1
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Alonso-Matilla R, Lam AR, Miettinen TP. Cell-intrinsic mechanical regulation of plasma membrane accumulation at the cytokinetic furrow. Proc Natl Acad Sci U S A 2024; 121:e2320769121. [PMID: 38990949 PMCID: PMC11260091 DOI: 10.1073/pnas.2320769121] [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: 11/26/2023] [Accepted: 06/11/2024] [Indexed: 07/13/2024] Open
Abstract
Cytokinesis is the process where the mother cell's cytoplasm separates into daughter cells. This is driven by an actomyosin contractile ring that produces cortical contractility and drives cleavage furrow ingression, resulting in the formation of a thin intercellular bridge. While cytoskeletal reorganization during cytokinesis has been extensively studied, less is known about the spatiotemporal dynamics of the plasma membrane. Here, we image and model plasma membrane lipid and protein dynamics on the cell surface during leukemia cell cytokinesis. We reveal an extensive accumulation and folding of the plasma membrane at the cleavage furrow and the intercellular bridge, accompanied by a depletion and unfolding of the plasma membrane at the cell poles. These membrane dynamics are caused by two actomyosin-driven biophysical mechanisms: the radial constriction of the cleavage furrow causes local compression of the apparent cell surface area and accumulation of the plasma membrane at the furrow, while actomyosin cortical flows drag the plasma membrane toward the cell division plane as the furrow ingresses. The magnitude of these effects depends on the plasma membrane fluidity, cortex adhesion, and cortical contractility. Overall, our work reveals cell-intrinsic mechanical regulation of plasma membrane accumulation at the cleavage furrow that is likely to generate localized differences in membrane tension across the cytokinetic cell. This may locally alter endocytosis, exocytosis, and mechanotransduction, while also serving as a self-protecting mechanism against cytokinesis failures that arise from high membrane tension at the intercellular bridge.
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Affiliation(s)
| | - Alice R. Lam
- Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Teemu P. Miettinen
- Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, Cambridge, MA02139
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2
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Vishen AS, Prost J, Sens P. Quantitative comparison of cell-cell detachment force in different experimental setups. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2024; 47:22. [PMID: 38563859 PMCID: PMC10987375 DOI: 10.1140/epje/s10189-024-00416-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2023] [Accepted: 03/12/2024] [Indexed: 04/04/2024]
Abstract
We compare three different setups for measuring cell-cell adhesion. We show that the measured strength depends on the type of setup that is used. For identical cells different assays measure different detachment forces. This can be understood from the fact that cell-cell detachment is a global property of the system. We also analyse the role of external force and line tension on contact angle and cell-cell detachment. Comparison with the experiments suggest that viscous forces play an important role in the process. We dedicate this article to Fyl Pincus who for many of us is an example to be followed not only for outstanding science but also for a marvelous human behavior.
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Affiliation(s)
- Amit Singh Vishen
- Max Planck Institute for the Physics of Complex Systems, 01187, Dresden, Germany.
| | - Jacques Prost
- Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University, CNRS UMR168, 75005, Paris, France
| | - Pierre Sens
- Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University, CNRS UMR168, 75005, Paris, France
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3
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Alonso-Matilla R, Lam A, Miettinen TP. Cell intrinsic mechanical regulation of plasma membrane accumulation at the cytokinetic furrow. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.11.13.566882. [PMID: 38014042 PMCID: PMC10680611 DOI: 10.1101/2023.11.13.566882] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2023]
Abstract
Cytokinesis is the process where the mother cell's cytoplasm separates into daughter cells. This is driven by an actomyosin contractile ring that produces cortical contractility and drives cleavage furrow ingression, resulting in the formation of a thin intercellular bridge. While cytoskeletal reorganization during cytokinesis has been extensively studied, little is known about the spatiotemporal dynamics of the plasma membrane. Here, we image and model plasma membrane lipid and protein dynamics on the cell surface during leukemia cell cytokinesis. We reveal an extensive accumulation and folding of plasma membrane at the cleavage furrow and the intercellular bridge, accompanied by a depletion and unfolding of plasma membrane at the cell poles. These membrane dynamics are caused by two actomyosin-driven biophysical mechanisms: the radial constriction of the cleavage furrow causes local compression of the apparent cell surface area and accumulation of the plasma membrane at the furrow, while actomyosin cortical flows drag the plasma membrane towards the cell division plane as the furrow ingresses. The magnitude of these effects depends on the plasma membrane fluidity, cortex adhesion and cortical contractility. Overall, our work reveals cell intrinsic mechanical regulation of plasma membrane accumulation at the cleavage furrow that is likely to generate localized differences in membrane tension across the cytokinetic cell. This may locally alter endocytosis, exocytosis and mechanotransduction, while also serving as a self-protecting mechanism against cytokinesis failures that arise from high membrane tension at the intercellular bridge.
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Affiliation(s)
- Roberto Alonso-Matilla
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
| | - Alice Lam
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Teemu P Miettinen
- Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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4
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Bovyn MJ, Haas PA. Shaping epithelial lumina under pressure. Biochem Soc Trans 2024; 52:BST20230632C. [PMID: 38415294 PMCID: PMC10903447 DOI: 10.1042/bst20230632c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2023] [Revised: 02/07/2024] [Accepted: 02/08/2024] [Indexed: 02/29/2024]
Abstract
The formation of fluid- or gas-filled lumina surrounded by epithelial cells pervades development and disease. We review the balance between lumen pressure and mechanical forces from the surrounding cells that governs lumen formation. We illustrate the mechanical side of this balance in several examples of increasing complexity, and discuss how recent work is beginning to elucidate how nonlinear and active mechanics and anisotropic biomechanical structures must conspire to overcome the isotropy of pressure to form complex, non-spherical lumina.
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Affiliation(s)
- Matthew J. Bovyn
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstraße 108, 01307 Dresden, Germany
| | - Pierre A. Haas
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstraße 108, 01307 Dresden, Germany
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5
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Blanc B, Agyapong JN, Hunter I, Galas JC, Fernandez-Nieves A, Fraden S. Collective chemomechanical oscillations in active hydrogels. Proc Natl Acad Sci U S A 2024; 121:e2313258121. [PMID: 38300869 PMCID: PMC10861864 DOI: 10.1073/pnas.2313258121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2023] [Accepted: 11/14/2023] [Indexed: 02/03/2024] Open
Abstract
We report on the collective response of an assembly of chemomechanical Belousov-Zhabotinsky (BZ) hydrogel beads. We first demonstrate that a single isolated spherical BZ hydrogel bead with a radius below a critical value does not oscillate, whereas an assembly of the same BZ hydrogel beads presents chemical oscillation. A BZ chemical model with an additional flux of chemicals out of the BZ hydrogel captures the experimentally observed transition from oxidized nonoscillating to oscillating BZ hydrogels and shows this transition is due to a flux of inhibitors out of the BZ hydrogel. The model also captures the role of neighboring BZ hydrogel beads in decreasing the critical size for an assembly of BZ hydrogel beads to oscillate. We finally leverage the quorum sensing behavior of the collective to trigger their chemomechanical oscillation and discuss how this collective effect can be used to enhance the oscillatory strain of these active BZ hydrogels. These findings could help guide the eventual fabrication of a swarm of autonomous, communicating, and motile hydrogels.
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Affiliation(s)
- Baptiste Blanc
- Laboratoire Jean Perrin, Sorbonne Université, CNRS, Institut de Biologie Paris-Seine (IBPS), Paris75005, France
- Department of Condensed Matter Physics, University of Barcelona, Barcelona08028, Spain
- Department of Physics, Brandeis University, Waltham, MA02454
| | - Johnson N. Agyapong
- Department of Physics, Brandeis University, Waltham, MA02454
- Department of Biomedical and Chemical Engineering, Syracuse University, Syracuse, NY13244
| | - Ian Hunter
- Department of Physics, Brandeis University, Waltham, MA02454
| | - Jean-Christophe Galas
- Laboratoire Jean Perrin, Sorbonne Université, CNRS, Institut de Biologie Paris-Seine (IBPS), Paris75005, France
| | - Alberto Fernandez-Nieves
- Department of Condensed Matter Physics, University of Barcelona, Barcelona08028, Spain
- Institute of Complex Systems, University of Barcelona, Barcelona08028, Spain
- Institució Catalanade Recerca i Estudis Avançats, Barcelona08010, Spain
| | - Seth Fraden
- Department of Physics, Brandeis University, Waltham, MA02454
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6
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Fossati M, Scheibner C, Fruchart M, Vitelli V. Odd elasticity and topological waves in active surfaces. Phys Rev E 2024; 109:024608. [PMID: 38491602 DOI: 10.1103/physreve.109.024608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Accepted: 01/12/2024] [Indexed: 03/18/2024]
Abstract
Odd elasticity describes active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new antisymmetric (odd) components appear in the elastic tensor. In this work we study the odd elasticity and non-Hermitian wave dynamics of active surfaces, specifically plates of moderate thickness. These odd moduli can endow the vibrational modes of the plate with a nonzero topological invariant known as the first Chern number. Within continuum elastic theory, we show that the Chern number is related to the presence of unidirectional shearing waves that are hosted at the plate's boundary. We show that the existence of these chiral edge waves hinges on a distinctive two-step mechanism. Unlike electronic Chern insulators where the magnetic field at the same time gaps the spectrum and imparts chirality, here the finite thickness of the sample gaps the shear modes, and the odd elasticity makes them chiral.
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Affiliation(s)
- Michele Fossati
- SISSA, Trieste 34136, Italy
- INFN Sezione di Trieste, Trieste 34127, Italy
| | - Colin Scheibner
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Michel Fruchart
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Vincenzo Vitelli
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
- Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, USA
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7
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Rombouts J, Elliott J, Erzberger A. Forceful patterning: theoretical principles of mechanochemical pattern formation. EMBO Rep 2023; 24:e57739. [PMID: 37916772 DOI: 10.15252/embr.202357739] [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: 06/30/2023] [Revised: 09/21/2023] [Accepted: 09/27/2023] [Indexed: 11/03/2023] Open
Abstract
Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.
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Affiliation(s)
- Jan Rombouts
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Developmental Biology Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
| | - Jenna Elliott
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
| | - Anna Erzberger
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
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8
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Mitchell NP, Cislo DJ. TubULAR: tracking in toto deformations of dynamic tissues via constrained maps. Nat Methods 2023; 20:1980-1988. [PMID: 38057529 PMCID: PMC10848277 DOI: 10.1038/s41592-023-02081-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2022] [Accepted: 10/10/2023] [Indexed: 12/08/2023]
Abstract
A common motif in biology is the arrangement of cells into tubes, which further transform into complex shapes. Traditionally, analysis of dynamic tissues has relied on inspecting static snapshots, live imaging of cross-sections or tracking isolated cells in three dimensions. However, capturing the interplay between in-plane and out-of-plane behaviors requires following the full surface as it deforms and integrating cell-scale motions into collective, tissue-scale deformations. Here, we present an analysis framework that builds in toto maps of tissue deformations by following tissue parcels in a static material frame of reference. Our approach then relates in-plane and out-of-plane behaviors and decomposes complex deformation maps into elementary contributions. The tube-like surface Lagrangian analysis resource (TubULAR) provides an open-source implementation accessible either as a standalone toolkit or as an extension of the ImSAnE package used in the developmental biology community. We demonstrate our approach by analyzing shape change in the embryonic Drosophila midgut and beating zebrafish heart. The method naturally generalizes to in vitro and synthetic systems and provides ready access to the mechanical mechanisms relating genetic patterning to organ shape change.
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Affiliation(s)
- Noah P Mitchell
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, CA, USA.
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA, USA.
| | - Dillon J Cislo
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA, USA.
- Center for Studies in Physics and Biology, The Rockefeller University, New York, NY, USA.
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9
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Maji A, Dasbiswas K, Rabin Y. Shape transitions in a network model of active elastic shells. SOFT MATTER 2023; 19:7216-7226. [PMID: 37724013 DOI: 10.1039/d3sm01041d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/20/2023]
Abstract
Morphogenesis involves the transformation of initially simple shapes, such as multicellular spheroids, into more complex 3D shapes. These shape changes are governed by mechanical forces including molecular motor-generated forces as well as hydrostatic fluid pressure, both of which are actively regulated in living matter through mechano-chemical feedback. Inspired by autonomous, biophysical shape change, such as occurring in the model organism hydra, we introduce a minimal, active, elastic model featuring a network of springs in a globe-like spherical shell geometry. In this model there is coupling between activity and the shape of the shell: if the local curvature of a filament represented by a spring falls below a critical value, its elastic constant is actively changed. This results in deformation of the springs that changes the shape of the shell. By combining excitation of springs and pressure regulation, we show that the shell undergoes a transition from spheroidal to either elongated ellipsoidal or a different spheroidal shape, depending on pressure. There exists a critical pressure at which there is an abrupt change from ellipsoids to spheroids, showing that pressure is potentially a sensitive switch for material shape. We thus offer biologically inspired design principles for autonomous shape transitions in active elastic shells.
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Affiliation(s)
- Ajoy Maji
- Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, 32000 Haifa, Israel
| | - Kinjal Dasbiswas
- Department of Physics, University of California, Merced, Merced, CA 95343, USA
| | - Yitzhak Rabin
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel.
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10
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Ledesma-Durán A, Juárez-Valencia LH. Diffusion coefficients and MSD measurements on curved membranes and porous media. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:70. [PMID: 37578670 DOI: 10.1140/epje/s10189-023-00329-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Accepted: 07/28/2023] [Indexed: 08/15/2023]
Abstract
We study some geometric aspects that influence the transport properties of particles that diffuse on curved surfaces. We compare different approaches to surface diffusion based on the Laplace-Beltrami operator adapted to predict concentration along entire membranes, confined subdomains along surfaces, or within porous media. Our goal is to summarize, firstly, how diffusion in these systems results in different types of diffusion coefficients and mean square displacement measurements, and secondly, how these two factors are affected by the concavity of the surface, the shape of the possible barriers or obstacles that form the available domains, the sinuosity, tortuosity, and constrictions of the trajectories and even how the observation plane affects the measurements of the diffusion. In addition to presenting a critical and organized comparison between different notions of MSD, in this review, we test the correspondence between theoretical predictions and numerical simulations by performing finite element simulations and illustrate some situations where diffusion theory can be applied. We briefly reviewed computational schemes for understanding surface diffusion and finally, discussed how this work contributes to understanding the role of surface diffusion transport properties in porous media and their relationship to other transport processes.
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Affiliation(s)
- Aldo Ledesma-Durán
- Departmento de Matemáticas, Universidad Autónoma Metropolitana, CDMX, Mexico
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11
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Hueschen CL, Dunn AR, Phillips R. Wildebeest herds on rolling hills: Flocking on arbitrary curved surfaces. Phys Rev E 2023; 108:024610. [PMID: 37723815 DOI: 10.1103/physreve.108.024610] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2022] [Accepted: 07/10/2023] [Indexed: 09/20/2023]
Abstract
The collective behavior of active agents, whether herds of wildebeest or microscopic actin filaments propelled by molecular motors, is an exciting frontier in biological and soft matter physics. Almost three decades ago, Toner and Tu developed a continuum theory of the collective action of flocks, or herds, that helped launch the modern field of active matter. One challenge faced when applying continuum active matter theories to living phenomena is the complex geometric structure of biological environments. Both macroscopic and microscopic herds move on asymmetric curved surfaces, like undulating grass plains or the surface layers of cells or embryos, which can render problems analytically intractable. In this paper, we present a formulation of the Toner-Tu flocking theory that uses the finite element method to solve the governing equations on arbitrary curved surfaces. First, we test the developed formalism and its numerical implementation in channel flow with scattering obstacles and on cylindrical and spherical surfaces, comparing our results to analytical solutions. We then progress to surfaces with arbitrary curvature, moving beyond previously accessible problems to explore herding behavior on a variety of landscapes. This approach allows the investigation of transients and dynamic solutions not revealed by analytic methods. It also enables versatile incorporation of new geometries and boundary conditions and efficient sweeps of parameter space. Looking forward, the paper presented here lays the groundwork for a dialogue between Toner-Tu theory and data on collective motion in biologically relevant geometries, from drone footage of migrating animal herds to movies of microscopic cytoskeletal flows within cells.
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Affiliation(s)
- Christina L Hueschen
- Department of Chemical Engineering, Stanford University, Palo Alto, California 94305, USA
| | - Alexander R Dunn
- Department of Chemical Engineering, Stanford University, Palo Alto, California 94305, USA
| | - Rob Phillips
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, California 91125, USA
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12
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Okuda S, Hiraiwa T. Modelling contractile ring formation and division to daughter cells for simulating proliferative multicellular dynamics. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:56. [PMID: 37466721 DOI: 10.1140/epje/s10189-023-00315-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Accepted: 06/24/2023] [Indexed: 07/20/2023]
Abstract
Cell proliferation is a fundamental process underlying embryogenesis, homeostasis, wound healing, and cancer. The process involves multiple events during each cell cycle, such as cell growth, contractile ring formation, and division to daughter cells, which affect the surrounding cell population geometrically and mechanically. However, existing methods do not comprehensively describe the dynamics of multicellular structures involving cell proliferation at a subcellular resolution. In this study, we present a novel model for proliferative multicellular dynamics at the subcellular level by building upon the nonconservative fluid membrane (NCF) model that we developed in earlier research. The NCF model utilizes a dynamically-rearranging closed triangular mesh to depict the shape of each cell, enabling us to analyze cell dynamics over extended periods beyond each cell cycle, during which cell surface components undergo dynamic turnover. The proposed model represents the process of cell proliferation by incorporating cell volume growth and contractile ring formation through an energy function and topologically dividing each cell at the cleavage furrow formed by the ring. Numerical simulations demonstrated that the model recapitulated the process of cell proliferation at subcellular resolution, including cell volume growth, cleavage furrow formation, and division to daughter cells. Further analyses suggested that the orientation of actomyosin stress in the contractile ring plays a crucial role in the cleavage furrow formation, i.e., circumferential orientation can form a cleavage furrow but isotropic orientation cannot. Furthermore, the model replicated tissue-scale multicellular dynamics, where the successive proliferation of adhesive cells led to the formation of a cell sheet and stratification on the substrate. Overall, the proposed model provides a basis for analyzing proliferative multicellular dynamics at subcellular resolution.
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Affiliation(s)
- Satoru Okuda
- Nano Life Science Institute, Kakuma-Machi, Kanazawa, Japan.
| | - Tetsuya Hiraiwa
- Mechanobiology Institute, National University of Singapore, Singapore, Singapore
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13
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Würthner L, Goychuk A, Frey E. Geometry-induced patterns through mechanochemical coupling. Phys Rev E 2023; 108:014404. [PMID: 37583206 DOI: 10.1103/physreve.108.014404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2022] [Accepted: 05/15/2023] [Indexed: 08/17/2023]
Abstract
Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic cell-shape changes. These changes in cell shape may in turn affect the dynamics of pattern-forming proteins, hence leading to an intricate feedback loop between cell shape and chemical dynamics. While several computational studies have examined the rich resulting dynamics, the underlying mechanisms are not yet fully understood. To elucidate some of these mechanisms, we explore a conceptual model for cell polarity on a dynamic one-dimensional manifold. Using concepts from differential geometry, we derive the equations governing mass-conserving reaction-diffusion systems on time-evolving manifolds. Analyzing these equations mathematically, we show that dynamic shape changes of the membrane can induce pattern-forming instabilities in parts of the membrane, which we refer to as regional instabilities. Deformations of the local membrane geometry can also (regionally) suppress pattern formation and spatially shift already existing patterns. We explain our findings by applying and generalizing the local equilibria theory of mass-conserving reaction-diffusion systems. This allows us to determine a simple onset criterion for geometry-induced pattern-forming instabilities, which is linked to the phase-space structure of the reaction-diffusion system. The feedback loop between membrane shape deformations and reaction-diffusion dynamics then leads to a surprisingly rich phenomenology of patterns, including oscillations, traveling waves, and standing waves, even if these patterns do not occur in systems with a fixed membrane shape. Our paper reveals that the local conformation of the membrane geometry acts as an important dynamical control parameter for pattern formation in mass-conserving reaction-diffusion systems.
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Affiliation(s)
- Laeschkir Würthner
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany
| | - Andriy Goychuk
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany
- Max Planck School Matter to Life, Hofgartenstraße 8, D-80539 Munich, Germany
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14
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Mendes TV, Ranft J, Berthoumieux H. Model of membrane deformations driven by a surface pH gradient. Phys Rev E 2023; 108:014113. [PMID: 37583220 DOI: 10.1103/physreve.108.014113] [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: 01/13/2023] [Accepted: 06/06/2023] [Indexed: 08/17/2023]
Abstract
Many cellular organelles are membrane-bound structures with complex membrane composition and shape. Their shapes have been observed to depend on the metabolic state of the organelle and the mechanisms that couple biochemical pathways and membrane shape are still actively investigated. Here, we study a model coupling inhomogeneities in the lipid composition and membrane geometry via a generalized Helfrich free energy. We derive the resulting stress tensor, the Green's function for a tubular membrane, and compute the phase diagram of the induced deformations. We then apply this model to study the deformation of mitochondria cristae described as membrane tubes supporting a pH gradient at its surface. This gradient in turn controls the lipid composition of the membrane via the protonation or deprotonation of cardiolipins, which are acid-based lipids known to be crucial for mitochondria shape and functioning. Our model predicts the appearance of tube deformations resembling the observed shape changes of cristea when submitted to a proton gradient.
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Affiliation(s)
- Toni V Mendes
- Laboratoire Ondes et Matière d'Aquitaine, Université de Bordeaux, Unité Mixte de Recherche 5798, CNRS, F-33400 Talence, France
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC, UMR 7600), F-75005 Paris, France
| | - Jonas Ranft
- Institut de Biologie de l'ENS, Ecole Normale Supérieure, CNRS, Inserm, Université PSL, 46 rue d'Ulm, F-75005 Paris, France
| | - Hélène Berthoumieux
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC, UMR 7600), F-75005 Paris, France
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, Berlin 14195, Germany
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15
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Sato K. A cell membrane model that reproduces cortical flow-driven cell migration and collective movement. Front Cell Dev Biol 2023; 11:1126819. [PMID: 37427380 PMCID: PMC10328438 DOI: 10.3389/fcell.2023.1126819] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2022] [Accepted: 05/30/2023] [Indexed: 07/11/2023] Open
Abstract
Many fundamental biological processes are dependent on cellular migration. Although the mechanical mechanisms of single-cell migration are relatively well understood, those underlying migration of multiple cells adhered to each other in a cluster, referred to as cluster migration, are poorly understood. A key reason for this knowledge gap is that many forces-including contraction forces from actomyosin networks, hydrostatic pressure from the cytosol, frictional forces from the substrate, and forces from adjacent cells-contribute to cell cluster movement, making it challenging to model, and ultimately elucidate, the final result of these forces. This paper describes a two-dimensional cell membrane model that represents cells on a substrate with polygons and expresses various mechanical forces on the cell surface, keeping these forces balanced at all times by neglecting cell inertia. The model is discrete but equivalent to a continuous model if appropriate replacement rules for cell surface segments are chosen. When cells are given a polarity, expressed by a direction-dependent surface tension reflecting the location dependence of contraction and adhesion on a cell boundary, the cell surface begins to flow from front to rear as a result of force balance. This flow produces unidirectional cell movement, not only for a single cell but also for multiple cells in a cluster, with migration speeds that coincide with analytical results from a continuous model. Further, if the direction of cell polarity is tilted with respect to the cluster center, surface flow induces cell cluster rotation. The reason why this model moves while keeping force balance on cell surface (i.e., under no net forces from outside) is because of the implicit inflow and outflow of cell surface components through the inside of the cell. An analytical formula connecting cell migration speed and turnover rate of cell surface components is presented.
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16
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Wang Z, Marchetti MC, Brauns F. Patterning of morphogenetic anisotropy fields. Proc Natl Acad Sci U S A 2023; 120:e2220167120. [PMID: 36947516 PMCID: PMC10068776 DOI: 10.1073/pnas.2220167120] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 02/15/2023] [Indexed: 03/23/2023] Open
Abstract
Orientational order, encoded in anisotropic fields, plays an important role during the development of an organism. A striking example of this is the freshwater polyp Hydra, where topological defects in the muscle fiber orientation have been shown to localize to key features of the body plan. This body plan is organized by morphogen concentration gradients, raising the question how muscle fiber orientation, morphogen gradients and body shape interact. Here, we introduce a minimal model that couples nematic orientational order to the gradient of a morphogen field. We show that on a planar surface, alignment to a radial concentration gradient can induce unbinding of topological defects, as observed during budding and tentacle formation in Hydra, and stabilize aster/vortex-like defects, as observed at a Hydra's mouth. On curved surfaces mimicking the morphologies of Hydra in various stages of development-from spheroid to adult-our model reproduces the experimentally observed reorganization of orientational order. Our results suggest how gradient alignment and curvature effects may work together to control orientational order during development and lay the foundations for future modeling efforts that will include the tissue mechanics that drive shape deformations.
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Affiliation(s)
- Zihang Wang
- Department of Physics, University of California, Santa Barbara, CA93106
| | | | - Fridtjof Brauns
- Department of Physics, University of California, Santa Barbara, CA93106
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA93106
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17
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Schamberger B, Ziege R, Anselme K, Ben Amar M, Bykowski M, Castro APG, Cipitria A, Coles RA, Dimova R, Eder M, Ehrig S, Escudero LM, Evans ME, Fernandes PR, Fratzl P, Geris L, Gierlinger N, Hannezo E, Iglič A, Kirkensgaard JJK, Kollmannsberger P, Kowalewska Ł, Kurniawan NA, Papantoniou I, Pieuchot L, Pires THV, Renner LD, Sageman-Furnas AO, Schröder-Turk GE, Sengupta A, Sharma VR, Tagua A, Tomba C, Trepat X, Waters SL, Yeo EF, Roschger A, Bidan CM, Dunlop JWC. Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2206110. [PMID: 36461812 DOI: 10.1002/adma.202206110] [Citation(s) in RCA: 33] [Impact Index Per Article: 33.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Revised: 11/22/2022] [Indexed: 06/17/2023]
Abstract
Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.
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Affiliation(s)
- Barbara Schamberger
- Department of the Chemistry and Physics of Materials, Paris-Lodron University of Salzburg, 5020, Salzburg, Austria
| | - Ricardo Ziege
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, 14476, Potsdam, Germany
| | - Karine Anselme
- IS2M (CNRS - UMR 7361), Université de Haute-Alsace, F-68100, Mulhouse, France
- Université de Strasbourg, F-67081, Strasbourg, France
| | - Martine Ben Amar
- Department of Physics, Laboratoire de Physique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005, Paris, France
| | - Michał Bykowski
- Department of Plant Anatomy and Cytology, Faculty of Biology, University of Warsaw, 02-096, Warsaw, Poland
| | - André P G Castro
- IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisboa, Portugal
- ESTS, Instituto Politécnico de Setúbal, 2914-761, Setúbal, Portugal
| | - Amaia Cipitria
- IS2M (CNRS - UMR 7361), Université de Haute-Alsace, F-68100, Mulhouse, France
- Group of Bioengineering in Regeneration and Cancer, Biodonostia Health Research Institute, 20014, San Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science, 48009, Bilbao, Spain
| | - Rhoslyn A Coles
- Cluster of Excellence, Matters of Activity, Humboldt-Universität zu Berlin, 10178, Berlin, Germany
| | - Rumiana Dimova
- Department of Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, 14476, Potsdam, Germany
| | - Michaela Eder
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, 14476, Potsdam, Germany
| | - Sebastian Ehrig
- Max Delbrück Center for Molecular Medicine, 13125, Berlin, Germany
- Berlin Institute for Medical Systems Biology, 10115, Berlin, Germany
| | - Luis M Escudero
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013, Seville, Spain
- Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), 28031, Madrid, Spain
| | - Myfanwy E Evans
- Institute for Mathematics, University of Potsdam, 14476, Potsdam, Germany
| | - Paulo R Fernandes
- IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisboa, Portugal
| | - Peter Fratzl
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, 14476, Potsdam, Germany
| | - Liesbet Geris
- Biomechanics Research Unit, GIGA In Silico Medicine, University of Liège, 4000, Liège, Belgium
| | - Notburga Gierlinger
- Institute of Biophysics, Department of Nanobiotechnology, University of Natural Resources and Life Sciences Vienna (Boku), 1190, Vienna, Austria
| | - Edouard Hannezo
- Institute of Science and Technology Austria, 3400, Klosterneuburg, Austria
| | - Aleš Iglič
- Laboratory of Physics, Faculty of Electrical engineering, University of Ljubljana, Tržaška 25, SI-1000, Ljubljana, Slovenia
| | - Jacob J K Kirkensgaard
- Condensed Matter Physics, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100, København Ø, Denmark
- Ingredients and Dairy Technology, Department of Food Science, University of Copenhagen, Rolighedsvej 26, 1958, Frederiksberg, Denmark
| | - Philip Kollmannsberger
- Center for Computational and Theoretical Biology, University of Würzburg, 97074, Würzburg, Germany
| | - Łucja Kowalewska
- Department of Plant Anatomy and Cytology, Faculty of Biology, University of Warsaw, 02-096, Warsaw, Poland
| | - Nicholas A Kurniawan
- Department of Biomedical Engineering and Institute for Complex Molecular Systems, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Ioannis Papantoniou
- Prometheus Division of Skeletal Tissue Engineering, KU Leuven, O&N1, Herestraat 49, PB 813, 3000, Leuven, Belgium
- Skeletal Biology and Engineering Research Center, Department of Development and Regeneration, KU Leuven, O&N1, Herestraat 49, PB 813, 3000, Leuven, Belgium
- Institute of Chemical Engineering Sciences, Foundation for Research and Technology (FORTH), Stadiou Str., 26504, Patras, Greece
| | - Laurent Pieuchot
- IS2M (CNRS - UMR 7361), Université de Haute-Alsace, F-68100, Mulhouse, France
- Université de Strasbourg, F-67081, Strasbourg, France
| | - Tiago H V Pires
- IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisboa, Portugal
| | - Lars D Renner
- Leibniz Institute of Polymer Research and the Max Bergmann Center of Biomaterials, 01069, Dresden, Germany
| | | | - Gerd E Schröder-Turk
- School of Physics, Chemistry and Mathematics, Murdoch University, 90 South St, Murdoch, WA, 6150, Australia
- Department of Materials Physics, Research School of Physics, The Australian National University, Canberra, ACT, 2600, Australia
| | - Anupam Sengupta
- Physics of Living Matter, Department of Physics and Materials Science, University of Luxembourg, L-1511, Luxembourg City, Grand Duchy of Luxembourg
| | - Vikas R Sharma
- Department of the Chemistry and Physics of Materials, Paris-Lodron University of Salzburg, 5020, Salzburg, Austria
| | - Antonio Tagua
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013, Seville, Spain
- Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), 28031, Madrid, Spain
| | - Caterina Tomba
- Univ Lyon, CNRS, INSA Lyon, Ecole Centrale de Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR5270, 69622, Villeurbanne, France
| | - Xavier Trepat
- ICREA at the Institute for Bioengineering of Catalonia, The Barcelona Institute for Science and Technology, 08028, Barcelona, Spain
- Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), 08028, Barcelona, Spain
| | - Sarah L Waters
- Mathematical Institute, University of Oxford, OX2 6GG, Oxford, UK
| | - Edwina F Yeo
- Mathematical Institute, University of Oxford, OX2 6GG, Oxford, UK
| | - Andreas Roschger
- Department of the Chemistry and Physics of Materials, Paris-Lodron University of Salzburg, 5020, Salzburg, Austria
| | - Cécile M Bidan
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, 14476, Potsdam, Germany
| | - John W C Dunlop
- Department of the Chemistry and Physics of Materials, Paris-Lodron University of Salzburg, 5020, Salzburg, Austria
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18
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Villedieu A, Alpar L, Gaugué I, Joudat A, Graner F, Bosveld F, Bellaïche Y. Homeotic compartment curvature and tension control spatiotemporal folding dynamics. Nat Commun 2023; 14:594. [PMID: 36737611 PMCID: PMC9898526 DOI: 10.1038/s41467-023-36305-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2022] [Accepted: 01/25/2023] [Indexed: 02/05/2023] Open
Abstract
Shape is a conspicuous and fundamental property of biological systems entailing the function of organs and tissues. While much emphasis has been put on how tissue tension and mechanical properties drive shape changes, whether and how a given tissue geometry influences subsequent morphogenesis remains poorly characterized. Here, we explored how curvature, a key descriptor of tissue geometry, impinges on the dynamics of epithelial tissue invagination. We found that the morphogenesis of the fold separating the adult Drosophila head and thorax segments is driven by the invagination of the Deformed (Dfd) homeotic compartment. Dfd controls invagination by modulating actomyosin organization and in-plane epithelial tension via the Tollo and Dystroglycan receptors. By experimentally introducing curvature heterogeneity within the homeotic compartment, we established that a curved tissue geometry converts the Dfd-dependent in-plane tension into an inward force driving folding. Accordingly, the interplay between in-plane tension and tissue curvature quantitatively explains the spatiotemporal folding dynamics. Collectively, our work highlights how genetic patterning and tissue geometry provide a simple design principle driving folding morphogenesis during development.
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Affiliation(s)
- Aurélien Villedieu
- Institut Curie, PSL Research University, CNRS UMR 3215, INSERM U934, F-75248 Paris Cedex 05, Paris, France.,Sorbonne Universités, UPMC Univ Paris 06, CNRS, CNRS UMR 3215, INSERM U934, F-75005, Paris, France
| | - Lale Alpar
- Institut Curie, PSL Research University, CNRS UMR 3215, INSERM U934, F-75248 Paris Cedex 05, Paris, France.,Sorbonne Universités, UPMC Univ Paris 06, CNRS, CNRS UMR 3215, INSERM U934, F-75005, Paris, France
| | - Isabelle Gaugué
- Institut Curie, PSL Research University, CNRS UMR 3215, INSERM U934, F-75248 Paris Cedex 05, Paris, France.,Sorbonne Universités, UPMC Univ Paris 06, CNRS, CNRS UMR 3215, INSERM U934, F-75005, Paris, France
| | - Amina Joudat
- Institut Curie, PSL Research University, CNRS UMR 3215, INSERM U934, F-75248 Paris Cedex 05, Paris, France.,Sorbonne Universités, UPMC Univ Paris 06, CNRS, CNRS UMR 3215, INSERM U934, F-75005, Paris, France
| | - François Graner
- Université Paris Cité, CNRS, Matière et Systèmes Complexes, F-75006, Paris, France
| | - Floris Bosveld
- Institut Curie, PSL Research University, CNRS UMR 3215, INSERM U934, F-75248 Paris Cedex 05, Paris, France. .,Sorbonne Universités, UPMC Univ Paris 06, CNRS, CNRS UMR 3215, INSERM U934, F-75005, Paris, France.
| | - Yohanns Bellaïche
- Institut Curie, PSL Research University, CNRS UMR 3215, INSERM U934, F-75248 Paris Cedex 05, Paris, France. .,Sorbonne Universités, UPMC Univ Paris 06, CNRS, CNRS UMR 3215, INSERM U934, F-75005, Paris, France.
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19
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Khoromskaia D, Salbreux G. Active morphogenesis of patterned epithelial shells. eLife 2023; 12:75878. [PMID: 36649186 PMCID: PMC9844985 DOI: 10.7554/elife.75878] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Accepted: 11/18/2022] [Indexed: 01/11/2023] Open
Abstract
Shape transformations of epithelial tissues in three dimensions, which are crucial for embryonic development or in vitro organoid growth, can result from active forces generated within the cytoskeleton of the epithelial cells. How the interplay of local differential tensions with tissue geometry and with external forces results in tissue-scale morphogenesis remains an open question. Here, we describe epithelial sheets as active viscoelastic surfaces and study their deformation under patterned internal tensions and bending moments. In addition to isotropic effects, we take into account nematic alignment in the plane of the tissue, which gives rise to shape-dependent, anisotropic active tensions and bending moments. We present phase diagrams of the mechanical equilibrium shapes of pre-patterned closed shells and explore their dynamical deformations. Our results show that a combination of nematic alignment and gradients in internal tensions and bending moments is sufficient to reproduce basic building blocks of epithelial morphogenesis, including fold formation, budding, neck formation, flattening, and tubulation.
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Affiliation(s)
| | - Guillaume Salbreux
- The Francis Crick InstituteLondonUnited Kingdom
- University of GenevaGenevaSwitzerland
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20
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Torres-Sánchez A, Kerr Winter M, Salbreux G. Interacting active surfaces: A model for three-dimensional cell aggregates. PLoS Comput Biol 2022; 18:e1010762. [PMID: 36525467 PMCID: PMC9803321 DOI: 10.1371/journal.pcbi.1010762] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Revised: 12/30/2022] [Accepted: 11/26/2022] [Indexed: 12/23/2022] Open
Abstract
We introduce a modelling and simulation framework for cell aggregates in three dimensions based on interacting active surfaces. Cell mechanics is captured by a physical description of the acto-myosin cortex that includes cortical flows, viscous forces, active tensions, and bending moments. Cells interact with each other via short-range forces capturing the effect of adhesion molecules. We discretise the model equations using a finite element method, and provide a parallel implementation in C++. We discuss examples of application of this framework to small and medium-sized aggregates: we consider the shape and dynamics of a cell doublet, a planar cell sheet, and a growing cell aggregate. This framework opens the door to the systematic exploration of the cell to tissue-scale mechanics of cell aggregates, which plays a key role in the morphogenesis of embryos and organoids.
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Affiliation(s)
| | - Max Kerr Winter
- Theoretical Physics of Biology laboratory, The Francis Crick Institute, London, United Kingdom
| | - Guillaume Salbreux
- Theoretical Physics of Biology laboratory, The Francis Crick Institute, London, United Kingdom
- Department of Genetics and Evolution, University of Geneva, Genève, Switzerland
- * E-mail:
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21
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Three-dimensional chiral morphodynamics of chemomechanical active shells. Proc Natl Acad Sci U S A 2022; 119:e2206159119. [PMID: 36442097 PMCID: PMC9894169 DOI: 10.1073/pnas.2206159119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
Morphogenesis of active shells such as cells is a fundamental chemomechanical process that often exhibits three-dimensional (3D) large deformations and chemical pattern dynamics simultaneously. Here, we establish a chemomechanical active shell theory accounting for mechanical feedback and biochemical regulation to investigate the symmetry-breaking and 3D chiral morphodynamics emerging in the cell cortex. The active bending and stretching of the elastic shells are regulated by biochemical signals like actomyosin and RhoA, which, in turn, exert mechanical feedback on the biochemical events via deformation-dependent diffusion and inhibition. We show that active deformations can trigger chemomechanical bifurcations, yielding pulse spiral waves and global oscillations, which, with increasing mechanical feedback, give way to traveling or standing waves subsequently. Mechanical feedback is also found to contribute to stabilizing the polarity of emerging patterns, thus ensuring robust morphogenesis. Our results reproduce and unravel the experimentally observed solitary and multiple spiral patterns, which initiate asymmetric cleavage in Xenopus and starfish embryogenesis. This study underscores the crucial roles of mechanical feedback in cell development and also suggests a chemomechanical framework allowing for 3D large deformation and chemical signaling to explore complex morphogenesis in living shell-like structures.
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22
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Callan-Jones A. Self-organization in amoeboid motility. Front Cell Dev Biol 2022; 10:1000071. [PMID: 36313569 PMCID: PMC9614430 DOI: 10.3389/fcell.2022.1000071] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Accepted: 10/03/2022] [Indexed: 11/13/2022] Open
Abstract
Amoeboid motility has come to refer to a spectrum of cell migration modes enabling a cell to move in the absence of strong, specific adhesion. To do so, cells have evolved a range of motile surface movements whose physical principles are now coming into view. In response to external cues, many cells—and some single-celled-organisms—have the capacity to turn off their default migration mode. and switch to an amoeboid mode. This implies a restructuring of the migration machinery at the cell scale and suggests a close link between cell polarization and migration mediated by self-organizing mechanisms. Here, I review recent theoretical models with the aim of providing an integrative, physical picture of amoeboid migration.
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23
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Vafa F, Mahadevan L. Active Nematic Defects and Epithelial Morphogenesis. PHYSICAL REVIEW LETTERS 2022; 129:098102. [PMID: 36083666 DOI: 10.1103/physrevlett.129.098102] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2021] [Revised: 04/11/2022] [Accepted: 05/25/2022] [Indexed: 06/15/2023]
Abstract
Inspired by recent experiments that highlight the role of nematic defects in the morphogenesis of epithelial tissues, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture. Allowing the surface to evolve via relaxational dynamics leads to a theory linking nematic defect dynamics, cellular division rates, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects. In an ex-vivo setting of cultured murine neural progenitor cells, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting, we show that the defect configuration consisting of a bound +1 defect state, which is stabilized by activity, surrounded by two -1/2 defects can create a stationary ring configuration of tentacles, consistent with observations of a basal marine invertebrate Hydra.
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Affiliation(s)
- Farzan Vafa
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
- Center of Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts 02138, USA
| | - L Mahadevan
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
- Departments of Physics, and Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA
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24
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Mechanical actuators in microglia dynamics and function. Eur J Cell Biol 2022; 101:151247. [DOI: 10.1016/j.ejcb.2022.151247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2022] [Revised: 05/16/2022] [Accepted: 06/01/2022] [Indexed: 11/24/2022] Open
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25
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Computer modeling reveals modalities to actuate mutable, active matter. Nat Commun 2022; 13:2689. [PMID: 35577807 PMCID: PMC9110741 DOI: 10.1038/s41467-022-30445-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Accepted: 04/27/2022] [Indexed: 11/22/2022] Open
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26
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Hoffmann LA, Carenza LN, Eckert J, Giomi L. Theory of defect-mediated morphogenesis. SCIENCE ADVANCES 2022; 8:eabk2712. [PMID: 35427161 PMCID: PMC9012457 DOI: 10.1126/sciadv.abk2712] [Citation(s) in RCA: 25] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Growing experimental evidence indicates that topological defects could serve as organizing centers in the morphogenesis of tissues. Here, we provide a quantitative explanation for this phenomenon, rooted in the buckling theory of deformable active polar liquid crystals. Using a combination of linear stability analysis and computational fluid dynamics, we demonstrate that active layers, such as confined cell monolayers, are unstable to the formation of protrusions in the presence of disclinations. The instability originates from an interplay between the focusing of the elastic forces, mediated by defects, and the renormalization of the system's surface tension by the active flow. The posttransitional regime is also characterized by several complex morphodynamical processes, such as oscillatory deformations, droplet nucleation, and active turbulence. Our findings offer an explanation of recent observations on tissue morphogenesis and shed light on the dynamics of active surfaces in general.
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Affiliation(s)
- Ludwig A. Hoffmann
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA, Leiden, Netherlands
| | - Livio Nicola Carenza
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA, Leiden, Netherlands
| | - Julia Eckert
- Physics of Life Processes, Leiden Institute of Physics, Universiteit Leiden, P.O. Box 9506, 2300 RA, Leiden, Netherlands
| | - Luca Giomi
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA, Leiden, Netherlands
- Corresponding author.
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27
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Abstract
We present an efficient model for describing morphogenesis and the emergence of spatiotemporal structures in synthetic chemical cells. This work is motivated by an experimental setup used for testing Turing's theory of morphogenesis. The model developed is based on the general theory of chemically active droplets, which combines the classical theory of phase separation with reaction-diffusion systems. Through the 2D calculations, we find the six spatiotemporal structures predicted by Turing in 1952 and experimentally observed, in a 1D array of droplets. Moreover, under Turing instability, with a determined chemical wavelength, the system undergoes morphogenesis. This theoretical approach provides a useful tool for understanding the physical differentiation through the direct calculation of the osmotic pressure in each cell as the chemical reaction occurs.
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Affiliation(s)
- Leonardo Silva-Dias
- Chemistry Department, Federal University of São Carlos, São Carlos, São Paulo 13 565-905, Brazil
| | - Alejandro Lopez-Castillo
- Chemistry Department, Federal University of São Carlos, São Carlos, São Paulo 13 565-905, Brazil
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28
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Ghosh S, Gutti S, Chaudhuri D. Pattern formation, localized and running pulsation on active spherical membranes. SOFT MATTER 2021; 17:10614-10627. [PMID: 34605510 DOI: 10.1039/d1sm00937k] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Active force generation by an actin-myosin cortex coupled to a cell membrane allows the cell to deform, respond to the environment, and mediate cell motility and division. Several membrane-bound activator proteins move along it and couple to the membrane curvature. Besides, they can act as nucleating sites for the growth of filamentous actin. Actin polymerization can generate a local outward push on the membrane. Inward pull from the contractile actomyosin cortex can propagate along the membrane via actin filaments. We use coupled evolution of fields to perform linear stability analysis and numerical calculations. As activity overcomes the stabilizing factors such as surface tension and bending rigidity, the spherical membrane shows instability towards pattern formation, localized pulsation, and running pulsation between poles. We present our results in terms of phase diagrams and evolutions of the coupled fields. They have relevance for living cells and can be verified in experiments on artificial cell-like constructs.
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Affiliation(s)
- Subhadip Ghosh
- Department of Physics, Faculty of Science, University of Zagreb, Bijenička cesta 32, 10000 Zagreb, Croatia.
| | - Sashideep Gutti
- BITS Pilani Hyderabad Campus, Hyderabad 500078, Telengana, India.
| | - Debasish Chaudhuri
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India
- Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India.
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29
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Paci G, Mao Y. Forced into shape: Mechanical forces in Drosophila development and homeostasis. Semin Cell Dev Biol 2021; 120:160-170. [PMID: 34092509 PMCID: PMC8681862 DOI: 10.1016/j.semcdb.2021.05.026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Revised: 05/19/2021] [Accepted: 05/20/2021] [Indexed: 12/03/2022]
Abstract
Mechanical forces play a central role in shaping tissues during development and maintaining epithelial integrity in homeostasis. In this review, we discuss the roles of mechanical forces in Drosophila development and homeostasis, starting from the interplay of mechanics with cell growth and division. We then discuss several examples of morphogenetic processes where complex 3D structures are shaped by mechanical forces, followed by a closer look at patterning processes. We also review the role of forces in homeostatic processes, including cell elimination and wound healing. Finally, we look at the interplay of mechanics and developmental robustness and discuss open questions in the field, as well as novel approaches that will help tackle them in the future.
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Affiliation(s)
- Giulia Paci
- MRC Laboratory for Molecular Cell Biology, University College London, Gower Street, London WC1E 6BT, UK; Institute for the Physics of Living Systems, University College London, Gower Street, London WC1E 6BT, UK
| | - Yanlan Mao
- MRC Laboratory for Molecular Cell Biology, University College London, Gower Street, London WC1E 6BT, UK; Institute for the Physics of Living Systems, University College London, Gower Street, London WC1E 6BT, UK.
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30
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Singh A, Incardona P, Sbalzarini IF. A C++ expression system for partial differential equations enables generic simulations of biological hydrodynamics. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:117. [PMID: 34554349 PMCID: PMC8460516 DOI: 10.1140/epje/s10189-021-00121-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Accepted: 08/31/2021] [Indexed: 06/13/2023]
Abstract
We present a user-friendly and intuitive C++ expression system to implement numerical simulations of continuum biological hydrodynamics. The expression system allows writing simulation programs in near-mathematical notation and makes codes more readable, more compact, and less error-prone. It also cleanly separates the implementation of the partial differential equation model from the implementation of the numerical methods used to discretize it. This allows changing either of them with minimal changes to the source code. The presented expression system is implemented in the high-performance computing platform OpenFPM, supporting simulations that transparently parallelize on multi-processor computer systems. We demonstrate that our expression system makes it easier to write scalable codes for simulating biological hydrodynamics in space and time. We showcase the present framework in numerical simulations of active polar fluids, as well as in classic simulations of fluid dynamics from the incompressible Navier-Stokes equations to Stokes flow in a ball. The presented expression system accelerates scalable simulations of spatio-temporal models that encode the physics and material properties of tissues in order to algorithmically study morphogenesis.
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Affiliation(s)
- Abhinav Singh
- Faculty of Computer Science, Technische Universität Dresden, Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
- Center for Systems Biology Dresden, Dresden, Germany
| | - Pietro Incardona
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
- Center for Systems Biology Dresden, Dresden, Germany
| | - Ivo F Sbalzarini
- Faculty of Computer Science, Technische Universität Dresden, Dresden, Germany.
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.
- Center for Systems Biology Dresden, Dresden, Germany.
- Cluster of Excellence Physics of Life, TU Dresden, Dresden, Germany.
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31
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Chemically controlled pattern formation in self-oscillating elastic shells. Proc Natl Acad Sci U S A 2021; 118:2025717118. [PMID: 33649242 DOI: 10.1073/pnas.2025717118] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Patterns and morphology develop in living systems such as embryos in response to chemical signals. To understand and exploit the interplay of chemical reactions with mechanical transformations, chemomechanical polymer systems have been synthesized by attaching chemicals into hydrogels. In this work, we design autonomous responsive elastic shells that undergo morphological changes induced by chemical reactions. We couple the local mechanical response of the gel with the chemical processes on the shell. This causes swelling and deswelling of the gel, generating diverse morphological changes, including periodic oscillations. We further introduce a mechanical instability and observe buckling-unbuckling dynamics with a response time delay. Moreover, we investigate the mechanical feedback on the chemical reaction and demonstrate the dynamic patterns triggered by an initial deformation. We show the chemical characteristics that account for the shell morphology and discuss the future designs for autonomous responsive materials.
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32
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Al-Izzi SC, Morris RG. Active flows and deformable surfaces in development. Semin Cell Dev Biol 2021; 120:44-52. [PMID: 34266757 DOI: 10.1016/j.semcdb.2021.07.001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Revised: 06/30/2021] [Accepted: 07/01/2021] [Indexed: 12/15/2022]
Abstract
We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients- active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.
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Affiliation(s)
- Sami C Al-Izzi
- School of Physics and EMBL Australia Node in Single Molecule Science, School of Medical Sciences, University of New South Wales - Sydney, 2052, Australia
| | - Richard G Morris
- School of Physics and EMBL Australia Node in Single Molecule Science, School of Medical Sciences, University of New South Wales - Sydney, 2052, Australia.
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33
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Oriola D, Spagnoli FM. Engineering life in synthetic systems. Development 2021; 148:270849. [PMID: 34251450 DOI: 10.1242/dev.199497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2021] [Accepted: 06/01/2021] [Indexed: 11/20/2022]
Abstract
The second EMBO-EMBL Symposium 'Synthetic Morphogenesis: From Gene Circuits to Tissue Architecture' was held virtually in March 2021, with participants from all over the world joining from the comfort of their sofas to discuss synthetic morphogenesis at large. Leading scientists from a range of disciplines, including developmental biology, physics, chemistry and computer science, covered a gamut of topics from the principles of cell and tissue organization, patterning and gene regulatory networks, to synthetic approaches for exploring evolutionary and developmental biology principles. Here, we describe some of the high points.
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Affiliation(s)
- David Oriola
- EMBL Barcelona, Dr Aiguader 88, 08003 Barcelona, Spain
| | - Francesca M Spagnoli
- Centre for Stem Cells and Regenerative Medicine, King's College London, Guy's Hospital, Floor 28, Tower Wing, Great Maze Pond, London SE1 9RT, UK
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34
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Patil N, Bonneau S, Joubert F, Bitbol AF, Berthoumieux H. Mitochondrial cristae modeled as an out-of-equilibrium membrane driven by a proton field. Phys Rev E 2021; 102:022401. [PMID: 32942462 DOI: 10.1103/physreve.102.022401] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2019] [Accepted: 06/27/2020] [Indexed: 01/27/2023]
Abstract
As the places where most of the fuel of the cell, namely, ATP, is synthesized, mitochondria are crucial organelles in eukaryotic cells. The shape of the invaginations of the mitochondria inner membrane, known as a crista, has been identified as a signature of the energetic state of the organelle. However, the interplay between the rate of ATP synthesis and the crista shape remains unclear. In this work, we investigate the crista membrane deformations using a pH-dependent Helfrich model, maintained out of equilibrium by a diffusive flux of protons. This model gives rise to shape changes of a cylindrical invagination, in particular to the formation of necks between wider zones under variable, and especially oscillating, proton flux.
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Affiliation(s)
- Nirbhay Patil
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC, UMR 7600), Sorbonne Université, CNRS, F-75005 Paris, France.,Laboratoire Jean Perrin (UMR 8237), Institut de Biologie Paris-Seine, Sorbonne Université, CNRS, F-75005 Paris, France
| | - Stéphanie Bonneau
- Laboratoire Jean Perrin (UMR 8237), Institut de Biologie Paris-Seine, Sorbonne Université, CNRS, F-75005 Paris, France
| | - Fréderic Joubert
- Laboratoire Jean Perrin (UMR 8237), Institut de Biologie Paris-Seine, Sorbonne Université, CNRS, F-75005 Paris, France
| | - Anne-Florence Bitbol
- Laboratoire Jean Perrin (UMR 8237), Institut de Biologie Paris-Seine, Sorbonne Université, CNRS, F-75005 Paris, France.,School of Life Sciences, Institute of Bioengineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Hélène Berthoumieux
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC, UMR 7600), Sorbonne Université, CNRS, F-75005 Paris, France
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35
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Zakharov A, Dasbiswas K. Modeling mechanochemical pattern formation in elastic sheets of biological matter. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:82. [PMID: 34159454 DOI: 10.1140/epje/s10189-021-00086-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2021] [Accepted: 06/07/2021] [Indexed: 06/13/2023]
Abstract
Inspired by active shape morphing in developing tissues and biomaterials, we investigate two generic mechanochemical models where the deformations of a thin elastic sheet are driven by, and in turn affect, the concentration gradients of a chemical signal. We develop numerical methods to study the coupled elastic deformations and chemical concentration kinetics, and illustrate with computations the formation of different patterns depending on shell thickness, strength of mechanochemical coupling and diffusivity. In the first model, the sheet curvature governs the production of a contractility inhibitor and depending on the threshold in the coupling, qualitatively different patterns occur. The second model is based on the stress-dependent activity of myosin motors and demonstrates how the concentration distribution patterns of molecular motors are affected by the long-range deformations generated by them. Since the propagation of mechanical deformations is typically faster than chemical kinetics (of molecular motors or signaling agents that affect motors), we describe in detail and implement a numerical method based on separation of timescales to effectively simulate such systems. We show that mechanochemical coupling leads to long-range propagation of patterns in disparate systems through elastic instabilities even without the diffusive or advective transport of the chemicals.
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Affiliation(s)
- Andrei Zakharov
- Department of Physics, University of California, Merced, CA, 95343, USA
| | - Kinjal Dasbiswas
- Department of Physics, University of California, Merced, CA, 95343, USA.
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36
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Gritti N, Oriola D, Trivedi V. Rethinking embryology in vitro: A synergy between engineering, data science and theory. Dev Biol 2021; 474:48-61. [DOI: 10.1016/j.ydbio.2020.10.013] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2020] [Revised: 10/21/2020] [Accepted: 10/26/2020] [Indexed: 02/06/2023]
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37
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Zakharov A, Dasbiswas K. Mechanochemical induction of wrinkling morphogenesis on elastic shells. SOFT MATTER 2021; 17:4738-4750. [PMID: 33978668 DOI: 10.1039/d1sm00003a] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Morphogenetic dynamics of tissue sheets require coordinated cell shape changes regulated by global patterning of mechanical forces. Inspired by such biological phenomena, we propose a minimal mechanochemical model based on the notion that cell shape changes are induced by diffusible biomolecules that influence tissue contractility in a concentration-dependent manner - and whose concentration is in turn affected by the macroscopic tissue shape. We perform computational simulations of thin shell elastic dynamics to reveal propagating chemical and three-dimensional deformation patterns arising due to a sequence of buckling instabilities. Depending on the concentration threshold that actuates cell shape change, we find qualitatively different patterns. The mechanochemically coupled patterning dynamics are distinct from those driven by purely mechanical or purely chemical factors, and emerge even without diffusion. Using numerical simulations and theoretical arguments, we analyze the elastic instabilities that result from our model and provide simple scaling laws to identify wrinkling morphologies.
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Affiliation(s)
- Andrei Zakharov
- Department of Physics, University of California, Merced, Merced, CA 95343, USA.
| | - Kinjal Dasbiswas
- Department of Physics, University of California, Merced, Merced, CA 95343, USA.
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38
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Frey F, Idema T. More than just a barrier: using physical models to couple membrane shape to cell function. SOFT MATTER 2021; 17:3533-3549. [PMID: 33503097 DOI: 10.1039/d0sm01758b] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The correct execution of many cellular processes, such as division and motility, requires the cell to adopt a specific shape. Physically, these shapes are determined by the interplay of the plasma membrane and internal cellular driving factors. While the plasma membrane defines the boundary of the cell, processes inside the cell can result in the generation of forces that deform the membrane. These processes include protein binding, the assembly of protein superstructures, and the growth and contraction of cytoskeletal networks. Due to the complexity of the cell, relating observed membrane deformations back to internal processes is a challenging problem. Here, we review cell shape changes in endocytosis, cell adhesion, cell migration and cell division and discuss how by modeling membrane deformations we can investigate the inner working principles of the cell.
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Affiliation(s)
- Felix Frey
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.
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39
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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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40
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Kuan HS, Pönisch W, Jülicher F, Zaburdaev V. Continuum Theory of Active Phase Separation in Cellular Aggregates. PHYSICAL REVIEW LETTERS 2021; 126:018102. [PMID: 33480767 DOI: 10.1103/physrevlett.126.018102] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Accepted: 11/29/2020] [Indexed: 06/12/2023]
Abstract
Dense cellular aggregates are common in biology, ranging from bacterial biofilms to organoids, cell spheroids, and tumors. Their dynamics, driven by intercellular forces, is intrinsically out of equilibrium. Motivated by bacterial colonies as a model system, we present a continuum theory to study dense, active, cellular aggregates. We describe the process of aggregate formation as an active phase separation phenomenon, while the merging of aggregates is rationalized as a coalescence of viscoelastic droplets where the key timescales are linked to the turnover of the active force. Our theory provides a general framework for studying the rheology and nonequilibrium dynamics of dense cellular aggregates.
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Affiliation(s)
- Hui-Shun Kuan
- Department of Biology, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Max Planck Zentrum für Physik und Medizin, 91058 Erlangen, Germany
| | - Wolfram Pönisch
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- MRC Laboratory for Molecular Cell Biology, University College London, WC1E 6BT London, United Kingdom
- Department of Physiology, Development and Neuroscience, University of Cambridge, CB2 3DY Cambridge, United Kingdom
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Center for Systems Biology Dresden, 01307 Dresden, Germany
- Cluster of Excellence Physics of Life, Technische Universität Dresden, 01307 Dresden, Germany
| | - Vasily Zaburdaev
- Department of Biology, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Max Planck Zentrum für Physik und Medizin, 91058 Erlangen, Germany
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41
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DiNapoli KT, Robinson DN, Iglesias PA. Tools for computational analysis of moving boundary problems in cellular mechanobiology. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2020; 13:e1514. [PMID: 33305503 DOI: 10.1002/wsbm.1514] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Revised: 10/08/2020] [Accepted: 10/20/2020] [Indexed: 12/29/2022]
Abstract
A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.
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Affiliation(s)
- Kathleen T DiNapoli
- Department of Cell Biology, Johns Hopkins School of Medicine, Baltimore, Maryland, USA
| | - Douglas N Robinson
- Department of Cell Biology, Johns Hopkins School of Medicine, Baltimore, Maryland, USA
| | - Pablo A Iglesias
- Department of Cell Biology, Johns Hopkins School of Medicine, Baltimore, Maryland, USA
- Department of Electrical & Computer Engineering, Johns Hopkins University, Baltimore, Maryland, USA
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42
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Martínez-Calvo A, Sevilla A. Universal Thinning of Liquid Filaments under Dominant Surface Forces. PHYSICAL REVIEW LETTERS 2020; 125:114502. [PMID: 32975989 DOI: 10.1103/physrevlett.125.114502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2019] [Accepted: 08/19/2020] [Indexed: 06/11/2023]
Abstract
Theory and numerical simulations of the thinning of liquid threads at high superficial concentration of surfactants suggest the existence of an asymptotic regime where surface tension balances surface viscous stresses, leading to an exponential thinning with an e-fold time F(Θ)(3μ_{s}+κ_{s})/σ, where μ_{s} and κ_{s} are the surface shear and dilatational viscosity coefficients, σ is the interfacial tension, Θ=κ_{s}/μ_{s}, and F(Θ) is a universal function. The potential use of this phenomenon to measure the surface viscosity coefficients is discussed.
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Affiliation(s)
- A Martínez-Calvo
- Grupo de Mecánica de Fluidos, Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid. Avda. de la Universidad 30, 28911 Leganés, Madrid, Spain
| | - A Sevilla
- Grupo de Mecánica de Fluidos, Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid. Avda. de la Universidad 30, 28911 Leganés, Madrid, Spain
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43
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Pimpale LG, Middelkoop TC, Mietke A, Grill SW. Cell lineage-dependent chiral actomyosin flows drive cellular rearrangements in early Caenorhabditis elegans development. eLife 2020; 9:54930. [PMID: 32644039 PMCID: PMC7394549 DOI: 10.7554/elife.54930] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Accepted: 07/05/2020] [Indexed: 12/15/2022] Open
Abstract
Proper positioning of cells is essential for many aspects of development. Daughter cell positions can be specified via orienting the cell division axis during cytokinesis. Rotatory actomyosin flows during division have been implied in specifying and reorienting the cell division axis, but how general such reorientation events are, and how they are controlled, remains unclear. We followed the first nine divisions of Caenorhabditis elegans embryo development and demonstrate that chiral counter-rotating flows arise systematically in early AB lineage, but not in early P/EMS lineage cell divisions. Combining our experiments with thin film active chiral fluid theory we identify a mechanism by which chiral counter-rotating actomyosin flows arise in the AB lineage only, and show that they drive lineage-specific spindle skew and cell reorientation events. In conclusion, our work sheds light on the physical processes that underlie chiral morphogenesis in early development.
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Affiliation(s)
- Lokesh G Pimpale
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.,Biotechnology Center, TU Dresden, Dresden, Germany.,Cluster of Excellence Physics of Life, TU Dresden, Dresden, Germany
| | - Teije C Middelkoop
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.,Biotechnology Center, TU Dresden, Dresden, Germany.,Cluster of Excellence Physics of Life, TU Dresden, Dresden, Germany
| | - Alexander Mietke
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.,Max Planck Institute for the Physics of Complex Systems, Dresden, Germany.,Chair of Scientific Computing for Systems Biology, Faculty of Computer Science, TU Dresden, Dresden, Germany.,Center for Systems Biology Dresden, Dresden, Germany.,Department of Mathematics, Massachusetts Institute of Technology, Cambridge, United States
| | - Stephan W Grill
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.,Biotechnology Center, TU Dresden, Dresden, Germany.,Cluster of Excellence Physics of Life, TU Dresden, Dresden, Germany
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44
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Loewe B, Serafin F, Shankar S, Bowick MJ, Marchetti MC. Shape and size changes of adherent elastic epithelia. SOFT MATTER 2020; 16:5282-5293. [PMID: 32462170 DOI: 10.1039/d0sm00239a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Epithelial tissues play a fundamental role in various morphogenetic events during development and early embryogenesis. Although epithelial monolayers are often modeled as two-dimensional (2D) elastic surfaces, they distinguish themselves from conventional thin elastic plates in three important ways- the presence of an apical-basal polarity, spatial variability of cellular thickness, and their nonequilibrium active nature. Here, we develop a minimal continuum model of a planar epithelial tissue as an active elastic material that incorporates all these features. We start from a full three-dimensional (3D) description of the tissue and derive an effective 2D model that captures, through the curvature of the apical surface, both the apical-basal asymmetry and the spatial geometry of the tissue. Crucially, variations of active stresses across the apical-basal axis lead to active torques that can drive curvature transitions. By identifying four distinct sources of activity, we find that bulk active stresses arising from actomyosin contractility and growth compete with boundary active tensions due to localized actomyosin cables and lamellipodial activity to generate the various states spanning the morphospace of a planar epithelium. Our treatment hence unifies 3D shape deformations through the coupled mechanics of apical curvature change and in-plane expansion/contraction of substrate-adhered tissues. Finally, we discuss the implications of our results for some biologically relevant processes such as tissue folding at the onset of lumen formation.
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Affiliation(s)
- Benjamin Loewe
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA.
| | - Francesco Serafin
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.
| | - Suraj Shankar
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
| | - Mark J Bowick
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - M Cristina Marchetti
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA.
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45
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Miller PW, Dunkel J. Gait-optimized locomotion of wave-driven soft sheets. SOFT MATTER 2020; 16:3991-3999. [PMID: 32255142 DOI: 10.1039/c9sm02103e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Inspired by the robust locomotion of limbless animals in a range of environments, the development of soft robots capable of moving by localized swelling, bending, and other forms of differential growth has become a target for soft matter research over the last decade. Engineered soft robots exhibit a wide range of morphologies, but theoretical investigations of soft robot locomotion have largely been limited to slender bodied or one-dimensional examples. Here, we demonstrate design principles regarding the locomotion of two-dimensional soft materials driven by morphoelastic waves along a dry substrate. Focusing on the essential common aspects of many natural and man-made soft actuators, a continuum model is developed which links the deformation of a thin elastic sheet to surface-bound excitation waves. Through a combination of analytic and numerical methods, we investigate the relationship between induced active stress and self-propulsion performance of self-propelling sheets driven by FitzHugh-Nagumo type chemical waves. Examining the role of both sheet geometry and terrain geography on locomotion, our results can provide guidance for the design of more efficient soft crawling devices.
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Affiliation(s)
- Pearson W Miller
- Department of Mathematics, 77 Massachusetts Avenue, Cambridge, MA, USA.
| | - Jörn Dunkel
- Department of Mathematics, 77 Massachusetts Avenue, Cambridge, MA, USA.
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46
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Mokbel M, Hosseini K, Aland S, Fischer-Friedrich E. The Poisson Ratio of the Cellular Actin Cortex Is Frequency Dependent. Biophys J 2020; 118:1968-1976. [PMID: 32208141 PMCID: PMC7175418 DOI: 10.1016/j.bpj.2020.03.002] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2019] [Revised: 02/06/2020] [Accepted: 03/02/2020] [Indexed: 10/24/2022] Open
Abstract
Cell shape changes are vital for many physiological processes such as cell proliferation, cell migration, and morphogenesis. They emerge from an orchestrated interplay of active cellular force generation and passive cellular force response, both crucially influenced by the actin cytoskeleton. To model cellular force response and deformation, cell mechanical models commonly describe the actin cytoskeleton as a contractile isotropic incompressible material. However, in particular at slow frequencies, there is no compelling reason to assume incompressibility because the water content of the cytoskeleton may change. Here, we challenge the assumption of incompressibility by comparing computer simulations of an isotropic actin cortex with tunable Poisson ratio to measured cellular force response. Comparing simulation results and experimental data, we determine the Poisson ratio of the cortex in a frequency-dependent manner. We find that the Poisson ratio of the cortex decreases in the measured frequency regime analogous to trends reported for the Poisson ratio of glassy materials. Our results therefore indicate that actin cortex compression or dilation is possible in response to acting forces at sufficiently fast timescales. This finding has important implications for the parameterization in active gel theories that describe actin cytoskeletal dynamics.
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Affiliation(s)
- Marcel Mokbel
- Faculty of Informatics/Mathematics, Hochschule für Technik und Wirtschaft, Dresden, Germany
| | - Kamran Hosseini
- Cluster of Excellence Physics of Life, Technische Universität Dresden, Dresden, Germany; Biotechnology Center, Technische Universität Dresden, Dresden, Germany
| | - Sebastian Aland
- Faculty of Informatics/Mathematics, Hochschule für Technik und Wirtschaft, Dresden, Germany.
| | - Elisabeth Fischer-Friedrich
- Cluster of Excellence Physics of Life, Technische Universität Dresden, Dresden, Germany; Biotechnology Center, Technische Universität Dresden, Dresden, Germany.
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Metselaar L, Yeomans JM, Doostmohammadi A. Topology and Morphology of Self-Deforming Active Shells. PHYSICAL REVIEW LETTERS 2019; 123:208001. [PMID: 31809098 DOI: 10.1103/physrevlett.123.208001] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2019] [Indexed: 06/10/2023]
Abstract
We present a generic framework for modeling three-dimensional deformable shells of active matter that captures the orientational dynamics of the active particles and hydrodynamic interactions on the shell and with the surrounding environment. We find that the cross talk between the self-induced flows of active particles and dynamic reshaping of the shell can result in conformations that are tunable by varying the form and magnitude of active stresses. We further demonstrate and explain how self-induced topological defects in the active layer can direct the morphodynamics of the shell. These findings are relevant to understanding morphological changes during organ development and the design of bioinspired materials that are capable of self-organization.
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Affiliation(s)
- Luuk Metselaar
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Julia M Yeomans
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Amin Doostmohammadi
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark
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48
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Mietke A, Jemseena V, Kumar KV, Sbalzarini IF, Jülicher F. Minimal Model of Cellular Symmetry Breaking. PHYSICAL REVIEW LETTERS 2019; 123:188101. [PMID: 31763902 DOI: 10.1103/physrevlett.123.188101] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2019] [Indexed: 06/10/2023]
Abstract
The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry-breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the self-organization of the cell cortex that is based on a hydrodynamic theory of curved active surfaces. Active stresses on this surface are regulated by a diffusing molecular species. We show that coupling of the active surface to a passive bulk fluid enables spontaneous polarization and the formation of a contractile ring on the surface via mechanochemical instabilities. We discuss the role of external fields in guiding such pattern formation. Our work reveals that key features of cellular symmetry breaking and cell division can emerge in a minimal model via general dynamic instabilities.
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Affiliation(s)
- Alexander Mietke
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Chair of Scientific Computing for Systems Biology, Faculty of Computer Science, TU Dresden, 01187 Dresden, Germany
- Center for Systems Biology Dresden, 01307 Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, 01307 Dresden, Germany
| | - V Jemseena
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, 560 089 Bengaluru, India
| | - K Vijay Kumar
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, 560 089 Bengaluru, India
| | - Ivo F Sbalzarini
- Chair of Scientific Computing for Systems Biology, Faculty of Computer Science, TU Dresden, 01187 Dresden, Germany
- Center for Systems Biology Dresden, 01307 Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, 01307 Dresden, Germany
- Cluster of Excellence Physics of Life, TU Dresden, 01307 Dresden, Germany
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Center for Systems Biology Dresden, 01307 Dresden, Germany
- Cluster of Excellence Physics of Life, TU Dresden, 01307 Dresden, Germany
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49
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Probing the Functional Role of Physical Motion in Development. Dev Cell 2019; 51:135-144. [PMID: 31639366 DOI: 10.1016/j.devcel.2019.10.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Revised: 08/15/2019] [Accepted: 09/30/2019] [Indexed: 01/16/2023]
Abstract
Spatiotemporal organization during development has frequently been proposed to be explainable by reaction-transport models, where biochemical reactions couple to physical motion. However, whereas genetic tools allow causality of molecular players to be dissected via perturbation experiments, the functional role of physical transport processes, such as diffusion and cytoplasmic streaming, frequently remains untestable. This Perspective explores the challenges of validating reaction-transport hypotheses and highlights new opportunities provided by perturbation approaches that specifically target physical transport mechanisms. Using these methods, experimental physics may begin to catch up with molecular biology and find ways to test roles of diffusion and flows in development.
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50
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Li Y, Ten Wolde PR. Shape Transformations of Vesicles Induced by Swim Pressure. PHYSICAL REVIEW LETTERS 2019; 123:148003. [PMID: 31702175 DOI: 10.1103/physrevlett.123.148003] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2019] [Indexed: 06/10/2023]
Abstract
While the behavior of vesicles in thermodynamic equilibrium has been studied extensively, how active forces control vesicle shape transformations is not understood. Here, we combine theory and simulations to study the shape behavior of vesicles containing active Brownian particles. We show that the combination of active forces, dimensionality, and membrane bending free energy creates a plethora of novel phase transitions. At low swim pressure, the vesicle exhibits a discontinuous transition from a spherical to a prolate shape, which has no counterpart in two dimensions. At high swim pressure it exhibits stochastic spatiotemporal oscillations. Our work helps researchers to understand and control the shape dynamics of membranes in active-matter systems.
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Affiliation(s)
- Yao Li
- AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
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