1
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Radhakrishnan K, Singh SP. Compression of a confined semiflexible polymer under direct and oscillating fields. Phys Rev E 2023; 108:014501. [PMID: 37583203 DOI: 10.1103/physreve.108.014501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2023] [Accepted: 06/19/2023] [Indexed: 08/17/2023]
Abstract
The folding transition of biopolymers from the coil to compact structures has attracted wide research interest in the past and is well studied in polymer physics. Recent seminal works on DNA in confined devices have shown that these long biopolymers tend to collapse under an external field, which is contrary to the previously reported stretching of the chain. In this work, we capture the compression of a confined semiflexible polymer under direct and oscillating fields using a coarse-grained computer simulation model in the presence of long-range hydrodynamics. In the case of a semiflexible polymer chain, the inhomogeneous hydrodynamic drag from the center to the periphery of the coil couples with the chain bending to cause a swirling movement of the chain segments, leading to structural intertwining and compaction. Contrarily, a flexible chain of the same length lacks such structural deformation and forms a well-established tadpole structure. While bending rigidity profoundly influences the chain's folding favorability, we also found that subject to the direct field, chains in stronger confinements exhibit substantial compaction, contrary to the one in moderate confinements or bulk where such compaction is absent. However, an alternating field within an optimum frequency can effectuate this compression even in moderate or no confinement. This field-induced collapse is a quintessential hydrodynamic phenomenon, resulting in intertwined knotted structures even for shorter chains, unlike other spontaneous knotting experiments where it happens exclusively for longer chains.
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Affiliation(s)
- Keerthi Radhakrishnan
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
| | - Sunil P Singh
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
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2
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Nie X, Xiong C, Zhou X, Liu Y. Phase transition of DNA knotting in spherical space. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:385101. [PMID: 35820412 DOI: 10.1088/1361-648x/ac808f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2022] [Accepted: 07/12/2022] [Indexed: 06/15/2023]
Abstract
Knots have been discovered in various biological systems, such as DNA. The knotting probability of DNA in free space depends non-monotonically on its bending rigidity and has a prominent peak. The current work aims to understand the underlying mechanism of the non-monotonic dependence of DNA knotting probability on bending rigidity. Monte Carlo simulations are performed on a closed DNA molecule confined in spherical space described by a worm-like chain model and a flexible kink model, respectively. The closed DNA's contour length and the spherical space radius both increase knotting probability, but also alter the unimodal dependence of knotting probability on bending rigidity. This is generalized using universal phase diagrams based on the two models. Under the flexible kink model, the total knotting probability of closed DNA is obviously increased at a relatively high excited energy. This supports the expectation that the entropy effect of knot size favours knot formation at a relatively low bending rigidity. In a given spherical space, the increasing contour length of closed DNA described by the worm-like chain model results in a visible shift in the knotting probability distribution. At the same time, the gyration radius of non-trivial closed DNA becomes comparable to that of trivial closed DNA, so that their ratio is not anti-correlated with average knot length. For closed DNA of various contour lengths, the relationship between average knot length and bending rigidity has a universal behaviour: the average knot length decreases to a local minimum at a bending rigidity of ∼5 and then gradually increases to a constant value. The existence of the local minimum is determined by the cut-off distance in repulsive Lennard-Jones potential. The bending rigidity corresponding to the beginning of the constant average knot length is consistent with that at the peak in the knotting distribution. At this point, the knot-size effect balances with the fragment free-energy effect and, at an even greater bending rigidity, knot length breathes around the average knot length value.
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Affiliation(s)
- Xiaolin Nie
- School of Physics and Electronic Science, Guizhou Normal University, Guiyang 550025, People's Republic of China
- College of Physics, Guizhou University, Guiyang 550025, People's Republic of China
| | - Caiyun Xiong
- College of Physics, Guizhou University, Guiyang 550025, People's Republic of China
| | - Xun Zhou
- School of Physics and Electronic Science, Guizhou Normal University, Guiyang 550025, People's Republic of China
| | - Yanhui Liu
- College of Physics, Guizhou University, Guiyang 550025, People's Republic of China
- Key Laboratory of Animal Genetics, Breeding and Reproduction in the Plateau Mountainous Region, Ministry of Education, Guizhou University, Guiyang 550025, People's Republic of China
- Kechuang Industrial Development Company Limited, Gui'an New Area, Guiyang 550025, People's Republic of China
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3
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Affiliation(s)
- Liang Dai
- Department of Physics, City University of Hong Kong, Hong Kong 999077, China
- Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
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4
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Park CB, Sung BJ. Effects of Packaging History on the Ejection of a Polymer Chain from a Small Confinement. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00857] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Affiliation(s)
- Chung Bin Park
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 04107, Republic of Korea
| | - Bong June Sung
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 04107, Republic of Korea
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5
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Zhu H, Tian F, Sun L, Wang S, Dai L. Revisiting the Non-monotonic Dependence of Polymer Knotting Probability on the Bending Stiffness. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02640] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Haoqi Zhu
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
| | - Fujia Tian
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
| | - Liang Sun
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
| | - Simin Wang
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
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6
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Lu L, Zhu H, Yuyuan Lu, An L, Dai L. Application of the Tube Model to Explain the Unexpected Decrease in Polymer Bending Energy Induced by Knot Formation. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01436] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Luwei Lu
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P.R. China
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P.R. China
- University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, P.R. China
| | - Haoqi Zhu
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P.R. China
- Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Yuyuan Lu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P.R. China
| | - Lijia An
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P.R. China
- University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, P.R. China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P.R. China
- Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
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7
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Polson JM, Hastie CG. Free energy of a knotted polymer confined to narrow cylindrical and conical channels. Phys Rev E 2020; 102:052502. [PMID: 33327190 DOI: 10.1103/physreve.102.052502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Accepted: 10/16/2020] [Indexed: 06/12/2023]
Abstract
Monte Carlo simulations are used to study the conformational behavior of a semiflexible polymer confined to cylindrical and conical channels. The channels are sufficiently narrow that the conditions for the Odijk regime are marginally satisfied. For cylindrical confinement, we examine polymers with a single knot of topology 3_{1}, 4_{1}, or 5_{1}, as well as unknotted polymers that are capable of forming S loops. We measure the variation of the free energy F with the end-to-end polymer extension length X and examine the effect of varying the polymer topology, persistence length P, and cylinder diameter D on the free-energy functions. Similarly, we characterize the behavior of the knot span along the channel. We find that increasing the knot complexity increases the typical size of the knot. In the regime of low X, where the knot/S-loop size is large, the conformational behavior is independent of polymer topology. In addition, the scaling properties of the free energy and knot span are in agreement with predictions from a theoretical model constructed using known properties of interacting polymers in the Odijk regime. We also examine the variation of F with the position of a knot in conical channels for various values of the cone angle α. The free energy decreases as the knot moves in a direction where the cone widens, and it also decreases with increasing α and with increasing knot complexity. The behavior is in agreement with predictions from a theoretical model in which the dominant contribution to the change in F is the change in the size of the hairpins as the knot moves to the wider region of the channel.
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Affiliation(s)
- James M Polson
- Department of Physics, University of Prince Edward Island, 550 University Ave., Charlottetown, Prince Edward Island, C1A 4P3, Canada
| | - Cameron G Hastie
- Department of Physics, University of Prince Edward Island, 550 University Ave., Charlottetown, Prince Edward Island, C1A 4P3, Canada
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8
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Affiliation(s)
- Liang Dai
- Department of Physics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China
| | - Beatrice W. Soh
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Patrick S. Doyle
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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9
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Foglino M, Locatelli E, Brackley CA, Michieletto D, Likos CN, Marenduzzo D. Non-equilibrium effects of molecular motors on polymers. SOFT MATTER 2019; 15:5995-6005. [PMID: 31292585 DOI: 10.1039/c9sm00273a] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We present a generic coarse-grained model to describe molecular motors acting on polymer substrates, mimicking, for example, RNA polymerase on DNA or kinesin on microtubules. The polymer is modeled as a connected chain of beads; motors are represented as freely diffusing beads which, upon encountering the substrate, bind to it through a short-ranged attractive potential. When bound, motors and polymer beads experience an equal and opposite active force, directed tangential to the polymer; this leads to motion of the motors along the polymer contour. The inclusion of explicit motors differentiates our model from other recent active polymer models. We study, by means of Langevin dynamics simulations, the effect of the motor activity on both the conformational and dynamical properties of the substrate. We find that activity leads, in addition to the expected enhancement of polymer diffusion, to an effective reduction of its persistence length. We discover that this effective "softening" is a consequence of the emergence of double-folded branches, or hairpins, and that it can be tuned by changing the number of motors or the force they generate. Finally, we investigate the effect of the motors on the probability of knot formation. Counter-intuitively our simulations reveal that, even though at equilibrium a more flexible substrate would show an increased knotting probability, motor activity leads to a marked decrease in the occurrence of knotted conformations with respect to equilibrium.
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Affiliation(s)
- M Foglino
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, UK
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10
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Young CD, Qian JR, Marvin M, Sing CE. Ring polymer dynamics and tumbling-stretch transitions in planar mixed flows. Phys Rev E 2019; 99:062502. [PMID: 31330603 DOI: 10.1103/physreve.99.062502] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2019] [Indexed: 06/10/2023]
Abstract
The properties of dilute polymer solutions are governed by the conformational dynamics of individual polymers which can be perturbed in the presence of an applied flow. Much of our understanding of dilute solutions comes from studying how flows manipulate the molecular features of polymer chains out of equilibrium, primarily focusing on linear polymer chains. Recently there has been an emerging interest in the dynamics of nonlinear architectures, particularly ring polymers, which exhibit surprising out-of-equilibrium dynamics in dilute solutions. In particular, it has been observed that hydrodynamics can couple to topology in planar elongational and shear flows, driving molecular expansion in the nonflow direction that is not observed for linear chains. In this paper, we extend our understanding of dilute ring polymer dynamics to mixed flows, which represent flow profiles intermediate between simple shear or planar elongation. We map the conformational behaviors at a number of flow geometries and strengths, demonstrating transitions between coiled, tumbling, and stretched regimes. Indeed, these observations are consistent with how linear chains respond to mixed flows. For both linear and ring polymers, we observe a marked first-order-like transition between tumbling and stretched polymers that we attribute to a dynamic energy barrier between the two states. This manifests as bimodal extension distributions in a narrow range of flow strengths and geometries, with the primary difference between rings and linear chains being the presence of molecular expansion in the vorticity direction.
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Affiliation(s)
- Charles D Young
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - June R Qian
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | | | - Charles E Sing
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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11
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543
| | - Patrick S. Doyle
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543
- Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139, United States
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12
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Liebetreu M, Ripoll M, Likos CN. Trefoil Knot Hydrodynamic Delocalization on Sheared Ring Polymers. ACS Macro Lett 2018; 7:447-452. [PMID: 35619341 DOI: 10.1021/acsmacrolett.8b00059] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
The behavior of unknotted and trefoil-knotted ring polymers under shear flow is here examined by means of mesoscopic simulations. In contrast to most polymers, ring polymers in a hydrodynamic solvent at high shear rates do not get shortened in the vorticity direction. This is a consequence of the backflow produced by the interaction of the sheared solvent with the end-free polymer topology. The extended structures of the ring in the vorticity-flow plane, when they are aligned in a constant velocity plane, favor ring contour fluctuations. This variety of conformations largely suppresses the tank-treading type of rotation with extended conformations in favor of the tumbling type of rotations, where stretched and collapsed conformations alternate. The extension of trefoil knots is also enhanced, so that the knots become delocalized. We anticipate that these effects, which disappear in the absence of hydrodynamic interactions, will have a crucial impact on the rheological properties of concentrated ring solutions, and will also influence the behavior of more complicated systems such as mixtures of polymers with different topologies.
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Affiliation(s)
- Maximilian Liebetreu
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Marisol Ripoll
- Forschungszentrum Jülich, Institute of Complex Systems, Theoretical Soft Matter and Biophysics, 52425 Jülich, Germany
| | - Christos N. Likos
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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13
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Abstract
The first synthetic molecular trefoil knot was prepared in the late 1980s. However, it is only in the last few years that more complex small-molecule knot topologies have been realized through chemical synthesis. The steric restrictions imposed on molecular strands by knotting can impart significant physical and chemical properties, including chirality, strong and selective ion binding, and catalytic activity. As the number and complexity of accessible molecular knot topologies increases, it will become increasingly useful for chemists to adopt the knot terminology employed by other disciplines. Here we give an overview of synthetic strategies towards molecular knots and outline the principles of knot, braid, and tangle theory appropriate to chemistry and molecular structure.
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Affiliation(s)
| | - David A. Leigh
- School of ChemistryUniversity of ManchesterOxford RoadManchesterM13 9PLUK
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14
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Affiliation(s)
- Stephen D. P. Fielden
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Großbritannien
| | - David A. Leigh
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Großbritannien
| | - Steffen L. Woltering
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Großbritannien
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15
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Coronel L, Orlandini E, Micheletti C. Non-monotonic knotting probability and knot length of semiflexible rings: the competing roles of entropy and bending energy. SOFT MATTER 2017; 13:4260-4267. [PMID: 28573303 DOI: 10.1039/c7sm00643h] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We consider self-avoiding rings of up to 1000 beads and study, by Monte Carlo techniques, how their equilibrium knotting properties depend on the bending rigidity. When the rings are taken from the rigid to fully-flexible limit, their average compactness increases, as expected. However, this progressive compactification is not parallelled by a steady increase of the abundance of knots. In fact the knotting probability, Pk, has a prominent maximum when the persistence length is a few times larger than the bead size. At similar bending rigidities, the knot length has, instead, a minimum. We show that the observed non-monotonicity of Pk arises from the competition between two effects. The first one is the entropic cost of introducing a knot. The second one is the gain in bending energy due to the presence of essential crossings. These, in fact, constrain the knotted region and keep it less bent than average. The two competing effects make knots maximally abundant when the persistence length is 5-10 times larger than the bead size. At such intermediate bending rigidities, knots in the chains of 500 and 1000 beads are 40 times more likely than in the fully-flexible limit.
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Affiliation(s)
- Lucia Coronel
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
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16
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Dai L, Doyle PS. Trapping a Knot into Tight Conformations by Intra-Chain Repulsions. Polymers (Basel) 2017; 9:E57. [PMID: 30970736 PMCID: PMC6432319 DOI: 10.3390/polym9020057] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2016] [Revised: 02/07/2017] [Accepted: 02/08/2017] [Indexed: 11/17/2022] Open
Abstract
Knots can occur in biopolymers such as DNA and peptides. In our previous study, we systematically investigated the effects of intra-chain interactions on knots and found that long-range repulsions can surprisingly tighten knots. Here, we use this knowledge to trap a knot into tight conformations in Langevin dynamics simulations. By trapping, we mean that the free energy landscape with respect to the knot size exhibits a potential well around a small knot size in the presence of long-range repulsions, and this potential can well lead to long-lived tight knots when its depth is comparable to or larger than thermal energy. We tune the strength of intra-chain repulsion such that a knot is weakly trapped. Driven by thermal fluctuations, the knot can escape from the trap and is then re-trapped. We find that the knot switches between tight and loose conformations-referred to as "knot breathing". We use a Yukawa potential to model screened electrostatic interactions to explore the relevance of knot trapping and breathing in charged biopolymers. We determine the minimal screened length and the minimal strength of repulsion for knot trapping. We find that Coulomb-induced knot trapping is possible to occur in single-stranded DNA and peptides for normal ionic strengths.
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543, Singapore.
| | - Patrick S Doyle
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543, Singapore.
- Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA.
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17
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543
| | - Patrick S. Doyle
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543
- Department
of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139, United States
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18
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D'Adamo G, Dietler G, Micheletti C. Tuning knot abundance in semiflexible chains with crowders of different sizes: a Monte Carlo study of DNA chains. SOFT MATTER 2016; 12:6708-6715. [PMID: 27443238 DOI: 10.1039/c6sm01327a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We use stochastic simulation techniques to sample the conformational space of linear semiflexible polymers in a crowded medium and study how the knotting properties depend on the crowder size and concentration. The abundance of physical knots in the chains, which for definiteness we model on 10 kb long DNA filaments, is shown to have a non-monotonic, unimodal dependence on the colloid diameter, dc. The maximum incidence of knots occurs when dc is about equal to half of the gyration radius of the isolated chain. The degree of enhancement of knots grows rapidly with the solution density and can be very conspicuous relative to the case of isolated chains with no crowders. For instance, at 30% volume fraction the relative increase is more than fourfold. This dramatic enhancement is shown to originate from the depletion-induced chain compaction over multiple and concurring length scales. The same effect accounts for the variations of the knot length that accompany the changes in knotting probability. The findings suggest that crowded media could be viably used as a passive physical means for controlling and modulating the incidence and length of knots in DNA and other types of semiflexible polymers.
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Affiliation(s)
- Giuseppe D'Adamo
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
| | - Giovanni Dietler
- Institut de Physique des Systèmes Biologiques, Ecole Polytechnique Fédérale de Lausanne, BSP, CH-1015 Lausanne, Switzerland
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
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19
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Orlandini E, Baiesi M, Zonta F. How Local Flexibility Affects Knot Positioning in Ring Polymers. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b00712] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Enzo Orlandini
- Department
of Physics and Astronomy, University of Padova, Via Marzolo 8, Padova, Italy
- INFN, Sezione
di Padova, Via Marzolo 8, Padova, Italy
| | - Marco Baiesi
- Department
of Physics and Astronomy, University of Padova, Via Marzolo 8, Padova, Italy
- INFN, Sezione
di Padova, Via Marzolo 8, Padova, Italy
| | - Francesco Zonta
- Shangai
Institute for Advanced Immunochemical Studies (SIAIS), ShanghaiTech University, No. 99 Haike Road, Pudong, Shanghai 201210, China
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20
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Caraglio M, Micheletti C, Orlandini E. Stretching Response of Knotted and Unknotted Polymer Chains. PHYSICAL REVIEW LETTERS 2015; 115:188301. [PMID: 26565504 DOI: 10.1103/physrevlett.115.188301] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2015] [Indexed: 06/05/2023]
Abstract
Recent theoretical and experimental advances have clarified the major effects of knotting on the properties of stretched chains. Yet, how knotted chains respond to weak mechanical stretching and how this behavior differs from the unknotted case are still open questions and we address them here by profiling the complete stretching response of chains of hundreds of monomers and different topology. We find that the ratio of the knotted and unknotted chain extensions varies nonmonotonically with the applied force. This surprising feature is shown to be a signature of the crossover between the well-known high-force stretching regime and the previously uncharacterized low-force one. The observed differences of knotted and unknotted chain response increases with knot complexity and are sufficiently marked that they could be harnessed in single-molecule contexts to infer the presence and complexity of physical knots in micron-long biomolecules.
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Affiliation(s)
- Michele Caraglio
- Dipartimento di Fisica e Astronomia Università di Padova and sezione CNISM, Via Marzolo 8, I-35131 Padova, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia Università di Padova and sezione INFN, Via Marzolo 8, I-35131 Padova, Italy
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21
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Poier P, Likos CN, Moreno A, Blaak R. An Anisotropic Effective Model for the Simulation of Semiflexible Ring Polymers. Macromolecules 2015; 48:4983-4997. [PMID: 26240439 PMCID: PMC4519991 DOI: 10.1021/acs.macromol.5b00603] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2015] [Revised: 05/29/2015] [Indexed: 01/27/2023]
Abstract
We derive and introduce anisotropic effective pair potentials to coarse-grain solutions of semiflexible ring polymers of various lengths. The system has been recently investigated by means of full monomer-resolved computer simulations, revealing a host of unusual features and structure formation, which, however, cannot be captured by a rotationally averaged effective pair potential between the rings' centers of mass [Bernabei M.; Soft Matter2013, 9, 1287]. Our new coarse-graining strategy is to picture each ring as a soft, penetrable disk. We demonstrate that for the short- and intermediate-length rings the new model is quite capable of capturing the physics in a quantitative fashion, whereas for the largest rings, which resemble flexible ones, it fails at high densities. Our work opens the way for the physical justification of general, anisotropic penetrable interaction potentials.
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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
| | - Angel
J. Moreno
- Centro de Física
de Materiales (CSIC-UPV/EHU) and Materials Physics Center (MPC), Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
- Donostia International
Physics Center, Paseo Manuel de Lardizabal
4, E-20018 San Sebastián, Spain
| | - Ronald Blaak
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
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22
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Dai L, Renner CB, Doyle PS. Origin of metastable knots in single flexible chains. PHYSICAL REVIEW LETTERS 2015; 114:037801. [PMID: 25659023 DOI: 10.1103/physrevlett.114.037801] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2014] [Indexed: 06/04/2023]
Abstract
Recent theoretical progress has explained the physics of knotting of semiflexible polymers, yet knotting of flexible polymers is relatively unexplored. We herein develop a new theory for the size distribution of knots on a flexible polymer and the existence of metastable knots. We show the free energy of a flexible molecule in a tube can be mapped to quantitatively reproduce the free energy distribution of a knot on a flexible chain. The size distribution of knots on flexible chains is expected to be universal and might be observed at a macroscopic scale, such as a string of hard balls.
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543, Singapore
| | - C Benjamin Renner
- Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139, USA
| | - Patrick S Doyle
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543, Singapore and Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139, USA
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23
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Narros A, Likos CN, Moreno AJ, Capone B. Multi-blob coarse graining for ring polymer solutions. SOFT MATTER 2014; 10:9601-9614. [PMID: 25356818 DOI: 10.1039/c4sm01904k] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present a multi-scale molecular modeling of concentrated solutions of unknotted and non-concatenated ring polymers under good solvent conditions. The approach is based on a multi-blob representation of each ring polymer, which is capable of overcoming the shortcomings of single-blob approaches that lose their validity at concentrations exceeding the overlap density of the solution [A. Narros, A. J. Moreno, and C. N. Likos, Soft Matter, 2010, 6, 2435]. By means of a first principles coarse-graining strategy based on analytically determined effective pair potentials between the blobs, computed at zero density, we quantitatively reproduce the single molecule and solution properties of a system with well-defined topological constraints. Detailed comparisons with the underlying, monomer-resolved model demonstrate the validity of our approach, which employs fully transferable pair potentials between connected and unconnected blobs. We demonstrate that the pair structure between the centers of mass of the rings is accurately reproduced by the multi-blob approach, thus opening the way for simulation of arbitrarily long polymers. Finally, we show the importance of the topological constraint of non-concatenation on the structure of the concentrated solution and in particular on the size of the correlation hole and the shrinkage of the rings as melt concentrations are approached.
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Affiliation(s)
- Arturo Narros
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria.
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24
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Baiesi M, Orlandini E, Stella AL. Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics. Macromolecules 2014. [DOI: 10.1021/ma5020287] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Marco Baiesi
- Department
of Physics and Astronomy, University of Padua, Via Marzolo 8, I-35131 Padova, Italy
- INFN - Sezione
di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Enzo Orlandini
- Department
of Physics and Astronomy, University of Padua, Via Marzolo 8, I-35131 Padova, Italy
- INFN - Sezione
di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Attilio L. Stella
- Department
of Physics and Astronomy, University of Padua, Via Marzolo 8, I-35131 Padova, Italy
- INFN - Sezione
di Padova, Via Marzolo 8, I-35131 Padova, Italy
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25
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Abstract
We present Brownian dynamics simulations of initially knotted double-stranded DNA molecules untying in elongational flows. We show that the motions of the knots are governed by a diffusion-convection equation by deriving scalings that collapse the simulation data. When being convected, all knots displace nonaffinely, and their rates of translation along the chain are topologically dictated. We discover that torus knots "corkscrew" when driven by flow, whereas nontorus knots do not. We show that a simple mechanism can explain a coupling between this rotation and the translation of a knot, explaining observed differences in knot translation rates. These types of knots are encountered in nanoscale manipulation of DNA, occur in biology at multiple length scales (DNA to umbilical cords), and are ubiquitous in daily life (e.g., hair). These results may have a broad impact on manipulations of such knots via flows, with applications to genomic sequencing and polymer processing.
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Affiliation(s)
- C. Benjamin Renner
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Patrick S. Doyle
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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26
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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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27
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Di Stefano M, Tubiana L, Di Ventra M, Micheletti C. Driving knots on DNA with AC/DC electric fields: topological friction and memory effects. SOFT MATTER 2014; 10:6491-6498. [PMID: 25048107 DOI: 10.1039/c4sm00160e] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The dynamical properties of entangled polyelectrolytes are investigated theoretically and computationally for a proposed novel micromanipulation setup. Specifically, we investigate the effects of DC and AC electric fields acting longitudinally on knotted DNA chains, modelled as semiflexible chains of charged beads, under mechanical tension. We consider various experimentally accessible values of the field amplitude and frequency as well as several of the simplest knot types. In particular, we consider both torus and twist knots because they are respectively known to be able or unable to slide along macroscopic threads and ropes. Strikingly, this qualitative distinction disappears in this microscopic context because all the considered knot types acquire a systematic drift in the direction of the electric force. Notably, the knot drift velocity and diffusion coefficient in zero field (both measurable also experimentally) can be used to define a characteristic "frictional" lengthscale for the various knot types. This previously unexplored length provides valuable information on the extent of self-interactions in the nominal knotted region. It is finally observed that the motion of a knot can effectively follow the AC field only if the driving period is larger than the knot relaxation time (for which the self-diffusion time provides an upper bound). These results suggest that salient aspects of the intrinsic dynamics of knots in DNA chains could be probed experimentally by means of external, time-dependent electric fields.
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Affiliation(s)
- Marco Di Stefano
- SISSA - Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy.
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28
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Affiliation(s)
- Liang Dai
- BioSystems
and Micromechanics IRG, Singapore—MIT Alliance for Research and Technology Centre, Singapore 117543, Singapore
| | - C. Benjamin Renner
- Department
of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139, United States
| | - Patrick S. Doyle
- BioSystems
and Micromechanics IRG, Singapore—MIT Alliance for Research and Technology Centre, Singapore 117543, Singapore
- Department
of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139, United States
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29
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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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30
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Tubiana L, Rosa A, Fragiacomo F, Micheletti C. Spontaneous Knotting and Unknotting of Flexible Linear Polymers: Equilibrium and Kinetic Aspects. Macromolecules 2013. [DOI: 10.1021/ma4002963] [Citation(s) in RCA: 64] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- L. Tubiana
- Department of Theoretical Physics, Jožef Stefan Institute, SI-1000 Ljubljana, Slovenia
| | - A. Rosa
- SISSA—Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea
265, 34136 Trieste, Italy
| | - F. Fragiacomo
- Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
| | - C. Micheletti
- SISSA—Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea
265, 34136 Trieste, Italy
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