1
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Polanowski P, Sikorski A. Coil-globule transition in two-dimensional polymer chains in an explicit solvent. SOFT MATTER 2023; 19:7979-7987. [PMID: 37818732 DOI: 10.1039/d3sm00975k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/13/2023]
Abstract
The structure of two-dimensional polymer chains in a solvent at different temperatures is still far from being fully understood. Computer simulations of high-density macromolecular systems require the use of appropriate algorithms, and therefore the simulations were carried out using the Cooperative Motion Algorithm. The polymer model studied was exactly two-dimensional, coarse-grained and based on a triangular lattice. The theta temperature and temperature of coil-to-globule transition, and critical exponents were determined. The differences between the structure of such a disk and that of a chain in a dense polymer liquid were shown.
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Affiliation(s)
- Piotr Polanowski
- Department of Molecular Physics, Łódź University of Technology, Żeromskiego 116, 90-543 Łódź, Poland
| | - Andrzej Sikorski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland.
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2
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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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3
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Olczyk P, Sikorski A. Structure of Strongly Adsorbed Polymer Systems: A Computer Simulation Study. MATERIALS (BASEL, SWITZERLAND) 2023; 16:5755. [PMID: 37687448 PMCID: PMC10488969 DOI: 10.3390/ma16175755] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2023] [Revised: 08/02/2023] [Accepted: 08/18/2023] [Indexed: 09/10/2023]
Abstract
The structure of very thin polymer films formed by strongly adsorbed macromolecules was studied by computer simulation. A coarse-grained model of strictly two-dimensional polymer systems was built, and its properties determined by an efficient Monte Carlo simulation algorithm. Properties of the model system were determined by means of Monte Carlo simulations with a sampling algorithm that combines Verdier-Stockmayer, pivot and reputation moves. The effects of temperature, chain length and polymer concentration on the macromolecular structure were investigated. It was shown that at low temperatures, the chain size increases with the concentration, that is, inversely with high temperatures. This behavior should be explained by the influence of inter-chain interactions.
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Affiliation(s)
- Patrycja Olczyk
- Faculty of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664 Warsaw, Poland
| | - Andrzej Sikorski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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4
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Hsieh MC, Tsao YH, Sheng YJ, Tsao HK. Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution. Polymers (Basel) 2023; 15:polym15092067. [PMID: 37177214 PMCID: PMC10181331 DOI: 10.3390/polym15092067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2023] [Revised: 04/24/2023] [Accepted: 04/24/2023] [Indexed: 05/15/2023] Open
Abstract
The transient elongational viscosity ηe(t) of the polymer melt is known to exhibit strain hardening, which depends on the strain rate ε˙. This phenomenon was elucidated by the difference of chain stretching in the entanglement network between extension and shear. However, to date, the microscopic evolution of polymer melt has not been fully statistically analyzed. In this work, the radial size distributions P(Rg,t) of linear polymers are explored by dissipative particle dynamics during the stretching processes. In uniaxial extensional flow, it is observed that the mean radius of gyration R¯g(t) and standard deviation σ(t) remain unchanged until the onset of strain hardening, corresponding to linear viscoelasticity. Both R¯g and σ rise rapidly in the non-linear regime, and bimodal size distribution can emerge. Moreover, the onset of strain hardening is found to be insensitive to the Hencky strain (ε˙Ht) and chain length (N).
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Affiliation(s)
- Ming-Chang Hsieh
- Department of Chemical Engineering, National Taiwan University, Taipei 106, Taiwan
| | - Yu-Hao Tsao
- Department of Chemical Engineering, National Taiwan University, Taipei 106, Taiwan
| | - Yu-Jane Sheng
- Department of Chemical Engineering, National Taiwan University, Taipei 106, Taiwan
| | - Heng-Kwong Tsao
- Department of Chemical and Materials Engineering, National Central University, Jhongli 320, Taiwan
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5
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Expansion of Single Chains Released from a Spherical Cavity. Polymers (Basel) 2022; 15:polym15010198. [PMID: 36616547 PMCID: PMC9824584 DOI: 10.3390/polym15010198] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2022] [Revised: 12/18/2022] [Accepted: 12/23/2022] [Indexed: 01/03/2023] Open
Abstract
A two-stage model is developed to explain the phenomena of chain expansion, released from a confining cavity. In the first stage, the chain is assumed to expand as a sphere, while in the second stage it expands like a coil. The kinetic equations for the variation of chain size are derived in the two stages by balancing the rate of the free energy change with the rate of the energy dissipation. Langevin dynamics simulations are then performed to examine the theory. We find that the expansion process is dominated by the second stage and the evolution of chain size follows, mainly, the predicted curve for coil expansion, which depends on the chain length and is not sensitive to the confining volume fraction. It permits to define the expansion time for the process. Further study reveals that the chain does undergo a spherical expansion in the first stage with the characteristic time much shorter than the one for the second stage. As a consequence, the first-stage variation of chain size can be regarded as an add-on to the principal curve of expansion designated by the second stage. The scaling behaviors and the associated scaling exponents are analyzed in details. The simulation results well support the theory.
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6
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Optimal Entanglement of Polymers Promotes the Formation of Highly Oriented Fibers. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00578] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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7
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Petrov A, Gavrilov AA, Chertovich A. An exotic microstructured globular state formed by a single multiblock copolymer chain. J Chem Phys 2022; 156:034903. [DOI: 10.1063/5.0072568] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Artem Petrov
- Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Alexey A. Gavrilov
- Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Alexander Chertovich
- Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
- Semenov Federal Research Center for Chemical Physics, 119991 Moscow, Russia
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8
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Wei J, Tian H, Zhou R, Shao Y, Song F, Gao YQ. Topological Constraints with Optimal Length Promote the Formation of Chromosomal Territories at Weakened Degree of Phase Separation. J Phys Chem B 2021; 125:9092-9101. [PMID: 34351763 DOI: 10.1021/acs.jpcb.1c03523] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
It is generally agreed that the nuclei of eukaryotic cells at interphase are partitioned into disjointed territories, with distinct regions occupied by certain chromosomes. However, the underlying mechanism for such territorialization is still under debate. Here we model chromosomes as coarse-grained block copolymers and to investigate the effect of loop domains (LDs) on the formation of compartments and territories based on dissipative particle dynamics. A critical length of LDs, which depends sensitively on the length of polymeric blocks, is obtained to minimize the degree of phase separation. This also applies to the two-polymer system: The critical length not only maximizes the degree of territorialization but also minimizes the degree of phase separation. Interestingly, by comparing with experimental data, we find the critical length for LDs and the corresponding length of blocks to be respectively very close to the mean length of topologically associating domains (TADs) and chromosomal segments with different densities of CpG islands for human chromosomes. The results indicate that topological constraints with optimal length can contribute to the formation of territories by weakening the degree of phase separation, which likely promotes the chromosomal flexibility in response to genetic regulations.
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Affiliation(s)
- Jiachen Wei
- State Key Laboratory of Nonlinear Mechanics and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China.,Shenzhen Bay Laboratory, 5F, No. 9 Duxue Road, Nanshan District, 518055 Shenzhen, Guangdong, China
| | - Hao Tian
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.,Biomedical Pioneering Innovation Center (BIOPIC), Peking University, Beijing 100871, China.,Beijing Advanced Innovation Center for Genomics (ICG), Peking University, Beijing 100871, China
| | - Rui Zhou
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.,Biomedical Pioneering Innovation Center (BIOPIC), Peking University, Beijing 100871, China.,Beijing Advanced Innovation Center for Genomics (ICG), Peking University, Beijing 100871, China
| | - Yingfeng Shao
- State Key Laboratory of Nonlinear Mechanics and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China.,School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Fan Song
- State Key Laboratory of Nonlinear Mechanics and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China.,School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yi Qin Gao
- Shenzhen Bay Laboratory, 5F, No. 9 Duxue Road, Nanshan District, 518055 Shenzhen, Guangdong, China.,Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.,Biomedical Pioneering Innovation Center (BIOPIC), Peking University, Beijing 100871, China.,Beijing Advanced Innovation Center for Genomics (ICG), Peking University, Beijing 100871, China
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9
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Kos PI, Ivanov VA, Chertovich AV. Crystallization of semiflexible polymers in melts and solutions. SOFT MATTER 2021; 17:2392-2403. [PMID: 33480911 DOI: 10.1039/d0sm01545h] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We studied the crystallization of semiflexible polymer chains in melts and poor-solvent solutions with different concentrations using dissipative particle dynamics (DPD) computer simulation techniques. We used the coarse-grained polymer model to reveal the general principles and microscopic scenario of crystallization in such systems at large time and length scales. It covers both primary and secondary nucleation as well as crystallites' merging. The parameters of the DPD model were chosen appropriately to reproduce the entanglements of polymer chains. We started from an initial homogeneous disordered solution of Gaussian chains and observed the initial stages of crystallization process caused in our model by orientational ordering of polymer chains and polymer-solvent phase separation. We found that the overall crystalline fraction at the end of the crystallization process decreases with the increasing polymer volume fraction while the steady-state crystallization speed at later stages does not depend on the polymer volume fraction. The average crystallite size has a maximal value in the systems with a polymer volume fraction from 0.7 to 0.95. In our model, these polymer concentrations represent an optimal value in the sense of balance between the amount of polymer material available to increase the crystallite size and chain entanglements, that prevent crystallites' growth and merging. On large time scales, our model allows us to observe lamellar thickening linear in logarithmic time scale.
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Affiliation(s)
- Pavel I Kos
- Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia. and N.N. Semenov Federal research center for Chemical Physics RAS, 119991 Moscow, Russia
| | - Viktor A Ivanov
- Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia. and Institute of Physics, Martin Luther University, 06099 Halle (Saale), Germany
| | - Alexander V Chertovich
- Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia. and N.N. Semenov Federal research center for Chemical Physics RAS, 119991 Moscow, Russia
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10
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Order and stochasticity in the folding of individual Drosophila genomes. Nat Commun 2021; 12:41. [PMID: 33397980 PMCID: PMC7782554 DOI: 10.1038/s41467-020-20292-z] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2020] [Accepted: 11/23/2020] [Indexed: 02/06/2023] Open
Abstract
Mammalian and Drosophila genomes are partitioned into topologically associating domains (TADs). Although this partitioning has been reported to be functionally relevant, it is unclear whether TADs represent true physical units located at the same genomic positions in each cell nucleus or emerge as an average of numerous alternative chromatin folding patterns in a cell population. Here, we use a single-nucleus Hi-C technique to construct high-resolution Hi-C maps in individual Drosophila genomes. These maps demonstrate chromatin compartmentalization at the megabase scale and partitioning of the genome into non-hierarchical TADs at the scale of 100 kb, which closely resembles the TAD profile in the bulk in situ Hi-C data. Over 40% of TAD boundaries are conserved between individual nuclei and possess a high level of active epigenetic marks. Polymer simulations demonstrate that chromatin folding is best described by the random walk model within TADs and is most suitably approximated by a crumpled globule build of Gaussian blobs at longer distances. We observe prominent cell-to-cell variability in the long-range contacts between either active genome loci or between Polycomb-bound regions, suggesting an important contribution of stochastic processes to the formation of the Drosophila 3D genome. Genomes are partitioned into topologically associating domains (TADs). Here the authors present single-nucleus Hi-C maps in Drosophila at 10 kb resolution, demonstrating the presence of chromatin compartments in individual nuclei, and partitioning of the genome into non-hierarchical TADs at the scale of 100 kb, which resembles population TAD profiles.
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11
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Schneider J, Meinel MK, Dittmar H, Müller-Plathe F. Different Stages of Polymer-Chain Collapse Following Solvent Quenching–Scaling Relations from Dissipative Particle Dynamics Simulations. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01315] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jurek Schneider
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
| | - Melissa K. Meinel
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
| | - Han Dittmar
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
| | - Florian Müller-Plathe
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
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12
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Petrov A, Kos P, Chertovich A. Kinetic mechanisms of crumpled globule formation. SOFT MATTER 2020; 16:2045-2054. [PMID: 31999294 DOI: 10.1039/c9sm01874c] [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
A homopolymer chain with beads forming pairwise reversible bonds is a well-known model in polymer physics. We studied the kinetics of homopolymer chain collapse, which was induced by pairwise reversible bond formation. We compared the kinetic mechanism of this coil-globule transition with the mechanism of collapse in a poor solvent. We discovered that if collapse of a spatially confined chain is induced by formation of long-living pairwise reversible bonds, the transient structures do not resemble classical pearl-necklace conformations formed during collapse in a poor solvent. However, both types of collapse lead to formation of a metastable state of a crumpled globule, which is one of the well-known models of interphase chromatin structure in different organisms. Moreover, we found that the stability and dynamics of this state can be controlled by the fraction of reversible bonds and bond lifetime.
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Affiliation(s)
- Artem Petrov
- Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia.
| | - Pavel Kos
- Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia. and Semenov Institute of Chemical Physics, 119991 Moscow, Russia
| | - Alexander Chertovich
- Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia. and Semenov Institute of Chemical Physics, 119991 Moscow, Russia
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13
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Scolari VF, Mercy G, Koszul R, Lesne A, Mozziconacci J. Kinetic Signature of Cooperativity in the Irreversible Collapse of a Polymer. PHYSICAL REVIEW LETTERS 2018; 121:057801. [PMID: 30118310 DOI: 10.1103/physrevlett.121.057801] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Revised: 04/11/2018] [Indexed: 06/08/2023]
Abstract
We investigate the kinetics of a polymer collapse due to the formation of irreversible cross-links between its monomers. Using the contact probability P(s) as a scale-dependent order parameter depending on the chemical distance s, our simulations show the emergence of a cooperative pearling instability. Namely, the polymer undergoes a sharp conformational transition to a set of absorbing states characterized by a length scale ξ corresponding to the mean pearl size. This length and the transition time depend on the polymer equilibrium dynamics and the cross-linking rate. We confirm experimentally this transition using a DNA conformation capture experiment in yeast.
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Affiliation(s)
- Vittore F Scolari
- Spatial Regulation of Genomes, Genomes and Genetics Department, Institut Pasteur, Paris 75015, France
- UMR3525, Centre National de la Recherche Scientifique, Paris 75015, France
| | - Guillaume Mercy
- Spatial Regulation of Genomes, Genomes and Genetics Department, Institut Pasteur, Paris 75015, France
- UMR3525, Centre National de la Recherche Scientifique, Paris 75015, France
| | - Romain Koszul
- Spatial Regulation of Genomes, Genomes and Genetics Department, Institut Pasteur, Paris 75015, France
- UMR3525, Centre National de la Recherche Scientifique, Paris 75015, France
| | - Annick Lesne
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, Paris F-75252, France
- Institut de Génétique Moléculaire de Montpellier, UMR 5535 CNRS, Montpellier, France
- University of Montpellier, Montpellier, France
| | - Julien Mozziconacci
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, Paris F-75252, France
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14
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Sazer S, Schiessel H. The biology and polymer physics underlying large-scale chromosome organization. Traffic 2018; 19:87-104. [PMID: 29105235 PMCID: PMC5846894 DOI: 10.1111/tra.12539] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2017] [Revised: 10/31/2017] [Accepted: 10/31/2017] [Indexed: 12/21/2022]
Abstract
Chromosome large-scale organization is a beautiful example of the interplay between physics and biology. DNA molecules are polymers and thus belong to the class of molecules for which physicists have developed models and formulated testable hypotheses to understand their arrangement and dynamic properties in solution, based on the principles of polymer physics. Biologists documented and discovered the biochemical basis for the structure, function and dynamic spatial organization of chromosomes in cells. The underlying principles of chromosome organization have recently been revealed in unprecedented detail using high-resolution chromosome capture technology that can simultaneously detect chromosome contact sites throughout the genome. These independent lines of investigation have now converged on a model in which DNA loops, generated by the loop extrusion mechanism, are the basic organizational and functional units of the chromosome.
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Affiliation(s)
- Shelley Sazer
- Verna and Marrs McLean Department of Biochemistry and Molecular BiologyBaylor College of MedicineHoustonTexas
| | - Helmut Schiessel
- Institute Lorentz for Theoretical PhysicsLeiden UniversityLeidenThe Netherlands
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15
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Markina A, Ivanov V, Komarov P, Larin S, Kenny JM, Lyulin S. Effect of polymer chain stiffness on initial stages of crystallization of polyetherimides: Coarse-grained computer simulation. ACTA ACUST UNITED AC 2017. [DOI: 10.1002/polb.24380] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
| | - Viktor Ivanov
- Moscow State University; Moscow 119991 Russian Federation
| | - Pavel Komarov
- Institute of Organoelement Compounds RAS; Moscow 119991 Russian Federation
- Tver State University; Tver 170100 Russian Federation
| | - Sergey Larin
- Institute of Macromolecular Compounds, RAS; St. Petersburg 199004 Russian Federation
| | - José Maria Kenny
- Institute of Macromolecular Compounds, RAS; St. Petersburg 199004 Russian Federation
- Materials Science and Technology Center, University of Perugia; Terni Italy
| | - Sergey Lyulin
- Institute of Macromolecular Compounds, RAS; St. Petersburg 199004 Russian Federation
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16
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Rudyak VY, Gavrilov AA, Guseva DV, Chertovich AV. Complex Curing Pathways and Their Influence on the Phthalonitrile Resin Hardening and Elasticity. MACROMOL THEOR SIMUL 2017. [DOI: 10.1002/mats.201700015] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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17
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Razin SV, Gavrilov AA, Kos P, Ulianov SV. Self-organization of a chromatin fibril into topologically-associated domains. RUSSIAN JOURNAL OF BIOORGANIC CHEMISTRY 2017. [DOI: 10.1134/s1068162017010083] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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18
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Astakhov AM, Ivanov VA, Vasilevskaya VV. Effect of correlations in the interaction along polymer chain on the globule structure. DOKLADY PHYSICAL CHEMISTRY 2017. [DOI: 10.1134/s001250161701002x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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19
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Kos PI, Chertovich AA. Concentrated dispersions and melts from block-copolymer micelles: Computer simulation. POLYMER SCIENCE SERIES A 2016. [DOI: 10.1134/s0965545x16050096] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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20
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Ulianov SV, Khrameeva EE, Gavrilov AA, Flyamer IM, Kos P, Mikhaleva EA, Penin AA, Logacheva MD, Imakaev MV, Chertovich A, Gelfand MS, Shevelyov YY, Razin SV. Active chromatin and transcription play a key role in chromosome partitioning into topologically associating domains. Genome Res 2015; 26:70-84. [PMID: 26518482 PMCID: PMC4691752 DOI: 10.1101/gr.196006.115] [Citation(s) in RCA: 243] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2015] [Accepted: 10/26/2015] [Indexed: 01/06/2023]
Abstract
Recent advances enabled by the Hi-C technique have unraveled many principles of chromosomal folding that were subsequently linked to disease and gene regulation. In particular, Hi-C revealed that chromosomes of animals are organized into topologically associating domains (TADs), evolutionary conserved compact chromatin domains that influence gene expression. Mechanisms that underlie partitioning of the genome into TADs remain poorly understood. To explore principles of TAD folding in Drosophila melanogaster, we performed Hi-C and poly(A)+ RNA-seq in four cell lines of various origins (S2, Kc167, DmBG3-c2, and OSC). Contrary to previous studies, we find that regions between TADs (i.e., the inter-TADs and TAD boundaries) in Drosophila are only weakly enriched with the insulator protein dCTCF, while another insulator protein Su(Hw) is preferentially present within TADs. However, Drosophila inter-TADs harbor active chromatin and constitutively transcribed (housekeeping) genes. Accordingly, we find that binding of insulator proteins dCTCF and Su(Hw) predicts TAD boundaries much worse than active chromatin marks do. Interestingly, inter-TADs correspond to decompacted inter-bands of polytene chromosomes, whereas TADs mostly correspond to densely packed bands. Collectively, our results suggest that TADs are condensed chromatin domains depleted in active chromatin marks, separated by regions of active chromatin. We propose the mechanism of TAD self-assembly based on the ability of nucleosomes from inactive chromatin to aggregate, and lack of this ability in acetylated nucleosomal arrays. Finally, we test this hypothesis by polymer simulations and find that TAD partitioning may be explained by different modes of inter-nucleosomal interactions for active and inactive chromatin.
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Affiliation(s)
- Sergey V Ulianov
- Institute of Gene Biology, RAS, 119334 Moscow, Russia; Department of Molecular Biology, Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Ekaterina E Khrameeva
- Skolkovo Institute of Science and Technology, 143026 Skolkovo, Russia; Institute for Information Transmission Problems (Kharkevich Institute), RAS, 127051 Moscow, Russia
| | | | - Ilya M Flyamer
- Institute of Gene Biology, RAS, 119334 Moscow, Russia; Department of Molecular Biology, Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Pavel Kos
- Physics Department, Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Elena A Mikhaleva
- Department of Molecular Genetics of Cell, Institute of Molecular Genetics, RAS, 123182 Moscow, Russia
| | - Aleksey A Penin
- Institute for Information Transmission Problems (Kharkevich Institute), RAS, 127051 Moscow, Russia; Department of Genetics, Faculty of Biology, Lomonosov Moscow State University, 119991 Moscow, Russia; A.N. Belozersky Institute of Physico-Chemical Biology, Lomonosov Moscow State University, 119234 Moscow, Russia
| | - Maria D Logacheva
- Institute for Information Transmission Problems (Kharkevich Institute), RAS, 127051 Moscow, Russia; A.N. Belozersky Institute of Physico-Chemical Biology, Lomonosov Moscow State University, 119234 Moscow, Russia; Pirogov Russian National Research Medical University, 117997 Moscow, Russia
| | - Maxim V Imakaev
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | | | - Mikhail S Gelfand
- Institute for Information Transmission Problems (Kharkevich Institute), RAS, 127051 Moscow, Russia; Faculty of Bioengineering and Bioinformatics, Lomonosov Moscow State University, 119234 Moscow, Russia
| | - Yuri Y Shevelyov
- Department of Molecular Genetics of Cell, Institute of Molecular Genetics, RAS, 123182 Moscow, Russia
| | - Sergey V Razin
- Institute of Gene Biology, RAS, 119334 Moscow, Russia; Department of Molecular Biology, Lomonosov Moscow State University, 119991 Moscow, Russia
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21
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Bunin G, Kardar M. Coalescence Model for Crumpled Globules Formed in Polymer Collapse. PHYSICAL REVIEW LETTERS 2015; 115:088303. [PMID: 26340216 DOI: 10.1103/physrevlett.115.088303] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2015] [Indexed: 06/05/2023]
Abstract
The rapid collapse of a polymer, due to external forces or changes in solvent, yields a long-lived "crumpled globule." The conjectured fractal structure shaped by hierarchical collapse dynamics has proved difficult to establish, even with large simulations. To unravel this puzzle, we study a coarse-grained model of in-falling spherical blobs that coalesce upon contact. Distances between pairs of monomers are assigned upon their initial coalescence, and do not "equilibrate" subsequently. Surprisingly, the model reproduces quantitatively the dependence of distance on segment length, suggesting that the slow approach to scaling is related to the wide distribution of blob sizes.
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Affiliation(s)
- Guy Bunin
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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22
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Tamm MV, Nazarov LI, Gavrilov AA, Chertovich AV. Anomalous diffusion in fractal globules. PHYSICAL REVIEW LETTERS 2015; 114:178102. [PMID: 25978267 DOI: 10.1103/physrevlett.114.178102] [Citation(s) in RCA: 56] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2014] [Indexed: 06/04/2023]
Abstract
The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics computer simulation for the thermal motion of monomers in the fractal globule state. Simulations starting from different entanglement-free initial states show good convergence which provides evidence supporting the existence of a unique metastable fractal globule state. We show monomer motion in this state to be subdiffusive described by ⟨X(2)(t)⟩∼t(αF) with αF close to 0.4. This result is in good agreement with existing experimental data on the chromatin dynamics, which makes an additional argument in support of the fractal globule model of chromatin packing.
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Affiliation(s)
- M V Tamm
- Physics Department, Moscow State University, 119991 Moscow, Russia
- Department of Applied Mathematics, National Research University Higher School of Economics, 101000 Moscow, Russia
| | - L I Nazarov
- Physics Department, Moscow State University, 119991 Moscow, Russia
| | - A A Gavrilov
- Physics Department, Moscow State University, 119991 Moscow, Russia
- Institute for Advanced Energy Related Nanomaterials, University of Ulm, D-89069 Ulm, Germany
| | - A V Chertovich
- Physics Department, Moscow State University, 119991 Moscow, Russia
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23
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Imakaev MV, Tchourine KM, Nechaev SK, Mirny LA. Effects of topological constraints on globular polymers. SOFT MATTER 2015; 11:665-671. [PMID: 25472862 DOI: 10.1039/c4sm02099e] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Topological constraints can affect both equilibrium and dynamic properties of polymer systems and can play a role in the organization of chromosomes. Despite many theoretical studies, the effects of topological constraints on the equilibrium state of a single compact polymer have not been systematically studied. Here we use simulations to address this longstanding problem. We find that sufficiently long unknotted polymers differ from knotted ones in the spatial and topological states of their subchains. The unknotted globule has subchains that are mostly unknotted and form asymptotically compact RG(s)∼s1/3 crumples. However, crumples display a high fractal dimension of the surface db=2.8, forming excessive contacts and interpenetrating each other. We conclude that this topologically constrained equilibrium state resembles a conjectured crumpled globule [Grosberg et al., Journal de Physique, 1988, 49, 2095], but differs from its idealized hierarchy of self-similar, isolated and compact crumples.
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