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Zhu Y, Zhu H, Tian F, Qiu Q, Dai L. Quantifying the effects of slit confinement on polymer knots using the tube model. Phys Rev E 2022; 105:024501. [PMID: 35291068 DOI: 10.1103/physreve.105.024501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 01/27/2022] [Indexed: 06/14/2023]
Abstract
Knots can spontaneously form in DNA, proteins, and other polymers and affect their properties. These knots often experience spatial confinement in biological systems and experiments. While confinement dramatically affects the knot behavior, the physical mechanisms underlying the confinement effects are not fully understood. In this work, we provide a simple physical picture of the polymer knots in slit confinement using the tube model. In the tube model, the polymer segments in the knot core are assumed to be confined in a virtual tube due to the topological restriction. We first perform Monte Carlo simulation of a flexible knotted chain confined in a slit. We find that with the decrease of the slit height from H=+∞ (the 3D case) to H=2a (the 2D case), the most probable knot size L_{knot}^{*} dramatically shrinks from (L_{knot}^{*})_{3D}≈140a to (L_{knot}^{*})_{2D}≈26a, where a is the monomer diameter of the flexible chain. Then we quantitatively explain the confinement-induced knot shrinking and knot deformation using the tube model. Our results for H=2a can be applied to a polymer knot on a surface, which resembles DNA knots measured by atomic force microscopy under the conditions that DNA molecules are weakly absorbed on the surface and reach equilibrium 2D conformations. This work demonstrates the effectiveness of the tube model in understanding polymer knots.
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Affiliation(s)
- Yongjian Zhu
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Haoqi Zhu
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Fujia Tian
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Qiyuan Qiu
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
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2
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Janse van Rensburg EJ, Orlandini E. Phase diagrams of confined square lattice linked polygons. Phys Rev E 2021; 104:064134. [PMID: 35030883 DOI: 10.1103/physreve.104.064134] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2021] [Accepted: 12/10/2021] [Indexed: 11/07/2022]
Abstract
The phase diagrams of two models of two confined and dense two-dimensional ring polymers are examined numerically. The ring polymers are modeled by square lattice polygons in a square cavity and are placed to be either unlinked or linked in the plane. The phase diagrams of the two models are found to be a function of the placement of the ring polymers and include multicritical points where first-order and continuous phase boundaries meet. We estimate numerically the critical exponents associated with the phase boundaries and the multicritical points.
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Affiliation(s)
- E J Janse van Rensburg
- Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada
| | - E Orlandini
- Dipartimento di Fisica e Astronomia "Galileo Galilei", Universitá degli studi di Padova, 8-35131 Padova, Italia
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Halun J, Karbowniczek P, Kuterba P, Danel Z. Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations. ENTROPY 2021; 23:e23020242. [PMID: 33669820 PMCID: PMC7922339 DOI: 10.3390/e23020242] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Revised: 02/06/2021] [Accepted: 02/08/2021] [Indexed: 12/03/2022]
Abstract
The calculations of the dimensionless layer monomer density profiles for a dilute solution of phantom ideal ring polymer chains and star polymers with f=4 arms in a Θ-solvent confined in a slit geometry of two parallel walls with repulsive surfaces and for the mixed case of one repulsive and the other inert surface were performed. Furthermore, taking into account the Derjaguin approximation, the dimensionless layer monomer density profiles for phantom ideal ring polymer chains and star polymers immersed in a solution of big colloidal particles with different adsorbing or repelling properties with respect to polymers were calculated. The density-force relation for the above-mentioned cases was analyzed, and the universal amplitude ratio B was obtained. Taking into account the small sphere expansion allowed obtaining the monomer density profiles for a dilute solution of phantom ideal ring polymers immersed in a solution of small spherical particles, or nano-particles of finite size, which are much smaller than the polymer size and the other characteristic mesoscopic length of the system. We performed molecular dynamics simulations of a dilute solution of linear, ring, and star-shaped polymers with N=300, 300 (360), and 1201 (4 × 300 + 1-star polymer with four arms) beads accordingly. The obtained analytical and numerical results for phantom ring and star polymers are compared with the results for linear polymer chains in confined geometries.
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Affiliation(s)
- Joanna Halun
- Institute of Nuclear Physics, Polish Academy of Sciences, 31-342 Cracow, Poland
- Correspondence:
| | - Pawel Karbowniczek
- Institute of Physics, Cracow University of Technology, 30-084 Cracow, Poland; (P.K.); (Z.D.)
| | - Piotr Kuterba
- Faculty of Physics, Astronomy and Applied Computer Sciences, Jagiellonian University in Cracow, 30-348 Cracow, Poland;
| | - Zoriana Danel
- Institute of Physics, Cracow University of Technology, 30-084 Cracow, Poland; (P.K.); (Z.D.)
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4
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Affiliation(s)
- Iurii Chubak
- Faculty of Physics, University of Vienna, Vienna, Austria
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5
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Dai L, Renner CB, Doyle PS. The polymer physics of single DNA confined in nanochannels. Adv Colloid Interface Sci 2016; 232:80-100. [PMID: 26782150 DOI: 10.1016/j.cis.2015.12.002] [Citation(s) in RCA: 82] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2015] [Revised: 12/01/2015] [Accepted: 12/01/2015] [Indexed: 11/17/2022]
Abstract
In recent years, applications and experimental studies of DNA in nanochannels have stimulated the investigation of the polymer physics of DNA in confinement. Recent advances in the physics of confined polymers, using DNA as a model polymer, have moved beyond the classic Odijk theory for the strong confinement, and the classic blob theory for the weak confinement. In this review, we present the current understanding of the behaviors of confined polymers while briefly reviewing classic theories. Three aspects of confined DNA are presented: static, dynamic, and topological properties. The relevant simulation methods are also summarized. In addition, comparisons of confined DNA with DNA under tension and DNA in semidilute solution are made to emphasize universal behaviors. Finally, an outlook of the possible future research for confined DNA is given.
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics (BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, 138602, Singapore
| | - C Benjamin Renner
- Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, United States
| | - Patrick S Doyle
- BioSystems and Micromechanics (BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, 138602, Singapore; Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, United States.
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Micheletti C, Orlandini E. Knotting and Unknotting Dynamics of DNA Strands in Nanochannels. ACS Macro Lett 2014; 3:876-880. [PMID: 35596352 DOI: 10.1021/mz500402s] [Citation(s) in RCA: 55] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
The self-knotting dynamics of DNA strands confined in nanochannels is studied with Brownian simulations. The model DNA chains are several microns long and placed inside channels that are 50-300 nm wide. This width range covers the transition between different metric scaling regimes and the concomitant drop of DNA knotting probability for channel widths below ∼75 nm. We find that knots typically originate from deep looping and backfoldings of the chain ends. Upon lowering the channel width, backfoldings become shallower and rarer and the lifetime of knots decreases while that of unknots increases. This lifetimes interplay causes the dramatic reduction of knots incidence for increasing confinement. The results can aid the design of nanochannels capable of harnessing the self-knotting dynamics to quench or relax the DNA topological state as desired.
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Affiliation(s)
- Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
| | - Enzo Orlandini
- Dipartimento
di Fisica, Sezione CNISM, and Università di Padova, via Marzolo 8, I-35131 Padova, Italy
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8
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Poier P, Likos CN, Matthews R. Influence of Rigidity and Knot Complexity on the Knotting of Confined Polymers. Macromolecules 2014; 47:3394-3400. [PMID: 24882882 PMCID: PMC4037316 DOI: 10.1021/ma5006414] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2014] [Revised: 05/05/2014] [Indexed: 02/01/2023]
Abstract
We employ computer simulations and thermodynamic integration to analyze the effects of bending rigidity and slit confinement on the free energy cost of tying knots, ΔFknotting, on polymer chains under tension. A tension-dependent, nonzero optimal stiffness κmin exists, for which ΔFknotting is minimal. For a polymer chain with several stiffness domains, each containing a large amount of monomers, the domain with stiffness κmin will be preferred by the knot. A local analysis of the bending in the interior of the knot reveals that local stretching of chains at the braid region is responsible for the fact that the tension-dependent optimal stiffness has a nonzero value. The reduction in ΔFknotting for a chain with optimal stiffness relative to the flexible chain can be enhanced by tuning the slit width of the 2D confinement and increasing the knot complexity. The optimal stiffness itself is independent of the knot types we considered, while confinement shifts it toward lower values.
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Affiliation(s)
- Peter Poier
- Faculty of Physics, University of Vienna , Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Christos N Likos
- Faculty of Physics, University of Vienna , Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Richard Matthews
- Faculty of Physics, University of Vienna , Boltzmanngasse 5, A-1090 Vienna, Austria
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Matthews R, Louis AA, Likos C. Effect of Bending Rigidity on the Knotting of a Polymer under Tension. ACS Macro Lett 2012; 1:1352-1356. [PMID: 23378936 PMCID: PMC3560425 DOI: 10.1021/mz300493d] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2012] [Accepted: 11/02/2012] [Indexed: 01/04/2023]
Abstract
A coarse-grained computational model is used to investigate how the bending rigidity of a polymer under tension affects the formation of a trefoil knot. Thermodynamic integration techniques are applied to demonstrate that the free-energy cost of forming a knot has a minimum at nonzero bending rigidity. The position of the minimum exhibits a power-law dependence on the applied tension. For knotted polymers with nonuniform bending rigidity, the knots preferentially localize in the region with a bending rigidity that minimizes the free energy.
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Affiliation(s)
- Richard Matthews
- Faculty
of Physics, University of Vienna, Boltzmanngasse
5, A-1090 Vienna, Austria
| | - Ard A. Louis
- Rudolf Peierls
Centre for Theoretical Physics, 1 Keble Road, Oxford
0X1 3NP, United Kingdom
| | - Christos
N. Likos
- Faculty
of Physics, University of Vienna, Boltzmanngasse
5, A-1090 Vienna, Austria
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Swetnam A, Brett C, Allen MP. Phase diagrams of knotted and unknotted ring polymers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031804. [PMID: 22587116 DOI: 10.1103/physreve.85.031804] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2012] [Indexed: 05/31/2023]
Abstract
The phase diagram for a lattice ring polymer under applied force, with variable solvent quality, for different topological knot states, is determined for the first time. In addition to eliminating pseudophases where the polymer is flattened into a single layer, it is found that nontrivial knots result in additional pseudophases under tensile force conditions.
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Affiliation(s)
- Adam Swetnam
- Department of Physics, University of Warwick, Coventry, United Kingdom
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Micheletti C, Orlandini E. Numerical Study of Linear and Circular Model DNA Chains Confined in a Slit: Metric and Topological Properties. Macromolecules 2012. [DOI: 10.1021/ma202503k] [Citation(s) in RCA: 61] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Cristian Micheletti
- SISSA—Scuola Internazionale Superiore di Studi Avanzati and CNR-IOM Democritos, Via Bonomea 265, 34136 Trieste, Italy
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia and Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
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