, New York 13902, United States
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28
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Li X, Schroeder CM, Dorfman KD. Modeling the stretching of wormlike chains in the presence of excluded volume. SOFT MATTER 2015; 11:5947-5954. [PMID: 26123827 DOI: 10.1039/c5sm01333j] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We propose an interpolation formula (the EV-WLC relation) for the force-extension behavior of wormlike chains in the presence of hard-core excluded volume interactions, analogous to the classic interpolation formula from Marko and Siggia for ideal wormlike chains. Using pruned-enriched Rosenbluth method (PERM) simulations of asymptotically long, discrete wormlike chains in an external force, we show that the error in the EV-WLC interpolation formula to describe discrete wormlike chains is systematically smaller than the error in the Marko-Siggia interpolation formula, except for the saturation region in which both formulas have the same limiting behavior. We anticipate that the EV-WLC interpolation formula will prove useful in the coarse-graining of wormlike chain models for dynamic simulations. Related results for the excess free energy due to excluded volume provide strong support for the physical basis of the Pincus regime.
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Affiliation(s)
- Xiaolan Li
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA.
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29
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Hsu HP. Monte Carlo simulations of lattice models for single polymer systems. J Chem Phys 2015; 141:164903. [PMID: 25362337 DOI: 10.1063/1.4899258] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Single linear polymer chains in dilute solutions under good solvent conditions are studied by Monte Carlo simulations with the pruned-enriched Rosenbluth method up to the chain length N~O(10(4)). Based on the standard simple cubic lattice model (SCLM) with fixed bond length and the bond fluctuation model (BFM) with bond lengths in a range between 2 and √10, we investigate the conformations of polymer chains described by self-avoiding walks on the simple cubic lattice, and by random walks and non-reversible random walks in the absence of excluded volume interactions. In addition to flexible chains, we also extend our study to semiflexible chains for different stiffness controlled by a bending potential. The persistence lengths of chains extracted from the orientational correlations are estimated for all cases. We show that chains based on the BFM are more flexible than those based on the SCLM for a fixed bending energy. The microscopic differences between these two lattice models are discussed and the theoretical predictions of scaling laws given in the literature are checked and verified. Our simulations clarify that a different mapping ratio between the coarse-grained models and the atomistically realistic description of polymers is required in a coarse-graining approach due to the different crossovers to the asymptotic behavior.
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Affiliation(s)
- Hsiao-Ping Hsu
- Max-Planck-Institut für Polymerforschung, Ackermannweg 10, D-55128 Mainz, Germany
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30
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Saleh OA. Perspective: Single polymer mechanics across the force regimes. J Chem Phys 2015; 142:194902. [DOI: 10.1063/1.4921348] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Affiliation(s)
- Omar A. Saleh
- Materials Department and BMSE Program, University of California, Santa Barbara, California 93106, USA
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31
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Alexeev AV, Maltseva DV, Ivanov VA, Klushin LI, Skvortsov AM. Force-extension curves for broken-rod macromolecules: Dramatic effects of different probing methods for two and three rods. J Chem Phys 2015; 142:164905. [PMID: 25933789 DOI: 10.1063/1.4919295] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study force-extension curves of a single semiflexible chain consisting of several rigid rods connected by flexible spacers. The atomic force microscopy and laser optical or magnetic tweezers apparatus stretching these rod-coil macromolecules are discussed. In addition, the stretching by external isotropic force is analyzed. The main attention is focused on computer simulation and analytical results. We demonstrate that the force-extension curves for rod-coil chains composed of two or three rods of equal length differ not only quantitatively but also qualitatively in different probe methods. These curves have an anomalous shape for a chain of two rods. End-to-end distributions of rod-coil chains are calculated by Monte Carlo method and compared with analytical equations. The influence of the spacer's length on the force-extension curves in different probe methods is analyzed. The results can be useful for interpreting experiments on the stretching of rod-coil block-copolymers.
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Affiliation(s)
- A V Alexeev
- Faculty of Physics, Moscow State University, 119991 Moscow, Russia
| | - D V Maltseva
- Faculty of Physics, Moscow State University, 119991 Moscow, Russia
| | - V A Ivanov
- Faculty of Physics, Moscow State University, 119991 Moscow, Russia
| | - L I Klushin
- Department of Physics, American University of Beirut, P.O. Box 11-0236, Beirut 1107 2020, Lebanon
| | - A M Skvortsov
- Chemical-Pharmaceutical Academy, Prof. Popova 14, 197022 St. Petersburg, Russia
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32
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Egorov SA, Hsu HP, Milchev A, Binder K. Semiflexible polymer brushes and the brush-mushroom crossover. SOFT MATTER 2015; 11:2604-2616. [PMID: 25687784 DOI: 10.1039/c4sm02862g] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Semiflexible polymers end-grafted to a repulsive planar substrate under good solvent conditions are studied by scaling arguments, computer simulations, and self-consistent field theory. Varying the chain length N, persistence length lp, and grafting density σg, the chain linear dimensions and distribution functions of all monomers and of the free chain ends are studied. Particular attention is paid to the limit of very small σg, where the grafted chains behave as "mushrooms" no longer interacting with each other. Unlike a flexible mushroom, which has a self-similar structure from the size (a) of an effective monomer up to the mushroom height (h/a ∝ N(v), ν ≈ 3/5), a semiflexible mushroom (like a free semiflexible chain) exhibits three different scaling regimes, h/a ∝ N for contour length L = Na < lp, a Gaussian regime, h/a ∝ (Llp)(1/2)/a for lp ≪ L ≪ R* ∝ (lp(2)/a), and a regime controlled by excluded volume, h/a ∝ (lp/a)(1/5)N(ν). The semiflexible brush is predicted to scale as h/a ∝ (lpaσg)(1/3)N in the excluded volume regime, and h/a ∝ (lpa(3)σ(2))(1/4)N in the Gaussian regime. Since in the volume taken by a semiflexible mushroom excluded-volume interactions are much weaker in comparison to a flexible mushroom, there occurs an additional regime where semiflexible mushrooms overlap without significant chain stretching. Moreover, since the size of a semiflexible mushroom is much larger than the size of a flexible mushroom with the same N, the crossover from mushroom to brush behavior is predicted to take place at much smaller densities than for fully flexible chains. The numerical results, however, confirm the scaling predictions only qualitatively; for chain lengths that are relevant for experiments, often intermediate effective exponents are observed due to extended crossovers.
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Affiliation(s)
- Sergei A Egorov
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, D-55128 Mainz, Germany
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33
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Luettmer-Strathmann J, Binder K. Transitions of tethered chain molecules under tension. J Chem Phys 2014; 141:114911. [DOI: 10.1063/1.4895729] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Affiliation(s)
- Jutta Luettmer-Strathmann
- Department of Physics and Department of Chemistry, The University of Akron, Akron, Ohio 44325-4001, USA
| | - Kurt Binder
- Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, D-55099 Mainz, Germany
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34
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Huang A, Bhattacharya A, Binder K. Conformations, transverse fluctuations, and crossover dynamics of a semi-flexible chain in two dimensions. J Chem Phys 2014; 140:214902. [DOI: 10.1063/1.4879537] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
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35
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Milchev A, Binder K. Unconventional ordering behavior of semi-flexible polymers in dense brushes under compression. SOFT MATTER 2014; 10:3783-3797. [PMID: 24700280 DOI: 10.1039/c3sm53133c] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Using a coarse-grained bead-spring model for semi-flexible macromolecules which form a polymer brush, the structure and dynamics of the polymers were investigated, varying the chain stiffness and the grafting density. The anchoring conditions for the grafted chains were chosen such that their first bonds were oriented along the normal to the substrate plane. The compression of such a semi-flexible brush by a planar piston was observed to be a two-stage process: for a small compression the chains were shown to contract by "buckling" deformation whereas for a larger compression the chains exhibited a collective (almost uniform) bending deformation. Thus, the stiff polymer brush underwent a 2nd order phase transition of collective bond reorientation. The pressure, required to keep the stiff brush at a given degree of compression, was thereby significantly smaller than for an otherwise identical brush made of entirely flexible polymer chains! While both the brush height and the chain linear dimensions in the z-direction perpendicular to the substrate increased monotonically with an increase in the chain stiffness, the lateral (xy) chain linear dimensions exhibited a maximum at an intermediate chain stiffness. Increasing the grafting density led to a strong decrease of these lateral dimensions which is compatible with an exponential decay. Also the recovery kinetics after removal of the compressing piston were studied, and were found to follow a power-law/exponential decay with time. A simple mean-field theoretical consideration, accounting for the buckling/bending behavior of semi-flexible polymer brushes under compression was suggested.
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Affiliation(s)
- Andrey Milchev
- Institute of Physical Chemistry, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
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36
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Adhikari R, Bhattacharya A. Driven translocation of a semi-flexible chain through a nanopore: a Brownian dynamics simulation study in two dimensions. J Chem Phys 2014; 138:204909. [PMID: 23742518 DOI: 10.1063/1.4807002] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study translocation dynamics of a semi-flexible polymer chain through a nanoscopic pore in two dimensions using Langevin dynamics simulation in presence of an external bias F inside the pore. For chain length N and stiffness parameter κb considered in this paper, we observe that the mean first passage time <τ> increases as <τ(κb)>~<τ(κb=0)>lp(aN) , where κb and lp are the stiffness parameter and persistence length, respectively, and aN is a constant that has a weak N dependence. We monitor the time dependence of the last monomer xN(t) at the cis compartment and calculate the tension propagation time (TP) ttp directly from simulation data for <xN(t)> ~ t as alluded in recent nonequlibrium TP theory [T. Sakaue, Phys. Rev. E 76, 021803 (2007)] and its modifications to Brownian dynamics tension propagation theory [T. Ikonen, A. Bhattacharya, T. Ala-Nissila, and W. Sung, Phys. Rev. E 85, 051803 (2012); and J. Chem. Phys. 137, 085101 (2012)] originally developed to study translocation of a fully flexible chain. We also measure ttp from peak position of the waiting time distribution W(s) of the translocation coordinate s (i.e., the monomer inside the pore), and explicitly demonstrate the underlying TP picture along the chain backbone of a translocating chain to be valid for semi-flexible chains as well. From the simulation data, we determine the dependence of ttp on chain persistence length lp and show that the ratio ttp∕<τ> is independent of the bias F.
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Affiliation(s)
- Ramesh Adhikari
- Department of Physics, University of Central Florida, Orlando, Florida 32816-2385, USA
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37
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Angelescu DG, Linse P. Monte Carlo Simulations of Multigraft Homopolymers in Good Solvent. Macromolecules 2013. [DOI: 10.1021/ma4021246] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Daniel G. Angelescu
- Romanian Academy,
“Ilie Murgulescu” Institute of Physical Chemistry, Splaiul Independentei 202, 060021 Bucharest, Romania
| | - Per Linse
- Physical Chemistry, Lund University, Box 124, SE-221 00 Lund, Sweden
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38
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Tree DR, Muralidhar A, Doyle PS, Dorfman KD. Is DNA a Good Model Polymer? Macromolecules 2013; 46:10.1021/ma401507f. [PMID: 24347685 PMCID: PMC3859536 DOI: 10.1021/ma401507f] [Citation(s) in RCA: 86] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
The details surrounding the cross-over from wormlike-specific to universal polymeric behavior has been the subject of debate and confusion even for the simple case of a dilute, unconfined wormlike chain. We have directly computed the polymer size, form factor, free energy and Kirkwood diffusivity for unconfined wormlike chains as a function of molecular weight, focusing on persistence lengths and effective widths that represent single-stranded and double-stranded DNA in a high ionic strength buffer. To do so, we use a chain-growth Monte Carlo algorithm, the Pruned-Enriched Rosenbluth Method (PERM), which allows us to estimate equilibrium and near-equilibrium dynamic properties of wormlike chains over an extremely large range of contour lengths. From our calculations, we find that very large DNA chains (≈ 1,000,000 base pairs depending on the choice of size metric) are required to reach flexible, swollen non-draining coils. Furthermore, our results indicate that the commonly used model polymer λ-DNA (48,500 base pairs) does not exhibit "ideal" scaling, but exists in the middle of the transition to long-chain behavior. We subsequently conclude that typical DNA used in experiments are too short to serve as an accurate model of long-chain, universal polymer behavior.
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Affiliation(s)
- Douglas R. Tree
- Department of Chemical Engineering and Materials Science, University of Minnesota
| | - Abhiram Muralidhar
- Department of Chemical Engineering and Materials Science, University of Minnesota
| | - Patrick S. Doyle
- Department of Chemical Engineering, Massachusetts Institute of Technology
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota
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39
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Hsu HP, Binder K. Semiflexible Macromolecules with Discrete Bond Angles Confined in Nanoslits: A Monte Carlo Test of Scaling Concepts. Macromolecules 2013. [DOI: 10.1021/ma401374e] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hsiao-Ping Hsu
- Institut
für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg
7, D-55099 Mainz, Germany
| | - Kurt Binder
- Institut
für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg
7, D-55099 Mainz, Germany
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40
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics
(BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, 3 Science Drive 2, Republic
of Singapore 117543
| | - Patrick S. Doyle
- BioSystems and Micromechanics
(BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, 3 Science Drive 2, Republic
of Singapore 117543
- Department
of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge,
Massachusetts 02139, United States
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41
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Ivanov VA, Martemyanova JA, Rodionova AS, Stukan MR. Computer simulation of stiff-chain polymers. POLYMER SCIENCE SERIES C 2013. [DOI: 10.1134/s1811238213060039] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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42
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Hsu HP, Paul W, Binder K. Estimation of persistence lengths of semiflexible polymers: Insight from simulations. POLYMER SCIENCE SERIES C 2013. [DOI: 10.1134/s1811238213060027] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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43
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Borówko M, Rżysko W, Sokołowski S, Sokołowska Z, Usatenko Z. Stretching tethered polymer chains: density functional approach. J Chem Phys 2013; 138:204707. [PMID: 23742500 DOI: 10.1063/1.4807086] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
We propose application of density functional theory to calculate the force acting on a selected segment of a tethered polymer chain that leads to stretching the chain. The density functional allows one to determine the effects due to the presence of other chains and solvent molecules. For high and moderate solvent densities the plot of the force versus the distance of the segment from the surface exhibits oscillatory behavior that has not been predicted by other approaches.
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Affiliation(s)
- M Borówko
- Department for the Modelling of Physico-Chemical Processes, MCS University, 20031 Lublin, Poland
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44
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Račko D, Cifra P. Segregation of semiflexible macromolecules in nanochannel. J Chem Phys 2013; 138:184904. [DOI: 10.1063/1.4803674] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
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45
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Hsu HP, Binder K. Effect of Chain Stiffness on the Adsorption Transition of Polymers. Macromolecules 2013. [DOI: 10.1021/ma400112q] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hsiao-Ping Hsu
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
| | - Kurt Binder
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
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46
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Hsu HP, Paul W, Binder K. Scattering function of semiflexible polymer chains under good solvent conditions. J Chem Phys 2013; 137:174902. [PMID: 23145745 DOI: 10.1063/1.4764300] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using the pruned-enriched Rosenbluth Monte Carlo algorithm, the scattering functions of semiflexible macromolecules in dilute solution under good solvent conditions are estimated both in d = 2 and d = 3 dimensions, considering also the effect of stretching forces. Using self-avoiding walks of up to N = 25,600 steps on the square and simple cubic lattices, variable chain stiffness is modeled by introducing an energy penalty ε(b) for chain bending; varying q(b) = exp (-ε(b)∕k(B)T) from q(b) = 1 (completely flexible chains) to q(b) = 0.005, the persistence length can be varied over two orders of magnitude. For unstretched semiflexible chains, we test the applicability of the Kratky-Porod worm-like chain model to describe the scattering function and discuss methods for extracting persistence length estimates from scattering. While in d = 2 the direct crossover from rod-like chains to self-avoiding walks invalidates the Kratky-Porod description, it holds in d = 3 for stiff chains if the number of Kuhn segments n(K) does not exceed a limiting value n(K)(*) (which depends on the persistence length). For stretched chains, the Pincus blob size enters as a further characteristic length scale. The anisotropy of the scattering is well described by the modified Debye function, if the actual observed chain extension <X> (end-to-end distance in the direction of the force) as well as the corresponding longitudinal and transverse linear dimensions <X(2)> - <X>(2), <R(g,⊥)(2)> are used.
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Affiliation(s)
- Hsiao-Ping Hsu
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany.
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47
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Valdman D, Lopez BJ, Valentine MT, Atzberger PJ. Force spectroscopy of complex biopolymers with heterogeneous elasticity. SOFT MATTER 2013; 9:772-778. [PMID: 24049545 PMCID: PMC3773885 DOI: 10.1039/c2sm27218k] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Cellular biopolymers can exhibit significant compositional heterogeneities as a result of the non-uniform binding of associated proteins, the formation of microstructural defects during filament assembly, or the imperfect bundling of filaments into composite structures of variable diameter. These can lead to significant variations in the local mechanical properties of biopolymers along their length. Existing spectral analysis methods assume filament homogeneity and therefore report only a single average stiffness for the entire filament. However, understanding how local effects modulate biopolymer mechanics in a spatially resolved manner is essential to understanding how binding and bundling proteins regulate biopolymer stiffness and function in cellular contexts. Here, we present a new method to determine the spatially varying material properties of individual complex biopolymers from the observation of passive thermal fluctuations of the filament conformation. We develop new statistical mechanics-based approaches for heterogeneous filaments that estimate local bending elasticities as a function of the filament arc-length. We validate this methodology using simulated polymers with known stiffness distributions, and find excellent agreement between derived and expected values. We then determine the bending elasticity of microtubule filaments of variable composition generated by repeated rounds of tubulin polymerization using either GTP or GMPCPP, a nonhydrolyzable GTP analog. Again, we find excellent agreement between mechanical and compositional heterogeneities.
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Affiliation(s)
- David Valdman
- Department of Mathematics, University of California, Santa Barbara, USA
| | - Benjamin J. Lopez
- Department of Mechanical Engineering, University of California, Santa Barbara, USA
| | - Megan T. Valentine
- Department of Mechanical Engineering, University of California, Santa Barbara, USA
| | - Paul J. Atzberger
- Department of Mathematics, University of California, Santa Barbara, USA
- Department of Mechanical Engineering, University of California, Santa Barbara, USA
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48
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Seaton DT, Schnabel S, Landau DP, Bachmann M. From flexible to stiff: systematic analysis of structural phases for single semiflexible polymers. PHYSICAL REVIEW LETTERS 2013; 110:028103. [PMID: 23383941 DOI: 10.1103/physrevlett.110.028103] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2012] [Indexed: 06/01/2023]
Abstract
Inspired by recent studies revealing unexpected pliability of semiflexible biomolecules like RNA and DNA, we systematically investigate the range of structural phases by means of a simple generic polymer model. Using a two-dimensional variant of Wang-Landau sampling to explore the conformational space in energy and stiffness within a single simulation, we identify the entire diversity of structures existing from the well-studied limit of flexible polymers to that of wormlike chains. We also discuss, in detail, the influence of finite-size effects in the formation of crystalline structures that are virtually inaccessible via conventional computational approaches.
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Affiliation(s)
- Daniel T Seaton
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
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49
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Cranford SW, Buehler MJ. Variation of Weak Polyelectrolyte Persistence Length through an Electrostatic Contour Length. Macromolecules 2012. [DOI: 10.1021/ma3008465] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Affiliation(s)
- Steven W. Cranford
- Center for Materials Science
and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United
States
- Laboratory for Atomistic and Molecular Mechanics, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 1-235A&B, Cambridge, Massachusetts 02139, United States
| | - Markus J. Buehler
- Center for Materials Science
and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United
States
- Laboratory for Atomistic and Molecular Mechanics, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 1-235A&B, Cambridge, Massachusetts 02139, United States
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50
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Milchev A, Binder K. Semiflexible polymers grafted to a solid planar substrate: Changing the structure from polymer brush to “polymer bristle”. J Chem Phys 2012; 136:194901. [DOI: 10.1063/1.4712138] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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