1
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Shin S, Shi G, Cho HW, Thirumalai D. Transcription-induced active forces suppress chromatin motion. Proc Natl Acad Sci U S A 2024; 121:e2307309121. [PMID: 38489381 PMCID: PMC10963020 DOI: 10.1073/pnas.2307309121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 02/06/2024] [Indexed: 03/17/2024] Open
Abstract
The organization of interphase chromosomes in a number of species is starting to emerge thanks to advances in a variety of experimental techniques. However, much less is known about the dynamics, especially in the functional states of chromatin. Some experiments have shown that the motility of individual loci in human interphase chromosome decreases during transcription and increases upon inhibiting transcription. This is a counterintuitive finding because it is thought that the active mechanical force (F) on the order of ten piconewtons, generated by RNA polymerase II (RNAPII) that is presumably transmitted to the gene-rich region of the chromatin, would render it more open, thus enhancing the mobility. We developed a minimal active copolymer model for interphase chromosomes to investigate how F affects the dynamical properties of chromatin. The movements of the loci in the gene-rich region are suppressed in an intermediate range of F and are enhanced at small F values, which has also been observed in experiments. In the intermediate F, the bond length between consecutive loci increases, becoming commensurate with the distance at the minimum of the attractive interaction between nonbonded loci. This results in a transient disorder-to-order transition, leading to a decreased mobility during transcription. Strikingly, the F-dependent change in the locus dynamics preserves the organization of the chromosome at [Formula: see text]. Transient ordering of the loci, which is not found in the polymers with random epigenetic profiles, in the gene-rich region might be a plausible mechanism for nucleating a dynamic network involving transcription factors, RNAPII, and chromatin.
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Affiliation(s)
- Sucheol Shin
- Department of Chemistry, The University of Texas at Austin, Austin, TX78712
| | - Guang Shi
- Department of Chemistry, The University of Texas at Austin, Austin, TX78712
- Department of Materials Science, University of Illinois, Urbana, IL61801
| | - Hyun Woo Cho
- Department of Fine Chemistry and Center for Functional Biomaterials, Seoul National University of Science and Technology, Seoul01811, Republic of Korea
| | - D. Thirumalai
- Department of Chemistry, The University of Texas at Austin, Austin, TX78712
- Department of Physics, The University of Texas at Austin, Austin, TX78712
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2
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Eshghi I, Zidovska A, Grosberg AY. Symmetry-based classification of forces driving chromatin dynamics. SOFT MATTER 2022; 18:8134-8146. [PMID: 36239271 DOI: 10.1039/d2sm00840h] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Chromatin - the functional form of DNA in the cell - exists in the form of a polymer immersed in a nucleoplasmic fluid inside the cell nucleus. Both chromatin and nucleoplasm are subject to active forces resulting from local biological processes. This activity leads to non-equilibrium phenomena, affecting chromatin organization and dynamics, yet the underlying physics is far from understood. Here, we expand upon a previously developed two-fluid model of chromatin and nucleoplasm by considering three types of activity in the form of force dipoles - two with both forces of the dipole acting on the same fluid (either polymer or nucleoplasm) and a third, with two forces pushing chromatin and solvent in opposite directions. We find that this latter type results in the most significant flows, dominating over most length scales of interest. Due to the friction between the fluids and their viscosity, we observe emergent screening length scales in the active flows of this system. We predict that the presence of different activity types and their relative strengths can be inferred from observing the power spectra of hydrodynamic fluctuations in the chromatin and the nucleoplasm.
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Affiliation(s)
- Iraj Eshghi
- Center for Soft Matter Research, Department of Physics, New York University, New York, NY 10003, USA.
| | - Alexandra Zidovska
- Center for Soft Matter Research, Department of Physics, New York University, New York, NY 10003, USA.
| | - Alexander Y Grosberg
- Center for Soft Matter Research, Department of Physics, New York University, New York, NY 10003, USA.
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3
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Ghosh A, Spakowitz AJ. Active and thermal fluctuations in multi-scale polymer structure and dynamics. SOFT MATTER 2022; 18:6629-6637. [PMID: 36000419 DOI: 10.1039/d2sm00593j] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The presence of athermal noise or biological fluctuations control and maintain crucial life-processes. In this work, we present an exact analytical treatment of the dynamic behavior of a flexible polymer chain that is subjected to both thermal and active forces. Our model for active forces incorporates temporal correlation associated with the characteristic time scale and processivity of enzymatic function (driven by ATP hydrolysis), leading to an active-force time scale that competes with relaxation processes within the polymer chain. We analyze the structure and dynamics of an active-Brownian polymer using our exact results for the dynamic structure factor and the looping time for the chain ends. The spectrum of relaxation times within a polymer chain implies two different behaviors at small and large length scales. Small length-scale relaxation is faster than the active-force time scale, and the dynamic and structural behavior at these scales are oblivious to active forces and, are thus governed by the true thermal temperature. Large length-scale behavior is governed by relaxation times that are much longer than the active-force time scale, resulting in an effective active-Brownian temperature that dramatically alters structural and dynamic behavior. These complex multi-scale effects imply a time-dependent temperature that governs living and non-equilibrium systems, serving as a unifying concept for interpreting and predicting their physical behavior.
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Affiliation(s)
- Ashesh Ghosh
- Department of Chemical Engineering, Stanford University, Stanford, California, USA.
| | - Andrew J Spakowitz
- Department of Chemical Engineering, Stanford University, Stanford, California, USA.
- Biophysics Program, Stanford University, Stanford, California, USA
- Department of Materials Science & Engineering, Stanford University, Stanford, California, USA
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4
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Yesbolatova AK, Arai R, Sakaue T, Kimura A. Formulation of Chromatin Mobility as a Function of Nuclear Size during C. elegans Embryogenesis Using Polymer Physics Theories. PHYSICAL REVIEW LETTERS 2022; 128:178101. [PMID: 35570447 DOI: 10.1103/physrevlett.128.178101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Accepted: 03/21/2022] [Indexed: 06/15/2023]
Abstract
During early embryogenesis of the nematode, Caenorhabditis elegans, the chromatin motion markedly decreases. Despite its biological implications, the underlying mechanism for this transition was unclear. By combining theory and experiment, we analyze the mean-square displacement (MSD) of the chromatin loci, and demonstrate that MSD-vs-time relationships in various nuclei collapse into a single master curve by normalizing them with the mesh size and the corresponding time scale. This enables us to identify the onset of the entangled dynamics with the size of tube diameter of chromatin polymer in the C. elegans embryo. Our dynamical scaling analysis predicts the transition between unentangled and entangled dynamics of chromatin polymers, the quantitative formula for MSD as a function of nuclear size and timescale, and provides testable hypotheses on chromatin mobility in other cell types and species.
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Affiliation(s)
- Aiya K Yesbolatova
- Department of Genetics, School of Life Science, The Graduate University for Advanced Studies, SOKENDAI, Mishima 411-8540, Japan
- Cell Architecture Laboratory, Department of Chromosome Science, National Institute of Genetics, Mishima 411-8540, Japan
| | - Ritsuko Arai
- Cell Architecture Laboratory, Department of Chromosome Science, National Institute of Genetics, Mishima 411-8540, Japan
| | - Takahiro Sakaue
- Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Kanagawa 252-5258, Japan
| | - Akatsuki Kimura
- Department of Genetics, School of Life Science, The Graduate University for Advanced Studies, SOKENDAI, Mishima 411-8540, Japan
- Cell Architecture Laboratory, Department of Chromosome Science, National Institute of Genetics, Mishima 411-8540, Japan
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5
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Sakaue T, Kimura A. Scaling Relationship in Chromatin as a Polymer. Results Probl Cell Differ 2022; 70:263-277. [PMID: 36348110 DOI: 10.1007/978-3-031-06573-6_8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Genomic DNA, which controls genetic information, is stored in the cell nucleus in eukaryotes. Chromatin moves dynamically in the nucleus, and this movement is closely related to the function of chromatin. However, the driving force of chromatin movement, its control mechanism, and the functional significance of movement are unclear. In addition to biochemical and genetic approaches such as identification and analysis of regulators, approaches based on the physical properties of chromatin and cell nuclei are indispensable for this understanding. In particular, the idea of polymer physics is expected to be effective. This paper introduces our efforts to combine biological experiments on chromatin kinetics with theoretical analysis based on polymer physics.
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Affiliation(s)
- Takahiro Sakaue
- Department of Physical Sciences, Aoyama Gakuin University, Sagamihara, Kanagawa, Japan.
| | - Akatsuki Kimura
- Cell Architecture Laboratory, National Institute of Genetics, Mishima, Japan.
- Department of Genetics, The Graduate University for Advanced Studies, Mishima, Japan.
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6
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Ghosh A, Spakowitz AJ. Statistical behavior of nonequilibrium and living biological systems subjected to active and thermal fluctuations. Phys Rev E 2022; 105:014415. [PMID: 35193230 DOI: 10.1103/physreve.105.014415] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2021] [Accepted: 12/24/2021] [Indexed: 06/14/2023]
Abstract
We present a path-integral formulation of the motion of a particle subjected to fluctuating active and thermal forces. This general framework predicts the statistical behavior associated with the stochastic trajectories of the particle, accounting for all possible realizations of Brownian and active forces, over an arbitrary potential landscape. Temporal correlations in the active forces result in non-Markovian statistics, necessitating the inclusion of a fixed active-force value at specified times within the statistical treatment. We specialize our theory to that of exponentially correlated active forces for a particle in a harmonic potential. We find the exact results for the statistical distributions for the initial position of the particle, accounting for the impact of the correlated active forces at all times prior to the initial time. Our theory is then used to find the two-point distribution for the active Brownian particle, which governs the joint probability that a particle begins and ends at specified locations. Analyses of the active Brownian statistics demonstrate that the impact of active forces can be interpreted through a time-dependent temperature whose influence depends on the competition of timescales of the active-force correlation and the relaxation time of the particle in the harmonic potential. The general results presented in this work are transferable to a broad range of nonequilibrium systems with active and Brownian motion, and the time-dependent temperature serves as a governing principle to describe the competition of timescales associated with active forces and internal relaxation processes.
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Affiliation(s)
- Ashesh Ghosh
- Department of Chemical Engineering, Stanford University, Stanford, California 94305, USA
| | - Andrew J Spakowitz
- Department of Chemical Engineering, Stanford University, Stanford, California 94305, USA
- Department of Materials Science, Stanford University, Stanford, California 94305, USA
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
- Biophysics Program, Stanford University, Stanford, California 94305, USA
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7
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Starkov D, Parfenyev V, Belan S. Conformational statistics of non-equilibrium polymer loops in Rouse model with active loop extrusion. J Chem Phys 2021; 154:164106. [PMID: 33940823 DOI: 10.1063/5.0048942] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Motivated by the recent experimental observations of the DNA loop extrusion by protein motors, in this paper, we investigate the statistical properties of the growing polymer loops within the ideal chain model. The loop conformation is characterized statistically by the mean gyration radius and the pairwise contact probabilities. It turns out that a single dimensionless parameter, which is given by the ratio of the loop relaxation time over the time elapsed since the start of extrusion, controls the crossover between near-equilibrium and highly non-equilibrium asymptotics in the statistics of the extruded loop, regardless of the specific time dependence of the extrusion velocity. In addition, we show that two-sided and one-sided loop extruding motors produce the loops with almost identical properties. Our predictions are based on two rigorous semi-analytical methods accompanied by asymptotic analysis of slow and fast extrusion limits.
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Affiliation(s)
- Dmitry Starkov
- Landau Institute for Theoretical Physics, Russian Academy of Sciences, 1-A Akademika Semenova av., 142432 Chernogolovka, Russia and National Research University Higher School of Economics, Faculty of Physics, Myasnitskaya 20, 101000 Moscow, Russia
| | - Vladimir Parfenyev
- Landau Institute for Theoretical Physics, Russian Academy of Sciences, 1-A Akademika Semenova av., 142432 Chernogolovka, Russia and National Research University Higher School of Economics, Faculty of Physics, Myasnitskaya 20, 101000 Moscow, Russia
| | - Sergey Belan
- Landau Institute for Theoretical Physics, Russian Academy of Sciences, 1-A Akademika Semenova av., 142432 Chernogolovka, Russia and National Research University Higher School of Economics, Faculty of Physics, Myasnitskaya 20, 101000 Moscow, Russia
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8
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Joo S, Durang X, Lee OC, Jeon JH. Anomalous diffusion of active Brownian particles cross-linked to a networked polymer: Langevin dynamics simulation and theory. SOFT MATTER 2020; 16:9188-9201. [PMID: 32840541 DOI: 10.1039/d0sm01200a] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Quantitatively understanding the dynamics of an active Brownian particle (ABP) interacting with a viscoelastic polymer environment is a scientific challenge. It is intimately related to several interdisciplinary topics such as the microrheology of active colloids in a polymer matrix and the athermal dynamics of the in vivo chromosomes or cytoskeletal networks. Based on Langevin dynamics simulation and analytic theory, here we explore such a viscoelastic active system in depth using a star polymer of functionality f with the center cross-linker particle being ABP. We observe that the ABP cross-linker, despite its self-propelled movement, attains an active subdiffusion with the scaling ΔR2(t) ∼ tα with α ≤ 1/2, through the viscoelastic feedback from the polymer. Counter-intuitively, the apparent anomaly exponent α becomes smaller as the ABP is driven by a larger propulsion velocity, but is independent of functionality f or the boundary conditions of the polymer. We set forth an exact theory and show that the motion of the active cross-linker is a Gaussian non-Markovian process characterized by two distinct power-law displacement correlations. At a moderate Péclet number, it seemingly behaves as fractional Brownian motion with a Hurst exponent H = α/2, whereas, at a high Péclet number, the self-propelled noise in the polymer environment leads to a logarithmic growth of the mean squared displacement (∼ln t) and a velocity autocorrelation decaying as -t-2. We demonstrate that the anomalous diffusion of the active cross-linker is precisely described by a fractional Langevin equation with two distinct random noises.
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Affiliation(s)
- Sungmin Joo
- Department of Physics, POSTECH, Pohang, Republic of Korea.
| | - Xavier Durang
- Department of Physics, POSTECH, Pohang, Republic of Korea.
| | - O-Chul Lee
- Department of Physics, POSTECH, Pohang, Republic of Korea.
| | - Jae-Hyung Jeon
- Department of Physics, POSTECH, Pohang, Republic of Korea.
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9
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Shaban HA, Barth R, Recoules L, Bystricky K. Hi-D: nanoscale mapping of nuclear dynamics in single living cells. Genome Biol 2020; 21:95. [PMID: 32312289 PMCID: PMC7168861 DOI: 10.1186/s13059-020-02002-6] [Citation(s) in RCA: 52] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2019] [Accepted: 03/20/2020] [Indexed: 02/06/2023] Open
Abstract
Bulk chromatin motion has not been analyzed at high resolution. We present Hi-D, a method to quantitatively map dynamics of chromatin and abundant nuclear proteins for every pixel simultaneously over the entire nucleus from fluorescence image series. Hi-D combines reconstruction of chromatin motion and classification of local diffusion processes by Bayesian inference. We show that DNA dynamics in the nuclear interior are spatially partitioned into 0.3-3-μm domains in a mosaic-like pattern, uncoupled from chromatin compaction. This pattern was remodeled in response to transcriptional activity. Hi-D can be applied to any dense and bulk structures opening new perspectives towards understanding motion of nuclear molecules.
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Affiliation(s)
- Haitham A Shaban
- Laboratoire de Biologie Moléculaire Eucaryote (LBME), Centre de Biologie Intégrative (CBI), CNRS, University of Toulouse, UPS, 31062, Toulouse, France.
- Spectroscopy Department, Physics Division, National Research Centre, 33 El Bohouth Str., P.O. 12622, Cairo, Egypt.
| | - Roman Barth
- Laboratoire de Biologie Moléculaire Eucaryote (LBME), Centre de Biologie Intégrative (CBI), CNRS, University of Toulouse, UPS, 31062, Toulouse, France
- Present Address: Bionanoscience Department, Faculty of Applied Sciences, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Ludmila Recoules
- Laboratoire de Biologie Moléculaire Eucaryote (LBME), Centre de Biologie Intégrative (CBI), CNRS, University of Toulouse, UPS, 31062, Toulouse, France
| | - Kerstin Bystricky
- Laboratoire de Biologie Moléculaire Eucaryote (LBME), Centre de Biologie Intégrative (CBI), CNRS, University of Toulouse, UPS, 31062, Toulouse, France.
- Institut Universitaire de France (IUF), Paris, France.
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10
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Cao X, Zhang B, Zhao N. Effective temperature scaled dynamics of a flexible polymer in an active bath. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1730992] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Xiuli Cao
- College of Chemistry, Sichuan University, Chengdu, China
| | - Bingjie Zhang
- College of Chemistry, Sichuan University, Chengdu, China
| | - Nanrong Zhao
- College of Chemistry, Sichuan University, Chengdu, China
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11
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Ito Y, Kimura A. Session 1SEA-physics of chromatin dynamics at the 57th Biophysical Society of Japan meeting. Biophys Rev 2020; 12:265-266. [PMID: 32056110 DOI: 10.1007/s12551-020-00642-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2020] [Accepted: 02/06/2020] [Indexed: 01/07/2023] Open
Affiliation(s)
- Yuma Ito
- School of Life Science and Technology, Tokyo Institute of Technology, Nagatsuta-cho, Midori, Yokohama, 226-8501, Japan
| | - Akatsuki Kimura
- Cell Architecture Laboratory, Department of Chromosome Science, National Institute of Genetics, Mishima, 411-8540, Japan. .,Department of Genetics, School of Life Science, The Graduate University for Advanced Studies, SOKENDAI, Mishima, 411-8540, Japan.
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12
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Put S, Sakaue T, Vanderzande C. Active dynamics and spatially coherent motion in chromosomes subject to enzymatic force dipoles. Phys Rev E 2019; 99:032421. [PMID: 30999440 DOI: 10.1103/physreve.99.032421] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2018] [Indexed: 06/09/2023]
Abstract
Inspired by recent experiments on chromosomal dynamics, we introduce an exactly solvable model for the interaction between a flexible polymer and a set of motorlike enzymes. The enzymes can bind and unbind to specific sites of the polymer and produce a dipolar force on two neighboring monomers when bound. We study the resulting nonequilibrium dynamics of the polymer and find that the motion of the monomers has several properties that were observed experimentally for chromosomal loci: a subdiffusive mean-square displacement and the appearance of regions of correlated motion. We also determine the velocity autocorrelation of the monomers and find that the underlying stochastic process is not fractional Brownian motion. Finally, we show that the active forces swell the polymer by an amount that becomes constant for large polymers.
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Affiliation(s)
- Stefanie Put
- Faculty of Sciences, Hasselt University, 3590 Diepenbeek, Belgium
| | - Takahiro Sakaue
- Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Kanagawa 252-5258, Japan
- PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan
| | - Carlo Vanderzande
- Faculty of Sciences, Hasselt University, 3590 Diepenbeek, Belgium
- Institute for Theoretical Physics, Katholieke Universiteit Leuven, 3001 Heverlee, Belgium
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13
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Inferring Active Noise Characteristics from the Paired Observations of Anomalous Diffusion. Polymers (Basel) 2018; 11:polym11010002. [PMID: 30959986 PMCID: PMC6401841 DOI: 10.3390/polym11010002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2018] [Revised: 12/17/2018] [Accepted: 12/17/2018] [Indexed: 11/24/2022] Open
Abstract
Anomalous diffusion has been most often argued in terms of a position fluctuation of a tracer. We here propose the other fluctuating observable, i.e., momentum transfer defined as the time integral of applied force to hold a tracer’s position. Being a conjugated variable, the momentum transfer is thought of as generating the anomalous diffusion paired with the position’s one. By putting together the paired anomalous diffusions, we aim to extract useful information in complex systems, which can be applied to experiments like tagged monomer observations in chromatin. The polymer being in the equilibrium, the mean square displacement (or variance) of position displacement or momentum transfer exhibits the sub- or superdiffusion, respectively, in which the sum of the anomalous diffusion indices is conserved quite generally, but the nonequilibrium media that generate the active noise may manifest the derivations from the equilibrium relation. We discuss the deviations that reflect the characteristics of the active noise.
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14
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Saintillan D, Shelley MJ, Zidovska A. Extensile motor activity drives coherent motions in a model of interphase chromatin. Proc Natl Acad Sci U S A 2018; 115:11442-11447. [PMID: 30348795 PMCID: PMC6233076 DOI: 10.1073/pnas.1807073115] [Citation(s) in RCA: 59] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The 3D spatiotemporal organization of the human genome inside the cell nucleus remains a major open question in cellular biology. In the time between two cell divisions, chromatin-the functional form of DNA in cells-fills the nucleus in its uncondensed polymeric form. Recent in vivo imaging experiments reveal that the chromatin moves coherently, having displacements with long-ranged correlations on the scale of micrometers and lasting for seconds. To elucidate the mechanism(s) behind these motions, we develop a coarse-grained active polymer model where chromatin is represented as a confined flexible chain acted upon by molecular motors that drive fluid flows by exerting dipolar forces on the system. Numerical simulations of this model account for steric and hydrodynamic interactions as well as internal chain mechanics. These demonstrate that coherent motions emerge in systems involving extensile dipoles and are accompanied by large-scale chain reconfigurations and nematic ordering. Comparisons with experiments show good qualitative agreement and support the hypothesis that self-organizing long-ranged hydrodynamic couplings between chromatin-associated active motor proteins are responsible for the observed coherent dynamics.
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Affiliation(s)
- David Saintillan
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093;
| | - Michael J Shelley
- Center for Computational Biology, Flatiron Institute, New York, NY 10010
- Courant Institute, New York University, New York, NY 10012
| | - Alexandra Zidovska
- Center for Soft Matter Research, Department of Physics, New York University, New York, NY 10003
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15
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Osmanović D. Properties of Rouse polymers with actively driven regions. J Chem Phys 2018; 149:164911. [DOI: 10.1063/1.5045686] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Dino Osmanović
- Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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16
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Carlon E, Orland H, Sakaue T, Vanderzande C. Effect of Memory and Active Forces on Transition Path Time Distributions. J Phys Chem B 2018; 122:11186-11194. [DOI: 10.1021/acs.jpcb.8b06379] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Affiliation(s)
- E. Carlon
- Institute for Theoretical Physics, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
| | - H. Orland
- Institut de Physique Théorique, CEA, CNRS, UMR3681, F-91191 Gif-sur-Yvette, France
- Beijing Computational Science Research Center, No.10 East Xibeiwang Road, Beijing 100193, China
| | - T. Sakaue
- Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagami-hara, Kanagawa 252-5258, Japan
- PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan
| | - C. Vanderzande
- Institute for Theoretical Physics, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
- Faculty of Sciences, Hasselt University, 3590 Diepenbeek, Belgium
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17
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Gnesotto FS, Mura F, Gladrow J, Broedersz CP. Broken detailed balance and non-equilibrium dynamics in living systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:066601. [PMID: 29504517 DOI: 10.1088/1361-6633/aab3ed] [Citation(s) in RCA: 116] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.
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Affiliation(s)
- F S Gnesotto
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
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18
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Grimm J, Dolgushev M. Dynamics of networks in a viscoelastic and active environment. SOFT MATTER 2018; 14:1171-1180. [PMID: 29349466 DOI: 10.1039/c7sm02050c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We investigate the dynamics of fractals and other networks in a viscoelastic and active environment. The viscoelastic dynamics is modeled based on the generalized Langevin equation, where the activity is introduced to it by means of the exponentially correlated noise. The intramolecular interactions are taken into account by the bead-spring picture. The microscopic connectivity (studied in the form of Vicsek fractals, of dual Sierpiński gaskets, of NTD trees, and of a family of deterministic small-world networks) reveals itself in the multiscale monomeric dynamics, which shows vastly different behaviors in the active and passive baths. In particular, the dynamics under active forces leads to a swelling that is characterized through power laws which are not present in the passive case. In all cases, the dynamics reflects the broad scaling behavior of the density of states and not necessarily the maximal relaxation time of the structures in a passive bath, as it is exemplified on the NTD trees.
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Affiliation(s)
- Jonas Grimm
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany.
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Gherardi M, Calabrese L, Tamm M, Cosentino Lagomarsino M. Model of chromosomal loci dynamics in bacteria as fractional diffusion with intermittent transport. Phys Rev E 2017; 96:042402. [PMID: 29347533 DOI: 10.1103/physreve.96.042402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2017] [Indexed: 06/07/2023]
Abstract
The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous work has shown that such rapid motions are ubiquitous, we still have little grasp on their physical nature, and no positive model is available that describes them. Here, we propose a minimal theoretical model for loci movements as a fractional Brownian motion subject to a constant but intermittent driving force, and compare simulations and analytical calculations to data from high-resolution dynamic tracking in E. coli. This analysis yields the characteristic time scales for intermittency. Finally, we discuss the possible shortcomings of this model, and show that an increase in the effective local noise felt by the chromosome associates to the active relocations.
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Affiliation(s)
- Marco Gherardi
- Sorbonne Universités, UPMC Univ Paris 06, 75005 Paris, France
- Physics Department, University of Milan, Via Celoria 16, 20133 Milano, Italy
| | - Ludovico Calabrese
- Physics Department, University of Milan, Via Celoria 16, 20133 Milano, Italy
| | - Mikhail Tamm
- Physics Department, University of Moscow, 119991 Moscow, Russia
- Department of Applied Mathematics, Higher School of Economics, 101000 Moscow, Russia
| | - Marco Cosentino Lagomarsino
- Sorbonne Universités, UPMC Univ Paris 06, 75005 Paris, France
- CNRS, UMR 7238, Paris, France
- IFOM, FIRC Institute of Molecular Oncology, 20139 Milan, Italy
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Saito T, Sakaue T. Complementary mode analyses between sub- and superdiffusion. Phys Rev E 2017; 95:042143. [PMID: 28505743 DOI: 10.1103/physreve.95.042143] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2016] [Indexed: 06/07/2023]
Abstract
Several subdiffusive stochastic processes in nature, e.g., the motion of a tagged monomer in polymers, the height fluctuation of interfaces, particle dynamics in single-file diffusion, etc., can be described rigorously or approximately by the superposition of various modes whose relaxation times are broadly distributed. In this paper, we propose a mode analysis generating superdiffusion, which is paired with or complementary to subdiffusion. The key point in our discussion lies in the identification of a pair of conjugated variables, which undergo sub- and superdiffusion, respectively. We provide a simple interpretation for the sub- and superdiffusion duality for these variables using the language of polymer physics. The analysis also suggests the usefulness of looking at the force fluctuation in experiments, where a polymer is driven by a constant velocity.
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Affiliation(s)
- Takuya Saito
- Earthquake Research Institute, University of Tokyo, Tokyo 113-0032, Japan
| | - Takahiro Sakaue
- Department of Physics, Kyushu University, Fukuoka 819-0395, Japan
- JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
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Abstract
We consider how active forces modeled as non-thermal random noise affect the average dynamical properties of a Rouse polymer. As the power spectrum of the noise is not known we keep the analytical treatment as generic as possible and then present results for a few examples of active noise. We discuss the connection between our results and recent experimental studies of dynamics of labeled DNA telomeres in living cells, and propose new chromatin tracking experiments that will allow one to determine the statistical properties of the active forces associated with chromatin remodeling processes.
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Affiliation(s)
- Dino Osmanović
- Department of Physics, and Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 52900, Israel.
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Shin J, Cherstvy AG, Kim WK, Zaburdaev V. Elasticity-based polymer sorting in active fluids: a Brownian dynamics study. Phys Chem Chem Phys 2017; 19:18338-18347. [DOI: 10.1039/c7cp02947k] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
While the dynamics of polymer chains in equilibrium media is well understood by now, the polymer dynamics in active non-equilibrium environments can be very different.
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Affiliation(s)
- Jaeoh Shin
- Max Planck Institute for the Physics of Complex Systems
- 01187 Dresden
- Germany
| | - Andrey G. Cherstvy
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Won Kyu Kim
- Institut für Weiche Materie and Funktionale Materialen
- Helmholtz-Zentrum Berlin
- 14109 Berlin
- Germany
| | - Vasily Zaburdaev
- Max Planck Institute for the Physics of Complex Systems
- 01187 Dresden
- Germany
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Dynamic Nucleosome Movement Provides Structural Information of Topological Chromatin Domains in Living Human Cells. PLoS Comput Biol 2016; 12:e1005136. [PMID: 27764097 PMCID: PMC5072619 DOI: 10.1371/journal.pcbi.1005136] [Citation(s) in RCA: 66] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2016] [Accepted: 09/10/2016] [Indexed: 01/15/2023] Open
Abstract
The mammalian genome is organized into submegabase-sized chromatin domains (CDs) including topologically associating domains, which have been identified using chromosome conformation capture-based methods. Single-nucleosome imaging in living mammalian cells has revealed subdiffusively dynamic nucleosome movement. It is unclear how single nucleosomes within CDs fluctuate and how the CD structure reflects the nucleosome movement. Here, we present a polymer model wherein CDs are characterized by fractal dimensions and the nucleosome fibers fluctuate in a viscoelastic medium with memory. We analytically show that the mean-squared displacement (MSD) of nucleosome fluctuations within CDs is subdiffusive. The diffusion coefficient and the subdiffusive exponent depend on the structural information of CDs. This analytical result enabled us to extract information from the single-nucleosome imaging data for HeLa cells. Our observation that the MSD is lower at the nuclear periphery region than the interior region indicates that CDs in the heterochromatin-rich nuclear periphery region are more compact than those in the euchromatin-rich interior region with respect to the fractal dimensions as well as the size. Finally, we evaluated that the average size of CDs is in the range of 100–500 nm and that the relaxation time of nucleosome movement within CDs is a few seconds. Our results provide physical and dynamic insights into the genome architecture in living cells. The mammalian genome is partitioned into topological chromatin domains (CDs) in the living cell nuclei. Gene expression is highly regulated within CDs according to their structure, whereas chromatin itself is highly dynamic. This raises the following question: how is the CD structure in such dynamic chromatin? We developed a conceptual framework that unifies chromatin dynamics and structure. Using a polymer model with a fractal domain structure in a viscoelastic medium, we analytically show that nucleosome movement is subdiffusive and depends on CD structure. Hence, structural information can be extracted based on nucleosome movement in living cells with single-particle tracking experiments. This framework provides physical insights into the relationship between dynamic genome organization and gene expression.
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