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Pobegalov G, Chu LY, Peters JM, Molodtsov MI. Single cohesin molecules generate force by two distinct mechanisms. Nat Commun 2023; 14:3946. [PMID: 37402740 DOI: 10.1038/s41467-023-39696-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Accepted: 06/23/2023] [Indexed: 07/06/2023] Open
Abstract
Spatial organization of DNA is facilitated by cohesin protein complexes that move on DNA and extrude DNA loops. How cohesin works mechanistically as a molecular machine is poorly understood. Here, we measure mechanical forces generated by conformational changes in single cohesin molecules. We show that bending of SMC coiled coils is driven by random thermal fluctuations leading to a ~32 nm head-hinge displacement that resists forces up to 1 pN; ATPase head engagement occurs in a single step of ~10 nm and is driven by an ATP dependent head-head movement, resisting forces up to 15 pN. Our molecular dynamic simulations show that the energy of head engagement can be stored in a mechanically strained conformation of NIPBL and released during disengagement. These findings reveal how single cohesin molecules generate force by two distinct mechanisms. We present a model, which proposes how this ability may power different aspects of cohesin-DNA interaction.
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Affiliation(s)
- Georgii Pobegalov
- The Francis Crick Institute, London, NW1 1AT, UK
- Department of Physics and Astronomy, University College London, London, WC1E 6BT, UK
| | - Lee-Ya Chu
- The Francis Crick Institute, London, NW1 1AT, UK
| | - Jan-Michael Peters
- Research Institute of Molecular Pathology (IMP), Vienna BioCenter, Vienna, 1030, Austria
| | - Maxim I Molodtsov
- The Francis Crick Institute, London, NW1 1AT, UK.
- Department of Physics and Astronomy, University College London, London, WC1E 6BT, UK.
- Research Institute of Molecular Pathology (IMP), Vienna BioCenter, Vienna, 1030, Austria.
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Rao A, Ramírez J, Olsen BD. Mechanisms of Self-Diffusion of Linear Associative Polymers Studied by Brownian Dynamics Simulation. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01508] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Ameya Rao
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Jorge Ramírez
- Department of Chemical Engineering, Universidad Politécnica de Madrid, Madrid 28006, Spain
| | - Bradley D. Olsen
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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Wakim JG, Sandholtz SH, Spakowitz AJ. Impact of chromosomal organization on epigenetic drift and domain stability revealed by physics-based simulations. Biophys J 2021; 120:4932-4943. [PMID: 34687722 DOI: 10.1016/j.bpj.2021.10.019] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Revised: 09/07/2021] [Accepted: 10/18/2021] [Indexed: 12/21/2022] Open
Abstract
We examine the relationship between the size of domains of epigenetic marks and the stability of those domains using our theoretical model that captures the physical mechanisms governing the maintenance of epigenetic modifications. We focus our study on histone H3 lysine-9 trimethylation, one of the most common and consequential epigenetic marks with roles in chromatin compaction and gene repression. Our model combines the effects of methyl spreading by methyltransferases and chromatin segregation into heterochromatin and euchromatin because of preferential heterochromatin protein 1 (HP1) binding. Our model indicates that, although large methylated domains are passed successfully from one chromatin generation to the next, small alterations to the methylation sequence are not maintained during chromatin replication. Using our predictive model, we investigate the size required for an epigenetic domain to persist over chromatin generations while surrounded by a much larger domain of opposite methylation and compaction state. We find that there is a critical size threshold in the hundreds-of-nucleosomes scale above which an epigenetic domain will be reliably maintained over generations. The precise size of the threshold differs for heterochromatic and euchromatic domains. Our results are consistent with natural alterations to the epigenetic sequence occurring during embryonic development and due to age-related epigenetic drift.
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Affiliation(s)
- Joseph G Wakim
- Department of Chemical Engineering, Stanford University, Stanford, California
| | | | - Andrew J Spakowitz
- Department of Chemical Engineering, Stanford University, Stanford, California; Department of Materials Science and Engineering, Stanford University, Stanford, California; Biophysics Program, Stanford University, Stanford, California; Department of Applied Physics, Stanford University, Stanford, California.
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Higashi TL, Pobegalov G, Tang M, Molodtsov MI, Uhlmann F. A Brownian ratchet model for DNA loop extrusion by the cohesin complex. eLife 2021; 10:e67530. [PMID: 34309513 PMCID: PMC8313234 DOI: 10.7554/elife.67530] [Citation(s) in RCA: 35] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2021] [Accepted: 06/10/2021] [Indexed: 12/12/2022] Open
Abstract
The cohesin complex topologically encircles DNA to promote sister chromatid cohesion. Alternatively, cohesin extrudes DNA loops, thought to reflect chromatin domain formation. Here, we propose a structure-based model explaining both activities. ATP and DNA binding promote cohesin conformational changes that guide DNA through a kleisin N-gate into a DNA gripping state. Two HEAT-repeat DNA binding modules, associated with cohesin's heads and hinge, are now juxtaposed. Gripping state disassembly, following ATP hydrolysis, triggers unidirectional hinge module movement, which completes topological DNA entry by directing DNA through the ATPase head gate. If head gate passage fails, hinge module motion creates a Brownian ratchet that, instead, drives loop extrusion. Molecular-mechanical simulations of gripping state formation and resolution cycles recapitulate experimentally observed DNA loop extrusion characteristics. Our model extends to asymmetric and symmetric loop extrusion, as well as z-loop formation. Loop extrusion by biased Brownian motion has important implications for chromosomal cohesin function.
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Affiliation(s)
- Torahiko L Higashi
- Chromosome Segregation Laboratory, The Francis Crick InstituteLondonUnited Kingdom
| | - Georgii Pobegalov
- Mechanobiology and Biophysics Laboratory, The Francis Crick InstituteLondonUnited Kingdom
- Department of Physics and Astronomy, University College LondonLondonUnited Kingdom
| | - Minzhe Tang
- Chromosome Segregation Laboratory, The Francis Crick InstituteLondonUnited Kingdom
| | - Maxim I Molodtsov
- Mechanobiology and Biophysics Laboratory, The Francis Crick InstituteLondonUnited Kingdom
- Department of Physics and Astronomy, University College LondonLondonUnited Kingdom
| | - Frank Uhlmann
- Chromosome Segregation Laboratory, The Francis Crick InstituteLondonUnited Kingdom
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Duarte LKR, Teixeira AVNC, Rizzi LG. Microrheology of semiflexible filament solutions based on relaxation simulations. SOFT MATTER 2021; 17:2920-2930. [PMID: 33587085 DOI: 10.1039/d0sm01976c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We present an efficient computational methodology to obtain the viscoelastic response of dilute solutions of semiflexible filaments. By considering an approach based on the fluctuation-dissipation theorem, we were able to evaluate the dynamical properties of probe particles immersed in solutions of semiflexible filaments from relaxation simulations with a relatively low computational cost and higher precision in comparison to those based on stochastic dynamics. We used a microrheological approach to obtain the complex shear modulus and the complex viscosity of the solution through its compliance which was obtained directly from the dynamical properties of a probe particle attached to an effective medium described by a mesoscopic model, i.e., an effective filament model (EFM). The relaxation simulations were applied to assess the effects of the bending energy on the viscoelasticity of the semiflexible filament solutions, and our methodology was validated by comparing the numerical results to the experimental data on DNA and collagen solutions.
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Affiliation(s)
- L K R Duarte
- Departamento de Física, Universidade Federal do Viçosa, CEP 36570-000, Viçosa, MG, Brazil. and Instituto Federal de Educação, Ciência e Tecnologia de Minas Gerais, CEP 35588-000, Arcos, MG, Brazil
| | - A V N C Teixeira
- Departamento de Física, Universidade Federal do Viçosa, CEP 36570-000, Viçosa, MG, Brazil.
| | - L G Rizzi
- Departamento de Física, Universidade Federal do Viçosa, CEP 36570-000, Viçosa, MG, Brazil.
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Hitching a Ride: Mechanics of Transport Initiation through Linker-Mediated Hitchhiking. Biophys J 2020; 118:1357-1369. [PMID: 32061275 DOI: 10.1016/j.bpj.2020.01.024] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Revised: 01/16/2020] [Accepted: 01/21/2020] [Indexed: 12/14/2022] Open
Abstract
In contrast to the canonical picture of transport by direct attachment to motor proteins, recent evidence shows that a number of intracellular "cargos" navigate the cytoplasm by hitchhiking on motor-driven "carrier" organelles. We describe a quantitative model of intracellular cargo transport via hitchhiking, examining the efficiency of hitchhiking initiation as a function of geometric and mechanical parameters. We focus specifically on the parameter regime relevant to the hitchhiking motion of peroxisome organelles in fungal hyphae. Our work predicts the dependence of transport initiation rates on the distribution of cytoskeletal tracks and carrier organelles, as well as the number, length, and flexibility of the linker proteins that mediate contact between the carrier and the hitchhiking cargo. Furthermore, we demonstrate that attaching organelles to microtubules can result in a substantial enhancement of the hitchhiking initiation rate in tubular geometries such as those found in fungal hyphae. This enhancement is expected to increase the overall transport rate of hitchhiking organelles and lead to greater efficiency in organelle dispersion. Our results leverage a quantitative physical model to highlight the importance of organelle encounter dynamics in noncanonical intracellular transport.
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Spakowitz AJ. Polymer physics across scales: Modeling the multiscale behavior of functional soft materials and biological systems. J Chem Phys 2019; 151:230902. [DOI: 10.1063/1.5126852] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- Andrew J. Spakowitz
- Department of Chemical Engineering, Stanford University, Stanford, California 94305, USA
- Department of Materials Science and Engineering, 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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Abstract
Predicting how epigenetic marks control the 3D organization of the genome is key to understanding how these marks regulate gene expression. We show that a physical model of a chromosome with experimentally measured local interactions segregates into euchromatin- and heterochromatin-like phases. The model reproduces many of the features of the large-scale organization of the chromosome as measured by Hi-C. Our work provides an estimate of the amount of epigenetic marking needed to segregate a gene into heterochromatin. We use a chromosome-scale simulation to show that the preferential binding of heterochromatin protein 1 (HP1) to regions high in histone methylation (specifically H3K9me3) results in phase segregation and reproduces features of the observed Hi-C contact map. Specifically, we perform Monte Carlo simulations with one computational bead per nucleosome and an H3K9me3 pattern based on published ChIP-seq signals. We implement a binding model in which HP1 preferentially binds to trimethylated histone tails and then oligomerizes to bridge together nucleosomes. We observe a phase reminiscent of heterochromatin—dense and high in H3K9me3—and another reminiscent of euchromatin—less dense and lacking H3K9me3. This segregation results in a plaid contact probability map that matches the general shape and position of published Hi-C data. Analysis suggests that a roughly 20-kb segment of H3K9me3 enrichment is required to drive segregation into the heterochromatic phase.
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Pilyugina E, Krajina B, Spakowitz AJ, Schieber JD. Buckling a Semiflexible Polymer Chain under Compression. Polymers (Basel) 2017; 9:polym9030099. [PMID: 30970780 PMCID: PMC6432112 DOI: 10.3390/polym9030099] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2017] [Revised: 03/02/2017] [Accepted: 03/03/2017] [Indexed: 02/07/2023] Open
Abstract
Instability and structural transitions arise in many important problems involving dynamics at molecular length scales. Buckling of an elastic rod under a compressive load offers a useful general picture of such a transition. However, the existing theoretical description of buckling is applicable in the load response of macroscopic structures, only when fluctuations can be neglected, whereas membranes, polymer brushes, filaments, and macromolecular chains undergo considerable Brownian fluctuations. We analyze here the buckling of a fluctuating semiflexible polymer experiencing a compressive load. Previous works rely on approximations to the polymer statistics, resulting in a range of predictions for the buckling transition that disagree on whether fluctuations elevate or depress the critical buckling force. In contrast, our theory exploits exact results for the statistical behavior of the worm-like chain model yielding unambiguous predictions about the buckling conditions and nature of the buckling transition. We find that a fluctuating polymer under compressive load requires a larger force to buckle than an elastic rod in the absence of fluctuations. The nature of the buckling transition exhibits a marked change from being distinctly second order in the absence of fluctuations to being a more gradual, compliant transition in the presence of fluctuations. We analyze the thermodynamic contributions throughout the buckling transition to demonstrate that the chain entropy favors the extended state over the buckled state, providing a thermodynamic justification of the elevated buckling force.
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Affiliation(s)
- Ekaterina Pilyugina
- Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, Chicago, IL 60616, USA.
- Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA.
| | - Brad Krajina
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA.
| | - Andrew J Spakowitz
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA.
- Department of Applied Physics, Stanford University, Stanford, CA 94305, USA.
- Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA.
- Biophysics Program, Stanford University, Stanford, CA 94305, USA.
| | - Jay D Schieber
- Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, Chicago, IL 60616, USA.
- Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA.
- Department of Physics, Illinois Institute of Technology, Chicago, IL 60616, USA.
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA.
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