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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Rauscher PM, de Pablo JJ. Random Knotting in Fractal Ring Polymers. Macromolecules 2022; 55:8409-8417. [PMID: 36186575 PMCID: PMC9520986 DOI: 10.1021/acs.macromol.2c01676] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2022] [Revised: 08/23/2022] [Indexed: 11/28/2022]
Abstract
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Many ring polymer
systems of physical and biological
interest exhibit
both pronounced topological effects and nontrivial self-similarity,
but the relationship between these two phenomena has not yet been
clearly established. Here, we use theory and simulation to formulate
such a connection by studying a fundamental topological property—the
random knotting probability—for ring polymers with varying
fractal dimension, df. Using straightforward scaling arguments, we generalize a classic
mathematical result, showing that the probability of a trivial knot
decays exponentially with chain size, N, for all
fractal dimensions: P0(N) ∝ exp(−N/N0). However, no such simple considerations can account for
the dependence of the knotting length, N0, on df, necessitating
a more involved analytical calculation. This analysis reveals a complicated
double-exponential dependence, which is well supported by numerical
data. By contrast, functional forms typical of simple scaling theories
fail to adequately describe the observations. These findings are equally
valid for two-dimensional ring polymer systems, where “knotting”
is defined as the intersection of any two segments.
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Affiliation(s)
- Phillip M. Rauscher
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Juan J. de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Materials Science Division (MSD) and Center for Molecular Engineering (CME), Argonne National Laboratory, Lemont, Illinois 60439, United States
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3
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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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4
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Wu J, Guo F, Li K, Zhang L. Sliding Dynamics of Ring Chains on Two Asymmetric/Symmetric Chains in a Simple Slide-Ring Gel. Polymers (Basel) 2021; 14:79. [PMID: 35012102 PMCID: PMC8747720 DOI: 10.3390/polym14010079] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Revised: 12/20/2021] [Accepted: 12/23/2021] [Indexed: 12/21/2022] Open
Abstract
The sliding dynamics along two asymmetric/symmetric axial chains of ring chains linked by a linear chainis investigated using molecular dynamics (MD) simulations. A novel sub-diffusion behavior is observed for ring chains sliding along eithera fixed rod-like chain or fluctuating axial chain on asymmetric/symmetric axial chainsat the intermediate time range due to their strongly interplay between two ring chains. However, two ring chains slide in the normal diffusion at along time range because their sliding dynamics can be regarded as an overall motion of two ring chains. For ring chains sliding on two symmetric/asymmetricaxial chains, the diffusion coefficient D of ring chains relies on the bending energy of axial chains (Kb) as well as the distance of two axial chains (d). There exists a maximum diffusion coefficient Dmax at d = d* in which ring chains slide at the fastest velocity due to the maximum conformational entropy for the linking chain between two ring chainsat d = d*. Ring chain slide on fixed rod-like axial chainsfaster in the symmetric axial chain case than that in the asymmetric axial chain case. However, ring chains slide on fluctuatingaxial chainsslower in the symmetric axial chain case than that in the asymmetric axial chain case. This investigation can provide insights into the effects of the linked chain conformation on the sliding dynamics of ring chains in a slide-ring gel.
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Affiliation(s)
| | | | | | - Linxi Zhang
- Department of Physics, Zhejiang University, Hangzhou 310027, China; (J.W.); (F.G.); (K.L.)
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5
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Bakhshandeh A, Segala M, Escobar Colla T. Equilibrium Conformations and Surface Charge Regulation of Spherical Polymer Brushes in Stretched Regimes. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c02077] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil
- Departamento de Físico-Química, Instituto de Química, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil
| | - Maximiliano Segala
- Instituto de Física, Universidade Federal de Ouro Preto, 35400-000 Ouro Preto, Minas Gerais, Brazil
- Departamento de Físico-Química, Instituto de Química, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil
| | - Thiago Escobar Colla
- Instituto de Física, Universidade Federal de Ouro Preto, 35400-000 Ouro Preto, Minas Gerais, Brazil
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6
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Guo F, Li K, Wu J, Wang Y, Zhang L. Sliding dynamics of ring chain on a knotted polymer in rotaxane. POLYMER 2021. [DOI: 10.1016/j.polymer.2021.124226] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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7
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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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8
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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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9
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Affiliation(s)
- Peter Cifra
- Polymer Institute Slovak Academy of Sciences Bratislava 84541 Slovakia
| | - Tomáš Bleha
- Polymer Institute Slovak Academy of Sciences Bratislava 84541 Slovakia
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10
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Wu Z, Alberti SAN, Schneider J, Müller-Plathe F. Knotting behaviour of polymer chains in the melt state for soft-core models with and without slip-springs. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:244001. [PMID: 33725671 DOI: 10.1088/1361-648x/abef25] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2020] [Accepted: 03/16/2021] [Indexed: 06/12/2023]
Abstract
We analyse the knotting behaviour of linear polymer melts in two types of soft-core models, namely dissipative-particle dynamics and hybrid-particle-field models, as well as their variants with slip-springs which are added to recover entangled polymer dynamics. The probability to form knots is found drastically higher in the hybrid-particle-field model compared to its parent hard-core molecular dynamics model. By comparing the knottedness in dissipative-particle dynamics and hybrid-particle-field models with and without slip-springs, we find the impact of slip-springs on the knotting properties to be negligible. As a dynamic property, we measure the characteristic time of knot formation and destruction, and find it to be (i) of the same order as single-monomer motion and (ii) independent of the chain length in all soft-core models. Knots are therefore formed and destroyed predominantly by the unphysical chain crossing. This work demonstrates that the addition of slip-springs does not alter the knotting behaviour, and it provides a general understanding of knotted structures in these two soft-core models of polymer melts.
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Affiliation(s)
- Zhenghao Wu
- Technical University of Darmstadt, Eduard-Zintl-Institute for Inorganic and Physical Chemistry and Profile Area Thermofluids and Interfaces, Alarich-Weiss-Strasse 8, D-64287 Darmstadt, Germany
| | - Simon A N Alberti
- Technical University of Darmstadt, Eduard-Zintl-Institute for Inorganic and Physical Chemistry and Profile Area Thermofluids and Interfaces, Alarich-Weiss-Strasse 8, D-64287 Darmstadt, Germany
| | - Jurek Schneider
- Technical University of Darmstadt, Eduard-Zintl-Institute for Inorganic and Physical Chemistry and Profile Area Thermofluids and Interfaces, Alarich-Weiss-Strasse 8, D-64287 Darmstadt, Germany
| | - Florian Müller-Plathe
- Technical University of Darmstadt, Eduard-Zintl-Institute for Inorganic and Physical Chemistry and Profile Area Thermofluids and Interfaces, Alarich-Weiss-Strasse 8, D-64287 Darmstadt, Germany
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11
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Tubiana L, Kobayashi H, Potestio R, Dünweg B, Kremer K, Virnau P, Daoulas K. Comparing equilibration schemes of high-molecular-weight polymer melts with topological indicators. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:204003. [PMID: 33765663 DOI: 10.1088/1361-648x/abf20c] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Accepted: 03/25/2021] [Indexed: 06/12/2023]
Abstract
Recent theoretical studies have demonstrated that the behaviour of molecular knots is a sensitive indicator of polymer structure. Here, we use knots to verify the ability of two state-of-the-art algorithms-configuration assembly and hierarchical backmapping-to equilibrate high-molecular-weight (MW) polymer melts. Specifically, we consider melts with MWs equivalent to several tens of entanglement lengths and various chain flexibilities, generated with both strategies. We compare their unknotting probability, unknotting length, knot spectra, and knot length distributions. The excellent agreement between the two independent methods with respect to knotting properties provides an additional strong validation of their ability to equilibrate dense high-MW polymeric liquids. By demonstrating this consistency of knotting behaviour, our study opens the way for studying topological properties of polymer melts beyond time and length scales accessible to brute-force molecular dynamics simulations.
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Affiliation(s)
- Luca Tubiana
- Physics Department, University of Trento, via Sommarive, 14 I-38123 Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Hideki Kobayashi
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Raffaello Potestio
- Physics Department, University of Trento, via Sommarive, 14 I-38123 Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy
| | - Burkhard Dünweg
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
- Department of Chemical Engineering, Monash University, Clayton, Victoria 3800, Australia
| | - Kurt Kremer
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Peter Virnau
- Institute of Physics, Johannes Gutenberg University, Staudingerweg 9, 55128 Mainz, Germany
| | - Kostas Daoulas
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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12
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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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13
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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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14
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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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15
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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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16
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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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17
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The Rabl configuration limits topological entanglement of chromosomes in budding yeast. Sci Rep 2019; 9:6795. [PMID: 31043625 PMCID: PMC6494875 DOI: 10.1038/s41598-019-42967-4] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2018] [Accepted: 03/27/2019] [Indexed: 11/25/2022] Open
Abstract
The three dimensional organization of genomes remains mostly unknown due to their high degree of condensation. Biophysical studies predict that condensation promotes the topological entanglement of chromatin fibers and the inhibition of function. How organisms balance between functionally active genomes and a high degree of condensation remains to be determined. Here we hypothesize that the Rabl configuration, characterized by the attachment of centromeres and telomeres to the nuclear envelope, helps to reduce the topological entanglement of chromosomes. To test this hypothesis we developed a novel method to quantify chromosome entanglement complexity in 3D reconstructions obtained from Chromosome Conformation Capture (CCC) data. Applying this method to published data of the yeast genome, we show that computational models implementing the attachment of telomeres or centromeres alone are not sufficient to obtain the reduced entanglement complexity observed in 3D reconstructions. It is only when the centromeres and telomeres are attached to the nuclear envelope (i.e. the Rabl configuration) that the complexity of entanglement of the genome is comparable to that of the 3D reconstructions. We therefore suggest that the Rabl configuration is an essential player in the simplification of the entanglement of chromatin fibers.
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18
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Abstract
We examine how channel confinement affects the equilibrium properties of topologically linked ring polymers and, by contrast, of equivalent unlinked rings, too. By performing extensive simulations of semiflexible rings of different chain length, N, and channel diameter, D, we discover three notable properties purely due to linking. First, upon entering the weak confinement regime, the length of the physically linked portion, lLKThe, becomes independent of chain length. Next, even when confinement is strong enough to pull apart and segregate unlinked rings, lLK stays much larger than in the highly stretched limit. Finally, at fixed N, lLK varies approximately as D0.5, and we provide a simple scaling argument for this power-law behavior. These properties, which may hold for different link topologies, can be tested by current experimental setups on DNA rings confined in microchannels. Moreover, they could be relevant for the efficient in vivo unlinking of newly replicated bacterial chromosomes.
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Zhang L, Lemonnier JF, Acocella A, Calvaresi M, Zerbetto F, Leigh DA. Effects of knot tightness at the molecular level. Proc Natl Acad Sci U S A 2019; 116:2452-2457. [PMID: 30683725 PMCID: PMC6377497 DOI: 10.1073/pnas.1815570116] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
Three 819 knots in closed-loop strands of different lengths (∼20, 23, and 26 nm) were used to experimentally assess the consequences of knot tightness at the molecular level. Through the use of 1H NMR, diffusion-ordered spectroscopy (DOSY), circular dichroism (CD), collision-induced dissociation mass spectrometry (CID-MS) and molecular dynamics (MD) simulations on the different-sized knots, we find that the structure, dynamics, and reactivity of the molecular chains are dramatically affected by the tightness of the knotting. The tautness of entanglement causes differences in conformation, enhances the expression of topological chirality, weakens covalent bonds, inhibits decomplexation events, and changes absorption properties. Understanding the effects of tightening nanoscale knots may usefully inform the design of knotted and entangled molecular materials.
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Affiliation(s)
- Liang Zhang
- School of Chemistry and Molecular Engineering, East China Normal University, 200062 Shanghai, China
- School of Chemistry, University of Manchester, M13 9PL Manchester, United Kingdom
| | | | - Angela Acocella
- Dipartimento di Chimica "G. Ciamician", Università di Bologna, 40126 Bologna, Italy
| | - Matteo Calvaresi
- Dipartimento di Chimica "G. Ciamician", Università di Bologna, 40126 Bologna, Italy
| | - Francesco Zerbetto
- Dipartimento di Chimica "G. Ciamician", Università di Bologna, 40126 Bologna, Italy
| | - David A Leigh
- School of Chemistry and Molecular Engineering, East China Normal University, 200062 Shanghai, China;
- School of Chemistry, University of Manchester, M13 9PL Manchester, United Kingdom
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20
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Cardelli C, Tubiana L, Bianco V, Nerattini F, Dellago C, Coluzza I. Heteropolymer Design and Folding of Arbitrary Topologies Reveals an Unexpected Role of Alphabet Size on the Knot Population. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01359] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Chiara Cardelli
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Luca Tubiana
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Valentino Bianco
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Francesca Nerattini
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Christoph Dellago
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Ivan Coluzza
- CIC biomaGUNE, Paseo Miramon 182, 20014 San Sebastian, Spain
- IKERBASQUE,
Basque
Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
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21
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Wu J, Cheng C, Liu G, Zhang P, Chen T. The folding pathways and thermodynamics of semiflexible polymers. J Chem Phys 2018; 148:184901. [PMID: 29764123 DOI: 10.1063/1.5018114] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.
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Affiliation(s)
- Jing Wu
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Chenqian Cheng
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Gaoyuan Liu
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Ping Zhang
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Tao Chen
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
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22
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Tubiana L, Polles G, Orlandini E, Micheletti C. KymoKnot: A web server and software package to identify and locate knots in trajectories of linear or circular polymers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:72. [PMID: 29884956 DOI: 10.1140/epje/i2018-11681-0] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Accepted: 05/18/2018] [Indexed: 06/08/2023]
Abstract
The KymoKnot software package and web server identifies and locates physical knots or proper knots in a series of polymer conformations. It is mainly intended as an analysis tool for trajectories of linear or circular polymers, but it can be used on single instances too, e.g. protein structures in PDB format. A key element of the software package is the so-called minimally interfering chain closure algorithm that is used to detect physical knots in open chains and to locate the knotted region in both open and closed chains. The web server offers a user-friendly graphical interface that identifies the knot type and highlights the knotted region on each frame of the trajectory, which the user can visualize interactively from various viewpoints. The dynamical evolution of the knotted region along the chain contour is presented as a kymograph. All data can be downloaded in text format. The KymoKnot package is licensed under the BSD 3-Clause licence. The server is publicly available at http://kymoknot.sissa.it/kymoknot/interactive.php .
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Affiliation(s)
- Luca Tubiana
- Computational Physics Department, University of Vienna, Sensengasse 8/10, 1090, Vienna, Austria.
| | - Guido Polles
- Molecular and Computational Biology, Department of Biological Sciences, University of Southern California, 90089, Los Angeles, CA, USA
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia and Sezione INFN, Università di Padova, Via Marzolo 8, 35131, Padova, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, Via Bonomea 265, I-34136, Trieste, Italy
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23
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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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24
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The energy cost of polypeptide knot formation and its folding consequences. Nat Commun 2017; 8:1581. [PMID: 29146980 PMCID: PMC5691195 DOI: 10.1038/s41467-017-01691-1] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2017] [Accepted: 10/09/2017] [Indexed: 11/08/2022] Open
Abstract
Knots are natural topologies of chains. Yet, little is known about spontaneous knot formation in a polypeptide chain—an event that can potentially impair its folding—and about the effect of a knot on the stability and folding kinetics of a protein. Here we used optical tweezers to show that the free energy cost to form a trefoil knot in the denatured state of a polypeptide chain of 120 residues is 5.8 ± 1 kcal mol−1. Monte Carlo dynamics of random chains predict this value, indicating that the free energy cost of knot formation is of entropic origin. This cost is predicted to remain above 3 kcal mol−1 for denatured proteins as large as 900 residues. Therefore, we conclude that naturally knotted proteins cannot attain their knot randomly in the unfolded state but must pay the cost of knotting through contacts along their folding landscape. The effect of knots on protein stability and folding kinetics is not well understood. Here the authors combine optical tweezer experiments and calculations to experimentally determine the energy cost for knot formation, which indicates that knotted proteins evolved specific folding pathways because knot formation in unfolded chains is unfavorable.
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25
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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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26
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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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27
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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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28
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Heinemann T, Klapp SHL. Coarse-graining strategy for molecular pair interactions: A reaction coordinate study for two- and three-dimensional systems. J Chem Phys 2017; 146:164107. [PMID: 28456203 DOI: 10.1063/1.4981207] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
We investigate and provide optimal sets of reaction coordinates for mixed pairs of molecules displaying polar, uniaxial, or spherical symmetry in two and three dimensions. These coordinates are non-redundant, i.e., they implicitly involve the molecules' symmetries. By tabulating pair interactions in these coordinates, resulting tables are thus minimal in length and require a minimal memory space. The intended fields of application are computer simulations of large ensembles of molecules or colloids with rather complex interactions in a fluid or liquid crystalline phase at low densities. Using effective interactions directly in the form of tables can help bridging the time and length scales without introducing errors stemming from any modeling procedure. Finally, we outline an exemplary computational methodology for gaining an effective pair potential in these coordinates, based on the Boltzmann inversion principle, by providing a step-by-step recipe.
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Affiliation(s)
- Thomas Heinemann
- Department of Chemistry, Seoul National University, Seoul 08826, Korea
| | - Sabine H L Klapp
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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29
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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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30
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Marenda M, Orlandini E, Micheletti C. Sorting ring polymers by knot type with modulated nanochannels. SOFT MATTER 2017; 13:795-802. [PMID: 28058437 DOI: 10.1039/c6sm02551j] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this theoretical study we discuss a novel method for sorting ring polymers according to their topological, knotted state. The proposed approach harnesses the rich dynamical behaviour of polymers confined inside spatially-modulated nanochannels. The longitudinal mobility of the rings is shown to have two key properties that are ideally suited for knot sorting. First, at fixed topology, the mobility has an intriguing oscillatory dependence on chain length. Second, the mobility ranking of different knot types is inverted upon increasing the chain length. We show that this complex interplay of channel geometry, chain length and topology can be rationalised within a simple theoretical framework based on Fick-Jacobs's diffusive theory. The results and the interpretative scheme ought to be useful for designing microfluidic devices with optimal topological sorting capabilities.
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Affiliation(s)
- Mattia Marenda
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia "Galileo Galilei", sezione CNISM, Università degli Studi di Padova, via Marzolo 8, I-35131 Padova, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
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31
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Najafi S, Podgornik R, Potestio R, Tubiana L. Role of Bending Energy and Knot Chirality in Knot Distribution and Their Effective Interaction along Stretched Semiflexible Polymers. Polymers (Basel) 2016; 8:polym8100347. [PMID: 30974623 PMCID: PMC6431951 DOI: 10.3390/polym8100347] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2016] [Revised: 08/25/2016] [Accepted: 09/15/2016] [Indexed: 12/20/2022] Open
Abstract
Knots appear frequently in semiflexible (bio)polymers, including double-stranded DNA, and their presence can affect the polymer’s physical and functional properties. In particular, it is possible and indeed often the case that multiple knots appear on a single chain, with effects which have only come under scrutiny in the last few years. In this manuscript, we study the interaction of two knots on a stretched semiflexible polymer, expanding some recent results on the topic. Specifically, we consider an idealization of a typical optical tweezers experiment and show how the bending rigidity of the chain—And consequently its persistence length—Influences the distribution of the entanglements; possibly more importantly, we observe and report how the relative chirality of the otherwise identical knots substantially modifies their interaction. We analyze the free energy of the chain and extract the effective interactions between embedded knots, rationalizing some of their pertinent features by means of simple effective models. We believe the salient aspect of the knot–knot interactions emerging from our study will be present in a large number of semiflexible polymers under tension, with important consequences for the characterization and manipulation of these systems—Be they artificial or biologica in origin—And for their technological application.
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Affiliation(s)
- Saeed Najafi
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
| | - Rudolf Podgornik
- Department of Physics, Faculty for Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia.
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia.
| | - Raffaello Potestio
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
| | - Luca Tubiana
- Computational Physics Group, University of Vienna, Sensengasse 8, 1090 Vienna, Austria.
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32
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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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33
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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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34
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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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35
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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: 73] [Impact Index Per Article: 9.1] [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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36
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Goff J, Sulaiman S, Arkles B, Lewicki JP. Soft Materials with Recoverable Shape Factors from Extreme Distortion States. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2016; 28:2393-8. [PMID: 26786598 PMCID: PMC4851117 DOI: 10.1002/adma.201503320] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Revised: 10/09/2015] [Indexed: 05/08/2023]
Abstract
Elastomeric polysiloxane nanocomposites with elongations of >5000% (more than 3× greater than any previously reported material) with excellent shape recovery are presented. Highly deformable materials are desirable for the fabrication of stretchable implants and microfluidic devices. No crosslinking or domain formation is observed by a variety of analytical techniques, suggesting that their elastomeric behavior is caused by polymer chain entanglements.
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Affiliation(s)
- Jonathan Goff
- Gelest Inc., 11 East Steel Rd., Morrisville, PA, 19067, USA
| | - Santy Sulaiman
- Gelest Inc., 11 East Steel Rd., Morrisville, PA, 19067, USA
| | - Barry Arkles
- Gelest Inc., 11 East Steel Rd., Morrisville, PA, 19067, USA
| | - James P Lewicki
- Lawrence Livermore National Laboratory, 700 East Ave., Livermore, CA, 94550, USA
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37
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Horner KE, Miller MA, Steed JW, Sutcliffe PM. Knot theory in modern chemistry. Chem Soc Rev 2016; 45:6432-6448. [DOI: 10.1039/c6cs00448b] [Citation(s) in RCA: 61] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
This tutorial review provides an introduction to the mathematics of knots and topological concepts in the context of the chemical sciences.
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Affiliation(s)
- Kate E. Horner
- SPOCK Group
- Department of Mathematical Sciences
- Durham University
- Durham
- UK
| | | | | | - Paul M. Sutcliffe
- SPOCK Group
- Department of Mathematical Sciences
- Durham University
- Durham
- UK
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38
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Suma A, Rosa A, Micheletti C. Pore Translocation of Knotted Polymer Chains: How Friction Depends on Knot Complexity. ACS Macro Lett 2015; 4:1420-1424. [PMID: 35614794 DOI: 10.1021/acsmacrolett.5b00747] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Knots can affect the capability of polymers to translocate through narrow pores in complex and counterintuitive ways that are still relatively unexplored. We report here on a systematic theoretical and computational investigation of the driven translocation of flexible chains accommodating a large repertoire of knots trapped at the pore entrance. These include composite knots, which are the most common form of spontaneous entanglement in long polymers. Two unexpected results emerge from this study. First, the high force translocation compliance does not decrease systematically with knot complexity. Second, the response of composite knots is so dependent on the order of their factor knots, that their hindrance can even be lower than some of their prime components. We show that the resulting rich and seemingly disparate phenomenology can be captured in a seamless framework based on the mechanism by which the tractive force is propagated along and past the knots. The quantitative scheme can be viably used for predictive purposes and, hence, ought to be useful in applicative contexts, too.
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Affiliation(s)
- Antonio Suma
- SISSA, International School for Advanced
Studies, via Bonomea 265, I-34136 Trieste, Italy
| | - Angelo Rosa
- SISSA, International School for Advanced
Studies, via Bonomea 265, I-34136 Trieste, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced
Studies, via Bonomea 265, I-34136 Trieste, Italy
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39
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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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40
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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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41
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Najafi S, Potestio R. Two Adhesive Sites Can Enhance the Knotting Probability of DNA. PLoS One 2015; 10:e0132132. [PMID: 26136125 PMCID: PMC4489926 DOI: 10.1371/journal.pone.0132132] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2015] [Accepted: 06/10/2015] [Indexed: 01/05/2023] Open
Abstract
Self-entanglement, or knotting, is entropically favored in long polymers. Relatively short polymers such as proteins can knot as well, but in this case the entanglement is mainly driven by fine-tuned, sequence-specific interactions. The relation between the sequence of a long polymer and its topological state is here investigated by means of a coarse-grained model of DNA. We demonstrate that the introduction of two adhesive regions along the sequence of a self-avoiding chain substantially increases the probability of forming a knot.
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Affiliation(s)
- Saeed Najafi
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Raffaello Potestio
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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42
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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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43
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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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44
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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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45
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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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46
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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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47
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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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