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Chen S, Markovich T, MacKintosh FC. Field Theory for Mechanical Criticality in Disordered Fiber Networks. PHYSICAL REVIEW LETTERS 2024; 133:028201. [PMID: 39073948 DOI: 10.1103/physrevlett.133.028201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2023] [Revised: 03/30/2024] [Accepted: 05/24/2024] [Indexed: 07/31/2024]
Abstract
Strain-controlled criticality governs the elasticity of jamming and fiber networks. While the upper critical dimension of jamming is believed to be d_{u}=2, non-mean-field exponents are observed in numerical studies of 2D and 3D fiber networks. The origins of this remains unclear. In this study we propose a minimal mean-field model for strain-controlled criticality of fiber networks. We then extend this to a phenomenological field theory, in which non-mean-field behavior emerges as a result of the disorder in the network structure. We predict that the upper critical dimension for such systems is d_{u}=4 using a Gaussian approximation. Moreover, we identify an order parameter for the phase transition, which has been lacking for fiber networks to date.
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Affiliation(s)
- Sihan Chen
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
- The James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Tomer Markovich
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel
- Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 69978, Israel
| | - Fred C MacKintosh
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- The Isaac Newton Institute for Mathematical Sciences, Cambridge University, Cambridge, United Kingdom
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2
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Hosaka Y, Golestanian R, Vilfan A. Lorentz Reciprocal Theorem in Fluids with Odd Viscosity. PHYSICAL REVIEW LETTERS 2023; 131:178303. [PMID: 37955478 DOI: 10.1103/physrevlett.131.178303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Accepted: 09/29/2023] [Indexed: 11/14/2023]
Abstract
The Lorentz reciprocal theorem-that is used to study various transport phenomena in hydrodynamics-is violated in chiral active fluids that feature odd viscosity with broken time-reversal and parity symmetries. Here, we show that the theorem can be generalized to fluids with odd viscosity by choosing an auxiliary problem with the opposite sign of the odd viscosity. We demonstrate the application of the theorem to two categories of microswimmers. Swimmers with prescribed surface velocity are not affected by odd viscosity, while those with prescribed active forces are. In particular, a torque dipole can lead to directed motion.
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Affiliation(s)
- Yuto Hosaka
- Max Planck Institute for Dynamics and Self-Organization (MPI-DS), Am Fassberg 17, 37077 Göttingen, Germany
| | - Ramin Golestanian
- Max Planck Institute for Dynamics and Self-Organization (MPI-DS), Am Fassberg 17, 37077 Göttingen, Germany
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- Institute for the Dynamics of Complex Systems, University of Göttingen, 37077 Göttingen, Germany
| | - Andrej Vilfan
- Max Planck Institute for Dynamics and Self-Organization (MPI-DS), Am Fassberg 17, 37077 Göttingen, Germany
- Jožef Stefan Institute, 1000 Ljubljana, Slovenia
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3
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Chen S, Markovich T, MacKintosh FC. Motor-free contractility of active biopolymer networks. Phys Rev E 2023; 108:044405. [PMID: 37978629 DOI: 10.1103/physreve.108.044405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Accepted: 09/19/2023] [Indexed: 11/19/2023]
Abstract
Contractility in animal cells is often generated by molecular motors such as myosin, which require polar substrates for their function. Motivated by recent experimental evidence of motor-independent contractility, we propose a robust motor-free mechanism that can generate contraction in biopolymer networks without the need for substrate polarity. We show that contractility is a natural consequence of active binding-unbinding of crosslinkers that breaks the principle of detailed balance, together with the asymmetric force-extension response of semiflexible biopolymers. We have extended our earlier work to discuss the motor-free contraction of viscoelastic biopolymer networks. We calculate the resulting contractile velocity using a microscopic model and show that it can be reduced to a simple coarse-grained model under certain limits. Our model may provide an explanation of recent reports of motor-independent contractility in cells. Our results also suggest a mechanism for generating contractile forces in synthetic active materials.
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Affiliation(s)
- Sihan Chen
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Tomer Markovich
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel
- Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 69978, Israel
| | - Fred C MacKintosh
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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4
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Cumberworth A, Ten Wolde PR. Constriction of Actin Rings by Passive Crosslinkers. PHYSICAL REVIEW LETTERS 2023; 131:038401. [PMID: 37540881 DOI: 10.1103/physrevlett.131.038401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 06/06/2023] [Indexed: 08/06/2023]
Abstract
In many organisms, cell division is driven by the constriction of a cytokinetic ring, which consists of actin filaments and crosslinking proteins. While it has long been believed that the constriction is driven by motor proteins, it has recently been discovered that passive crosslinkers that do not turn over fuel are able to generate enough force to constrict actin filament rings. To study the ring constriction dynamics, we develop a model that includes the driving force of crosslinker condensation and the opposing forces of friction and filament bending. We analyze the constriction force as a function of ring topology and crosslinker concentration, and predict forces that are sufficient to constrict an unadorned plasma membrane. Our model also predicts that actin-filament sliding arises from an interplay between filament rotation and crosslinker hopping, producing frictional forces that are low compared with those of crosslinker-mediated microtubule sliding.
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Benoist F, Saggiorato G, Lenz M. Generic stress rectification in nonlinear elastic media. SOFT MATTER 2023; 19:2970-2976. [PMID: 37014008 PMCID: PMC10131159 DOI: 10.1039/d2sm01606k] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Stress propagation in nonlinear media is crucial in cell biology, where molecular motors exert anisotropic force dipoles on the fibrous cytoskeleton. While the force dipoles can be either contractile or expansile, a medium made of fibers which buckle under compression rectifies these stresses towards a biologically crucial contraction. A general understanding of this rectification phenomenon as a function of the medium's elasticity is however lacking. Here we use theoretical continuum elasticity to show that rectification is actually a very general effect in nonlinear materials subjected to anisotropic internal stresses. We analytically show that both bucklable and constitutively linear materials subjected to geometrical nonlinearities rectify small forces towards contraction, while granular-like materials rectify towards expansion. Using simulations, we moreover show that these results extend to larger forces. Beyond fiber networks, these results could shed light on the propagation of stresses in brittle or granular materials following a local plastic rearrangement.
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Affiliation(s)
- Félix Benoist
- Université Paris-Saclay, CNRS, LPTMS, 91400, Orsay, France.
| | | | - Martin Lenz
- Université Paris-Saclay, CNRS, LPTMS, 91400, Orsay, France.
- PMMH, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris, F-, 75005, Paris, France
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6
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Baldauf L, van Buren L, Fanalista F, Koenderink GH. Actomyosin-Driven Division of a Synthetic Cell. ACS Synth Biol 2022; 11:3120-3133. [PMID: 36164967 PMCID: PMC9594324 DOI: 10.1021/acssynbio.2c00287] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Indexed: 01/24/2023]
Abstract
One of the major challenges of bottom-up synthetic biology is rebuilding a minimal cell division machinery. From a reconstitution perspective, the animal cell division apparatus is mechanically the simplest and therefore attractive to rebuild. An actin-based ring produces contractile force to constrict the membrane. By contrast, microbes and plant cells have a cell wall, so division requires concerted membrane constriction and cell wall synthesis. Furthermore, reconstitution of the actin division machinery helps in understanding the physical and molecular mechanisms of cytokinesis in animal cells and thus our own cells. In this review, we describe the state-of-the-art research on reconstitution of minimal actin-mediated cytokinetic machineries. Based on the conceptual requirements that we obtained from the physics of the shape changes involved in cell division, we propose two major routes for building a minimal actin apparatus capable of division. Importantly, we acknowledge both the passive and active roles that the confining lipid membrane can play in synthetic cytokinesis. We conclude this review by identifying the most pressing challenges for future reconstitution work, thereby laying out a roadmap for building a synthetic cell equipped with a minimal actin division machinery.
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Affiliation(s)
| | | | - Federico Fanalista
- Department of Bionanoscience,
Kavli Institute of Nanoscience Delft, Delft
University of Technology, 2629 HZ Delft, The Netherlands
| | - Gijsje Hendrika Koenderink
- Department of Bionanoscience,
Kavli Institute of Nanoscience Delft, Delft
University of Technology, 2629 HZ Delft, The Netherlands
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7
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Chen S, Broedersz CP, Markovich T, MacKintosh FC. Nonlinear stress relaxation of transiently crosslinked biopolymer networks. Phys Rev E 2021; 104:034418. [PMID: 34654176 DOI: 10.1103/physreve.104.034418] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Accepted: 08/22/2021] [Indexed: 11/07/2022]
Abstract
A long-standing puzzle in the rheology of living cells is the origin of the experimentally observed long-time stress relaxation. The mechanics of the cell is largely dictated by the cytoskeleton, which is a biopolymer network consisting of transient crosslinkers, allowing for stress relaxation over time. Moreover, these networks are internally stressed due to the presence of molecular motors. In this work we propose a theoretical model that uses a mode-dependent mobility to describe the stress relaxation of such prestressed transient networks. Our theoretical predictions agree favorably with experimental data of reconstituted cytoskeletal networks and may provide an explanation for the slow stress relaxation observed in cells.
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Affiliation(s)
- Sihan Chen
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Chase P Broedersz
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands.,Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
| | - Tomer Markovich
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Fred C MacKintosh
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA.,Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA.,Department of Chemistry, Rice University, Houston, Texas 77005, USA
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Kučera O, Siahaan V, Janda D, Dijkstra SH, Pilátová E, Zatecka E, Diez S, Braun M, Lansky Z. Anillin propels myosin-independent constriction of actin rings. Nat Commun 2021; 12:4595. [PMID: 34321459 PMCID: PMC8319318 DOI: 10.1038/s41467-021-24474-1] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Accepted: 06/21/2021] [Indexed: 02/07/2023] Open
Abstract
Constriction of the cytokinetic ring, a circular structure of actin filaments, is an essential step during cell division. Mechanical forces driving the constriction are attributed to myosin motor proteins, which slide actin filaments along each other. However, in multiple organisms, ring constriction has been reported to be myosin independent. How actin rings constrict in the absence of motor activity remains unclear. Here, we demonstrate that anillin, a non-motor actin crosslinker, indispensable during cytokinesis, autonomously propels the contractility of actin bundles. Anillin generates contractile forces of tens of pico-Newtons to maximise the lengths of overlaps between bundled actin filaments. The contractility is enhanced by actin disassembly. When multiple actin filaments are arranged into a ring, this contractility leads to ring constriction. Our results indicate that passive actin crosslinkers can substitute for the activity of molecular motors to generate contractile forces in a variety of actin networks, including the cytokinetic ring.
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Affiliation(s)
- Ondřej Kučera
- grid.418095.10000 0001 1015 3316Institute of Biotechnology, Czech Academy of Sciences, BIOCEV, Vestec, Prague West, Czechia ,grid.5583.b0000 0001 2299 8025Present Address: CytoMorpho Lab, Laboratoire Physiologie Cellulaire & Végétale, Institut de recherche interdisciplinaire de Grenoble, Commissariat à l’énergie atomique et aux énergies alternatives (CEA), Grenoble, France
| | - Valerie Siahaan
- grid.418095.10000 0001 1015 3316Institute of Biotechnology, Czech Academy of Sciences, BIOCEV, Vestec, Prague West, Czechia
| | - Daniel Janda
- grid.418095.10000 0001 1015 3316Institute of Biotechnology, Czech Academy of Sciences, BIOCEV, Vestec, Prague West, Czechia
| | - Sietske H. Dijkstra
- grid.418095.10000 0001 1015 3316Institute of Biotechnology, Czech Academy of Sciences, BIOCEV, Vestec, Prague West, Czechia
| | - Eliška Pilátová
- grid.418095.10000 0001 1015 3316Institute of Biotechnology, Czech Academy of Sciences, BIOCEV, Vestec, Prague West, Czechia
| | - Eva Zatecka
- grid.418095.10000 0001 1015 3316Institute of Biotechnology, Czech Academy of Sciences, BIOCEV, Vestec, Prague West, Czechia
| | - Stefan Diez
- grid.4488.00000 0001 2111 7257B CUBE – Center for Molecular Bioengineering, TU Dresden, Dresden, Germany ,grid.419537.d0000 0001 2113 4567Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany ,grid.4488.00000 0001 2111 7257Cluster of Excellence Physics of Life, Technische Universität Dresden, Dresden, Germany
| | - Marcus Braun
- grid.418095.10000 0001 1015 3316Institute of Biotechnology, Czech Academy of Sciences, BIOCEV, Vestec, Prague West, Czechia
| | - Zdenek Lansky
- grid.418095.10000 0001 1015 3316Institute of Biotechnology, Czech Academy of Sciences, BIOCEV, Vestec, Prague West, Czechia
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Markovich T, Lubensky TC. Odd Viscosity in Active Matter: Microscopic Origin and 3D Effects. PHYSICAL REVIEW LETTERS 2021; 127:048001. [PMID: 34355935 DOI: 10.1103/physrevlett.127.048001] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Revised: 04/19/2021] [Accepted: 06/03/2021] [Indexed: 06/13/2023]
Abstract
In common fluids, viscosity is associated with dissipation. However, when time-reversal symmetry is broken a new type of nondissipative "viscosity" emerges. Recent theories and experiments on classical 2D systems with active spinning particles have heightened interest in "odd viscosity," but a microscopic theory for it in active materials is still absent. Here, we present such first-principles microscopic Hamiltonian theory, valid for both 2D and 3D, showing that odd viscosity is present in any system, even at zero temperature, with globally or locally aligned spinning components. Our work substantially extends the applicability of odd viscosity into 3D fluids, and specifically to internally driven active materials, such as living matter (e.g., actomyosin gels). We find intriguing 3D effects of odd viscosity such as propagation of anisotropic bulk shear waves and breakdown of Bernoulli's principle.
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Affiliation(s)
- Tomer Markovich
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Tom C Lubensky
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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10
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The Actomyosin Cortex of Cells: A Thin Film of Active Matter. J Indian Inst Sci 2021. [DOI: 10.1007/s41745-020-00220-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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