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Craig EM, Oprea F, Alam S, Grodsky A, Miller KE. A simple active fluid model unites cytokinesis, cell crawling, and axonal outgrowth. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.05.22.595337. [PMID: 38826455 PMCID: PMC11142150 DOI: 10.1101/2024.05.22.595337] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2024]
Abstract
Axonal outgrowth, cell crawling, and cytokinesis utilize actomyosin, microtubule-based motors, cytoskeletal dynamics, and substrate adhesions to produce traction forces and bulk cellular motion. While it has long been appreciated that growth cones resemble crawling cells and that the mechanisms that drive cytokinesis help power cell crawling, they are typically viewed as unique processes. To better understand the relationship between these modes of motility, here, we developed a unified active fluid model of cytokinesis, amoeboid migration, mesenchymal migration, neuronal migration, and axonal outgrowth in terms of cytoskeletal flow, adhesions, viscosity, and force generation. Using numerical modeling, we fit subcellular velocity profiles of the motions of cytoskeletal structures and docked organelles from previously published studies to infer underlying patterns of force generation and adhesion. Our results indicate that, during cytokinesis, there is a primary converge zone at the cleavage furrow that drives flow towards it; adhesions are symmetric across the cell, and as a result, cells are stationary. In mesenchymal, amoeboid, and neuronal migration, the site of the converge zone shifts, and differences in adhesion between the front and back of the cell drive crawling. During neuronal migration and axonal outgrowth, the primary convergence zone lies within the growth cone, which drives actin retrograde flow in the P-domain and bulk anterograde flow of the axonal shaft. They differ in that during neuronal migration, the cell body is weakly attached to the substrate and thus moves forward at the same velocity as the axon. In contrast, during axonal outgrowth, the cell body strongly adheres to the substrate and remains stationary, resulting in a decrease in flow velocity away from the growth cone. The simplicity with which cytokinesis, cell crawling, and axonal outgrowth can be modeled by varying coefficients in a simple model suggests a deep connection between them.
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Affiliation(s)
- Erin M Craig
- Central Washington University, Department of Physics, 400 E. University Way, Ellensburg, WA 98926-7422, USA
| | - Francesca Oprea
- Department of Integrative Biology, Michigan State University, East Lansing, MI 48824, USA
| | - Sajid Alam
- Department of Integrative Biology, Michigan State University, East Lansing, MI 48824, USA
| | - Ania Grodsky
- Department of Integrative Biology, Michigan State University, East Lansing, MI 48824, USA
| | - Kyle E Miller
- Department of Integrative Biology, Michigan State University, East Lansing, MI 48824, USA
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2
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Yeh YT, Del Álamo JC, Caffrey CR. Biomechanics of parasite migration within hosts. Trends Parasitol 2024; 40:164-175. [PMID: 38172015 DOI: 10.1016/j.pt.2023.12.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2023] [Revised: 11/30/2023] [Accepted: 12/01/2023] [Indexed: 01/05/2024]
Abstract
The dissemination of protozoan and metazoan parasites through host tissues is hindered by cellular barriers, dense extracellular matrices, and fluid forces in the bloodstream. To overcome these diverse biophysical impediments, parasites implement versatile migratory strategies. Parasite-exerted mechanical forces and upregulation of the host's cellular contractile machinery are the motors for these strategies, and these are comparably better characterized for protozoa than for helminths. Using the examples of the protozoans, Toxoplasma gondii and Plasmodium, and the metazoan, Schistosoma mansoni, we highlight how quantitative tools such as traction force and reflection interference contrast microscopies have improved our understanding of how parasites alter host mechanobiology to promote their migration.
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Affiliation(s)
- Yi-Ting Yeh
- Department of Mechanical Engineering, University of Washington, Seattle, WA 98109, USA; Center for Cardiovascular Biology, University of Washington, Seattle, WA 98109, USA.
| | - Juan C Del Álamo
- Department of Mechanical Engineering, University of Washington, Seattle, WA 98109, USA; Center for Cardiovascular Biology, University of Washington, Seattle, WA 98109, USA; Division of Cardiology, University of Washington, Seattle, WA 98109, USA; Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 93093, USA
| | - Conor R Caffrey
- Center for Discovery and Innovation in Parasitic Diseases, Skaggs School of Pharmacy and Pharmaceutical Sciences, 9500 Gilman Drive, MC0657, University of California San Diego, La Jolla, CA 92093, USA
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3
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Mittal N, Michels EB, Massey AE, Qiu Y, Royer-Weeden SP, Smith BR, Cartagena-Rivera AX, Han SJ. Myosin-independent stiffness sensing by fibroblasts is regulated by the viscoelasticity of flowing actin. COMMUNICATIONS MATERIALS 2024; 5:6. [PMID: 38741699 PMCID: PMC11090405 DOI: 10.1038/s43246-024-00444-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Accepted: 01/02/2024] [Indexed: 05/16/2024]
Abstract
The stiffness of the extracellular matrix induces differential tension within integrin-based adhesions, triggering differential mechanoresponses. However, it has been unclear if the stiffness-dependent differential tension is induced solely by myosin activity. Here, we report that in the absence of myosin contractility, 3T3 fibroblasts still transmit stiffness-dependent differential levels of traction. This myosin-independent differential traction is regulated by polymerizing actin assisted by actin nucleators Arp2/3 and formin where formin has a stronger contribution than Arp2/3 to both traction and actin flow. Intriguingly, despite only slight changes in F-actin flow speed observed in cells with the combined inhibition of Arp2/3 and myosin compared to cells with sole myosin inhibition, they show a 4-times reduction in traction than cells with myosin-only inhibition. Our analyses indicate that traditional models based on rigid F-actin are inadequate for capturing such dramatic force reduction with similar actin flow. Instead, incorporating the F-actin network's viscoelastic properties is crucial. Our new model including the F-actin viscoelasticity reveals that Arp2/3 and formin enhance stiffness sensitivity by mechanically reinforcing the F-actin network, thereby facilitating more effective transmission of flow-induced forces. This model is validated by cell stiffness measurement with atomic force microscopy and experimental observation of model-predicted stiffness-dependent actin flow fluctuation.
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Affiliation(s)
- Nikhil Mittal
- Department of Biomedical Engineering, Michigan Technological University, Houghton, MI, USA
- Health Research Institute, Michigan Technological University, Houghton, MI, USA
| | - Etienne B. Michels
- Department of Biomedical Engineering, Michigan Technological University, Houghton, MI, USA
| | - Andrew E. Massey
- Section on Mechanobiology, National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health, Bethesda, MD, USA
| | - Yunxiu Qiu
- Department of Biomedical Engineering, Michigan State University, Lansing, MI, USA
| | - Shaina P. Royer-Weeden
- Department of Biomedical Engineering, Michigan Technological University, Houghton, MI, USA
| | - Bryan R. Smith
- Department of Biomedical Engineering, Michigan State University, Lansing, MI, USA
| | - Alexander X. Cartagena-Rivera
- Section on Mechanobiology, National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health, Bethesda, MD, USA
| | - Sangyoon J. Han
- Department of Biomedical Engineering, Michigan Technological University, Houghton, MI, USA
- Health Research Institute, Michigan Technological University, Houghton, MI, USA
- Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, Houghton, MI, USA
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4
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Kechagia Z, Sáez P, Gómez-González M, Canales B, Viswanadha S, Zamarbide M, Andreu I, Koorman T, Beedle AEM, Elosegui-Artola A, Derksen PWB, Trepat X, Arroyo M, Roca-Cusachs P. The laminin-keratin link shields the nucleus from mechanical deformation and signalling. NATURE MATERIALS 2023; 22:1409-1420. [PMID: 37709930 PMCID: PMC10627833 DOI: 10.1038/s41563-023-01657-3] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 07/31/2023] [Indexed: 09/16/2023]
Abstract
The mechanical properties of the extracellular matrix dictate tissue behaviour. In epithelial tissues, laminin is a very abundant extracellular matrix component and a key supporting element. Here we show that laminin hinders the mechanoresponses of breast epithelial cells by shielding the nucleus from mechanical deformation. Coating substrates with laminin-111-unlike fibronectin or collagen I-impairs cell response to substrate rigidity and YAP nuclear localization. Blocking the laminin-specific integrin β4 increases nuclear YAP ratios in a rigidity-dependent manner without affecting the cell forces or focal adhesions. By combining mechanical perturbations and mathematical modelling, we show that β4 integrins establish a mechanical linkage between the substrate and keratin cytoskeleton, which stiffens the network and shields the nucleus from actomyosin-mediated mechanical deformation. In turn, this affects the nuclear YAP mechanoresponses, chromatin methylation and cell invasion in three dimensions. Our results demonstrate a mechanism by which tissues can regulate their sensitivity to mechanical signals.
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Affiliation(s)
- Zanetta Kechagia
- Institute for Bioengineering of Catalonia (IBEC), Barcelona Institute of Science and Technology (BIST), Barcelona, Spain.
| | - Pablo Sáez
- Laboratori de Càlcul Numèric (LàCaN), Universitat Politècnica de Catalunya, Barcelona, Spain
- Institut de Matemátiques de la UPC-BarcelonaTech (IMTech), Barcelona, Spain
| | - Manuel Gómez-González
- Institute for Bioengineering of Catalonia (IBEC), Barcelona Institute of Science and Technology (BIST), Barcelona, Spain
| | - Brenda Canales
- Cell and Tissue Mechanobiology Laboratory, The Francis Crick Institute, London, UK
- Department of Physics, King's College London, London, UK
| | - Srivatsava Viswanadha
- Institute for Bioengineering of Catalonia (IBEC), Barcelona Institute of Science and Technology (BIST), Barcelona, Spain
| | | | - Ion Andreu
- Institute for Bioengineering of Catalonia (IBEC), Barcelona Institute of Science and Technology (BIST), Barcelona, Spain
- Instituto Biofisika (UPV/EHU, CSIC), University of the Basque Country, Leioa, Spain
- Ikerbasque, Basque Foundation for Science, Bilbao, Spain
| | - Thijs Koorman
- Department of Pathology, University Medical Center Utrecht, Utrecht, The Netherlands
| | - Amy E M Beedle
- Institute for Bioengineering of Catalonia (IBEC), Barcelona Institute of Science and Technology (BIST), Barcelona, Spain
- Department of Physics, King's College London, London, UK
| | - Alberto Elosegui-Artola
- Cell and Tissue Mechanobiology Laboratory, The Francis Crick Institute, London, UK
- Department of Physics, King's College London, London, UK
| | - Patrick W B Derksen
- Department of Pathology, University Medical Center Utrecht, Utrecht, The Netherlands
| | - Xavier Trepat
- Institute for Bioengineering of Catalonia (IBEC), Barcelona Institute of Science and Technology (BIST), Barcelona, Spain
- University of Barcelona, Barcelona, Spain
- Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Barcelona, Spain
- Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain
| | - Marino Arroyo
- Institute for Bioengineering of Catalonia (IBEC), Barcelona Institute of Science and Technology (BIST), Barcelona, Spain
- Laboratori de Càlcul Numèric (LàCaN), Universitat Politècnica de Catalunya, Barcelona, Spain
- Institut de Matemátiques de la UPC-BarcelonaTech (IMTech), Barcelona, Spain
- Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, Spain
| | - Pere Roca-Cusachs
- Institute for Bioengineering of Catalonia (IBEC), Barcelona Institute of Science and Technology (BIST), Barcelona, Spain.
- University of Barcelona, Barcelona, Spain.
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5
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Giverso C, Jankowiak G, Preziosi L, Schmeiser C. The Influence of Nucleus Mechanics in Modelling Adhesion-independent Cell Migration in Structured and Confined Environments. Bull Math Biol 2023; 85:88. [PMID: 37626216 PMCID: PMC10457269 DOI: 10.1007/s11538-023-01187-8] [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: 10/08/2022] [Accepted: 07/17/2023] [Indexed: 08/27/2023]
Abstract
Recent biological experiments (Lämmermann et al. in Nature 453(7191):51-55, 2008; Reversat et al. in Nature 7813:582-585, 2020; Balzer et al. in ASEB J Off Publ Fed Am Soc Exp Biol 26(10):4045-4056, 2012) have shown that certain types of cells are able to move in structured and confined environments even without the activation of focal adhesion. Focusing on this particular phenomenon and based on previous works (Jankowiak et al. in Math Models Methods Appl Sci 30(03):513-537, 2020), we derive a novel two-dimensional mechanical model, which relies on the following physical ingredients: the asymmetrical renewal of the actin cortex supporting the membrane, resulting in a backward flow of material; the mechanical description of the nuclear membrane and the inner nuclear material; the microtubule network guiding nucleus location; the contact interactions between the cell and the external environment. The resulting fourth order system of partial differential equations is then solved numerically to conduct a study of the qualitative effects of the model parameters, mainly those governing the mechanical properties of the nucleus and the geometry of the confining structure. Coherently with biological observations, we find that cells characterized by a stiff nucleus are unable to migrate in channels that can be crossed by cells with a softer nucleus. Regarding the geometry, cell velocity and ability to migrate are influenced by the width of the channel and the wavelength of the external structure. Even though still preliminary, these results may be potentially useful in determining the physical limit of cell migration in confined environments and in designing scaffolds for tissue engineering.
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Affiliation(s)
- Chiara Giverso
- Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Gaspard Jankowiak
- Department of Mathematics and Statistics, University of Konstanz, 78457 Constance, Germany
| | - Luigi Preziosi
- Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Christian Schmeiser
- Faculty of Mathematics, University of Vienna, Oskar-Morgenstern Platz 1, 1090 Wien, Austria
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6
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Sáez P, Venturini C. Positive, negative and controlled durotaxis. SOFT MATTER 2023; 19:2993-3001. [PMID: 37016959 DOI: 10.1039/d2sm01326f] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Cell migration is a physical process central to life. Among others, it regulates embryogenesis, tissue regeneration, and tumor growth. Therefore, understanding and controlling cell migration represent fundamental challenges in science. Specifically, the ability of cells to follow stiffness gradients, known as durotaxis, is ubiquitous across most cell types. Even so, certain cells follow positive stiffness gradients while others move along negative gradients. How the physical mechanisms involved in cell migration work to enable a wide range of durotactic responses is still poorly understood. Here, we provide a mechanistic rationale for durotaxis by integrating stochastic clutch models for cell adhesion with an active gel theory of cell migration. We show that positive and negative durotaxis found across cell types are explained by asymmetries in the cell adhesion dynamics. We rationalize durotaxis by asymmetric mechanotransduction in the cell adhesion behavior that further polarizes the intracellular retrograde flow and the protruding velocity at the cell membrane. Our theoretical framework confirms previous experimental observations and explains positive and negative durotaxis. Moreover, we show how durotaxis can be engineered to manipulate cell migration, which has important implications in biology, medicine, and bioengineering.
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Affiliation(s)
- P Sáez
- Laboratori de Càlcul Numèric (LaCaN), Universitat Politècnica de Catalunya, Barcelona, Spain.
- E.T.S. de Ingeniería de Caminos, Universitat Politècnica de Catalunya, Barcelona, Spain
- Institut de Matemàtiques de la UPC-BarcelonaTech (IMTech), Universitat Politècnica de Catalunya, Barcelona, Spain
| | - C Venturini
- Laboratori de Càlcul Numèric (LaCaN), Universitat Politècnica de Catalunya, Barcelona, Spain.
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7
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Stolarska MA, Rammohan AR. On the significance of membrane unfolding in mechanosensitive cell spreading: Its individual and synergistic effects. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:2408-2438. [PMID: 36899540 DOI: 10.3934/mbe.2023113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Mechanosensitivity of cell spread area to substrate stiffness has been established both through experiments and different types of mathematical models of varying complexity including both the mechanics and biochemical reactions in the cell. What has not been addressed in previous mathematical models is the role of cell membrane dynamics on cell spreading, and an investigation of this issue is the goal of this work. We start with a simple mechanical model of cell spreading on a deformable substrate and progressively layer mechanisms to account for the traction dependent growth of focal adhesions, focal adhesion induced actin polymerization, membrane unfolding/exocytosis and contractility. This layering approach is intended to progressively help in understanding the role each mechanism plays in reproducing experimentally observed cell spread areas. To model membrane unfolding we introduce a novel approach based on defining an active rate of membrane deformation that is dependent on membrane tension. Our modeling approach allows us to show that tension-dependent membrane unfolding plays a critical role in achieving the large cell spread areas experimentally observed on stiff substrates. We also demonstrate that coupling between membrane unfolding and focal adhesion induced polymerization works synergistically to further enhance cell spread area sensitivity to substrate stiffness. This enhancement has to do with the fact that the peripheral velocity of spreading cells is associated with contributions from the different mechanisms by either enhancing the polymerization velocity at the leading edge or slowing down of the retrograde flow of actin within the cell. The temporal evolution of this balance in the model corresponds to the three-phase behavior observed experimentally during spreading. In the initial phase membrane unfolding is found to be particularly important.
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Affiliation(s)
- Magdalena A Stolarska
- Department of Mathematics, 2115 Summit Ave., University of St. Thomas, St. Paul, MN 55105, USA
| | - Aravind R Rammohan
- Corning Life Sciences, Corning Inc., 836 North St, Tewksbury, MA 01876, USA
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8
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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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9
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Stepien TL, Secomb TW. Spreading mechanics and differentiation of astrocytes during retinal development. J Theor Biol 2022; 549:111208. [DOI: 10.1016/j.jtbi.2022.111208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Revised: 05/27/2022] [Accepted: 06/21/2022] [Indexed: 11/30/2022]
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10
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Chelly H, Recho P. Cell motility as an energy minimization process. Phys Rev E 2022; 105:064401. [PMID: 35854577 DOI: 10.1103/physreve.105.064401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Accepted: 05/12/2022] [Indexed: 06/15/2023]
Abstract
The dynamics of active matter driven by interacting molecular motors has a nonpotential structure at the local scale. However, we show that there exists a quasipotential effectively describing the collective self-organization of the motors propelling a cell at a continuum active gel level. Such a model allows us to understand cell motility as an active phase transition problem between the static and motile steady-state configurations that minimize the quasipotential. In particular, both configurations can coexist in a metastable fashion and a small stochastic disorder in the gel is sufficient to trigger an intermittent cell dynamics where either static or motile phases are more probable, depending on which state is the global minimum of the quasipotential.
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Affiliation(s)
- H Chelly
- Univ. Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
| | - P Recho
- Univ. Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
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11
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Zhou L, Feng S, Li L, Lü S, Zhang Y, Long M. Two Complementary Signaling Pathways Depict Eukaryotic Chemotaxis: A Mechanochemical Coupling Model. Front Cell Dev Biol 2021; 9:786254. [PMID: 34869388 PMCID: PMC8635958 DOI: 10.3389/fcell.2021.786254] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Accepted: 10/21/2021] [Indexed: 01/16/2023] Open
Abstract
Many eukaryotic cells, including neutrophils and Dictyostelium cells, are able to undergo correlated random migration in the absence of directional cues while reacting to shallow gradients of chemoattractants with exquisite precision. Although progress has been made with regard to molecular identities, it remains elusive how molecular mechanics are integrated with cell mechanics to initiate and manipulate cell motility. Here, we propose a two dimensional (2D) cell migration model wherein a multilayered dynamic seesaw mechanism is accompanied by a mechanical strain-based inhibition mechanism. In biology, these two mechanisms can be mapped onto the biochemical feedback between phosphoinositides (PIs) and Rho GTPase and the mechanical interplay between filamin A (FLNa) and FilGAP. Cell migration and the accompanying morphological changes are demonstrated in numerical simulations using a particle-spring model, and the diffusion in the cell membrane are simulations using a one dimensional (1D) finite differences method (FDM). The fine balance established between endogenous signaling and a mechanically governed inactivation scheme ensures the endogenous cycle of self-organizing pseudopods, accounting for the correlated random migration. Furthermore, this model cell manifests directional and adaptable responses to shallow graded signaling, depending on the overwhelming effect of the graded stimuli guidance on strain-based inhibition. Finally, the model cell becomes trapped within an obstacle-ridden spatial region, manifesting a shuttle run for local explorations and can chemotactically “escape”, illustrating again the balance required in the complementary signaling pathways.
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Affiliation(s)
- Lüwen Zhou
- Smart Materials and Advanced Structure Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo Zhejiang, China.,Key Laboratory of Microgravity (National Microgravity Laboratory), and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Center for Biomechanics and Bioengineering, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China
| | - Shiliang Feng
- Smart Materials and Advanced Structure Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo Zhejiang, China.,Key Laboratory of Microgravity (National Microgravity Laboratory), and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Center for Biomechanics and Bioengineering, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China
| | - Long Li
- State Key Laboratory of Nonlinear Mechanics (LNM) and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China
| | - Shouqin Lü
- Key Laboratory of Microgravity (National Microgravity Laboratory), and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Center for Biomechanics and Bioengineering, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China.,School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China
| | - Yan Zhang
- Key Laboratory of Microgravity (National Microgravity Laboratory), and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Center for Biomechanics and Bioengineering, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China.,School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China
| | - Mian Long
- Key Laboratory of Microgravity (National Microgravity Laboratory), and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Center for Biomechanics and Bioengineering, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China.,School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China
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12
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Ghabache E, Cao Y, Miao Y, Groisman A, Devreotes PN, Rappel W. Coupling traction force patterns and actomyosin wave dynamics reveals mechanics of cell motion. Mol Syst Biol 2021; 17:e10505. [PMID: 34898015 PMCID: PMC8666840 DOI: 10.15252/msb.202110505] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Revised: 11/18/2021] [Accepted: 11/19/2021] [Indexed: 11/13/2022] Open
Abstract
Motile cells can use and switch between different modes of migration. Here, we use traction force microscopy and fluorescent labeling of actin and myosin to quantify and correlate traction force patterns and cytoskeletal distributions in Dictyostelium discoideum cells that move and switch between keratocyte-like fan-shaped, oscillatory, and amoeboid modes. We find that the wave dynamics of the cytoskeletal components critically determine the traction force pattern, cell morphology, and migration mode. Furthermore, we find that fan-shaped cells can exhibit two different propulsion mechanisms, each with a distinct traction force pattern. Finally, the traction force patterns can be recapitulated using a computational model, which uses the experimentally determined spatiotemporal distributions of actin and myosin forces and a viscous cytoskeletal network. Our results suggest that cell motion can be generated by friction between the flow of this network and the substrate.
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Affiliation(s)
| | - Yuansheng Cao
- Department of PhysicsUniversity of California, San DiegoLa JollaCAUSA
| | - Yuchuan Miao
- Department of Cell BiologySchool of MedicineJohns Hopkins UniversityBaltimoreMDUSA
| | - Alex Groisman
- Department of PhysicsUniversity of California, San DiegoLa JollaCAUSA
| | - Peter N Devreotes
- Department of Cell BiologySchool of MedicineJohns Hopkins UniversityBaltimoreMDUSA
| | - Wouter‐Jan Rappel
- Department of PhysicsUniversity of California, San DiegoLa JollaCAUSA
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13
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Rutkowski DM, Vavylonis D. Discrete mechanical model of lamellipodial actin network implements molecular clutch mechanism and generates arcs and microspikes. PLoS Comput Biol 2021; 17:e1009506. [PMID: 34662335 PMCID: PMC8553091 DOI: 10.1371/journal.pcbi.1009506] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Revised: 10/28/2021] [Accepted: 09/30/2021] [Indexed: 01/03/2023] Open
Abstract
Mechanical forces, actin filament turnover, and adhesion to the extracellular environment regulate lamellipodial protrusions. Computational and mathematical models at the continuum level have been used to investigate the molecular clutch mechanism, calculating the stress profile through the lamellipodium and around focal adhesions. However, the forces and deformations of individual actin filaments have not been considered while interactions between actin networks and actin bundles is not easily accounted with such methods. We develop a filament-level model of a lamellipodial actin network undergoing retrograde flow using 3D Brownian dynamics. Retrograde flow is promoted in simulations by pushing forces from the leading edge (due to actin polymerization), pulling forces (due to molecular motors), and opposed by viscous drag in cytoplasm and focal adhesions. Simulated networks have densities similar to measurements in prior electron micrographs. Connectivity between individual actin segments is maintained by permanent and dynamic crosslinkers. Remodeling of the network occurs via the addition of single actin filaments near the leading edge and via filament bond severing. We investigated how several parameters affect the stress distribution, network deformation and retrograde flow speed. The model captures the decrease in retrograde flow upon increase of focal adhesion strength. The stress profile changes from compression to extension across the leading edge, with regions of filament bending around focal adhesions. The model reproduces the observed reduction in retrograde flow speed upon exposure to cytochalasin D, which halts actin polymerization. Changes in crosslinker concentration and dynamics, as well as in the orientation pattern of newly added filaments demonstrate the model's ability to generate bundles of filaments perpendicular (actin arcs) or parallel (microspikes) to the protruding direction.
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14
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Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment. AXIOMS 2021. [DOI: 10.3390/axioms10040243] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
The present work is motivated by the development of a mathematical model mimicking the mechanisms observed in lab-on-chip experiments, made to reproduce on microfluidic chips the in vivo reality. Here we consider the Cancer-on-Chip experiment where tumor cells are treated with chemotherapy drug and secrete chemical signals in the environment attracting multiple immune cell species. The in silico model here proposed goes towards the construction of a “digital twin” of the experimental immune cells in the chip environment to better understand the complex mechanisms of immunosurveillance. To this aim, we develop a tumor-immune microfluidic hybrid PDE–ODE model to describe the concentration of chemicals in the Cancer-on-Chip environment and immune cells migration. The development of a trustable simulation algorithm, able to reproduce the immunocompetent dynamics observed in the chip, requires an efficient tool for the calibration of the model parameters. In this respect, the present paper represents a first methodological work to test the feasibility and the soundness of the calibration technique here proposed, based on a multidimensional spline interpolation technique for the time-varying velocity field surfaces obtained from cell trajectories.
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15
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Drozdowski OM, Ziebert F, Schwarz US. Optogenetic control of intracellular flows and cell migration: A comprehensive mathematical analysis with a minimal active gel model. Phys Rev E 2021; 104:024406. [PMID: 34525652 DOI: 10.1103/physreve.104.024406] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2021] [Accepted: 07/14/2021] [Indexed: 12/23/2022]
Abstract
The actin cytoskeleton of cells is in continuous motion due to both polymerization of new filaments and their contraction by myosin II molecular motors. Through adhesion to the substrate, such intracellular flow can be converted into cell migration. Recently, optogenetics has emerged as a new powerful experimental method to control both actin polymerization and myosin II contraction. While optogenetic control of polymerization can initiate cell migration by generating protrusion, it is less clear if and how optogenetic control of contraction can also affect cell migration. Here we analyze the latter situation using a minimal variant of active gel theory into which we include optogenetic activation as a spatiotemporally constrained perturbation. The model can describe the symmetrical flow of the actomyosin system observed in optogenetic experiments, but not the long-lasting polarization required for cell migration. Motile solutions become possible if cytoskeletal polymerization is included through the boundary conditions. Optogenetic activation of contraction can then initiate locomotion in a symmetrically spreading cell and strengthen motility in an asymmetrically polymerizing one. If designed appropriately, it can also arrest motility even for protrusive boundaries.
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Affiliation(s)
- Oliver M Drozdowski
- Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, 69120 Heidelberg, Germany and BioQuant, Heidelberg University, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany
| | - Falko Ziebert
- Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, 69120 Heidelberg, Germany and BioQuant, Heidelberg University, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany
| | - Ulrich S Schwarz
- Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, 69120 Heidelberg, Germany and BioQuant, Heidelberg University, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany
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16
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Lou SS, Kennard AS, Koslover EF, Gutierrez E, Groisman A, Theriot JA. Elastic wrinkling of keratocyte lamellipodia driven by myosin-induced contractile stress. Biophys J 2021; 120:1578-1591. [PMID: 33631203 DOI: 10.1016/j.bpj.2021.02.022] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2020] [Revised: 02/01/2021] [Accepted: 02/03/2021] [Indexed: 11/16/2022] Open
Abstract
During actin-based cell migration, the actin cytoskeleton in the lamellipodium both generates and responds to force, which has functional consequences for the ability of the cell to extend protrusions. However, the material properties of the lamellipodial actin network and its response to stress on the timescale of motility are incompletely understood. Here, we describe a dynamic wrinkling phenotype in the lamellipodium of fish keratocytes, in which the actin sheet buckles upward away from the ventral membrane of the cell, forming a periodic pattern of wrinkles perpendicular to the cell's leading edge. Cells maintain an approximately constant wrinkle wavelength over time despite new wrinkle formation and the lateral movement of wrinkles in the cell frame of reference, suggesting that cells have a preferred or characteristic wrinkle wavelength. Generation of wrinkles is dependent upon myosin contractility, and their wavelength scales directly with the density of the actin network and inversely with cell adhesion. These results are consistent with a simple physical model for wrinkling in an elastic sheet under compression and suggest that the lamellipodial cytoskeleton behaves as an elastic material on the timescale of cell migration despite rapid actin turnover.
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Affiliation(s)
- Sunny S Lou
- Department of Chemical and Systems Biology, Stanford University, Stanford, California
| | - Andrew S Kennard
- Program in Biophysics, Stanford University, Stanford, California; Department of Biology and Howard Hughes Medical Institute, University of Washington, Seattle, Washington
| | - Elena F Koslover
- Department of Physics, University of California, San Diego, San Diego, California
| | - Edgar Gutierrez
- Department of Physics, University of California, San Diego, San Diego, California
| | - Alexander Groisman
- Department of Physics, University of California, San Diego, San Diego, California
| | - Julie A Theriot
- Department of Biology and Howard Hughes Medical Institute, University of Washington, Seattle, Washington.
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17
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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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18
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Zhao J, Manuchehrfar F, Liang J. Cell-substrate mechanics guide collective cell migration through intercellular adhesion: a dynamic finite element cellular model. Biomech Model Mechanobiol 2020; 19:1781-1796. [PMID: 32108272 PMCID: PMC7990038 DOI: 10.1007/s10237-020-01308-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2019] [Accepted: 02/13/2020] [Indexed: 01/23/2023]
Abstract
During the process of tissue formation and regeneration, cells migrate collectively while remaining connected through intercellular adhesions. However, the roles of cell-substrate and cell-cell mechanical interactions in regulating collective cell migration are still unclear. In this study, we employ a newly developed finite element cellular model to study collective cell migration by exploring the effects of mechanical feedback between cell and substrate and mechanical signal transmission between adjacent cells. Our viscoelastic model of cells consists many triangular elements and is of high resolution. Cadherin adhesion between cells is modeled explicitly as linear springs at subcellular level. In addition, we incorporate a mechano-chemical feedback loop between cell-substrate mechanics and Rac-mediated cell protrusion. Our model can reproduce a number of experimentally observed patterns of collective cell migration during wound healing, including cell migration persistence, separation distance between cell pairs and migration direction. Moreover, we demonstrate that cell protrusion determined by the cell-substrate mechanics plays an important role in guiding persistent and oriented collective cell migration. Furthermore, this guidance cue can be maintained and transmitted to submarginal cells of long distance through intercellular adhesions. Our study illustrates that our finite element cellular model can be employed to study broad problems of complex tissue in dynamic changes at subcellular level.
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Affiliation(s)
- Jieling Zhao
- INRIA de Paris and Sorbonne Universités UPMC, LJLL Team Mamba, Paris, France.
| | - Farid Manuchehrfar
- Department of Bioengineering, University of Illinois at Chicago, Chicago, USA
| | - Jie Liang
- Department of Bioengineering, University of Illinois at Chicago, Chicago, USA
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19
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Wolgemuth CW, Sun SX. Active random forces can drive differential cellular positioning and enhance motor-driven transport. Mol Biol Cell 2020; 31:2283-2288. [PMID: 32726176 PMCID: PMC7550702 DOI: 10.1091/mbc.e19-11-0629] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Cells are remarkable machines capable of performing an exquisite range of functions, many of which depend crucially on the activity of molecular motors that generate forces. Recent experiments have shown that intracellular random movements are not solely thermal in nature but also arise from stochasticity in the forces from these molecular motors. Here we consider the effects of these nonthermal random forces. We show that stochastic motor force not only enhances diffusion but also leads to size-dependent transport of objects that depends on the local density of the cytoskeletal filaments on which motors operate. As a consequence, we find that objects that are larger than the mesh size of the cytoskeleton should be attracted to regions of high cytoskeletal density, while objects that are smaller than the mesh size will preferentially avoid these regions. These results suggest a mechanism for size-based organelle positioning and also suggest that motor-driven random forces can additionally enhance motor-driven transport.
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Affiliation(s)
- Charles W Wolgemuth
- Johns Hopkins Physical Sciences-Oncology Center, Johns Hopkins University, Baltimore, MD 21218.,Departments of Physics and Molecular and Cellular Biology, University of Arizona, Tucson, AZ 85721
| | - Sean X Sun
- Johns Hopkins Physical Sciences-Oncology Center, Johns Hopkins University, Baltimore, MD 21218.,Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218
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20
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Moure A, Gomez H. Influence of myosin activity and mechanical impact on keratocyte polarization. SOFT MATTER 2020; 16:5177-5194. [PMID: 32459252 DOI: 10.1039/d0sm00473a] [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
In cell migration, polarization is the process by which a stationary cell breaks symmetry and initiates motion. Although a lot is known about the mechanisms involved in cell polarization, the role played by myosin contraction remains unclear. In addition, cell polarization by mechanical impact has received little attention. Here, we study the influence of myosin activity on cell polarization and the initiation of motion induced by mechanical cues using a computational model for keratocytes. The model accounts for cell deformation, the dynamics of myosin and the signaling protein RhoA (a member of the Rho GTPases family), as well as the forces acting on the actomyosin network. Our results show that the attainment of a steady polarized state depends on the strength of myosin down- or up-regulation and that myosin upregulation favors cell polarization. Our results also confirm the existence of a threshold level for cell polarization, which is determined by the level of polarization of the Rho GTPases at the time the external stimuli vanish. In all, this paper shows that capturing the interactions between the signaling proteins (Rho GTPases for keratocytes) and the compounds of the motile machinery in a moving cell is crucial to study cell polarization.
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Affiliation(s)
- Adrian Moure
- School of Mechanical Engineering, Purdue University, West Lafayette, 47907 IN, USA.
| | - Hector Gomez
- School of Mechanical Engineering, Purdue University, West Lafayette, 47907 IN, USA. and Weldon School of Biomedical Engineering, Purdue University, West Lafayette, 47907 IN, USA and Purdue University Center for Cancer Research, Purdue University, West Lafayette, 47906 IN, USA
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21
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Zhang Z, Rosakis P, Hou TY, Ravichandran G. A minimal mechanosensing model predicts keratocyte evolution on flexible substrates. J R Soc Interface 2020; 17:20200175. [PMID: 32370690 DOI: 10.1098/rsif.2020.0175] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
A mathematical model is proposed for shape evolution and locomotion of fish epidermal keratocytes on elastic substrates. The model is based on mechanosensing concepts: cells apply contractile forces onto the elastic substrate, while cell shape evolution depends locally on the substrate stress generated by themselves or external mechanical stimuli acting on the substrate. We use the level set method to study the behaviour of the model numerically, and predict a number of distinct phenomena observed in experiments, such as (i) symmetry breaking from the stationary centrosymmetric to the well-known steadily propagating crescent shape, (ii) asymmetric bipedal oscillations and travelling waves in the lamellipodium leading edge, (iii) response to remote mechanical stress externally applied to the substrate (tensotaxis) and (iv) changing direction of motion towards an interface with a rigid substrate (durotaxis).
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Affiliation(s)
- Zhiwen Zhang
- Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR
| | - Phoebus Rosakis
- Department of Mathematics and Applied Mathematics, University of Crete, Heraklion 70013 Crete, Greece.,Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Voutes 70013 Crete, Greece
| | - Thomas Y Hou
- Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125, USA
| | - Guruswami Ravichandran
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
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22
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Mogilner A, Barnhart EL, Keren K. Experiment, theory, and the keratocyte: An ode to a simple model for cell motility. Semin Cell Dev Biol 2020; 100:143-151. [DOI: 10.1016/j.semcdb.2019.10.019] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Revised: 09/27/2019] [Accepted: 10/31/2019] [Indexed: 01/20/2023]
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23
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Bonilla-Quintana M, Wörgötter F, Tetzlaff C, Fauth M. Modeling the Shape of Synaptic Spines by Their Actin Dynamics. Front Synaptic Neurosci 2020; 12:9. [PMID: 32218728 PMCID: PMC7078677 DOI: 10.3389/fnsyn.2020.00009] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2019] [Accepted: 02/24/2020] [Indexed: 01/05/2023] Open
Abstract
Dendritic spines are the morphological basis of excitatory synapses in the cortex and their size and shape correlates with functional synaptic properties. Recent experiments show that spines exhibit large shape fluctuations that are not related to activity-dependent plasticity but nonetheless might influence memory storage at their synapses. To investigate the determinants of such spontaneous fluctuations, we propose a mathematical model for the dynamics of the spine shape and analyze it in 2D-related to experimental microscopic imagery-and in 3D. We show that the spine shape is governed by a local imbalance between membrane tension and the expansive force from actin bundles that originates from discrete actin polymerization foci. Experiments have shown that only few such polymerization foci co-exist at any time in a spine, each having limited life time. The model shows that the momentarily existing set of such foci pushes the membrane along certain directions until foci are replaced and other directions may now be affected. We explore these relations in depth and use our model to predict shape and temporal characteristics of spines from the different biophysical parameters involved in actin polymerization. Approximating the model by a single recursive equation we finally demonstrate that the temporal evolution of the number of active foci is sufficient to predict the size of the model-spines. Thus, our model provides the first platform to study the relation between molecular and morphological properties of the spine with a high degree of biophysical detail.
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Affiliation(s)
- Mayte Bonilla-Quintana
- Department for Computational Neuroscience, Third Institute of Physics-Biophysics, Georg-August-University, Göttingen, Germany
| | - Florentin Wörgötter
- Department for Computational Neuroscience, Third Institute of Physics-Biophysics, Georg-August-University, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Georg-August-University, Göttingen, Germany
| | - Christian Tetzlaff
- Department for Computational Neuroscience, Third Institute of Physics-Biophysics, Georg-August-University, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Georg-August-University, Göttingen, Germany
| | - Michael Fauth
- Department for Computational Neuroscience, Third Institute of Physics-Biophysics, Georg-August-University, Göttingen, Germany
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24
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Recho P, Putelat T, Truskinovsky L. Active gel segment behaving as an active particle. Phys Rev E 2020; 100:062403. [PMID: 31962422 DOI: 10.1103/physreve.100.062403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2019] [Indexed: 12/14/2022]
Abstract
We reduce a one-dimensional model of an active segment (AS), which is used, for instance, in the description of contraction-driven cell motility, to a zero-dimensional model of an active particle (AP) characterized by two internal degrees of freedom: position and polarity. Both models give rise to hysteretic force-velocity relations showing that an active agent can support two opposite polarities under the same external force and that it can maintain the same polarity while being dragged by external forces with opposite orientations. This double bistability results in a rich dynamic repertoire which we illustrate by studying static, stalled, motile, and periodically repolarizing regimes displayed by an active agent confined in a viscoelastic environment. We show that the AS and AP models can be calibrated to generate quantitatively similar dynamic responses.
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Affiliation(s)
- P Recho
- LIPhy, CNRS-UMR 5588, Université Grenoble Alpes, F-38000 Grenoble, France
| | - T Putelat
- SAS, Rothamsted Research, Harpenden, AL5 2JQ, United Kingdom.,DEM, Queen's School of Engineering, University of Bristol, Bristol, BS8 1TR, United Kingdom
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25
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Xiong L, Cao Y, Cooper R, Rappel WJ, Hasty J, Tsimring L. Flower-like patterns in multi-species bacterial colonies. eLife 2020; 9:e48885. [PMID: 31933477 PMCID: PMC6959979 DOI: 10.7554/elife.48885] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2019] [Accepted: 11/16/2019] [Indexed: 11/13/2022] Open
Abstract
Diverse interactions among species within bacterial colonies lead to intricate spatiotemporal dynamics, which can affect their growth and survival. Here, we describe the emergence of complex structures in a colony grown from mixtures of motile and non-motile bacterial species on a soft agar surface. Time-lapse imaging shows that non-motile bacteria 'hitchhike' on the motile bacteria as the latter migrate outward. The non-motile bacteria accumulate at the boundary of the colony and trigger an instability that leaves behind striking flower-like patterns. The mechanism of the front instability governing this pattern formation is elucidated by a mathematical model for the frictional motion of the colony interface, with friction depending on the local concentration of the non-motile species. A more elaborate two-dimensional phase-field model that explicitly accounts for the interplay between growth, mechanical stress from the motile species, and friction provided by the non-motile species, fully reproduces the observed flower-like patterns.
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Affiliation(s)
- Liyang Xiong
- Department of PhysicsUniversity of California, San DiegoLa JollaUnited States
- BioCircuits InstituteUniversity of California, San DiegoLa JollaUnited States
| | - Yuansheng Cao
- Department of PhysicsUniversity of California, San DiegoLa JollaUnited States
| | - Robert Cooper
- BioCircuits InstituteUniversity of California, San DiegoLa JollaUnited States
| | - Wouter-Jan Rappel
- Department of PhysicsUniversity of California, San DiegoLa JollaUnited States
| | - Jeff Hasty
- BioCircuits InstituteUniversity of California, San DiegoLa JollaUnited States
- The San Diego Center for Systems BiologySan DiegoUnited States
- Molecular Biology Section, Division of Biological SciencesUniversity of California, San DiegoLa JollaUnited States
- Department of BioengineeringUniversity of California, San DiegoLa JollaUnited States
| | - Lev Tsimring
- BioCircuits InstituteUniversity of California, San DiegoLa JollaUnited States
- The San Diego Center for Systems BiologySan DiegoUnited States
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26
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Moure A, Gomez H. Dual role of the nucleus in cell migration on planar substrates. Biomech Model Mechanobiol 2020; 19:1491-1508. [PMID: 31907682 DOI: 10.1007/s10237-019-01283-6] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2019] [Accepted: 12/21/2019] [Indexed: 01/09/2023]
Abstract
Cell migration is essential to sustain life. There have been significant advances in the understanding of the mechanisms that control cell crawling, but the role of the nucleus remains poorly understood. The nucleus exerts a tight control of cell migration in 3D environments, but its influence in 2D migration on planar substrates remains unclear. Here, we study the role of the cell nucleus in 2D cell migration using a computational model of fish keratocytes. Our results indicate that the apparently minor role played by the nucleus emerges from two antagonist effects: While the nucleus modifies the spatial distributions of actin and myosin in a way that reduces cell velocity (e.g., the nucleus displaces myosin to the sides and front of the cell), its mechanical connection with the cytoskeleton alters the intracellular stresses promoting cell migration. Overall, the favorable effect of the nucleus-cytoskeleton connection prevails, which may explain why regular cells usually move faster than enucleated cells.
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Affiliation(s)
- Adrian Moure
- School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47907, USA.
| | - Hector Gomez
- School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47907, USA.,Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, 47907, USA.,Purdue University Center for Cancer Research, Purdue University, West Lafayette, IN, 47906, USA
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27
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Farutin A, Étienne J, Misbah C, Recho P. Crawling in a Fluid. PHYSICAL REVIEW LETTERS 2019; 123:118101. [PMID: 31573254 DOI: 10.1103/physrevlett.123.118101] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2019] [Indexed: 06/10/2023]
Abstract
There is increasing evidence that mammalian cells not only crawl on substrates but can also swim in fluids. To elucidate the mechanisms of the onset of motility of cells in suspension, a model which couples actin and myosin kinetics to fluid flow is proposed and solved for a spherical shape. The swimming speed is extracted in terms of key parameters. We analytically find super- and subcritical bifurcations from a nonmotile to a motile state and also spontaneous polarity oscillations that arise from a Hopf bifurcation. Relaxing the spherical assumption, the obtained shapes show appealing trends.
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Affiliation(s)
| | | | - Chaouqi Misbah
- Univ. Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
| | - Pierre Recho
- Univ. Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
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28
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De PS, De R. Stick-slip dynamics of migrating cells on viscoelastic substrates. Phys Rev E 2019; 100:012409. [PMID: 31499904 DOI: 10.1103/physreve.100.012409] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2019] [Indexed: 01/14/2023]
Abstract
Stick-slip motion, a common phenomenon observed during crawling of cells, is found to be strongly sensitive to the substrate stiffness. Stick-slip behaviors have previously been investigated typically using purely elastic substrates. For a more realistic understanding of this phenomenon, we propose a theoretical model to study the dynamics on a viscoelastic substrate. Our model, based on a reaction-diffusion framework, incorporates known important interactions such as retrograde flow of actin, myosin contractility, force-dependent assembly, and disassembly of focal adhesions coupled with cell-substrate interaction. We show that consideration of a viscoelastic substrate not only captures the usually observed stick-slip jumps but also predicts the existence of an optimal substrate viscosity corresponding to maximum traction force and minimum retrograde flow which was hitherto unexplored. Moreover, our theory predicts the time evolution of individual bond force that characterizes the stick-slip patterns on soft versus stiff substrates. Our analysis also elucidates how the duration of the stick-slip cycles are affected by various cellular parameters.
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Affiliation(s)
- Partho Sakha De
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal, India
| | - Rumi De
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal, India
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29
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Cao Y, Karmakar R, Ghabache E, Gutierrez E, Zhao Y, Groisman A, Levine H, Camley BA, Rappel WJ. Cell motility dependence on adhesive wetting. SOFT MATTER 2019; 15:2043-2050. [PMID: 30724956 DOI: 10.1039/c8sm01832d] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Adhesive cell-substrate interactions are crucial for cell motility and are responsible for the necessary traction that propels cells. These interactions can also change the shape of the cell, analogous to liquid droplet wetting on adhesive substrates. To address how these shape changes affect cell migration and cell speed we model motility using deformable, 2D cross-sections of cells in which adhesion and frictional forces between cell and substrate can be varied separately. Our simulations show that increasing the adhesion results in increased spreading of cells and larger cell speeds. We propose an analytical model which shows that the cell speed is inversely proportional to an effective height of the cell and that increasing this height results in increased internal shear stress. The numerical and analytical results are confirmed in experiments on motile eukaryotic cells.
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Affiliation(s)
- Yuansheng Cao
- Department of Physics, University of California, San Diego, La Jolla, California 92093, USA.
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30
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Di Costanzo E, Giacomello A, Messina E, Natalini R, Pontrelli G, Rossi F, Smits R, Twarogowska M. A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres). MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2018; 35:121-144. [PMID: 28115549 DOI: 10.1093/imammb/dqw022] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2015] [Accepted: 11/28/2016] [Indexed: 11/13/2022]
Abstract
We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model, cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment. Numerical simulations show the structure and the development of the clustered progenitors and are in a good agreement with the results obtained from in vitro experiments.
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Affiliation(s)
- Ezio Di Costanzo
- Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche, Rome, Italy
| | - Alessandro Giacomello
- Department of Molecular Medicine, Pasteur Institute Cenci-Bolognetti Foundation, Sapienza University of Rome, Rome, Italy
| | - Elisa Messina
- Department of Pediatric Cardiology, Sapienza University of Rome, Rome, Italy
| | - Roberto Natalini
- Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche, Rome, Italy
| | - Giuseppe Pontrelli
- Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche, Rome, Italy
| | - Fabrizio Rossi
- Department of Molecular Medicine, Pasteur Institute Cenci-Bolognetti Foundation, Sapienza University of Rome, Rome, Italy
| | - Robert Smits
- Department of Mathematical Sciences, New Mexico State University, Las Cruces, USA
| | - Monika Twarogowska
- Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche, Rome, Italy
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31
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Sfakianakis N, Brunk A. Stability, Convergence, and Sensitivity Analysis of the FBLM and the Corresponding FEM. Bull Math Biol 2018; 80:2789-2827. [PMID: 30159856 DOI: 10.1007/s11538-018-0460-0] [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: 09/12/2017] [Accepted: 06/29/2018] [Indexed: 10/28/2022]
Abstract
We study in this paper the filament-based lamellipodium model (FBLM) and the corresponding finite element method (FEM) used to solve it. We investigate fundamental numerical properties of the FEM and justify its further use with the FBLM. We show that the FEM satisfies a time step stability condition that is consistent with the nature of the problem and propose a particular strategy to automatically adapt the time step of the method. We show that the FEM converges with respect to the (two-dimensional) space discretization in a series of characteristic and representative chemotaxis and haptotaxis experiments. We embed and couple the FBLM with a complex and adaptive extracellular environment comprised of chemical and adhesion components that are described by their macroscopic density and study their combined time evolution. With this combination, we study the sensitivity of the FBLM on several of its controlling parameters and discuss their influence in the dynamics of the model and its future evolution. We finally perform a number of numerical experiments that reproduce biological cases and compare the results with the ones reported in the literature.
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Affiliation(s)
- N Sfakianakis
- Institute of Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 205, 69120, Heidelberg, Germany.
| | - A Brunk
- Institute of Mathematics, Johannes Gutenberg-University, Staudingerweg 9, 55128, Mainz, Germany
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32
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Agosti A, Ambrosi D, Turzi S. Strain energy storage and dissipation rate in active cell mechanics. Phys Rev E 2018; 97:052410. [PMID: 29906906 DOI: 10.1103/physreve.97.052410] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Indexed: 01/07/2023]
Abstract
When living cells are observed at rest on a flat substrate, they can typically exhibit a rounded (symmetric) or an elongated (polarized) shape. Although the cells are apparently at rest, the active stress generated by the molecular motors continuously stretches and drifts the actin network, the cytoskeleton of the cell. In this paper we theoretically compare the energy stored and dissipated in this active system in two geometric configurations of interest: symmetric and polarized. We find that the stored energy is larger for a radially symmetric cell at low activation regime, while the polar configuration has larger strain energy when the active stress is beyond a critical threshold. Conversely, the dissipation of energy in a symmetric cell is always larger than that of a nonsymmetric one. By a combination of symmetry arguments and competition between surface and bulk stress, we argue that radial symmetry is an energetically expensive metastable state that provides access to an infinite number of lower-energy states, the polarized configurations.
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Affiliation(s)
- A Agosti
- Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - D Ambrosi
- DISMA, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - S Turzi
- Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
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33
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Three-dimensional simulation of obstacle-mediated chemotaxis. Biomech Model Mechanobiol 2018; 17:1243-1268. [DOI: 10.1007/s10237-018-1023-x] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2017] [Accepted: 04/25/2018] [Indexed: 01/07/2023]
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34
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Rajagopal V, Holmes WR, Lee PVS. Computational modeling of single-cell mechanics and cytoskeletal mechanobiology. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2018; 10:e1407. [PMID: 29195023 PMCID: PMC5836888 DOI: 10.1002/wsbm.1407] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Revised: 08/19/2017] [Accepted: 09/07/2017] [Indexed: 01/10/2023]
Abstract
Cellular cytoskeletal mechanics plays a major role in many aspects of human health from organ development to wound healing, tissue homeostasis and cancer metastasis. We summarize the state-of-the-art techniques for mathematically modeling cellular stiffness and mechanics and the cytoskeletal components and factors that regulate them. We highlight key experiments that have assisted model parameterization and compare the advantages of different models that have been used to recapitulate these experiments. An overview of feed-forward mechanisms from signaling to cytoskeleton remodeling is provided, followed by a discussion of the rapidly growing niche of encapsulating feedback mechanisms from cytoskeletal and cell mechanics to signaling. We discuss broad areas of advancement that could accelerate research and understanding of cellular mechanobiology. A precise understanding of the molecular mechanisms that affect cell and tissue mechanics and function will underpin innovations in medical device technologies of the future. WIREs Syst Biol Med 2018, 10:e1407. doi: 10.1002/wsbm.1407 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.
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Affiliation(s)
- Vijay Rajagopal
- Cell Structure and Mechanobiology Group, Department of Biomedical EngineeringUniversity of MelbourneMelbourneAustralia
| | - William R. Holmes
- Department of Physics and AstronomyVanderbilt UniversityNashvilleTNUSA
| | - Peter Vee Sin Lee
- Cell and Tissue Biomechanics Laboratory, Department of Biomedical EngineeringUniversity of MelbourneMelbourneAustralia
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35
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Nikmaneshi M, Firoozabadi B, Saidi M. Fully-coupled mathematical modeling of actomyosin-cytosolic two-phase flow in a highly deformable moving Keratocyte cell. J Biomech 2018; 67:37-45. [DOI: 10.1016/j.jbiomech.2017.11.025] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2017] [Revised: 11/16/2017] [Accepted: 11/22/2017] [Indexed: 11/28/2022]
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36
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Putelat T, Recho P, Truskinovsky L. Mechanical stress as a regulator of cell motility. Phys Rev E 2018; 97:012410. [PMID: 29448458 DOI: 10.1103/physreve.97.012410] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2017] [Indexed: 06/08/2023]
Abstract
The motility of a cell can be triggered or inhibited not only by an applied force but also by a mechanically neutral force couple. This type of loading, represented by an applied stress and commonly interpreted as either squeezing or stretching, can originate from extrinsic interaction of a cell with its neighbors. To quantify the effect of applied stresses on cell motility we use an analytically transparent one-dimensional model accounting for active myosin contraction and induced actin turnover. We show that stretching can polarize static cells and initiate cell motility while squeezing can symmetrize and arrest moving cells. We show further that sufficiently strong squeezing can lead to the loss of cell integrity. The overall behavior of the system depends on the two dimensionless parameters characterizing internal driving (chemical activity) and external loading (applied stress). We construct a phase diagram in this parameter space distinguishing between static, motile, and collapsed states. The obtained results are relevant for the mechanical understanding of contact inhibition and the epithelial-to-mesenchymal transition.
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Affiliation(s)
- T Putelat
- DEM, Queen's School of Engineering, University of Bristol, Bristol BS8 1TR, United Kingdom
| | - P Recho
- LIPhy, CNRS-UMR 5588, Université Grenoble Alpes, F-38000 Grenoble, France
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37
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Nickaeen M, Novak IL, Pulford S, Rumack A, Brandon J, Slepchenko BM, Mogilner A. A free-boundary model of a motile cell explains turning behavior. PLoS Comput Biol 2017; 13:e1005862. [PMID: 29136638 PMCID: PMC5705165 DOI: 10.1371/journal.pcbi.1005862] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Revised: 11/28/2017] [Accepted: 10/31/2017] [Indexed: 01/14/2023] Open
Abstract
To understand shapes and movements of cells undergoing lamellipodial motility, we systematically explore minimal free-boundary models of actin-myosin contractility consisting of the force-balance and myosin transport equations. The models account for isotropic contraction proportional to myosin density, viscous stresses in the actin network, and constant-strength viscous-like adhesion. The contraction generates a spatially graded centripetal actin flow, which in turn reinforces the contraction via myosin redistribution and causes retraction of the lamellipodial boundary. Actin protrusion at the boundary counters the retraction, and the balance of the protrusion and retraction shapes the lamellipodium. The model analysis shows that initiation of motility critically depends on three dimensionless parameter combinations, which represent myosin-dependent contractility, a characteristic viscosity-adhesion length, and a rate of actin protrusion. When the contractility is sufficiently strong, cells break symmetry and move steadily along either straight or circular trajectories, and the motile behavior is sensitive to conditions at the cell boundary. Scanning of a model parameter space shows that the contractile mechanism of motility supports robust cell turning in conditions where short viscosity-adhesion lengths and fast protrusion cause an accumulation of myosin in a small region at the cell rear, destabilizing the axial symmetry of a moving cell. To understand shapes and movements of simple motile cells, we systematically explore minimal models describing a cell as a two-dimensional actin-myosin gel with a free boundary. The models account for actin-myosin contraction balanced by viscous stresses in the actin gel and uniform adhesion. The myosin contraction causes the lamellipodial boundary to retract. Actin protrusion at the boundary counters the retraction, and the balance of protrusion and retraction shapes the cell. The models reproduce a variety of motile shapes observed experimentally. The analysis shows that the mechanical state of a cell depends on a small number of parameters. We find that when the contractility is sufficiently strong, cells break symmetry and move steadily along either straight or circular trajectory. Scanning model parameters shows that the contractile mechanism of motility supports robust cell turning behavior in conditions where deformable actin gel and fast protrusion destabilize the axial symmetry of a moving cell.
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Affiliation(s)
- Masoud Nickaeen
- Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, CT, United States of America
| | - Igor L. Novak
- Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, CT, United States of America
| | - Stephanie Pulford
- Center for Engineering Learning & Teaching, University of Washington, Seattle, WA, United States of America
| | - Aaron Rumack
- Department of Computer Science, Cornell University, Ithaca, NY, United States of America
| | - Jamie Brandon
- Department of Mathematics, Adrian College, Adrian, MI, United States of America
| | - Boris M. Slepchenko
- Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, CT, United States of America
| | - Alex Mogilner
- Courant Institute and Department of Biology, New York University, New York, NY, United States of America
- * E-mail:
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38
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Abaurrea Velasco C, Dehghani Ghahnaviyeh S, Nejat Pishkenari H, Auth T, Gompper G. Complex self-propelled rings: a minimal model for cell motility. SOFT MATTER 2017; 13:5865-5876. [PMID: 28766641 DOI: 10.1039/c7sm00439g] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Collective behavior of active matter is observed for self-propelled particles, such as vibrated disks and active Brownian particles, as well as for cytoskeletal filaments in motile cells. Here, a system of quasi two-dimensional penetrable self-propelled rods inside rigid rings is used to construct a complex self-propelled particle. The rods interact sterically with each other and with a stationary or mobile ring via a separation-shifted Lennard-Jones potential. They either have a sliding attachment to the inside of the ring at one of their ends, or can move freely within the ring confinement. We study the inner structure and dynamics of the mobile self-propelled rings. We find that these complex particles cannot only be characterized as active Brownian particles, but can also exhibit cell-like motility: random walks, persistent motion, circling, and run-and-circle motion.
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Affiliation(s)
- Clara Abaurrea Velasco
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany.
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39
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Antagonistic Behaviors of NMY-1 and NMY-2 Maintain Ring Channels in the C. elegans Gonad. Biophys J 2017; 111:2202-2213. [PMID: 27851943 DOI: 10.1016/j.bpj.2016.10.011] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2015] [Revised: 09/30/2016] [Accepted: 10/05/2016] [Indexed: 11/23/2022] Open
Abstract
Contractile rings play critical roles in a number of biological processes, including oogenesis, wound healing, and cytokinesis. In many cases, the activity of motor proteins such as nonmuscle myosins is required for appropriate constriction of these contractile rings. In the gonad of the nematode worm Caenorhabditis elegans, ring channels are a specialized form of contractile ring that are maintained at a constant diameter before oogenesis. We propose a model of ring channel maintenance that explicitly incorporates force generation by motor proteins that can act normally or tangentially to the ring channel opening. We find that both modes of force generation are needed to maintain the ring channels. We demonstrate experimentally that the type II myosins NMY-1 and NMY-2 antagonize each other in the ring channels by producing force in perpendicular directions: the experimental depletion of NMY-1/theoretical decrease in orthogonal force allows premature ring constriction and cellularization, whereas the experimental depletion of NMY-2/theoretical decrease in tangential force opens the ring channels and prevents cellularization. Together, our experimental and theoretical results show that both forces, mediated by NMY-1 and NMY-2, are crucial for maintaining the appropriate ring channel diameter and dynamics throughout the gonad.
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40
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Priya R, Gomez GA, Budnar S, Acharya BR, Czirok A, Yap AS, Neufeld Z. Bistable front dynamics in a contractile medium: Travelling wave fronts and cortical advection define stable zones of RhoA signaling at epithelial adherens junctions. PLoS Comput Biol 2017; 13:e1005411. [PMID: 28273072 PMCID: PMC5362241 DOI: 10.1371/journal.pcbi.1005411] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2016] [Revised: 03/22/2017] [Accepted: 02/07/2017] [Indexed: 12/24/2022] Open
Abstract
Mechanical coherence of cell layers is essential for epithelia to function as tissue barriers and to control active tissue dynamics during morphogenesis. RhoA signaling at adherens junctions plays a key role in this process by coupling cadherin-based cell-cell adhesion together with actomyosin contractility. Here we propose and analyze a mathematical model representing core interactions involved in the spatial localization of junctional RhoA signaling. We demonstrate how the interplay between biochemical signaling through positive feedback, combined with diffusion on the cell membrane and mechanical forces generated in the cortex, can determine the spatial distribution of RhoA signaling at cell-cell junctions. This dynamical mechanism relies on the balance between a propagating bistable signal that is opposed by an advective flow generated by an actomyosin stress gradient. Experimental observations on the behavior of the system when contractility is inhibited are in qualitative agreement with the predictions of the model.
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Affiliation(s)
- Rashmi Priya
- Institute for Molecular Bioscience, Division of Cell Biology and Molecular Medicine, The University of Queensland, St. Lucia, Brisbane, Queensland, Australia
| | - Guillermo A. Gomez
- Institute for Molecular Bioscience, Division of Cell Biology and Molecular Medicine, The University of Queensland, St. Lucia, Brisbane, Queensland, Australia
| | - Srikanth Budnar
- Institute for Molecular Bioscience, Division of Cell Biology and Molecular Medicine, The University of Queensland, St. Lucia, Brisbane, Queensland, Australia
| | - Bipul R. Acharya
- Institute for Molecular Bioscience, Division of Cell Biology and Molecular Medicine, The University of Queensland, St. Lucia, Brisbane, Queensland, Australia
| | - Andras Czirok
- Department of Anatomy and Cell Biology, University of Kansas Medical Center, Kansas City, Kansas, United States of America
| | - Alpha S. Yap
- Institute for Molecular Bioscience, Division of Cell Biology and Molecular Medicine, The University of Queensland, St. Lucia, Brisbane, Queensland, Australia
| | - Zoltan Neufeld
- School of Mathematics and Physics, The University of Queensland, St. Lucia, Brisbane, Queensland, Australia
- * E-mail:
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41
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Camley BA, Rappel WJ. Physical models of collective cell motility: from cell to tissue. JOURNAL OF PHYSICS D: APPLIED PHYSICS 2017; 50:113002. [PMID: 28989187 PMCID: PMC5625300 DOI: 10.1088/1361-6463/aa56fe] [Citation(s) in RCA: 89] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
In this article, we review physics-based models of collective cell motility. We discuss a range of techniques at different scales, ranging from models that represent cells as simple self-propelled particles to phase field models that can represent a cell's shape and dynamics in great detail. We also extensively review the ways in which cells within a tissue choose their direction, the statistics of cell motion, and some simple examples of how cell-cell signaling can interact with collective cell motility. This review also covers in more detail selected recent works on collective cell motion of small numbers of cells on micropatterns, in wound healing, and the chemotaxis of clusters of cells.
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42
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Camley BA, Zhao Y, Li B, Levine H, Rappel WJ. Crawling and turning in a minimal reaction-diffusion cell motility model: Coupling cell shape and biochemistry. Phys Rev E 2017; 95:012401. [PMID: 28208438 DOI: 10.1103/physreve.95.012401] [Citation(s) in RCA: 43] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2016] [Indexed: 11/07/2022]
Abstract
We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical polarity, which controls the locations where actin polymerization occurs, and the physical properties of the cell, including its membrane tension. We find in our model both highly persistent trajectories, in which the cell crawls in a straight line, and turning trajectories, where the cell transitions from crawling in a line to crawling in a circle. We discuss the controlling variables for this turning instability and argue that turning arises from a coupling between the reaction-diffusion mechanism and the shape of the cell. This emphasizes the surprising features that can arise from simple links between cell mechanics and biochemistry. Our results suggest that similar instabilities may be present in a broad class of biochemical descriptions of cell polarity.
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Affiliation(s)
- Brian A Camley
- Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
| | - Yanxiang Zhao
- Department of Mathematics, The George Washington University, Washington, DC 20052, USA
| | - Bo Li
- Department of Mathematics and Graduate Program in Quantitative Biology, University of California, San Diego, La Jolla, California 92093, USA
| | - Herbert Levine
- Department of Bioengineering, Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Wouter-Jan Rappel
- Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
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43
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Moure A, Gomez H. Computational model for amoeboid motion: Coupling membrane and cytosol dynamics. Phys Rev E 2016; 94:042423. [PMID: 27841601 DOI: 10.1103/physreve.94.042423] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2016] [Indexed: 12/12/2022]
Abstract
A distinguishing feature of amoeboid motion is that the migrating cell undergoes large deformations, caused by the emergence and retraction of actin-rich protrusions, called pseudopods. Here, we propose a cell motility model that represents pseudopod dynamics, as well as its interaction with membrane signaling molecules. The model accounts for internal and external forces, such as protrusion, contraction, adhesion, surface tension, or those arising from cell-obstacle contacts. By coupling the membrane and cytosol interactions we are able to reproduce a realistic picture of amoeboid motion. The model results are in quantitative agreement with experiments and show how cells may take advantage of the geometry of their microenvironment to migrate more efficiently.
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Affiliation(s)
- Adrian Moure
- Universidade da Coruña, Campus de Elviña, 15071, A Coruña, Spain
| | - Hector Gomez
- Universidade da Coruña, Campus de Elviña, 15071, A Coruña, Spain
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44
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Ghasemi V A, Firoozabadi B, Saidi MS. Theoretical modeling of actin-retrograde-flow passing clusters of confined T cell receptors. Math Biosci 2016; 283:1-6. [PMID: 27720878 DOI: 10.1016/j.mbs.2016.09.020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2016] [Revised: 09/15/2016] [Accepted: 09/28/2016] [Indexed: 11/17/2022]
Abstract
Through the activation process of T cells, actin filaments move from the cell periphery toward the cell center. The moving filaments engage with T cell receptors and thus contribute to transportation of the signaling molecules. To study the connection between the moving actin filaments and T cell receptors, an experiment available in the literature has measured filaments flow velocity passing over a region of confined clusters of receptors. It shows that flow velocity decreases in the proximity of the receptors, and then regains its normal value after traversing the region, suggesting a dissipative friction-like connection. In this work, we develop a minimal theoretical model to re-examine this experiment. The model brings the insight that, in contrast to the first impression that the experiment gives, the direct necessity of having a minimum in the velocity profile is not the locally high friction region, but a combined driving force of push from upstream and pull from within and downstream of the system. The predicted driving force integrates our current understanding of the spatially dependent role of the myosin motor proteins and the actin-polymerization-machinery, which make the pulling and pushing forces, respectively.
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Affiliation(s)
- A Ghasemi V
- School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran.
| | - B Firoozabadi
- School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran.
| | - M S Saidi
- School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran.
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45
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Roux C, Duperray A, Laurent VM, Michel R, Peschetola V, Verdier C, Étienne J. Prediction of traction forces of motile cells. Interface Focus 2016; 6:20160042. [PMID: 27708765 DOI: 10.1098/rsfs.2016.0042] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
When crawling on a flat substrate, living cells exert forces on it via adhesive contacts, enabling them to build up tension within their cytoskeleton and to change shape. The measurement of these forces has been made possible by traction force microscopy (TFM), a technique which has allowed us to obtain time-resolved traction force maps during cell migration. This cell 'footprint' is, however, not sufficient to understand the details of the mechanics of migration, that is how cytoskeletal elements (respectively, adhesion complexes) are put under tension and reinforce or deform (respectively, mature and/or unbind) as a result. In a recent paper, we have validated a rheological model of actomyosin linking tension, deformation and myosin activity. Here, we complement this model with tentative models of the mechanics of adhesion and explore how closely these models can predict the traction forces that we recover from experimental measurements during cell migration. The resulting mathematical problem is a PDE set on the experimentally observed domain, which we solve using a finite-element approach. The four parameters of the model can then be adjusted by comparison with experimental results on a single frame of an experiment, and then used to test the predictive power of the model for following frames and other experiments. It is found that the basic pattern of traction forces is robustly predicted by the model and fixed parameters as a function of current geometry only.
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Affiliation(s)
- Clément Roux
- Laboratoire interdisciplinaire de physique (LIPHY), University Grenoble Alpes, 38000 Grenoble, France; Laboratoire interdisciplinaire de physique (LIPHY), CNRS, 38000 Grenoble, France
| | - Alain Duperray
- IAB, University Grenoble Alpes, 38000 Grenoble, France; IAB, INSERM, 38000 Grenoble, France
| | - Valérie M Laurent
- Laboratoire interdisciplinaire de physique (LIPHY), University Grenoble Alpes, 38000 Grenoble, France; Laboratoire interdisciplinaire de physique (LIPHY), CNRS, 38000 Grenoble, France
| | - Richard Michel
- Laboratoire interdisciplinaire de physique (LIPHY), University Grenoble Alpes, 38000 Grenoble, France; Laboratoire interdisciplinaire de physique (LIPHY), CNRS, 38000 Grenoble, France
| | - Valentina Peschetola
- Laboratoire interdisciplinaire de physique (LIPHY), University Grenoble Alpes, 38000 Grenoble, France; Laboratoire interdisciplinaire de physique (LIPHY), CNRS, 38000 Grenoble, France
| | - Claude Verdier
- Laboratoire interdisciplinaire de physique (LIPHY), University Grenoble Alpes, 38000 Grenoble, France; Laboratoire interdisciplinaire de physique (LIPHY), CNRS, 38000 Grenoble, France
| | - Jocelyn Étienne
- Laboratoire interdisciplinaire de physique (LIPHY), University Grenoble Alpes, 38000 Grenoble, France; Laboratoire interdisciplinaire de physique (LIPHY), CNRS, 38000 Grenoble, France
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46
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Oelz D, Mogilner A. Actomyosin contraction, aggregation and traveling waves in a treadmilling actin array. PHYSICA D. NONLINEAR PHENOMENA 2016; 318-319:70-83. [PMID: 26989275 PMCID: PMC4789780 DOI: 10.1016/j.physd.2015.10.005] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We use perturbation theory to derive a continuum model for the dynamic actomyosin bundle/ring in the regime of very strong crosslinking. Actin treadmilling is essential for contraction. Linear stability analysis and numerical solutions of the model equations reveal that when the actin treadmilling is very slow, actin and myosin aggregate into equidistantly spaced peaks. When treadmilling is significant, actin filament of one polarity are distributed evenly, while filaments of the opposite polarity develop a shock wave moving with the treadmilling velocity. Myosin aggregates into a sharp peak surfing the crest of the actin wave. Any actomyosin aggregation diminishes contractile stress. The easiest way to maintain higher contraction is to upregulate the actomyosin turnover which destabilizes nontrivial patterns and stabilizes the homogeneous actomyosin distributions. We discuss the model's implications for the experiment.
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Affiliation(s)
- Dietmar Oelz
- Courant Inst. of Math. Sciences, New York University, 251
Mercer St, New York, NY 10012
| | - Alex Mogilner
- Courant Inst. of Math. Sciences, New York University, 251
Mercer St, New York, NY 10012
- Department of Biology, New York University
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47
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Recho P, Jerusalem A, Goriely A. Growth, collapse, and stalling in a mechanical model for neurite motility. Phys Rev E 2016; 93:032410. [PMID: 27078393 DOI: 10.1103/physreve.93.032410] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2015] [Indexed: 06/05/2023]
Abstract
Neurites, the long cellular protrusions that form the routes of the neuronal network, are capable of actively extending during early morphogenesis or regenerating after trauma. To perform this task, they rely on their cytoskeleton for mechanical support. In this paper, we present a three-component active gel model that describes neurites in the three robust mechanical states observed experimentally: collapsed, static, and motile. These states arise from an interplay between the physical forces driven by the growth of the microtubule-rich inner core of the neurite and the acto-myosin contractility of its surrounding cortical membrane. In particular, static states appear as a mechanical balance between traction and compression of these two parallel structures. The model predicts how the response of a neurite to a towing force depends on the force magnitude and recovers the response of neurites to several drug treatments that modulate the cytoskeleton active and passive properties.
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Affiliation(s)
- Pierre Recho
- Mathematical Institute, University of Oxford, Oxford OX26GG, United Kingdom
| | - Antoine Jerusalem
- Department of Engineering Science, University of Oxford, Oxford OX13PJ, United Kingdom
| | - Alain Goriely
- Mathematical Institute, University of Oxford, Oxford OX26GG, United Kingdom
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Sehring IM, Recho P, Denker E, Kourakis M, Mathiesen B, Hannezo E, Dong B, Jiang D. Assembly and positioning of actomyosin rings by contractility and planar cell polarity. eLife 2015; 4:e09206. [PMID: 26486861 PMCID: PMC4612727 DOI: 10.7554/elife.09206] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2015] [Accepted: 09/02/2015] [Indexed: 12/23/2022] Open
Abstract
The actomyosin cytoskeleton is a primary force-generating mechanism in morphogenesis, thus a robust spatial control of cytoskeletal positioning is essential. In this report, we demonstrate that actomyosin contractility and planar cell polarity (PCP) interact in post-mitotic Ciona notochord cells to self-assemble and reposition actomyosin rings, which play an essential role for cell elongation. Intriguingly, rings always form at the cells' anterior edge before migrating towards the center as contractility increases, reflecting a novel dynamical property of the cortex. Our drug and genetic manipulations uncover a tug-of-war between contractility, which localizes cortical flows toward the equator and PCP, which tries to reposition them. We develop a simple model of the physical forces underlying this tug-of-war, which quantitatively reproduces our results. We thus propose a quantitative framework for dissecting the relative contribution of contractility and PCP to the self-assembly and repositioning of cytoskeletal structures, which should be applicable to other morphogenetic events.
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Affiliation(s)
- Ivonne M Sehring
- Sars International Centre for Marine Molecular Biology, University of Bergen, Bergen, Norway
| | - Pierre Recho
- Department of Physico-Chemistry of Living Matter, Institut Curie, Paris, France.,Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Elsa Denker
- Sars International Centre for Marine Molecular Biology, University of Bergen, Bergen, Norway
| | - Matthew Kourakis
- Department of Molecular, Cellular and Developmental Biology, University of California, Santa Barbara, Santa Barbara, United States
| | - Birthe Mathiesen
- Sars International Centre for Marine Molecular Biology, University of Bergen, Bergen, Norway
| | - Edouard Hannezo
- Department of Physico-Chemistry of Living Matter, Institut Curie, Paris, France.,The Gurdon Institute, University of Cambridge, Cambridge, United Kingdom
| | - Bo Dong
- Ministry of Education Key Laboratory of Marine Genetics and Breeding, College of Marine Life Sciences, Ocean University of China, Qingdao, China.,Laboratory for Marine Biology and Biotechnology, Qingdao National Laboratory for Marine Science and Technology,
| | - Di Jiang
- Sars International Centre for Marine Molecular Biology, University of Bergen, Bergen, Norway
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Doostmohammadi A, Thampi SP, Saw TB, Lim CT, Ladoux B, Yeomans JM. Celebrating Soft Matter's 10th Anniversary: Cell division: a source of active stress in cellular monolayers. SOFT MATTER 2015; 11:7328-7336. [PMID: 26265162 DOI: 10.1039/c5sm01382h] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We introduce the notion of cell division-induced activity and show that the cell division generates extensile forces and drives dynamical patterns in cell assemblies. Extending the hydrodynamic models of lyotropic active nematics we describe turbulent-like velocity fields that are generated by the cell division in a confluent monolayer of cells. We show that the experimentally measured flow field of dividing Madin-Darby Canine Kidney (MDCK) cells is reproduced by our modeling approach. Division-induced activity acts together with intrinsic activity of the cells in extensile and contractile cell assemblies to change the flow and director patterns and the density of topological defects. Finally we model the evolution of the boundary of a cellular colony and compare the fingering instabilities induced by cell division to experimental observations on the expansion of MDCK cell cultures.
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Affiliation(s)
- Amin Doostmohammadi
- The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK.
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50
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Verkhovsky AB. The mechanisms of spatial and temporal patterning of cell-edge dynamics. Curr Opin Cell Biol 2015; 36:113-21. [PMID: 26432504 DOI: 10.1016/j.ceb.2015.09.001] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2015] [Revised: 09/11/2015] [Accepted: 09/11/2015] [Indexed: 01/14/2023]
Abstract
Adherent cells migrate and change their shape by means of protrusion and retraction at their edges. When and where these activities occur defines the shape of the cell and the way it moves. Despite a great deal of knowledge about the structural organization, components, and biochemical reactions involved in protrusion and retraction, the origins of their spatial and temporal patterns are still poorly understood. Chemical signaling circuitry is believed to be an important source of patterning, but recent studies highlighted mechanisms based on physical forces, motion, and mechanical feedback.
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Affiliation(s)
- Alexander B Verkhovsky
- Laboratory of Physics of Living Matter, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
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