1
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Marcato D, Giacometti A, Maritan A, Rosa A. Phase behaviour of semiflexible lattice polymers in poor-solvent solution: Mean-field theory and Monte Carlo simulations. J Chem Phys 2023; 159:154901. [PMID: 37843062 DOI: 10.1063/5.0171911] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 09/22/2023] [Indexed: 10/17/2023] Open
Abstract
We study a solution of interacting semiflexible polymers with curvature energy in poor-solvent conditions on the d-dimensional cubic lattice using mean-field theory and Monte Carlo computer simulations. Building upon past studies on a single chain, we construct a field-theory representation of the system and solve it within a mean-field approximation supported by Monte Carlo simulations in d = 3. A gas-liquid transition is found in the temperature-density plane that is then interpreted in terms of real systems. Interestingly, we find this transition to be independent of the bending rigidity. Past classical Flory-Huggins and Flory mean-field results are shown to be particular cases of this more general framework. Perspectives in terms of guiding experimental results towards optimal conditions are also proposed.
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Affiliation(s)
- Davide Marcato
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari Venezia, 30123 Venezia, Italy
- European Centre for Living Technology (ECLT) Ca' Bottacin, 3911 Dorsoduro Calle Crosera, 30123 Venezia, Italy
| | - Amos Maritan
- Laboratory of Interdisciplinary Physics, Department of Physics and Astronomy "G. Galilei," University of Padova, Padova, Italy and INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - Angelo Rosa
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
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2
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Nguyen NTT, Ngo AT, Hoang TX. Energetic preference and topological constraint effects on the formation of DNA twisted toroidal bundles. J Chem Phys 2023; 158:114904. [PMID: 36948817 DOI: 10.1063/5.0134710] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/06/2023] Open
Abstract
DNA toroids are compact torus-shaped bundles formed by one or multiple DNA molecules being condensed from the solution due to various condensing agents. It has been shown that the DNA toroidal bundles are twisted. However, the global conformations of DNA inside these bundles are still not well understood. In this study, we investigate this issue by solving different models for the toroidal bundles and performing replica-exchange molecular dynamics (REMD) simulations for self-attractive stiff polymers of various chain lengths. We find that a moderate degree of twisting is energetically favorable for toroidal bundles, yielding optimal configurations of lower energies than for other bundles corresponding to spool-like and constant radius of curvature arrangements. The REMD simulations show that the ground states of the stiff polymers are twisted toroidal bundles with the average twist degrees close to those predicted by the theoretical model. Constant-temperature simulations show that twisted toroidal bundles can be formed through successive processes of nucleation, growth, quick tightening, and slow tightening of the toroid, with the two last processes facilitating the polymer threading through the toroid's hole. A relatively long chain of 512 beads has an increased dynamical difficulty to access the twisted bundle states due to the polymer's topological constraint. Interestingly, we also observed significantly twisted toroidal bundles with a sharp U-shaped region in the polymer conformation. It is suggested that this U-shaped region makes the formation of twisted bundles easier by effectively reducing the polymer length. This effect can be equivalent to having multiple chains in the toroid.
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Affiliation(s)
- Nhung T T Nguyen
- Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi 11108, Vietnam
| | - Anh T Ngo
- Chemical Engineering Department, University of Illinois at Chicago, Chicago, Illinois 60608, USA
| | - Trinh X Hoang
- Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi 11108, Vietnam
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3
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Boehm BJ, McNeill CR, Huang DM. Competing single-chain folding and multi-chain aggregation pathways control solution-phase aggregate morphology of organic semiconducting polymers. NANOSCALE 2022; 14:18070-18086. [PMID: 36448546 DOI: 10.1039/d2nr04750k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Understanding the solution-phase behaviour of organic semiconducting polymers is important for systematically improving the performance of devices based on solution-processed thin films of these molecules. Conventional polymer theory predicts that polymer conformations become more compact as solvent quality decreases, but recent experiments have shown the high-performance organic-semiconducting polymer P(NDI2OD-T2) to form extended rod-like aggregates much larger than a single chain in poor solvents, with the formation of these extended aggregates correlated with enhanced electron mobility in films deposited from these solutions. We explain the unexpected formation of extended aggregates using a novel coarse-grained simulation model of P(NDI2OD-T2) that we have developed to study the effect of solvent quality on its solution-phase behaviour. In poor solvents, we find that aggregation through only a few monomers gives effectively inseparable chains, leading to the formation of extended structures of partially overlapping chains via non-equilibrium assembly. This behaviour requires that multi-chain aggregation occurs faster than chain folding, which we show is the case for the chain lengths and concentrations shown experimentally to form rod-like aggregates. This kinetically controlled process introduces a dependence of aggregate structure on concentration, chain length, and chain flexibility, which we show is able to reconcile experimental findings and is generalisable to the solution-phase assembly of other semiflexible polymers.
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Affiliation(s)
- Belinda J Boehm
- Department of Chemistry, School of Physical Sciences, The University of Adelaide, SA 5005, Australia.
| | - Christopher R McNeill
- Department of Materials Science and Engineering, Monash University, Clayton, VIC 3800, Australia
| | - David M Huang
- Department of Chemistry, School of Physical Sciences, The University of Adelaide, SA 5005, Australia.
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4
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Du J, Yin H, Zhu H, Wan T, Wang B, Qi H, Lu Y, Dai L, Chen T. Forming a Double-Helix Phase of Single Polymer Chains by the Cooperation between Local Structure and Nonlocal Attraction. PHYSICAL REVIEW LETTERS 2022; 128:197801. [PMID: 35622042 DOI: 10.1103/physrevlett.128.197801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2021] [Revised: 03/01/2022] [Accepted: 03/25/2022] [Indexed: 06/15/2023]
Abstract
Double-helix structures, such as DNA, are formed in nature to realize many unique functions. Inspired by this, researchers are pursuing strategies to design such structures from polymers. A key question is whether the double helix can be formed from the self-folding of a single polymer chain without specific interactions. Here, using Langevin dynamics simulation and theoretical analysis, we find that a stable double-helix phase can be achieved by the self-folding of single semiflexible polymers as a result of the cooperation between local structure and nonlocal attraction. The critical temperature of double-helix formation approximately follows T^{cri}∼ln(k_{θ}) and T^{cri}∼ln(k_{τ}), where k_{θ} and k_{τ} are the polymer bending and torsion stiffness, respectively. Furthermore, the double helix can exhibit major and minor grooves due to symmetric break for better packing. Our results provide a novel guide to the experimental design of the double helix.
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Affiliation(s)
- Jiang Du
- College of Chemistry and Materials Science, Northwest University, Xi'an 710127, China
| | - Hongmei Yin
- College of Chemistry and Materials Science, Northwest University, Xi'an 710127, China
| | - Haoqi Zhu
- Department of Physics, City University of Hong Kong, Hong Kong 999077, China
| | - Tiantian Wan
- College of Chemistry and Materials Science, Northwest University, Xi'an 710127, China
| | - Binzhou Wang
- College of Chemistry and Materials Science, Northwest University, Xi'an 710127, China
| | - Hongtao Qi
- College of Chemistry and Materials Science, Northwest University, Xi'an 710127, China
| | - Yanfang Lu
- College of Chemistry and Materials Science, Northwest University, Xi'an 710127, China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Hong Kong 999077, China
| | - Tao Chen
- College of Chemistry and Materials Science, Northwest University, Xi'an 710127, China
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5
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Yevdokimov YM, Skuridin SG, Salyanov VI, Kats EI. Observations of three "re-entrant" twisted structures in double-stranded DNA dispersion particles. EUROPEAN BIOPHYSICS JOURNAL : EBJ 2022; 51:85-94. [PMID: 34839370 DOI: 10.1007/s00249-021-01578-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Revised: 09/11/2021] [Accepted: 11/14/2021] [Indexed: 06/13/2023]
Abstract
In this work we report on observations of new twisted (cholesteric-like) structures in liquid-crystalline dispersion particles with a hexagonal packing of double-stranded (ds) DNA molecules. Heating up to 80 °C of the DNA dispersion formed in a aqueous-salt solution with a high osmotic pressure (concentration) of poly(ethylene glycol) induces the formation of a new, optically active, spirally twisted structure of these molecules ("re-entrant" cholesteric structure (rest-A structure)). Cooling of this dispersion up to 22 °C is accompanied by the formation of an additional "re-entrant" cholesteric structure (rest-B). Modification of particles of the ds DNA dispersion (with rest-B structure) by replacing Na+ cations by multi-charged Gd3+ cations results in the third " re-entrant" structure (rest-C) despite a high density packing of ds nucleic acid molecules.
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Affiliation(s)
- Yuri M Yevdokimov
- Engelhardt Institute of Molecular Biology of the Russian Academy of Sciences, Vavilova st. 32, Moscow, Russia, 119991
| | - Sergey G Skuridin
- Engelhardt Institute of Molecular Biology of the Russian Academy of Sciences, Vavilova st. 32, Moscow, Russia, 119991.
| | - Viktor I Salyanov
- Engelhardt Institute of Molecular Biology of the Russian Academy of Sciences, Vavilova st. 32, Moscow, Russia, 119991
| | - Efim I Kats
- Landau Institute for Theoretical Physics of the Russian Academy of Sciences, academician Semenov ave. 1-A, Chernogolovka, Moscow Region, Russia, 142432
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6
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Hu R, Gao L, Cai C, Lin J, Chen Z, Wang L. Intermicellar Polymerization and Intramicellar Cyclization: A Supramolecular Ring–Chain Competition Reaction. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01020] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Rui Hu
- Shanghai Key Laboratory of Advanced Polymeric Materials, Key Laboratory for Ultrafine Materials of Ministry of Education, Frontiers Science Center for Materiobiology and Dynamic Chemistry, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Liang Gao
- Shanghai Key Laboratory of Advanced Polymeric Materials, Key Laboratory for Ultrafine Materials of Ministry of Education, Frontiers Science Center for Materiobiology and Dynamic Chemistry, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Chunhua Cai
- Shanghai Key Laboratory of Advanced Polymeric Materials, Key Laboratory for Ultrafine Materials of Ministry of Education, Frontiers Science Center for Materiobiology and Dynamic Chemistry, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Jiaping Lin
- Shanghai Key Laboratory of Advanced Polymeric Materials, Key Laboratory for Ultrafine Materials of Ministry of Education, Frontiers Science Center for Materiobiology and Dynamic Chemistry, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Zuowei Chen
- Shanghai Key Laboratory of Advanced Polymeric Materials, Key Laboratory for Ultrafine Materials of Ministry of Education, Frontiers Science Center for Materiobiology and Dynamic Chemistry, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Liquan Wang
- Shanghai Key Laboratory of Advanced Polymeric Materials, Key Laboratory for Ultrafine Materials of Ministry of Education, Frontiers Science Center for Materiobiology and Dynamic Chemistry, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China
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7
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Gao L, Hu R, Xu P, Lin J, Zhang L, Wang L. Supramolecular cyclization of semiflexible cylindrical micelles assembled from rod-coil graft copolymers. NANOSCALE 2020; 12:296-305. [PMID: 31825050 DOI: 10.1039/c9nr07930k] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Uniform toroidal micelles can be constructed via the supramolecular cyclization of semiflexible cylindrical micelles, but revealing the conditions under which the cyclization occurs and the mechanism underlying the cyclization remains a challenge. In this study, we performed Brownian dynamics simulations of the supramolecular cyclization of semiflexible cylindrical micelles formed by rod-coil graft copolymers to obtain the cyclization conditions and understand the cyclization mechanism. It was found that the balance of the bending energy of the polymer backbones with the self-attraction energy between the pendant groups on the polymer backbones plays an important role in the cyclization process. A theoretical model based on this balance is developed to explain the cyclization mechanism, and the conditions required for realizing the supramolecular cyclization are obtained. The proposed mechanism is supported by our experimental findings regarding the supramolecular cyclization of polypeptide cylindrical micelles. The cyclization conditions and the revealed mechanism can guide further preparation of uniform toroidal micelles from semiflexible cylindrical micelles in an end-to-end closure manner.
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Affiliation(s)
- Liang Gao
- Shanghai Key Laboratory of Advanced Polymeric Materials, Key Laboratory for Ultrafine Materials of Ministry of Education, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China.
| | - Rui Hu
- Shanghai Key Laboratory of Advanced Polymeric Materials, Key Laboratory for Ultrafine Materials of Ministry of Education, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China.
| | - Pengfei Xu
- Shanghai Key Laboratory of Advanced Polymeric Materials, Key Laboratory for Ultrafine Materials of Ministry of Education, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China.
| | - Jiaping Lin
- Shanghai Key Laboratory of Advanced Polymeric Materials, Key Laboratory for Ultrafine Materials of Ministry of Education, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China.
| | - Liangshun Zhang
- Shanghai Key Laboratory of Advanced Polymeric Materials, Key Laboratory for Ultrafine Materials of Ministry of Education, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China.
| | - Liquan Wang
- Shanghai Key Laboratory of Advanced Polymeric Materials, Key Laboratory for Ultrafine Materials of Ministry of Education, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China.
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8
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Škrbić T, Banavar JR, Giacometti A. Chain stiffness bridges conventional polymer and bio-molecular phases. J Chem Phys 2019; 151:174901. [PMID: 31703491 DOI: 10.1063/1.5123720] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
Chain molecules play important roles in industry and in living cells. Our focus here is on distinct ways of modeling the stiffness inherent in a chain molecule. We consider three types of stiffnesses-one yielding an energy penalty for local bends (energetic stiffness) and the other two forbidding certain classes of chain conformations (entropic stiffness). Using detailed Wang-Landau microcanonical Monte Carlo simulations, we study the interplay between the nature of the stiffness and the ground state conformation of a self-attracting chain. We find a wide range of ground state conformations, including a coil, a globule, a toroid, rods, helices, and zig-zag strands resembling β-sheets, as well as knotted conformations allowing us to bridge conventional polymer phases and biomolecular phases. An analytical mapping is derived between the persistence lengths stemming from energetic and entropic stiffness. Our study shows unambiguously that different stiffnesses play different physical roles and have very distinct effects on the nature of the ground state of the conformation of a chain, even if they lead to identical persistence lengths.
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Affiliation(s)
- Tatjana Škrbić
- Department of Physics and Institute for Theoretical Science, 1274 University of Oregon, Eugene, Oregon 97403-1274, USA
| | - Jayanth R Banavar
- Department of Physics and Institute for Theoretical Science, 1274 University of Oregon, Eugene, Oregon 97403-1274, USA
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy
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9
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Gordievskaya YD, Kramarenko EY. Effect of the Fraction and Size of Polar Groups on the Formation of Compact Conformations of a Polymer Chain with Variable Stiffness in Low-Polar Media. POLYMER SCIENCE SERIES B 2019. [DOI: 10.1134/s1560090419060046] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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10
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Abstract
In this review, we compare the circular dichroism (CD) spectra of liquid-crystalline dispersion (LCD) particles formed in PEG-containing aqueous-salt solutions with the purpose of determining the packing of ds DNA molecules in these particles. Depending on the osmotic pressure of the solution, the phase exclusion of ds DNA molecules at room temperature results in the formation of LCD particles with the cholesteric or the hexagonal packing of molecules. The heating of dispersion particles with the hexagonal packing of the ds DNA molecules results in a new phase transition, accompanied by an appearance of a new optically active phase of ds DNA molecules. Our results are rationalized by way of a concept of orientationally ordered “quasinematic” layers formed by ds DNA molecules, with a parallel alignment in the hexagonal structure. These layers can adopt a twisted configuration with a temperature increase; and as a result of this process, a new, helicoidal structure of dispersion particle is formed (termed as the “re-entrant” cholesteric phase). To prove the cholesteric pattern of ds DNA molecules in this phase, the “liquid-like” state of the dispersion particles was transformed into its “rigid” counterpart.
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11
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Liu L, Hyeon C. From octopus to dendrite—Semiflexible polyelectrolyte brush condensates in trivalent counterion solution. J Chem Phys 2018; 149:163302. [DOI: 10.1063/1.5027161] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Affiliation(s)
- Lei Liu
- Korea Institute for Advanced Study, Seoul 02455, South Korea
| | - Changbong Hyeon
- Korea Institute for Advanced Study, Seoul 02455, South Korea
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12
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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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13
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Pyrlin SV, Hine NDM, Kleij AW, Ramos MMD. Self-assembly of bis-salphen compounds: from semiflexible chains to webs of nanorings. SOFT MATTER 2018; 14:1181-1194. [PMID: 29349462 DOI: 10.1039/c7sm02371e] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The recently-observed self-assembly of certain salphen-based compounds into neuron-like networks of microrings interconnected with nano-thin strings may suggest a new highly-potent tool for nanoscale patterning. However, the mechanism behind such phenomena needs to be clarified before they can be applied in materials design. Here we show that, in contrast with what was initially presumed, the emergence of a "rings-and-rods" pattern is unlikely to be explained by merging, collapse and piercing of vesicles as in previously reported cases of nanorings self-assembly via non-bonding interactions. We propose an alternative explanation: the compounds under study form a 1D coordination polymer, the fibres of which are elastic enough to fold into toroidal globules upon solvent evaporation, while being able to link separate chains into extended networks. This becomes possible because the structure of the compound's scaffold is found to adopt a very different conformation from that inferred in the original work. Based on ab initio and molecular dynamics calculations we propose a step-by-step description of self-assembly process of a supramolecular structure which explains all the observed phenomena in a simple and clear way. The individual roles of the compound' s scaffold structure, coordination centres, functional groups and solvent effects are also explained, opening a route to control the morphology of self-assembled networks and to synthesize new compounds exhibiting similar behaviour.
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Affiliation(s)
- Sergey V Pyrlin
- Department of Physics and Center of Physics, University of Minho, Campus de Gualtar, Braga 4710-057, Portugal.
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14
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Nguyen VD, Nguyen TT, Carloni P. DNA like-charge attraction and overcharging by divalent counterions in the presence of divalent co-ions. J Biol Phys 2017; 43:185-195. [PMID: 28190162 DOI: 10.1007/s10867-017-9443-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2016] [Accepted: 01/09/2017] [Indexed: 01/04/2023] Open
Abstract
Strongly correlated electrostatics of DNA systems has drawn the interest of many groups, especially the condensation and overcharging of DNA by multivalent counterions. By adding counterions of different valencies and shapes, one can enhance or reduce DNA overcharging. In this paper, we focus on the effect of multivalent co-ions, specifically divalent co-ions such as SO[Formula: see text]. A computational experiment of DNA condensation using Monte Carlo simulation in grand canonical ensemble is carried out where the DNA system is in equilibrium with a bulk solution containing a mixture of salt of different valency of co-ions. Compared to systems with purely monovalent co-ions, the influence of divalent co-ions shows up in multiple aspects. Divalent co-ions lead to an increase of monovalent salt in the DNA condensate. Because monovalent salts mostly participate in linear screening of electrostatic interactions in the system, more monovalent salt molecules enter the condensate leads to screening out of short-range DNA-DNA like charge attraction and weaker DNA condensation free energy. The overcharging of DNA by multivalent counterions is also reduced in the presence of divalent co-ions. Strong repulsions between DNA and divalent co-ions and among divalent co-ions themselves lead to a depletion of negative ions near the DNA surface as compared to the case without divalent co-ions. At large distances, the DNA-DNA repulsive interaction is stronger in the presence of divalent co-ions, suggesting that divalent co-ions' role is not only that of simple stronger linear screening.
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Affiliation(s)
- Viet Duc Nguyen
- Faculty of Physics, VNU University of Science, Vietnam National University, 334 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam
| | - Toan T Nguyen
- Faculty of Physics, VNU University of Science, Vietnam National University, 334 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam.
- VNU Key Laboratory "Multiscale Simulation of Complex Systems", VNU University of Science, Vietnam National University, 334 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam.
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, GA, 30332-0430, USA.
| | - Paolo Carloni
- VNU Key Laboratory "Multiscale Simulation of Complex Systems", VNU University of Science, Vietnam National University, 334 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam
- Computational Biomedicine, Institute for Advanced Simulation IAS-5, and Institute of Neuroscience and Medicine INM-9, Forschungszentrum Julich, 52425, Julich, Germany
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15
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Lima CHM, Rocha MS, Ramos EB. Unfolding DNA condensates produced by DNA-like charged depletants: A force spectroscopy study. J Chem Phys 2017; 146:054901. [DOI: 10.1063/1.4975103] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Škrbić T, Hoang TX, Giacometti A. Effective stiffness and formation of secondary structures in a protein-like model. J Chem Phys 2016; 145:084904. [DOI: 10.1063/1.4961387] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tatjana Škrbić
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari di Venezia, Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy
| | - Trinh X. Hoang
- Center for Computational Physics, Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi, Vietnam
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari di Venezia, Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy
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17
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Benetatos P, Jho Y. Bundling in semiflexible polymers: A theoretical overview. Adv Colloid Interface Sci 2016; 232:114-126. [PMID: 26813628 DOI: 10.1016/j.cis.2016.01.001] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2015] [Revised: 12/07/2015] [Accepted: 01/02/2016] [Indexed: 01/07/2023]
Abstract
Supramolecular assemblies of polymers are key modules to sustain the structure of cells and their function. The main elements of these assemblies are charged semiflexible polymers (polyelectrolytes) generally interacting via a long(er)-range repulsion and a short(er)-range attraction. The most common supramolecular structure formed by these polymers is the bundle. In the present paper, we critically review some recent theoretical and computational advances on the problem of bundle formation, and point a few promising directions for future work.
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Affiliation(s)
- Panayotis Benetatos
- Department of Physics, Kyungpook National University, 80 Daehakro, Bukgu, Daegu, 702-701, South Korea
| | - YongSeok Jho
- Asia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk, 790-784, South Korea; Department of Physics, Pohang University of Science and Technology, 790-784, South Korea.
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Stanković I, Dašić M, Messina R. Structure and cohesive energy of dipolar helices. SOFT MATTER 2016; 12:3056-3065. [PMID: 26890916 DOI: 10.1039/c5sm02774h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
This paper deals with the investigation of cohesive energy in dipolar helices made up of hard spheres. Such tubular helical structures are ubiquitous objects in biological systems. We observe a complex dependence of cohesive energy on surface packing fraction and dipole moment distribution. As far as single helices are concerned, the lowest cohesive energy is achieved at the highest surface packing fraction. Besides, a striking non-monotonic behavior is reported for the cohesive energy as a function of the surface packing fraction. For multiple helices, we discover a new phase, exhibiting markedly higher cohesive energy. This phase is referred to as ZZ tube consisting of stacked crown rings (reminiscent of a pile of zig-zag rings), resulting in a local triangular arrangement with densely packed filaments parallel to the tube axis.
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Affiliation(s)
- Igor Stanković
- Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia.
| | - Miljan Dašić
- Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia.
| | - René Messina
- Institut de Chimie, Physique et Matériaux (ICPM), Université de Lorraine, 1 Bd. Arago, 57070 Metz, France
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Nguyen TT. Grand-canonical simulation of DNA condensation with two salts, effect of divalent counterion size. J Chem Phys 2016; 144:065102. [DOI: 10.1063/1.4940312] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Toan T. Nguyen
- Faculty of Physics, Hanoi University of Science, Vietnam National University, 334 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam and School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332-0430, USA
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Cortini R, Caré BR, Victor JM, Barbi M. Theory and simulations of toroidal and rod-like structures in single-molecule DNA condensation. J Chem Phys 2015; 142:105102. [PMID: 25770562 DOI: 10.1063/1.4914513] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
DNA condensation by multivalent cations plays a crucial role in genome packaging in viruses and sperm heads, and has been extensively studied using single-molecule experimental methods. In those experiments, the values of the critical condensation forces have been used to estimate the amplitude of the attractive DNA-DNA interactions. Here, to describe these experiments, we developed an analytical model and a rigid body Langevin dynamics assay to investigate the behavior of a polymer with self-interactions, in the presence of a traction force applied at its extremities. We model self-interactions using a pairwise attractive potential, thereby treating the counterions implicitly. The analytical model allows to accurately predict the equilibrium structures of toroidal and rod-like condensed structures, and the dependence of the critical condensation force on the DNA length. We find that the critical condensation force depends strongly on the length of the DNA, and finite-size effects are important for molecules of length up to 10(5)μm. Our Langevin dynamics simulations show that the force-extension behavior of the rod-like structures is very different from the toroidal ones, so that their presence in experiments should be easily detectable. In double-stranded DNA condensation experiments, the signature of the presence of rod-like structures was not unambiguously detected, suggesting that the polyamines used to condense DNA may protect it from bending sharply as needed in the rod-like structures.
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Affiliation(s)
- Ruggero Cortini
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600,Université Pierre et Marie Curie, Sorbonne Université, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Bertrand R Caré
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600,Université Pierre et Marie Curie, Sorbonne Université, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Jean-Marc Victor
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600,Université Pierre et Marie Curie, Sorbonne Université, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Maria Barbi
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600,Université Pierre et Marie Curie, Sorbonne Université, 4 place Jussieu, 75252 Paris Cedex 05, France
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Hoang TX, Trinh HL, Giacometti A, Podgornik R, Banavar JR, Maritan A. Phase diagram of the ground states of DNA condensates. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:060701. [PMID: 26764619 DOI: 10.1103/physreve.92.060701] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2015] [Indexed: 06/05/2023]
Abstract
The phase diagram of the ground states of DNA in a bad solvent is studied for a semiflexible polymer model with a generalized local elastic bending potential characterized by a nonlinearity parameter x and effective self-attraction promoting compaction. x=1 corresponds to the wormlike chain model. Surprisingly, the phase diagram as well as the transition lines between the ground states are found to be a function of x. The model provides a simple explanation for the results of prior experimental and computational studies and makes predictions for the specific geometries of the ground states. The results underscore the impact of the form of the microscopic bending energy at macroscopic observable scales.
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Affiliation(s)
- Trinh X Hoang
- Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi, Vietnam
| | - Hoa Lan Trinh
- Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi, Vietnam
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Universita' Ca' Foscari Venezia, I-30123 Venezia, Italy
| | - Rudolf Podgornik
- Department of Theoretical Physics, J. Stefan Institute and Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Jayanth R Banavar
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Amos Maritan
- Dipartimento di Fisica e Astronomia, Università di Padova, CNISM and INFN, via Marzolo 8, I-35131 Padova, Italy
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Lu BS, Podgornik R. Effective interactions between fluid membranes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022112. [PMID: 26382349 DOI: 10.1103/physreve.92.022112] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2015] [Indexed: 06/05/2023]
Abstract
A self-consistent theory is proposed for the general problem of interacting undulating fluid membranes subject to the constraint that they do not interpenetrate. We implement the steric constraint via an exact functional integral representation and, through the use of a saddle-point approximation, transform it into a novel effective steric potential. The steric potential is found to consist of two contributions: one generated by zero-mode fluctuations of the membranes and the other by thermal bending fluctuations. For membranes of cross-sectional area S, we find that the bending fluctuation part scales with the intermembrane separation d as d-2 for d≪√S but crosses over to d-4 scaling for d≫√S, whereas the zero-mode part of the steric potential always scales as d-2. For membranes interacting exclusively via the steric potential, we obtain closed-form expressions for the effective interaction potential and for the rms undulation amplitude σ, which becomes small at low temperatures T and/or large bending stiffnesses κ. Moreover, σ scales as d for d≪√S but saturates at √kBTS/κ for d≫√S. In addition, using variational Gaussian theory, we apply our self-consistent treatment to study intermembrane interactions subject to different types of potentials: (i) the Moreira-Netz potential for a pair of strongly charged membranes with an intervening solution of multivalent counterions, (ii) an attractive square well, (iii) the Morse potential, and (iv) a combination of hydration and van der Waals interactions.
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Affiliation(s)
- Bing-Sui Lu
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia and Department of Theoretical Physics, J. Stefan Institute, 1000 Ljubljana, Slovenia
| | - Rudolf Podgornik
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia and Department of Theoretical Physics, J. Stefan Institute, 1000 Ljubljana, Slovenia
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