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Junier I, Ghobadpour E, Espeli O, Everaers R. DNA supercoiling in bacteria: state of play and challenges from a viewpoint of physics based modeling. Front Microbiol 2023; 14:1192831. [PMID: 37965550 PMCID: PMC10642903 DOI: 10.3389/fmicb.2023.1192831] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 09/25/2023] [Indexed: 11/16/2023] Open
Abstract
DNA supercoiling is central to many fundamental processes of living organisms. Its average level along the chromosome and over time reflects the dynamic equilibrium of opposite activities of topoisomerases, which are required to relax mechanical stresses that are inevitably produced during DNA replication and gene transcription. Supercoiling affects all scales of the spatio-temporal organization of bacterial DNA, from the base pair to the large scale chromosome conformation. Highlighted in vitro and in vivo in the 1960s and 1970s, respectively, the first physical models were proposed concomitantly in order to predict the deformation properties of the double helix. About fifteen years later, polymer physics models demonstrated on larger scales the plectonemic nature and the tree-like organization of supercoiled DNA. Since then, many works have tried to establish a better understanding of the multiple structuring and physiological properties of bacterial DNA in thermodynamic equilibrium and far from equilibrium. The purpose of this essay is to address upcoming challenges by thoroughly exploring the relevance, predictive capacity, and limitations of current physical models, with a specific focus on structural properties beyond the scale of the double helix. We discuss more particularly the problem of DNA conformations, the interplay between DNA supercoiling with gene transcription and DNA replication, its role on nucleoid formation and, finally, the problem of scaling up models. Our primary objective is to foster increased collaboration between physicists and biologists. To achieve this, we have reduced the respective jargon to a minimum and we provide some explanatory background material for the two communities.
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Affiliation(s)
- Ivan Junier
- CNRS, UMR 5525, VetAgro Sup, Grenoble INP, TIMC, Université Grenoble Alpes, Grenoble, France
| | - Elham Ghobadpour
- CNRS, UMR 5525, VetAgro Sup, Grenoble INP, TIMC, Université Grenoble Alpes, Grenoble, France
- École Normale Supérieure (ENS) de Lyon, CNRS, Laboratoire de Physique and Centre Blaise Pascal de l'ENS de Lyon, Lyon, France
| | - Olivier Espeli
- Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS, INSERM, Université PSL, Paris, France
| | - Ralf Everaers
- École Normale Supérieure (ENS) de Lyon, CNRS, Laboratoire de Physique and Centre Blaise Pascal de l'ENS de Lyon, Lyon, France
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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: 38] [Impact Index Per Article: 7.6] [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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Lepage T, Junier I. Modeling Bacterial DNA: Simulation of Self-Avoiding Supercoiled Worm-Like Chains Including Structural Transitions of the Helix. Methods Mol Biol 2017; 1624:323-337. [PMID: 28842893 DOI: 10.1007/978-1-4939-7098-8_23] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
Under supercoiling constraints, naked DNA, such as a large part of bacterial DNA, folds into braided structures called plectonemes. The double-helix can also undergo local structural transitions, leading to the formation of denaturation bubbles and other alternative structures. Various polymer models have been developed to capture these properties, with Monte-Carlo (MC) approaches dedicated to the inference of thermodynamic properties. In this chapter, we explain how to perform such Monte-Carlo simulations, following two objectives. On one hand, we present the self-avoiding supercoiled Worm-Like Chain (ssWLC) model, which is known to capture the folding properties of supercoiled DNA, and provide a detailed explanation of a standard MC simulation method. On the other hand, we explain how to extend this ssWLC model to include structural transitions of the helix.
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Affiliation(s)
- Thibaut Lepage
- CNRS, TIMC-IMAG, F-38000, Grenoble, France.,University of Grenoble Alpes, TIMC-IMAG, F-38000, Grenoble, France
| | - Ivan Junier
- CNRS, TIMC-IMAG, F-38000, Grenoble, France. .,University of Grenoble Alpes, TIMC-IMAG, F-38000, Grenoble, France.
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Ozboyaci M, Martinez M, Wade RC. An Efficient Low Storage and Memory Treatment of Gridded Interaction Fields for Simulations of Macromolecular Association. J Chem Theory Comput 2016; 12:4563-77. [DOI: 10.1021/acs.jctc.6b00350] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Musa Ozboyaci
- Heidelberg Institute for Theoretical Studies (HITS), Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany
- Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences, Heidelberg University, INF 205, 69120 Heidelberg, Germany
| | - Michael Martinez
- Heidelberg Institute for Theoretical Studies (HITS), Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany
| | - Rebecca C. Wade
- Heidelberg Institute for Theoretical Studies (HITS), Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany
- Zentrum für Molekulare Biologie der Universität Heidelberg, DKFZ-ZMBH Allianz, INF 282, 69120 Heidelberg, Germany
- Interdisciplinary Center for Scientific Computing, Heidelberg University, INF 205, 69120 Heidelberg, Germany
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Lepage T, Képès F, Junier I. Thermodynamics of long supercoiled molecules: insights from highly efficient Monte Carlo simulations. Biophys J 2016; 109:135-43. [PMID: 26153710 DOI: 10.1016/j.bpj.2015.06.005] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2014] [Revised: 05/26/2015] [Accepted: 06/02/2015] [Indexed: 12/21/2022] Open
Abstract
Supercoiled DNA polymer models for which the torsional energy depends on the total twist of molecules (Tw) are a priori well suited for thermodynamic analysis of long molecules. So far, nevertheless, the exact determination of Tw in these models has been based on a computation of the writhe of the molecules (Wr) by exploiting the conservation of the linking number, Lk=Tw+Wr, which reflects topological constraints coming from the helical nature of DNA. Because Wr is equal to the number of times the main axis of a DNA molecule winds around itself, current Monte Carlo algorithms have a quadratic time complexity, O(L(2)), with respect to the contour length (L) of the molecules. Here, we present an efficient method to compute Tw exactly, leading in principle to algorithms with a linear complexity, which in practice is O(L(1.2)). Specifically, we use a discrete wormlike chain that includes the explicit double-helix structure of DNA and where the linking number is conserved by continuously preventing the generation of twist between any two consecutive cylinders of the discretized chain. As an application, we show that long (up to 21 kbp) linear molecules stretched by mechanical forces akin to magnetic tweezers contain, in the buckling regime, multiple and branched plectonemes that often coexist with curls and helices, and whose length and number are in good agreement with experiments. By attaching the ends of the molecules to a reservoir of twists with which these can exchange helix turns, we also show how to compute the torques in these models. As an example, we report values that are in good agreement with experiments and that concern the longest molecules that have been studied so far (16 kbp).
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Affiliation(s)
- Thibaut Lepage
- Institute of Systems and Synthetic Biology, Genopole, CNRS, University of Évry, Évry, France; Laboratoire Adaptation et Pathogénie des Micro-organismes-UMR 5163, Université Grenoble 1, CNRS, Grenoble, France
| | - François Képès
- Institute of Systems and Synthetic Biology, Genopole, CNRS, University of Évry, Évry, France; Department of BioEngineering, Imperial College London, London, United Kingdom
| | - Ivan Junier
- Laboratoire Adaptation et Pathogénie des Micro-organismes-UMR 5163, Université Grenoble 1, CNRS, Grenoble, France; Centre for Genomic Regulation (CRG), Barcelona, Spain; Universitat Pompeu Fabra (UPF), Barcelona, Spain.
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Cortini R, Caré BR, Victor JM, Barbi M. Theory and simulations of toroidal and rod-like structures in single-molecule DNA condensation. J Chem Phys 2015; 142:105102. [PMID: 25770562 DOI: 10.1063/1.4914513] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
DNA condensation by multivalent cations plays a crucial role in genome packaging in viruses and sperm heads, and has been extensively studied using single-molecule experimental methods. In those experiments, the values of the critical condensation forces have been used to estimate the amplitude of the attractive DNA-DNA interactions. Here, to describe these experiments, we developed an analytical model and a rigid body Langevin dynamics assay to investigate the behavior of a polymer with self-interactions, in the presence of a traction force applied at its extremities. We model self-interactions using a pairwise attractive potential, thereby treating the counterions implicitly. The analytical model allows to accurately predict the equilibrium structures of toroidal and rod-like condensed structures, and the dependence of the critical condensation force on the DNA length. We find that the critical condensation force depends strongly on the length of the DNA, and finite-size effects are important for molecules of length up to 10(5)μm. Our Langevin dynamics simulations show that the force-extension behavior of the rod-like structures is very different from the toroidal ones, so that their presence in experiments should be easily detectable. In double-stranded DNA condensation experiments, the signature of the presence of rod-like structures was not unambiguously detected, suggesting that the polyamines used to condense DNA may protect it from bending sharply as needed in the rod-like structures.
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Affiliation(s)
- Ruggero Cortini
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600,Université Pierre et Marie Curie, Sorbonne Université, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Bertrand R Caré
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600,Université Pierre et Marie Curie, Sorbonne Université, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Jean-Marc Victor
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600,Université Pierre et Marie Curie, Sorbonne Université, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Maria Barbi
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600,Université Pierre et Marie Curie, Sorbonne Université, 4 place Jussieu, 75252 Paris Cedex 05, France
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Dršata T, Lankaš F. Multiscale modelling of DNA mechanics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:323102. [PMID: 26194779 DOI: 10.1088/0953-8984/27/32/323102] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Mechanical properties of DNA are important not only in a wide range of biological processes but also in the emerging field of DNA nanotechnology. We review some of the recent developments in modeling these properties, emphasizing the multiscale nature of the problem. Modern atomic resolution, explicit solvent molecular dynamics simulations have contributed to our understanding of DNA fine structure and conformational polymorphism. These simulations may serve as data sources to parameterize rigid base models which themselves have undergone major development. A consistent buildup of larger entities involving multiple rigid bases enables us to describe DNA at more global scales. Free energy methods to impose large strains on DNA, as well as bead models and other approaches, are also briefly discussed.
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Affiliation(s)
- Tomáš Dršata
- Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo nám. 2, 166 10 Prague, Czech Republic. Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University Prague, Albertov 6, 128 43 Prague, Czech Republic
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