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De Belly H, Weiner OD. Follow the flow: Actin and membrane act as an integrated system to globally coordinate cell shape and movement. Curr Opin Cell Biol 2024; 89:102392. [PMID: 38991476 DOI: 10.1016/j.ceb.2024.102392] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2024] [Revised: 06/01/2024] [Accepted: 06/06/2024] [Indexed: 07/13/2024]
Abstract
Migratory cells are polarized with protrusive fronts and contractile rears. This spatial organization necessitates long-range coordination of the signals that organize protrusions and contractions. Cells leverage reciprocal interactions of short-range biochemical signals and long-range mechanical forces for this integration. The interface between the plasma membrane and actin cortex is where this communication occurs. Here, we review how the membrane and cortex form an integrated system for long-range coordination of cell polarity. We highlight the role of membrane-to-cortex-attachment proteins as regulators of tension transmission across the cell and discuss the interplay between actin-membrane and polarity signaling complexes. Rather than presenting an exhaustive list of recent findings, we focus on important gaps in our current understanding.
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Affiliation(s)
- Henry De Belly
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, USA; Department of Biochemistry and Biophysics, University of California, San Francisco, San Francisco, CA, USA.
| | - Orion D Weiner
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, USA; Department of Biochemistry and Biophysics, University of California, San Francisco, San Francisco, CA, USA.
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2
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De Belly H, Yan S, Borja da Rocha H, Ichbiah S, Town JP, Zager PJ, Estrada DC, Meyer K, Turlier H, Bustamante C, Weiner OD. Cell protrusions and contractions generate long-range membrane tension propagation. Cell 2023; 186:3049-3061.e15. [PMID: 37311454 PMCID: PMC10330871 DOI: 10.1016/j.cell.2023.05.014] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Revised: 03/10/2023] [Accepted: 05/11/2023] [Indexed: 06/15/2023]
Abstract
Membrane tension is thought to be a long-range integrator of cell physiology. Membrane tension has been proposed to enable cell polarity during migration through front-back coordination and long-range protrusion competition. These roles necessitate effective tension transmission across the cell. However, conflicting observations have left the field divided as to whether cell membranes support or resist tension propagation. This discrepancy likely originates from the use of exogenous forces that may not accurately mimic endogenous forces. We overcome this complication by leveraging optogenetics to directly control localized actin-based protrusions or actomyosin contractions while simultaneously monitoring the propagation of membrane tension using dual-trap optical tweezers. Surprisingly, actin-driven protrusions and actomyosin contractions both elicit rapid global membrane tension propagation, whereas forces applied to cell membranes alone do not. We present a simple unifying mechanical model in which mechanical forces that engage the actin cortex drive rapid, robust membrane tension propagation through long-range membrane flows.
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Affiliation(s)
- Henry De Belly
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, USA; Department of Biochemistry and Biophysics, University of California, San Francisco, San Francisco, CA, USA
| | - Shannon Yan
- Department of Molecular and Cell Biology, University of California, Berkeley, Berkeley, CA 94720, USA; California Institute for Quantitative Biosciences, University of California, Berkeley, Berkeley, CA 94720, USA
| | - Hudson Borja da Rocha
- Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS, Inserm, Université PSL, Paris, France
| | - Sacha Ichbiah
- Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS, Inserm, Université PSL, Paris, France
| | - Jason P Town
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, USA; Department of Biochemistry and Biophysics, University of California, San Francisco, San Francisco, CA, USA
| | - Patrick J Zager
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, USA; Department of Biochemistry and Biophysics, University of California, San Francisco, San Francisco, CA, USA
| | - Dorothy C Estrada
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, USA; Department of Biochemistry and Biophysics, University of California, San Francisco, San Francisco, CA, USA
| | - Kirstin Meyer
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, USA; Department of Biochemistry and Biophysics, University of California, San Francisco, San Francisco, CA, USA
| | - Hervé Turlier
- Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS, Inserm, Université PSL, Paris, France.
| | - Carlos Bustamante
- Department of Molecular and Cell Biology, University of California, Berkeley, Berkeley, CA 94720, USA; California Institute for Quantitative Biosciences, University of California, Berkeley, Berkeley, CA 94720, USA; Jason L. Choy Laboratory of Single-Molecule Biophysics, University of California, Berkeley, Berkeley, CA, USA; Department of Physics, University of California, Berkeley, Berkeley, CA, USA; Howard Hughes Medical Institute, University of California, Berkeley, Berkeley, CA, USA; Kavli Energy Nanoscience Institute, University of California, Berkeley, Berkeley, CA, USA.
| | - Orion D Weiner
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, USA; Department of Biochemistry and Biophysics, University of California, San Francisco, San Francisco, CA, USA.
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3
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Gomez D, Lam KY, Mori Y. Front propagation in the shadow wave-pinning model. J Math Biol 2023; 86:72. [PMID: 37037923 DOI: 10.1007/s00285-023-01908-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2022] [Revised: 02/08/2023] [Accepted: 03/22/2023] [Indexed: 04/12/2023]
Abstract
In this paper we consider a non-local bistable reaction-diffusion equation which is a simplified version of the wave-pinning model of cell polarization. In the small diffusion limit, a typical solution u(x, t) of this model approaches one of the stable states of the bistable nonlinearity in different parts of the spatial domain [Formula: see text], separated by an interface moving at a normal velocity regulated by the integral [Formula: see text]. In what is often referred to as wave-pinning, feedback between mass-conservation and bistablity causes the interface to slow and approach a fixed limit. In the limit of a small diffusivity [Formula: see text], we prove that for any [Formula: see text] the interface can be estimated within [Formula: see text] of the location as predicted using formal asymptotics. We also discuss the sharpness of our result by comparing the formal asymptotic results with numerical simulations.
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Affiliation(s)
- Daniel Gomez
- Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104-6395, USA.
| | - King-Yeung Lam
- Department of Mathematics, The Ohio State University, Columbus, OH, 43210-1174, USA
| | - Yoichiro Mori
- Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104-6395, USA
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4
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Li JH, Trivedi V, Diz-Muñoz A. Understanding the interplay of membrane trafficking, cell surface mechanics, and stem cell differentiation. Semin Cell Dev Biol 2023; 133:123-134. [PMID: 35641408 PMCID: PMC9703995 DOI: 10.1016/j.semcdb.2022.05.010] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Revised: 04/08/2022] [Accepted: 05/14/2022] [Indexed: 01/17/2023]
Abstract
Stem cells can generate a diversity of cell types during development, regeneration and adult tissue homeostasis. Differentiation changes not only the cell fate in terms of gene expression but also the physical properties and functions of cells, e.g. the secretory activity, cell shape, or mechanics. Conversely, these activities and properties can also regulate differentiation itself. Membrane trafficking is known to modulate signal transduction and thus has the potential to control stem cell differentiation. On the other hand, membrane trafficking, particularly from and to the plasma membrane, depends on the mechanical properties of the cell surface such as tension within the plasma membrane or the cortex. Indeed, recent findings demonstrate that cell surface mechanics can also control cell fate. Here, we review the bidirectional relationships between these three fundamental cellular functions, i.e. membrane trafficking, cell surface mechanics, and stem cell differentiation. Furthermore, we discuss commonly used methods in each field and how combining them with new tools will enhance our understanding of their interplay. Understanding how membrane trafficking and cell surface mechanics can guide stem cell fate holds great potential as these concepts could be exploited for directed differentiation of stem cells for the fields of tissue engineering and regenerative medicine.
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Affiliation(s)
- Jia Hui Li
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Meyerhofstraße 1, Heidelberg 69117, Germany
| | - Vikas Trivedi
- EMBL, PRBB, Dr. Aiguader, 88, Barcelona 08003, Spain,Developmental Biology Unit, EMBL, Meyerhofstraße 1, Heidelberg 69117, Germany
| | - Alba Diz-Muñoz
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Meyerhofstraße 1, Heidelberg 69117, Germany.
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5
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Merino-Casallo F, Gomez-Benito MJ, Hervas-Raluy S, Garcia-Aznar JM. Unravelling cell migration: defining movement from the cell surface. Cell Adh Migr 2022; 16:25-64. [PMID: 35499121 PMCID: PMC9067518 DOI: 10.1080/19336918.2022.2055520] [Citation(s) in RCA: 22] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 03/10/2022] [Indexed: 12/13/2022] Open
Abstract
Cell motility is essential for life and development. Unfortunately, cell migration is also linked to several pathological processes, such as cancer metastasis. Cells' ability to migrate relies on many actors. Cells change their migratory strategy based on their phenotype and the properties of the surrounding microenvironment. Cell migration is, therefore, an extremely complex phenomenon. Researchers have investigated cell motility for more than a century. Recent discoveries have uncovered some of the mysteries associated with the mechanisms involved in cell migration, such as intracellular signaling and cell mechanics. These findings involve different players, including transmembrane receptors, adhesive complexes, cytoskeletal components , the nucleus, and the extracellular matrix. This review aims to give a global overview of our current understanding of cell migration.
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Affiliation(s)
- Francisco Merino-Casallo
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza, Spain
- Department of Mechanical Engineering, University of Zaragoza, Zaragoza, Spain
| | - Maria Jose Gomez-Benito
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza, Spain
- Department of Mechanical Engineering, University of Zaragoza, Zaragoza, Spain
| | - Silvia Hervas-Raluy
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza, Spain
- Department of Mechanical Engineering, University of Zaragoza, Zaragoza, Spain
| | - Jose Manuel Garcia-Aznar
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza, Spain
- Department of Mechanical Engineering, University of Zaragoza, Zaragoza, Spain
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6
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Merino-Casallo F, Gomez-Benito MJ, Martinez-Cantin R, Garcia-Aznar JM. A mechanistic protrusive-based model for 3D cell migration. Eur J Cell Biol 2022; 101:151255. [PMID: 35843121 DOI: 10.1016/j.ejcb.2022.151255] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Revised: 06/15/2022] [Accepted: 07/01/2022] [Indexed: 11/17/2022] Open
Abstract
Cell migration is essential for a variety of biological processes, such as embryogenesis, wound healing, and the immune response. After more than a century of research-mainly on flat surfaces-, there are still many unknowns about cell motility. In particular, regarding how cells migrate within 3D matrices, which more accurately replicate in vivo conditions. We present a novel in silico model of 3D mesenchymal cell migration regulated by the chemical and mechanical profile of the surrounding environment. This in silico model considers cell's adhesive and nuclear phenotypes, the effects of the steric hindrance of the matrix, and cells ability to degradate the ECM. These factors are crucial when investigating the increasing difficulty that migrating cells find to squeeze their nuclei through dense matrices, which may act as physical barriers. Our results agree with previous in vitro observations where fibroblasts cultured in collagen-based hydrogels did not durotax toward regions with higher collagen concentrations. Instead, they exhibited an adurotactic behavior, following a more random trajectory. Overall, cell's migratory response in 3D domains depends on its phenotype, and the properties of the surrounding environment, that is, 3D cell motion is strongly dependent on the context.
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Affiliation(s)
- Francisco Merino-Casallo
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza 50018, Spain; Department of Mechanical Engineering, Universidad de Zaragoza, Zaragoza 50009, Spain
| | - Maria Jose Gomez-Benito
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza 50018, Spain; Department of Mechanical Engineering, Universidad de Zaragoza, Zaragoza 50009, Spain
| | - Ruben Martinez-Cantin
- Robotics, Perception and Real Time Group (RoPeRT), Aragon Institute of Engineering Research (I3A), Zaragoza 50018, Spain; Department of Computer Science and System Engineering, Universidad de Zaragoza, Zaragoza 50009, Spain
| | - Jose Manuel Garcia-Aznar
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza 50018, Spain; Department of Mechanical Engineering, Universidad de Zaragoza, Zaragoza 50009, Spain.
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7
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The many faces of membrane tension: Challenges across systems and scales. BIOCHIMICA ET BIOPHYSICA ACTA. BIOMEMBRANES 2022; 1864:183897. [PMID: 35231438 DOI: 10.1016/j.bbamem.2022.183897] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Revised: 02/09/2022] [Accepted: 02/16/2022] [Indexed: 01/27/2023]
Abstract
Our understanding of the role of membrane tension in the field of membrane biophysics is rapidly evolving from a passive construct to an active player in a variety of cellular phenomena. Membrane tension has been shown to be a key regulator of many cellular processes ranging including trafficking, ion channel activation, and the invasion of red blood cells by malaria parasites. Recent experimental advances in cells, including the development of a fluorescent tension reporter, have shown that membrane tension is heterogeneous. In this mini-review, I summarize the recent advances in membrane tension measurements and discuss the contributions from different cellular constituents such as the cortical cytoskeleton. Then, I will explore how these different complexities can be considered in biophysical models of different scales. Finally, I will elaborate on the need for iterations between models and experiments as technologies in both fields advance to enable us to obtain critical insights into the physiological role of membrane tension as a critical component of mechanotransduction.
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8
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Rajagopal V, Arumugam S, Hunter PJ, Khadangi A, Chung J, Pan M. The Cell Physiome: What Do We Need in a Computational Physiology Framework for Predicting Single-Cell Biology? Annu Rev Biomed Data Sci 2022; 5:341-366. [PMID: 35576556 DOI: 10.1146/annurev-biodatasci-072018-021246] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Modern biology and biomedicine are undergoing a big data explosion, needing advanced computational algorithms to extract mechanistic insights on the physiological state of living cells. We present the motivation for the Cell Physiome project: a framework and approach for creating, sharing, and using biophysics-based computational models of single-cell physiology. Using examples in calcium signaling, bioenergetics, and endosomal trafficking, we highlight the need for spatially detailed, biophysics-based computational models to uncover new mechanisms underlying cell biology. We review progress and challenges to date toward creating cell physiome models. We then introduce bond graphs as an efficient way to create cell physiome models that integrate chemical, mechanical, electromagnetic, and thermal processes while maintaining mass and energy balance. Bond graphs enhance modularization and reusability of computational models of cells at scale. We conclude with a look forward at steps that will help fully realize this exciting new field of mechanistic biomedical data science. Expected final online publication date for the Annual Review of Biomedical Data Science, Volume 5 is August 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Vijay Rajagopal
- Department of Biomedical Engineering, University of Melbourne, Melbourne, Victoria, Australia;
| | - Senthil Arumugam
- Cellular Physiology Lab, Monash Biomedicine Discovery Institute, Faculty of Medicine, Nursing and Health Sciences; European Molecular Biological Laboratory (EMBL) Australia; and Australian Research Council Centre of Excellence in Advanced Molecular Imaging, Monash University, Clayton/Melbourne, Victoria, Australia
| | - Peter J Hunter
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Afshin Khadangi
- Department of Biomedical Engineering, University of Melbourne, Melbourne, Victoria, Australia;
| | - Joshua Chung
- Department of Biomedical Engineering, University of Melbourne, Melbourne, Victoria, Australia;
| | - Michael Pan
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria, Australia
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9
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Harcha PA, López-López T, Palacios AG, Sáez PJ. Pannexin Channel Regulation of Cell Migration: Focus on Immune Cells. Front Immunol 2022; 12:750480. [PMID: 34975840 PMCID: PMC8716617 DOI: 10.3389/fimmu.2021.750480] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2021] [Accepted: 11/15/2021] [Indexed: 12/12/2022] Open
Abstract
The role of Pannexin (PANX) channels during collective and single cell migration is increasingly recognized. Amongst many functions that are relevant to cell migration, here we focus on the role of PANX-mediated adenine nucleotide release and associated autocrine and paracrine signaling. We also summarize the contribution of PANXs with the cytoskeleton, which is also key regulator of cell migration. PANXs, as mechanosensitive ATP releasing channels, provide a unique link between cell migration and purinergic communication. The functional association with several purinergic receptors, together with a plethora of signals that modulate their opening, allows PANX channels to integrate physical and chemical cues during inflammation. Ubiquitously expressed in almost all immune cells, PANX1 opening has been reported in different immunological contexts. Immune activation is the epitome coordination between cell communication and migration, as leukocytes (i.e., T cells, dendritic cells) exchange information while migrating towards the injury site. In the current review, we summarized the contribution of PANX channels during immune cell migration and recruitment; although we also compile the available evidence for non-immune cells (including fibroblasts, keratinocytes, astrocytes, and cancer cells). Finally, we discuss the current evidence of PANX1 and PANX3 channels as a both positive and/or negative regulator in different inflammatory conditions, proposing a general mechanism of these channels contribution during cell migration.
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Affiliation(s)
- Paloma A Harcha
- Centro Interdisciplinario de Neurociencia de Valparaíso, Instituto de Neurociencia, Facultad de Ciencias, Universidad de Valparaíso, Valparaíso, Chile
| | - Tamara López-López
- Cell Communication and Migration Laboratory, Institute of Biochemistry and Molecular Cell Biology, Center for Experimental Medicine, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
| | - Adrián G Palacios
- Centro Interdisciplinario de Neurociencia de Valparaíso, Instituto de Neurociencia, Facultad de Ciencias, Universidad de Valparaíso, Valparaíso, Chile
| | - Pablo J Sáez
- Cell Communication and Migration Laboratory, Institute of Biochemistry and Molecular Cell Biology, Center for Experimental Medicine, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
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10
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Cortical tension initiates the positive feedback loop between cadherin and F-actin. Biophys J 2022; 121:596-606. [PMID: 35031276 PMCID: PMC8874026 DOI: 10.1016/j.bpj.2022.01.006] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Revised: 11/30/2021] [Accepted: 01/10/2022] [Indexed: 11/20/2022] Open
Abstract
Adherens junctions physically link two cells at their contact interface via extracellular binding between cadherin molecules and intracellular interactions between cadherins and the actin cytoskeleton. Cadherin and actomyosin cytoskeletal dynamics are regulated reciprocally by mechanical and chemical signals, which subsequently determine the strength of cell-cell adhesions and the emergent organization and stiffness of the tissues they form. However, an understanding of the integrated system is lacking. We present a new mechanistic computational model of intercellular junction maturation in a cell doublet to investigate the mechanochemical cross talk that regulates adherens junction formation and homeostasis. The model couples a two-dimensional lattice-based simulation of cadherin dynamics with a reaction-diffusion representation of the reorganising actomyosin network through its regulation by Rho signalling at the intracellular junction. We demonstrate that local immobilization of cadherin induces cluster formation in a cis-less-dependent manner. We then recapitulate the process of cell-cell contact formation. Our model suggests that cortical tension applied on the contact rim can explain the ring distribution of cadherin and actin filaments (F-actin) on the cell-cell contact of the cell doublet. Furthermore, we propose and test the hypothesis that cadherin and F-actin interact like a positive feedback loop, which is necessary for formation of the ring structure. Different patterns of cadherin distribution were observed as an emergent property of disturbances of this positive feedback loop. We discuss these findings in light of available experimental observations on underlying mechanisms related to cadherin/F-actin binding and the mechanical environment.
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11
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Rens EG, Edelstein-Keshet L. Cellular Tango: how extracellular matrix adhesion choreographs Rac-Rho signaling and cell movement. Phys Biol 2021; 18. [PMID: 34544056 DOI: 10.1088/1478-3975/ac2888] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2021] [Accepted: 09/20/2021] [Indexed: 12/14/2022]
Abstract
The small GTPases Rac and Rho are known to regulate eukaryotic cell shape, promoting front protrusion (Rac) or rear retraction (Rho) of the cell edge. Such cell deformation changes the contact and adhesion of cell to the extracellular matrix (ECM), while ECM signaling through integrin receptors also affects GTPase activity. We develop and investigate a model for this three-way feedback loop in 1D and 2D spatial domains, as well as in a fully deforming 2D cell shapes with detailed adhesion-bond biophysics. The model consists of reaction-diffusion equations solved numerically with open-source software, Morpheus, and with custom-built cellular Potts model simulations. We find a variety of patterns and cell behaviors, including persistent polarity, flipped front-back cell polarity oscillations, spiral waves, and random protrusion-retraction. We show that the observed spatial patterns depend on the cell shape, and vice versa.
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Affiliation(s)
- Elisabeth G Rens
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.,Department of Mathematics, University of British Columbia, Vancouver, Canada
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12
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MacDonald JS, Bourgault Y, Lutscher F. Moving-habitat models: A numerical approach. Math Biosci 2021; 341:108711. [PMID: 34547364 DOI: 10.1016/j.mbs.2021.108711] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Revised: 09/09/2021] [Accepted: 09/09/2021] [Indexed: 10/20/2022]
Abstract
As the global climate changes, biological populations have to adapt in place or move in space to stay within their preferred temperature regime. Empirical evidence suggests that shifting speeds of temperature isoclines are location and elevation dependent and may accelerate over time. We present a mathematical tool to study transient behaviour of population dynamics within such moving habitats to discern between populations at high and low risk of extinction. We introduce a system of reaction-diffusion equations to study the impact of varying shifting speeds on the persistence and distribution of a single species. Our model includes habitat dependent movement behaviour and habitat preference of individuals. These assumptions result in a jump in density across habitat types and generalize previous studies. We build and validate a numerical finite difference scheme to solve the resulting equations. Our numerical scheme uses a coordinate system where the location of the moving suitable habitat is fixed in space and a modification of a finite difference scheme to capture the jump in density. We explore a variety of shifting-speed scenarios and contribute insights into the mechanisms that support population persistence through time in shifting habitats. One common finding is that a strong bias for the suitable habitat helps the population persist at faster shifting speeds, yet sustains a smaller total population at slower shifting speeds.
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Affiliation(s)
- Jane S MacDonald
- University of Ottawa, Department of Mathematics and Statistics, 150 Louis-Pasteur Pvt, K1N 6N5, Ottawa, Canada.
| | - Yves Bourgault
- University of Ottawa, Department of Mathematics and Statistics, 150 Louis-Pasteur Pvt, K1N 6N5, Ottawa, Canada.
| | - Frithjof Lutscher
- University of Ottawa, Department of Mathematics and Statistics, 150 Louis-Pasteur Pvt, K1N 6N5, Ottawa, Canada; University of Ottawa, Department of Biology, Canada.
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13
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Three-dimensional stochastic simulation of chemoattractant-mediated excitability in cells. PLoS Comput Biol 2021; 17:e1008803. [PMID: 34260581 PMCID: PMC8330952 DOI: 10.1371/journal.pcbi.1008803] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Revised: 08/03/2021] [Accepted: 06/08/2021] [Indexed: 01/21/2023] Open
Abstract
During the last decade, a consensus has emerged that the stochastic triggering of an excitable system drives pseudopod formation and subsequent migration of amoeboid cells. The presence of chemoattractant stimuli alters the threshold for triggering this activity and can bias the direction of migration. Though noise plays an important role in these behaviors, mathematical models have typically ignored its origin and merely introduced it as an external signal into a series of reaction-diffusion equations. Here we consider a more realistic description based on a reaction-diffusion master equation formalism to implement these networks. In this scheme, noise arises naturally from a stochastic description of the various reaction and diffusion terms. Working on a three-dimensional geometry in which separate compartments are divided into a tetrahedral mesh, we implement a modular description of the system, consisting of G-protein coupled receptor signaling (GPCR), a local excitation-global inhibition mechanism (LEGI), and signal transduction excitable network (STEN). Our models implement detailed biochemical descriptions whenever this information is available, such as in the GPCR and G-protein interactions. In contrast, where the biochemical entities are less certain, such as the LEGI mechanism, we consider various possible schemes and highlight the differences between them. Our simulations show that even when the LEGI mechanism displays perfect adaptation in terms of the mean level of proteins, the variance shows a dose-dependence. This differs between the various models considered, suggesting a possible means for determining experimentally among the various potential networks. Overall, our simulations recreate temporal and spatial patterns observed experimentally in both wild-type and perturbed cells, providing further evidence for the excitable system paradigm. Moreover, because of the overall importance and ubiquity of the modules we consider, including GPCR signaling and adaptation, our results will be of interest beyond the field of directed migration. Though the term noise usually carries negative connotations, it can also contribute positively to the characteristic dynamics of a system. In biological systems, where noise arises from the stochastic interactions between molecules, its study is usually confined to genetic regulatory systems in which copy numbers are small and fluctuations large. However, noise can have important roles when the number of signaling molecules is large. The extension of pseudopods and the subsequent motion of amoeboid cells arises from the noise-induced trigger of an excitable system. Chemoattractant signals bias this triggering thereby directing cell motion. To date, this paradigm has not been tested by mathematical models that account accurately for the noise that arises in the corresponding reactions. In this study, we employ a reaction-diffusion master equation approach to investigate the effects of noise. Using a modular approach and a three-dimensional cell model with specific subdomains attributed to the cell membrane and cortex, we explore the spatiotemporal dynamics of the system. Our simulations recreate many experimentally-observed cell behaviors thereby supporting the biased-excitable network hypothesis.
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14
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Tambyah TA, Murphy RJ, Buenzli PR, Simpson MJ. A free boundary mechanobiological model of epithelial tissues. Proc Math Phys Eng Sci 2020; 476:20200528. [PMID: 33362419 PMCID: PMC7735320 DOI: 10.1098/rspa.2020.0528] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Accepted: 10/21/2020] [Indexed: 12/12/2022] Open
Abstract
In this study, we couple intracellular signalling and cell-based mechanical properties to develop a novel free boundary mechanobiological model of epithelial tissue dynamics. Mechanobiological coupling is introduced at the cell level in a discrete modelling framework, and new reaction-diffusion equations are derived to describe tissue-level outcomes. The free boundary evolves as a result of the underlying biological mechanisms included in the discrete model. To demonstrate the accuracy of the continuum model, we compare numerical solutions of the discrete and continuum models for two different signalling pathways. First, we study the Rac-Rho pathway where cell- and tissue-level mechanics are directly related to intracellular signalling. Second, we study an activator-inhibitor system which gives rise to spatial and temporal patterning related to Turing patterns. In all cases, the continuum model and free boundary condition accurately reflect the cell-level processes included in the discrete model.
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Affiliation(s)
| | | | | | - Matthew J. Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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