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Socol M, Wang R, Jost D, Carrivain P, Vaillant C, Le Cam E, Dahirel V, Normand C, Bystricky K, Victor JM, Gadal O, Bancaud A. Rouse model with transient intramolecular contacts on a timescale of seconds recapitulates folding and fluctuation of yeast chromosomes. Nucleic Acids Res 2019; 47:6195-6207. [PMID: 31114898 PMCID: PMC6614813 DOI: 10.1093/nar/gkz374] [Citation(s) in RCA: 35] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2019] [Revised: 04/25/2019] [Accepted: 05/09/2019] [Indexed: 01/08/2023] Open
Abstract
DNA folding and dynamics along with major nuclear functions are determined by chromosome structural properties, which remain, thus far, elusive in vivo. Here, we combine polymer modeling and single particle tracking experiments to determine the physico-chemical parameters of chromatin in vitro and in living yeast. We find that the motion of reconstituted chromatin fibers can be recapitulated by the Rouse model using mechanical parameters of nucleosome arrays deduced from structural simulations. Conversely, we report that the Rouse model shows some inconsistencies to analyze the motion and structural properties inferred from yeast chromosomes determined with chromosome conformation capture techniques (specifically, Hi-C). We hence introduce the Rouse model with Transient Internal Contacts (RouseTIC), in which random association and dissociation occurs along the chromosome contour. The parametrization of this model by fitting motion and Hi-C data allows us to measure the kinetic parameters of the contact formation reaction. Chromosome contacts appear to be transient; associated to a lifetime of seconds and characterized by an attractive energy of -0.3 to -0.5 kBT. We suggest attributing this energy to the occurrence of histone tail-DNA contacts and notice that its amplitude sets chromosomes in 'theta' conditions, in which they are poised for compartmentalization and phase separation.
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Affiliation(s)
- Marius Socol
- LAAS-CNRS, Université de Toulouse, CNRS, F-31400 Toulouse, France
- IRIM, CNRS, University of Montpellier, France
| | - Renjie Wang
- Laboratoire de Biologie Moléculaire Eucaryote (LBME), Centre de Biologie Intégrative (CBI), Université de Toulouse, CNRS, UPS, F-31062 Toulouse, France
- Material Science & Engineering School, Henan University of Technology, 450001 Zhengzhou, P.R. China
| | - Daniel Jost
- Univ. Grenoble Alpes, CNRS, CHU Grenoble Alpes, Grenoble INP, TIMC-IMAG, F-38000 Grenoble, France
| | - Pascal Carrivain
- Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS UMR 5672, Lyon 69007, France
| | - Cédric Vaillant
- Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS UMR 5672, Lyon 69007, France
| | - Eric Le Cam
- Genome Maintenance and Molecular Microscopy UMR8126, CNRS, Université Paris-Sud, Université Paris-Saclay, Gustave Roussy, F-94805 Villejuif Cedex France
| | - Vincent Dahirel
- Sorbonne Université, CNRS, Physicochimie des Electrolytes et Nanosystèmes interfaciaux, laboratoire PHENIX, F-75005 Paris, France
| | - Christophe Normand
- Laboratoire de Biologie Moléculaire Eucaryote (LBME), Centre de Biologie Intégrative (CBI), Université de Toulouse, CNRS, UPS, F-31062 Toulouse, France
| | - Kerstin Bystricky
- Laboratoire de Biologie Moléculaire Eucaryote (LBME), Centre de Biologie Intégrative (CBI), Université de Toulouse, CNRS, UPS, F-31062 Toulouse, France
| | - Jean-Marc Victor
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, F-75005 Paris, France
| | - Olivier Gadal
- Laboratoire de Biologie Moléculaire Eucaryote (LBME), Centre de Biologie Intégrative (CBI), Université de Toulouse, CNRS, UPS, F-31062 Toulouse, France
| | - Aurélien Bancaud
- LAAS-CNRS, Université de Toulouse, CNRS, F-31400 Toulouse, France
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Guérin T. Analytical expressions for the closure probability of a stiff wormlike chain for finite capture radius. Phys Rev E 2017; 96:022501. [PMID: 28950625 DOI: 10.1103/physreve.96.022501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2015] [Indexed: 11/07/2022]
Abstract
Estimating the probability that two monomers of the same polymer chain are close together is a key ingredient to characterize intramolecular reactions and polymer looping. In the case of stiff wormlike polymers (rigid fluctuating elastic rods), for which end-to-end encounters are rare events, we derive an explicit analytical formula for the probability η(r_{c}) that the distance between the chain extremities is smaller than some capture radius r_{c}. The formula is asymptotically exact in the limit of stiff chains, and it leads to the identification of two distinct scaling regimes for the closure factor, originating from a strong variation of the fluctuations of the chain orientation at closure. Our theory is compatible with existing analytical results from the literature that cover the cases of a vanishing capture radius and of nearly fully extended chains.
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Affiliation(s)
- T Guérin
- Laboratoire Ondes et Matiere d'Aquitaine, CNRS UMR 5798, Université de Bordeaux, Talence, France
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Detcheverry F. Unimodal and bimodal random motions of independent exponential steps. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:114. [PMID: 25412824 DOI: 10.1140/epje/i2014-14114-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2014] [Revised: 10/06/2014] [Accepted: 10/22/2014] [Indexed: 06/04/2023]
Abstract
We consider random walks that arise from the repetition of independent, statistically identical steps, whose nature may be arbitrary. Such unimodal motions appear in a variety of contexts, including particle propagation, cell motility, swimming of micro-organisms, animal motion and foraging strategies. Building on general frameworks, we focus on the case where step duration is exponentially distributed. We explore systematically unimodal processes whose steps are ballistic, diffusive, cyclic or governed by rotational diffusion, and give the exact propagator in Fourier-Laplace domain, from which the moments and the diffusion coefficient are obtained. We also address bimodal processes, where two kinds of step are taken in turn, and show that the mean square displacement, the quantity of prime importance in experiments, is simply related to those of unimodal motions.
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Affiliation(s)
- F Detcheverry
- Institut Lumière Matière, UMR5306 Université Claude Bernard Lyon 1-CNRS, Université de Lyon, 69622, Villeurbanne, France,
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Pritchard RH, Huang YYS, Terentjev EM. Mechanics of biological networks: from the cell cytoskeleton to connective tissue. SOFT MATTER 2014; 10:1864-84. [PMID: 24652375 DOI: 10.1039/c3sm52769g] [Citation(s) in RCA: 107] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
From the cell cytoskeleton to connective tissues, fibrous networks are ubiquitous in metazoan life as the key promoters of mechanical strength, support and integrity. In recent decades, the application of physics to biological systems has made substantial strides in elucidating the striking mechanical phenomena observed in such networks, explaining strain stiffening, power law rheology and cytoskeletal fluidisation - all key to the biological function of individual cells and tissues. In this review we focus on the current progress in the field, with a primer into the basic physics of individual filaments and the networks they form. This is followed by a discussion of biological networks in the context of a broad spread of recent in vitro and in vivo experiments.
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Affiliation(s)
- Robyn H Pritchard
- Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK.
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Klotzsch E, Schoen I, Ries J, Renn A, Sandoghdar V, Vogel V. Conformational distribution of surface-adsorbed fibronectin molecules explored by single molecule localization microscopy. Biomater Sci 2014; 2:883-892. [DOI: 10.1039/c3bm60262a] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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6
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Lee CF. Length distribution of stiff, self-assembled polymers at thermal equilibrium. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:415101. [PMID: 22945455 DOI: 10.1088/0953-8984/24/41/415101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We investigate the length distribution of self-assembled, long and stiff polymers at thermal equilibrium. Our analysis is based on calculating the partition functions of stiff polymers of variable lengths in the elastic regime. Our conclusion is that the length distribution of this self-assembled system follows closely the exponential distribution, except at the short length limit. We then discuss the implications of our results on the experimentally observed length distributions in amyloid fibrils.
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Affiliation(s)
- Chiu Fan Lee
- Department of Bioengineering, Imperial College London, South Kensington Campus, London, UK.
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Affiliation(s)
- Tetsuya Hiraiwa
- Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
| | - Takao Ohta
- Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
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8
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Affiliation(s)
- J. R. Blundell
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
| | - E. M. Terentjev
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
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Rechendorff K, Witz G, Adamcik J, Dietler G. Persistence length and scaling properties of single-stranded DNA adsorbed on modified graphite. J Chem Phys 2009; 131:095103. [DOI: 10.1063/1.3216111] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Errami J, Peyrard M, Theodorakopoulos N. Modeling DNA beacons at the mesoscopic scale. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2007; 23:397-411. [PMID: 17728978 DOI: 10.1140/epje/i2007-10200-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2007] [Accepted: 06/29/2007] [Indexed: 05/17/2023]
Abstract
We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer models; alternative calculations performed using the freely rotating chain and the discrete Kratky-Porod models are reported. Stem formation is modeled according to the Peyrard-Bishop-Dauxois Hamiltonian. The kinetics of opening and closing is described in terms of a diffusion-controlled motion in an effective free-energy landscape. Melting profiles, dependence of melting temperature on loop length, and kinetic time scales are in semiquantitative agreement with experimental data obtained from fluorescent DNA beacons forming poly(T) loops. Variation in strand rigidity is not sufficient to account for the large activation enthalpy of closing and the strong loop length dependence observed in hairpins forming poly(A) loops. Implications for modeling single strands of DNA or RNA are discussed.
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Affiliation(s)
- J Errami
- Laboratoire de Physique, ENS-Lyon, 46 allée d'Italie, 69364, Lyon Cedex 07, France
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Chaudhuri D. Semiflexible polymers: dependence on ensemble and boundary orientations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:021803. [PMID: 17358360 DOI: 10.1103/physreve.75.021803] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2006] [Indexed: 05/14/2023]
Abstract
We show that the mechanical properties of a worm-like-chain (WLC) polymer, of contour length L and persistence length lambda such that t=L/lambda approximately O(1), depend both on the ensemble and the constraint on end orientations. In the Helmholtz ensemble, multiple minima in the free energy near t=4 persists for all kinds of orientational boundary conditions. The qualitative features of projected probability distribution of end-to-end vector depend crucially on the embedding dimensions. A mapping of the WLC model, to a quantum particle moving on the surface of a unit sphere, is used to obtain the statistical and mechanical properties of the polymer under various boundary conditions and ensembles. The results show excellent agreement with Monte Carlo simulations.
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Affiliation(s)
- Debasish Chaudhuri
- Department of Biological Physics, Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
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Ishimoto Y, Kikuchi N. Low-energy states of a semiflexible polymer chain with attraction and the whip-toroid transitions. J Chem Phys 2006; 125:074905. [PMID: 16942378 DOI: 10.1063/1.2335455] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We establish a general model for the whip-toroid transitions of a semiflexible homopolymer chain using the path integral method and the O3 nonlinear sigma model on a line segment with the local inextensibility constraint. We exactly solve the energy levels of classical solutions and show that some of its classical configurations exhibit toroidal forms, and the system has phase transitions from a whip to toroidal states with a conformation parameter c = (W2l)(L2pi)2. We also discuss the stability of the toroid states and propose the low-energy effective Green's function. Finally, with the finite size effect on the toroid states, predicted toroidal properties are successfully compared to experimental results of DNA condensation.
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Affiliation(s)
- Y Ishimoto
- Theoretical Physics Laboratory, RIKEN, Wako 351-0198, Japan.
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Wiggins PA, Nelson PC. Generalized theory of semiflexible polymers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:031906. [PMID: 16605557 DOI: 10.1103/physreve.73.031906] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2005] [Indexed: 05/08/2023]
Abstract
DNA bending on length scales shorter than a persistence length plays an integral role in the translation of genetic information from DNA to cellular function. Quantitative experimental studies of these biological systems have led to a renewed interest in the polymer mechanics relevant for describing the conformational free energy of DNA bending induced by protein-DNA complexes. Recent experimental results from DNA cyclization studies have cast doubt on the applicability of the canonical semiflexible polymer theory, the wormlike chain (WLC) model, to DNA bending on biologically relevant length scales. This paper develops a theory of the chain statistics of a class of generalized semiflexible polymer models. Our focus is on the theoretical development of these models and the calculation of experimental observables. To illustrate our methods, we focus on a specific, illustrative model of DNA bending. We show that the WLC model generically describes the long-length-scale chain statistics of semiflexible polymers, as predicted by renormalization group arguments. In particular, we show that either the WLC or our present model adequately describes force-extension, solution scattering, and long-contour-length cyclization experiments, regardless of the details of DNA bend elasticity. In contrast, experiments sensitive to short-length-scale chain behavior can in principle reveal dramatic departures from the linear elastic behavior assumed in the WLC model. We demonstrate this explicitly by showing that our toy model can reproduce the anomalously large short-contour-length cyclization factors recently measured by Cloutier and Widom. Finally, we discuss the applicability of these models to DNA chain statistics in the context of future experiments.
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Affiliation(s)
- Paul A Wiggins
- Division of Physics, Mathematics, & Astronomy, California Institute of Technology, Pasadena, California 91125, USA.
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