1
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Heyn JCJ, Rädler JO, Falcke M. Mesenchymal cell migration on one-dimensional micropatterns. Front Cell Dev Biol 2024; 12:1352279. [PMID: 38694822 PMCID: PMC11062138 DOI: 10.3389/fcell.2024.1352279] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Accepted: 03/29/2024] [Indexed: 05/04/2024] Open
Abstract
Quantitative studies of mesenchymal cell motion are important to elucidate cytoskeleton function and mechanisms of cell migration. To this end, confinement of cell motion to one dimension (1D) significantly simplifies the problem of cell shape in experimental and theoretical investigations. Here we review 1D migration assays employing micro-fabricated lanes and reflect on the advantages of such platforms. Data are analyzed using biophysical models of cell migration that reproduce the rich scenario of morphodynamic behavior found in 1D. We describe basic model assumptions and model behavior. It appears that mechanical models explain the occurrence of universal relations conserved across different cell lines such as the adhesion-velocity relation and the universal correlation between speed and persistence (UCSP). We highlight the unique opportunity of reproducible and standardized 1D assays to validate theory based on statistical measures from large data of trajectories and discuss the potential of experimental settings embedding controlled perturbations to probe response in migratory behavior.
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Affiliation(s)
- Johannes C. J. Heyn
- Fakultät für Physik, Ludwig-Maximilians-Universität München (LMU), Munich, Germany
| | - Joachim O. Rädler
- Fakultät für Physik, Ludwig-Maximilians-Universität München (LMU), Munich, Germany
| | - Martin Falcke
- Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany
- Department of Physics, Humboldt University, Berlin, Germany
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2
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Stock C. pH-regulated single cell migration. Pflugers Arch 2024; 476:639-658. [PMID: 38214759 PMCID: PMC11006768 DOI: 10.1007/s00424-024-02907-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2023] [Revised: 12/21/2023] [Accepted: 01/02/2024] [Indexed: 01/13/2024]
Abstract
Over the last two decades, extra- and intracellular pH have emerged as fundamental regulators of cell motility. Fundamental physiological and pathological processes relying on appropriate cell migration, such as embryonic development, wound healing, and a proper immune defense on the one hand, and autoimmune diseases, metastatic cancer, and the progression of certain parasitic diseases on the other, depend on surrounding pH. In addition, migrating single cells create their own localized pH nanodomains at their surface and in the cytosol. By this means, the migrating cells locally modulate their adhesion to, and the re-arrangement and digestion of, the extracellular matrix. At the same time, the cytosolic nanodomains tune cytoskeletal dynamics along the direction of movement resulting in concerted lamellipodia protrusion and rear end retraction. Extracellular pH gradients as found in wounds, inflamed tissues, or the periphery of tumors stimulate directed cell migration, and long-term exposure to acidic conditions can engender a more migratory and invasive phenotype persisting for hours up to several generations of cells after they have left the acidic milieu. In the present review, the different variants of pH-dependent single cell migration are described. The underlying pH-dependent molecular mechanisms such as conformational changes of adhesion molecules, matrix protease activity, actin (de-)polymerization, and signaling events are explained, and molecular pH sensors stimulated by H+ signaling are presented.
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Affiliation(s)
- Christian Stock
- Department of Gastroenterology, Hepatology, Infectiology & Endocrinology, Hannover Medical School, Carl-Neuberg-Str. 1, 30625, Hannover, Germany.
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3
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Lin Y, Pal DS, Banerjee P, Banerjee T, Qin G, Deng Y, Borleis J, Iglesias PA, Devreotes PN. Ras-mediated homeostatic control of front-back signaling dictates cell polarity. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.08.30.555648. [PMID: 37693515 PMCID: PMC10491231 DOI: 10.1101/2023.08.30.555648] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/12/2023]
Abstract
Studies in the model systems, Dictyostelium amoebae and HL-60 neutrophils, have shown that local Ras activity directly regulates cell motility or polarity. Localized Ras activation on the membrane is spatiotemporally regulated by its activators, RasGEFs, and inhibitors, RasGAPs, which might be expected to create a stable 'front' and 'back', respectively, in migrating cells. Focusing on C2GAPB in amoebae and RASAL3 in neutrophils, we investigated how Ras activity along the cortex controls polarity. Since existing gene knockout and overexpression studies can be circumvented, we chose optogenetic approaches to assess the immediate, local effects of these Ras regulators on the cell cortex. In both cellular systems, optically targeting the respective RasGAPs to the cell front extinguished existing protrusions and changed the direction of migration, as might be expected. However, when the expression of C2GAPB was induced globally, amoebae polarized within hours. Furthermore, within minutes of globally recruiting either C2GAPB in amoebae or RASAL3 in neutrophils, each cell type polarized and moved more rapidly. Targeting the RasGAPs to the cell backs exaggerated these effects on migration and polarity. Overall, in both cell types, RasGAP-mediated polarization was brought about by increased actomyosin contractility at the back and sustained, localized F-actin polymerization at the front. These experimental results were accurately captured by computational simulations in which Ras levels control front and back feedback loops. The discovery that context-dependent Ras activity on the cell cortex has counterintuitive, unanticipated effects on cell polarity can have important implications for future drug-design strategies targeting oncogenic Ras.
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4
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Beta C, Edelstein-Keshet L, Gov N, Yochelis A. From actin waves to mechanism and back: How theory aids biological understanding. eLife 2023; 12:e87181. [PMID: 37428017 DOI: 10.7554/elife.87181] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 06/01/2023] [Indexed: 07/11/2023] Open
Abstract
Actin dynamics in cell motility, division, and phagocytosis is regulated by complex factors with multiple feedback loops, often leading to emergent dynamic patterns in the form of propagating waves of actin polymerization activity that are poorly understood. Many in the actin wave community have attempted to discern the underlying mechanisms using experiments and/or mathematical models and theory. Here, we survey methods and hypotheses for actin waves based on signaling networks, mechano-chemical effects, and transport characteristics, with examples drawn from Dictyostelium discoideum, human neutrophils, Caenorhabditis elegans, and Xenopus laevis oocytes. While experimentalists focus on the details of molecular components, theorists pose a central question of universality: Are there generic, model-independent, underlying principles, or just boundless cell-specific details? We argue that mathematical methods are equally important for understanding the emergence, evolution, and persistence of actin waves and conclude with a few challenges for future studies.
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Affiliation(s)
- Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
| | | | - Nir Gov
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Arik Yochelis
- Swiss Institute for Dryland Environmental and Energy Research, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion, Israel
- Department of Physics, Ben-Gurion University of the Negev, Be'er Sheva, Israel
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5
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Banerjee T, Matsuoka S, Biswas D, Miao Y, Pal DS, Kamimura Y, Ueda M, Devreotes PN, Iglesias PA. A dynamic partitioning mechanism polarizes membrane protein distribution. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.01.03.522496. [PMID: 36712016 PMCID: PMC9881856 DOI: 10.1101/2023.01.03.522496] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
The plasma membrane is widely regarded as the hub of the signal transduction network activities that drives numerous physiological responses, including cell polarity and migration. Yet, the symmetry breaking process in the membrane, that leads to dynamic compartmentalization of different proteins, remains poorly understood. Using multimodal live-cell imaging, here we first show that multiple endogenous and synthetic lipid-anchored proteins, despite maintaining stable tight association with the inner leaflet of the plasma membrane, were unexpectedly depleted from the membrane domains where the signaling network was spontaneously activated such as in the new protrusions as well as within the propagating ventral waves. Although their asymmetric patterns resembled those of standard peripheral "back" proteins such as PTEN, unlike the latter, these lipidated proteins did not dissociate from the membrane upon global receptor activation. Our experiments not only discounted the possibility of recurrent reversible translocation from membrane to cytosol as it occurs for weakly bound peripheral membrane proteins, but also ruled out the necessity of directed vesicular trafficking and cytoskeletal supramolecular structure-based restrictions in driving these dynamic symmetry breaking events. Selective photoconversion-based protein tracking assays suggested that these asymmetric patterns instead originate from the inherent ability of these membrane proteins to "dynamically partition" into distinct domains within the plane of the membrane. Consistently, single-molecule measurements showed that these lipid-anchored molecules have substantially dissimilar diffusion profiles in different regions of the membrane. When these profiles were incorporated into an excitable network-based stochastic reaction-diffusion model of the system, simulations revealed that our proposed "dynamic partitioning" mechanism is sufficient to give rise to familiar asymmetric propagating wave patterns. Moreover, we demonstrated that normally uniform integral and lipid-anchored membrane proteins in Dictyostelium and mammalian neutrophil cells can be induced to partition spatiotemporally to form polarized patterns, by optogenetically recruiting membrane domain-specific peptides to these proteins. Together, our results indicate "dynamic partitioning" as a new mechanism of plasma membrane organization, that can account for large-scale compartmentalization of a wide array of lipid-anchored and integral membrane proteins in different physiological processes.
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6
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Tarama M, Mori K, Yamamoto R. Mechanochemical subcellular-element model of crawling cells. Front Cell Dev Biol 2022; 10:1046053. [PMID: 36544905 PMCID: PMC9760904 DOI: 10.3389/fcell.2022.1046053] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Accepted: 11/11/2022] [Indexed: 12/12/2022] Open
Abstract
Constructing physical models of living cells and tissues is an extremely challenging task because of the high complexities of both intra- and intercellular processes. In addition, the force that a single cell generates vanishes in total due to the law of action and reaction. The typical mechanics of cell crawling involve periodic changes in the cell shape and in the adhesion characteristics of the cell to the substrate. However, the basic physical mechanisms by which a single cell coordinates these processes cooperatively to achieve autonomous migration are not yet well understood. To obtain a clearer grasp of how the intracellular force is converted to directional motion, we develop a basic mechanochemical model of a crawling cell based on subcellular elements with the focus on the dependence of the protrusion and contraction as well as the adhesion and de-adhesion processes on intracellular biochemical signals. By introducing reaction-diffusion equations that reproduce traveling waves of local chemical concentrations, we clarify that the chemical dependence of the cell-substrate adhesion dynamics determines the crawling direction and distance with one chemical wave. Finally, we also perform multipole analysis of the traction force to compare it with the experimental results. Our present work sheds light on how intracellular chemical reactions are converted to a directional cell migration under the force-free condition. Although the detailed mechanisms of actual cells are far more complicated than our simple model, we believe that this mechanochemical model is a good prototype for more realistic models.
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Affiliation(s)
- Mitsusuke Tarama
- Department of Physics, Kyushu University, Fukuoka, Japan,*Correspondence: Mitsusuke Tarama,
| | - Kenji Mori
- Department of Chemical Engineering, Kyoto University, Kyoto, Japan
| | - Ryoichi Yamamoto
- Department of Chemical Engineering, Kyoto University, Kyoto, Japan
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7
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Banerjee T, Biswas D, Pal DS, Miao Y, Iglesias PA, Devreotes PN. Spatiotemporal dynamics of membrane surface charge regulates cell polarity and migration. Nat Cell Biol 2022; 24:1499-1515. [PMID: 36202973 PMCID: PMC10029748 DOI: 10.1038/s41556-022-00997-7] [Citation(s) in RCA: 27] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2021] [Accepted: 08/18/2022] [Indexed: 12/12/2022]
Abstract
During cell migration and polarization, numerous signal transduction and cytoskeletal components self-organize to generate localized protrusions. Although biochemical and genetic analyses have delineated many specific interactions, how the activation and localization of so many different molecules are spatiotemporally orchestrated at the subcellular level has remained unclear. Here we show that the regulation of negative surface charge on the inner leaflet of the plasma membrane plays an integrative role in the molecular interactions. Surface charge, or zeta potential, is transiently lowered at new protrusions and within cortical waves of Ras/PI3K/TORC2/F-actin network activation. Rapid alterations of inner leaflet anionic phospholipids-such as PI(4,5)P2, PI(3,4)P2, phosphatidylserine and phosphatidic acid-collectively contribute to the surface charge changes. Abruptly reducing the surface charge by recruiting positively charged optogenetic actuators was sufficient to trigger the entire biochemical network, initiate de novo protrusions and abrogate pre-existing polarity. These effects were blocked by genetic or pharmacological inhibition of key signalling components such as AKT and PI3K/TORC2. Conversely, increasing the negative surface charge deactivated the network and locally suppressed chemoattractant-induced protrusions or subverted EGF-induced ERK activation. Computational simulations involving excitable biochemical networks demonstrated that slight changes in feedback loops, induced by recruitment of the charged actuators, could lead to outsized effects on system activation. We propose that key signalling network components act on, and are in turn acted upon, by surface charge, closing feedback loops, which bring about the global-scale molecular self-organization required for spontaneous protrusion formation, cell migration and polarity establishment.
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Affiliation(s)
- Tatsat Banerjee
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
- Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - Debojyoti Biswas
- Department of Electrical and Computer Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - Dhiman Sankar Pal
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
| | - Yuchuan Miao
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
- Department of Biological Chemistry, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
| | - Pablo A Iglesias
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
- Department of Electrical and Computer Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - Peter N Devreotes
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA.
- Department of Biological Chemistry, School of Medicine, Johns Hopkins University, Baltimore, MD, USA.
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8
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Yochelis A, Flemming S, Beta C. Versatile Patterns in the Actin Cortex of Motile Cells: Self-Organized Pulses Can Coexist with Macropinocytic Ring-Shaped Waves. PHYSICAL REVIEW LETTERS 2022; 129:088101. [PMID: 36053696 DOI: 10.1103/physrevlett.129.088101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2022] [Accepted: 08/03/2022] [Indexed: 06/15/2023]
Abstract
Self-organized patterns in the actin cytoskeleton are essential for eukaryotic cellular life. They are the building blocks of many functional structures that often operate simultaneously to facilitate, for example, nutrient uptake and movement of cells. However, identifying how qualitatively distinct actin patterns can coexist remains a challenge. Using bifurcation theory of a mass conserved activator-inhibitor system, we uncover a generic mechanism of how different actin waves-traveling waves and excitable pulses-organize and simultaneously emerge. Live-cell imaging experiments indeed reveal that narrow, planar, and fast-moving excitable pulses may coexist with ring-shaped macropinocytic actin waves in the cortex of motile amoeboid cells.
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Affiliation(s)
- Arik Yochelis
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
- Department of Physics, Ben-Gurion University of the Negev, Be'er Sheva 8410501, Israel
| | - Sven Flemming
- Institute of Physics and Astronomy, University of Potsdam, Potsdam 14476, Germany
| | - Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, Potsdam 14476, Germany
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9
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Michaud A, Leda M, Swider ZT, Kim S, He J, Landino J, Valley JR, Huisken J, Goryachev AB, von Dassow G, Bement WM. A versatile cortical pattern-forming circuit based on Rho, F-actin, Ect2, and RGA-3/4. J Cell Biol 2022; 221:213290. [PMID: 35708547 PMCID: PMC9206115 DOI: 10.1083/jcb.202203017] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Revised: 05/09/2022] [Accepted: 05/30/2022] [Indexed: 01/16/2023] Open
Abstract
Many cells can generate complementary traveling waves of actin filaments (F-actin) and cytoskeletal regulators. This phenomenon, termed cortical excitability, results from coupled positive and negative feedback loops of cytoskeletal regulators. The nature of these feedback loops, however, remains poorly understood. We assessed the role of the Rho GAP RGA-3/4 in the cortical excitability that accompanies cytokinesis in both frog and starfish. RGA-3/4 localizes to the cytokinetic apparatus, “chases” Rho waves in an F-actin–dependent manner, and when coexpressed with the Rho GEF Ect2, is sufficient to convert the normally quiescent, immature Xenopus oocyte cortex into a dramatically excited state. Experiments and modeling show that changing the ratio of RGA-3/4 to Ect2 produces cortical behaviors ranging from pulses to complex waves of Rho activity. We conclude that RGA-3/4, Ect2, Rho, and F-actin form the core of a versatile circuit that drives a diverse range of cortical behaviors, and we demonstrate that the immature oocyte is a powerful model for characterizing these dynamics.
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Affiliation(s)
- Ani Michaud
- Cellular and Molecular Biology Graduate Program, University of Wisconsin-Madison, Madison, WI.,Center for Quantitative Cell Imaging, University of Wisconsin-Madison, Madison, WI
| | - Marcin Leda
- Center for Synthetic and Systems Biology, University of Edinburgh, Edinburgh, UK
| | - Zachary T Swider
- Cellular and Molecular Biology Graduate Program, University of Wisconsin-Madison, Madison, WI.,Center for Quantitative Cell Imaging, University of Wisconsin-Madison, Madison, WI
| | - Songeun Kim
- Cellular and Molecular Biology Graduate Program, University of Wisconsin-Madison, Madison, WI.,Center for Quantitative Cell Imaging, University of Wisconsin-Madison, Madison, WI
| | - Jiaye He
- Department of Integrative Biology, University of Wisconsin-Madison, Madison, WI.,Morgridge Institute for Research, University of Wisconsin-Madison, Madison, WI
| | - Jennifer Landino
- Department of Molecular, Cellular, and Developmental Biology, University of Michigan-Ann Arbor, Ann Arbor, MI
| | - Jenna R Valley
- Oregon Institute of Marine Biology, University of Oregon, Charleston, OR
| | - Jan Huisken
- Department of Integrative Biology, University of Wisconsin-Madison, Madison, WI.,Morgridge Institute for Research, University of Wisconsin-Madison, Madison, WI
| | - Andrew B Goryachev
- Center for Synthetic and Systems Biology, University of Edinburgh, Edinburgh, UK
| | - George von Dassow
- Oregon Institute of Marine Biology, University of Oregon, Charleston, OR
| | - William M Bement
- Center for Quantitative Cell Imaging, University of Wisconsin-Madison, Madison, WI.,Department of Integrative Biology, University of Wisconsin-Madison, Madison, WI
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10
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Swider ZT, Michaud A, Leda M, Landino J, Goryachev AB, Bement WM. Cell cycle and developmental control of cortical excitability in Xenopus laevis. Mol Biol Cell 2022; 33:ar73. [PMID: 35594176 PMCID: PMC9635278 DOI: 10.1091/mbc.e22-01-0025] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Interest in cortical excitability—the ability of the cell cortex to generate traveling waves of protein activity—has grown considerably over the past 20 years. Attributing biological functions to cortical excitability requires an understanding of the natural behavior of excitable waves and the ability to accurately quantify wave properties. Here we have investigated and quantified the onset of cortical excitability in Xenopus laevis eggs and embryos and the changes in cortical excitability throughout early development. We found that cortical excitability begins to manifest shortly after egg activation. Further, we identified a close relationship between wave properties—such as wave frequency and amplitude—and cell cycle progression as well as cell size. Finally, we identified quantitative differences between cortical excitability in the cleavage furrow relative to nonfurrow cortical excitability and showed that these wave regimes are mutually exclusive.
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Affiliation(s)
- Zachary T Swider
- Cellular and Molecular Biology Graduate Program, University of Wisconsin-Madison Madison, WI 53706.,Center for Quantitative Cell Imaging, University of Wisconsin-Madison Madison, WI 53706
| | - Ani Michaud
- Cellular and Molecular Biology Graduate Program, University of Wisconsin-Madison Madison, WI 53706.,Center for Quantitative Cell Imaging, University of Wisconsin-Madison Madison, WI 53706
| | - Marcin Leda
- Centre for Synthetic and Systems Biology, University of Edinburgh, Edinburgh EH9 3BF, UK
| | - Jennifer Landino
- Department of Molecular, Cellular, and Developmental Biology, University of Michigan-Ann Arbor, Ann Arbor, MI 48109
| | - Andrew B Goryachev
- Centre for Synthetic and Systems Biology, University of Edinburgh, Edinburgh EH9 3BF, UK
| | - William M Bement
- Cellular and Molecular Biology Graduate Program, University of Wisconsin-Madison Madison, WI 53706.,Center for Quantitative Cell Imaging, University of Wisconsin-Madison Madison, WI 53706.,Department of Integrative Biology, University of Wisconsin-Madison Madison, WI 53706
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11
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Yang Q, Miao Y, Campanello LJ, Hourwitz MJ, Abubaker-Sharif B, Bull AL, Devreotes PN, Fourkas JT, Losert W. Cortical waves mediate the cellular response to electric fields. eLife 2022; 11:73198. [PMID: 35318938 PMCID: PMC8942472 DOI: 10.7554/elife.73198] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2021] [Accepted: 03/08/2022] [Indexed: 11/13/2022] Open
Abstract
Electrotaxis, the directional migration of cells in a constant electric field, is important in regeneration, development, and wound healing. Electrotaxis has a slower response and a smaller dynamic range than guidance by other cues, suggesting that the mechanism of electrotaxis shares both similarities and differences with chemical-gradient-sensing pathways. We examine a mechanism centered on the excitable system consisting of cortical waves of biochemical signals coupled to cytoskeletal reorganization, which has been implicated in random cell motility. We use electro-fused giant Dictyostelium discoideum cells to decouple waves from cell motion and employ nanotopographic surfaces to limit wave dimensions and lifetimes. We demonstrate that wave propagation in these cells is guided by electric fields. The wave area and lifetime gradually increase in the first 10 min after an electric field is turned on, leading to more abundant and wider protrusions in the cell region nearest the cathode. The wave directions display 'U-turn' behavior upon field reversal, and this switch occurs more quickly on nanotopography. Our results suggest that electric fields guide cells by controlling waves of signal transduction and cytoskeletal activity, which underlie cellular protrusions. Whereas surface receptor occupancy triggers both rapid activation and slower polarization of signaling pathways, electric fields appear to act primarily on polarization, explaining why cells respond to electric fields more slowly than to other guidance cues.
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Affiliation(s)
- Qixin Yang
- Department of Physics, University of Maryland, College Park, United States.,Institute for Physical Science and Technology, University of Maryland, College Park, United States
| | - Yuchuan Miao
- Department of Cell Biology, Johns Hopkins University, Baltimore, United States
| | - Leonard J Campanello
- Department of Physics, University of Maryland, College Park, United States.,Institute for Physical Science and Technology, University of Maryland, College Park, United States
| | - Matt J Hourwitz
- Department of Chemistry & Biochemistry, University of Maryland, College Park, United States
| | | | - Abby L Bull
- Department of Physics, University of Maryland, College Park, United States.,Institute for Physical Science and Technology, University of Maryland, College Park, United States
| | - Peter N Devreotes
- Department of Cell Biology, Johns Hopkins University, Baltimore, United States
| | - John T Fourkas
- Institute for Physical Science and Technology, University of Maryland, College Park, United States.,Department of Chemistry & Biochemistry, University of Maryland, College Park, United States
| | - Wolfgang Losert
- Department of Physics, University of Maryland, College Park, United States.,Institute for Physical Science and Technology, University of Maryland, College Park, United States
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12
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Gerisch G, Prassler J, Ecke M. Patterning of the cell cortex and the localization of cleavage furrows in multi-nucleate cells. J Cell Sci 2022; 135:275044. [PMID: 35274133 PMCID: PMC9016623 DOI: 10.1242/jcs.259648] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Accepted: 03/07/2022] [Indexed: 12/03/2022] Open
Abstract
In multi-nucleate cells of Dictyostelium, cytokinesis is performed by unilateral cleavage furrows that ingress the large cells from their border. We use a septase (sepA)-null mutant with delayed cytokinesis to show that in anaphase a pattern is generated in the cell cortex of cortexillin and myosin II. In multi-nucleate cells, these proteins decorate the entire cell cortex except circular zones around the centrosomes. Unilateral cleavage furrows are initiated at spaces free of microtubule asters and invade the cells along trails of cortexillin and myosin II accumulation. Where these areas widen, the cleavage furrow may branch or expand. When two furrows meet, they fuse, thus separating portions of the multi-nucleate cell from each other. Unilateral furrows are distinguished from the contractile ring of a normal furrow by their expansion rather than constriction. This is particularly evident for expanding ring-shaped furrows that are formed in the centre of a large multi-nucleate cell. Our data suggest that the myosin II-enriched area in multi-nucleate cells is a contractile sheet that pulls on the unilateral furrows and, in that way, expands them. Summary: Multi-nucleate Dictyostelium cells divide by unilateral cleavage furrows that progress and expand according to a pattern of cortexillin and myosin II that is determined by microtubule asters at the spindle poles.
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Affiliation(s)
- Günther Gerisch
- Max Planck Institute of Biochemistry, Am Klopferspitz 18, D-82152 Martinsried, Germany
| | - Jana Prassler
- Max Planck Institute of Biochemistry, Am Klopferspitz 18, D-82152 Martinsried, Germany
| | - Mary Ecke
- Max Planck Institute of Biochemistry, Am Klopferspitz 18, D-82152 Martinsried, Germany
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13
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Saito N, Sawai S. Three-dimensional morphodynamic simulations of macropinocytic cups. iScience 2021; 24:103087. [PMID: 34755081 PMCID: PMC8560551 DOI: 10.1016/j.isci.2021.103087] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Revised: 08/13/2021] [Accepted: 09/01/2021] [Indexed: 12/02/2022] Open
Abstract
Macropinocytosis refers to the non-specific uptake of extracellular fluid, which plays ubiquitous roles in cell growth, immune surveillance, and virus entry. Despite its widespread occurrence, it remains unclear how its initial cup-shaped plasma membrane extensions form without any external solid support, as opposed to the process of particle uptake during phagocytosis. Here, by developing a computational framework that describes the coupling between the bistable reaction-diffusion processes of active signaling patches and membrane deformation, we demonstrated that the protrusive force localized to the edge of the patches can give rise to a self-enclosing cup structure, without further assumptions of local bending or contraction. Efficient uptake requires a balance among the patch size, magnitude of protrusive force, and cortical tension. Furthermore, our model exhibits cyclic cup formation, coexistence of multiple cups, and cup-splitting, indicating that these complex morphologies self-organize via a common mutually-dependent process of reaction-diffusion and membrane deformation.
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Affiliation(s)
- Nen Saito
- Exploratory Research Center on Life and Living Systems, National Institutes of Natural Sciences, 5-1 Higashiyama, Myodaiji-cho, Okazaki, Aichi 444-8787, Japan
| | - Satoshi Sawai
- Department of Basic Science, University of Tokyo, Meguro-ku, Tokyo 153-8902, Japan
- Research Center for Complex Systems Biology, Graduate School of Arts and Sciences, University of Tokyo, Meguro-ku, Tokyo 153-8902, Japan
- Department of Biological Sciences, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
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14
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Kuhn J, Lin Y, Devreotes PN. Using Live-Cell Imaging and Synthetic Biology to Probe Directed Migration in Dictyostelium. Front Cell Dev Biol 2021; 9:740205. [PMID: 34676215 PMCID: PMC8523838 DOI: 10.3389/fcell.2021.740205] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Accepted: 09/08/2021] [Indexed: 12/30/2022] Open
Abstract
For decades, the social amoeba Dictyostelium discoideum has been an invaluable tool for dissecting the biology of eukaryotic cells. Its short growth cycle and genetic tractability make it ideal for a variety of biochemical, cell biological, and biophysical assays. Dictyostelium have been widely used as a model of eukaryotic cell motility because the signaling and mechanical networks which they use to steer and produce forward motion are highly conserved. Because these migration networks consist of hundreds of interconnected proteins, perturbing individual molecules can have subtle effects or alter cell morphology and signaling in major unpredictable ways. Therefore, to fully understand this network, we must be able to quantitatively assess the consequences of abrupt modifications. This ability will allow us better control cell migration, which is critical for development and disease, in vivo. Here, we review recent advances in imaging, synthetic biology, and computational analysis which enable researchers to tune the activity of individual molecules in single living cells and precisely measure the effects on cellular motility and signaling. We also provide practical advice and resources to assist in applying these approaches in Dictyostelium.
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15
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Ecke M, Prassler J, Gerisch G. Genetic Instability Due to Spindle Anomalies Visualized in Mutants of Dictyostelium. Cells 2021; 10:cells10092240. [PMID: 34571889 PMCID: PMC8469108 DOI: 10.3390/cells10092240] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Revised: 08/20/2021] [Accepted: 08/24/2021] [Indexed: 11/24/2022] Open
Abstract
Aberrant centrosome activities in mutants of Dictyostelium discoideum result in anomalies of mitotic spindles that affect the reliability of chromosome segregation. Genetic instabilities caused by these deficiencies are tolerated in multinucleate cells, which can be produced by electric-pulse induced cell fusion as a source for aberrations in the mitotic apparatus of the mutant cells. Dual-color fluorescence labeling of the microtubule system and the chromosomes in live cells revealed the variability of spindle arrangements, of centrosome-nuclear interactions, and of chromosome segregation in the atypical mitoses observed.
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16
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Li X, Pal DS, Biswas D, Iglesias PA, Devreotes PN. Reverse fountain flow of phosphatidylinositol-3,4-bisphosphate polarizes migrating cells. EMBO J 2021; 40:e105094. [PMID: 33586225 PMCID: PMC7883298 DOI: 10.15252/embj.2020105094] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2020] [Revised: 11/06/2020] [Accepted: 11/18/2020] [Indexed: 12/22/2022] Open
Abstract
The ability of cells to polarize and move toward external stimuli plays a crucial role in development, as well as in normal and pathological physiology. Migrating cells maintain dynamic complementary distributions of Ras activity and of the phospholipid phosphatidylinositol‐3,4‐bisphosphate (PI(3,4)P2). Here, we show that lagging‐edge component PI(3,4)P2 also localizes to retracting leading‐edge protrusions and nascent macropinosomes, even in the absence of phosphatidylinositol 3,4,5‐trisphosphate (PIP3). Once internalized, macropinosomes break up into smaller PI(3,4)P2‐enriched vesicles, which fuse with the plasma membrane at the rear of the cell. Subsequently, the phosphoinositide diffuses toward the front of the cell, where it is degraded. Computational modeling confirms that this cycle gives rise to stable back‐to‐front gradient. These results uncover a surprising “reverse‐fountain flow” of PI(3,4)P2 that regulates polarity.
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Affiliation(s)
- Xiaoguang Li
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA.,Department of Biological Chemistry, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
| | - Dhiman Sankar Pal
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
| | - Debojyoti Biswas
- Department of Electrical and Computer Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - Pablo A Iglesias
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA.,Department of Electrical and Computer Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - Peter N Devreotes
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
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17
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van Haastert PJM. Unified control of amoeboid pseudopod extension in multiple organisms by branched F-actin in the front and parallel F-actin/myosin in the cortex. PLoS One 2020; 15:e0243442. [PMID: 33296414 PMCID: PMC7725310 DOI: 10.1371/journal.pone.0243442] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Accepted: 11/23/2020] [Indexed: 02/06/2023] Open
Abstract
The trajectory of moving eukaryotic cells depends on the kinetics and direction of extending pseudopods. The direction of pseudopods has been well studied to unravel mechanisms for chemotaxis, wound healing and inflammation. However, the kinetics of pseudopod extension-when and why do pseudopods start and stop- is equally important, but is largely unknown. Here the START and STOP of about 4000 pseudopods was determined in four different species, at four conditions and in nine mutants (fast amoeboids Dictyostelium and neutrophils, slow mesenchymal stem cells, and fungus B.d. chytrid with pseudopod and a flagellum). The START of a first pseudopod is a random event with a probability that is species-specific (23%/s for neutrophils). In all species and conditions, the START of a second pseudopod is strongly inhibited by the extending first pseudopod, which depends on parallel filamentous actin/myosin in the cell cortex. Pseudopods extend at a constant rate by polymerization of branched F-actin at the pseudopod tip, which requires the Scar complex. The STOP of pseudopod extension is induced by multiple inhibitory processes that evolve during pseudopod extension and mainly depend on the increasing size of the pseudopod. Surprisingly, no differences in pseudopod kinetics are detectable between polarized, unpolarized or chemotactic cells, and also not between different species except for small differences in numerical values. This suggests that the analysis has uncovered the fundament of cell movement with distinct roles for stimulatory branched F-actin in the protrusion and inhibitory parallel F-actin in the contractile cortex.
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18
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Wu M, Liu J. Mechanobiology in cortical waves and oscillations. Curr Opin Cell Biol 2020; 68:45-54. [PMID: 33039945 DOI: 10.1016/j.ceb.2020.08.017] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Revised: 08/25/2020] [Accepted: 08/27/2020] [Indexed: 12/18/2022]
Abstract
Cortical actin waves have emerged as a widely prevalent phenomena and brought pattern formation to many fields of cell biology. Cortical excitabilities, reminiscent of the electric excitability in neurons, are likely fundamental property of the cell cortex. Although they have been mostly considered to be biochemical in nature, accumulating evidence support the role of mechanics in the pattern formation process. Both pattern formation and mechanobiology approach biological phenomena at the collective level, either by looking at the mesoscale dynamical behavior of molecular networks or by using collective physical properties to characterize biological systems. As such they are very different from the traditional reductionist, bottom-up view of biology, which brings new challenges and potential opportunities. In this essay, we aim to provide our perspectives on what the proposed mechanochemical feedbacks are and open questions regarding their role in cortical excitable and oscillatory dynamics.
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Affiliation(s)
- Min Wu
- Department of Cell Biology, Yale University School of Medicine, 333 Cedar Street, New Haven, CT, 06520-8002, USA..
| | - Jian Liu
- Department of Cell Biology, School of Medicine, Johns Hopkins University, 855 N Wolfe Street, Baltimore, MD, 21025, USA
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19
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van Haastert PJM. Symmetry Breaking during Cell Movement in the Context of Excitability, Kinetic Fine-Tuning and Memory of Pseudopod Formation. Cells 2020; 9:E1809. [PMID: 32751539 PMCID: PMC7465517 DOI: 10.3390/cells9081809] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2020] [Revised: 07/28/2020] [Accepted: 07/29/2020] [Indexed: 11/16/2022] Open
Abstract
The path of moving eukaryotic cells depends on the kinetics and direction of extending pseudopods. Amoeboid cells constantly change their shape with pseudopods extending in different directions. Detailed analysis has revealed that time, place and direction of pseudopod extension are not random, but highly ordered with strong prevalence for only one extending pseudopod, with defined life-times, and with reoccurring events in time and space indicative of memory. Important components are Ras activation and the formation of branched F-actin in the extending pseudopod and inhibition of pseudopod formation in the contractile cortex of parallel F-actin/myosin. In biology, order very often comes with symmetry. In this essay, I discuss cell movement and the dynamics of pseudopod extension from the perspective of symmetry and symmetry changes of Ras activation and the formation of branched F-actin in the extending pseudopod. Combining symmetry of Ras activation with kinetics and memory of pseudopod extension results in a refined model of amoeboid movement that appears to be largely conserved in the fast moving Dictyostelium and neutrophils, the slow moving mesenchymal stem cells and the fungus B.d. chytrid.
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Affiliation(s)
- Peter J M van Haastert
- Department of Cell Biochemistry, University of Groningen, Nijenborgh 7, 9747 AG Groningen, The Netherlands
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20
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Pal DS, Li X, Banerjee T, Miao Y, Devreotes PN. The excitable signal transduction networks: movers and shapers of eukaryotic cell migration. THE INTERNATIONAL JOURNAL OF DEVELOPMENTAL BIOLOGY 2020; 63:407-416. [PMID: 31840779 DOI: 10.1387/ijdb.190265pd] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
In response to a variety of external cues, eukaryotic cells display varied migratory modes to perform their physiological functions during development and in the adult. Aberrations in cell migration result in embryonic defects and cancer metastasis. The molecular components involved in cell migration are remarkably conserved between the social amoeba Dictyostelium and mammalian cells. This makes the amoeba an excellent model system for studies of eukaryotic cell migration. These migration-associated components can be grouped into three networks: input, signal transduction and cytoskeletal. In migrating cells, signal transduction events such as Ras or PI3K activity occur at the protrusion tips, referred to as 'front', whereas events such as dissociation of PTEN from these regions are referred to as 'back'. Asymmetric distribution of such front and back events is crucial for establishing polarity and guiding cell migration. The triggering of these signaling events displays properties of biochemical excitability including all-or-nothing responsiveness to suprathreshold stimuli, refractoriness, and wave propagation. These signal transduction waves originate from a point and propagate towards the edge of the cell, thereby driving cytoskeletal activity and cellular protrusions. Any change in the threshold for network activation alters the range of the propagating waves and the size of cellular protrusions which gives rise to various migratory modes in cells. Thus, this review highlights excitable signal transduction networks as key players for coordinating cytoskeletal activities to drive cell migration in all eukaryotes.
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Affiliation(s)
- Dhiman S Pal
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
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21
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Beta C, Gov NS, Yochelis A. Why a Large-Scale Mode Can Be Essential for Understanding Intracellular Actin Waves. Cells 2020; 9:cells9061533. [PMID: 32585983 PMCID: PMC7349605 DOI: 10.3390/cells9061533] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2020] [Revised: 06/16/2020] [Accepted: 06/18/2020] [Indexed: 01/18/2023] Open
Abstract
During the last decade, intracellular actin waves have attracted much attention due to their essential role in various cellular functions, ranging from motility to cytokinesis. Experimental methods have advanced significantly and can capture the dynamics of actin waves over a large range of spatio-temporal scales. However, the corresponding coarse-grained theory mostly avoids the full complexity of this multi-scale phenomenon. In this perspective, we focus on a minimal continuum model of activator-inhibitor type and highlight the qualitative role of mass conservation, which is typically overlooked. Specifically, our interest is to connect between the mathematical mechanisms of pattern formation in the presence of a large-scale mode, due to mass conservation, and distinct behaviors of actin waves.
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Affiliation(s)
- Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany;
| | - Nir S. Gov
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel;
| | - Arik Yochelis
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research (BIDR), Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva 8410501, Israel
- Correspondence:
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22
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Cell-Substrate Patterns Driven by Curvature-Sensitive Actin Polymerization: Waves and Podosomes. Cells 2020; 9:cells9030782. [PMID: 32210185 PMCID: PMC7140849 DOI: 10.3390/cells9030782] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2020] [Revised: 03/14/2020] [Accepted: 03/17/2020] [Indexed: 12/20/2022] Open
Abstract
Cells adhered to an external solid substrate are observed to exhibit rich dynamics of actin structures on the basal membrane, which are distinct from those observed on the dorsal (free) membrane. Here we explore the dynamics of curved membrane proteins, or protein complexes, that recruit actin polymerization when the membrane is confined by the solid substrate. Such curved proteins can induce the spontaneous formation of membrane protrusions on the dorsal side of cells. However, on the basal side of the cells, such protrusions can only extend as far as the solid substrate and this constraint can convert such protrusions into propagating wave-like structures. We also demonstrate that adhesion molecules can stabilize localized protrusions that resemble some features of podosomes. This coupling of curvature and actin forces may underlie the differences in the observed actin-membrane dynamics between the basal and dorsal sides of adhered cells.
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23
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Abstract
Cytokinesis-the division of a cell into two daughter cells-is a key step in cell growth and proliferation. It typically occurs in synchrony with the cell cycle to ensure that a complete copy of the genetic information is passed on to the next generation of daughter cells. In animal cells, cytokinesis commonly relies on an actomyosin contractile ring that drives equatorial furrowing and separation into the two daughter cells. However, also contractile ring-independent forms of cell division are known that depend on substrate-mediated traction forces. Here, we report evidence of an as yet unknown type of contractile ring-independent cytokinesis that we termed wave-mediated cytofission. It is driven by self-organized cortical actin waves that travel across the ventral membrane of oversized, multinucleated Dictyostelium discoideum cells. Upon collision with the cell border, waves may initiate the formation of protrusions that elongate and eventually pinch off to form separate daughter cells. They are composed of a stable elongated wave segment that is enclosed by a cell membrane and moves in a highly persistent fashion. We rationalize our observations based on a noisy excitable reaction-diffusion model in combination with a dynamic phase field to account for the cell shape and demonstrate that daughter cells emerging from wave-mediated cytofission exhibit a well-controlled size.
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24
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Ecke M, Prassler J, Tanribil P, Müller-Taubenberger A, Körber S, Faix J, Gerisch G. Formins specify membrane patterns generated by propagating actin waves. Mol Biol Cell 2020; 31:373-385. [PMID: 31940262 PMCID: PMC7183788 DOI: 10.1091/mbc.e19-08-0460] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2019] [Revised: 01/07/2020] [Accepted: 01/08/2020] [Indexed: 12/18/2022] Open
Abstract
Circular actin waves separate two distinct areas on the substrate-attached cell surface from each other: an external area from an inner territory that is circumscribed by the wave. These areas differ in composition of actin-associated proteins and of phosphoinositides in the membrane. At the propagating wave, one area is converted into the other. By photo-conversion of Eos-actin and analysis of actin network structures we show that both in the inner territory and the external area the actin network is subject to continuous turnover. To address the question of whether areas in the wave pattern are specified by particular actin polymerizing machines, we locate five members of the formin family to specific regions of the wave landscape using TIRF microscopy and constitutively active formin constructs tagged with fluorescent protein. Formin ForB favors the actin wave and ForG the inner territory, whereas ForA, ForE, and ForH are more strongly recruited to the external area. Fluctuations of membrane binding peculiar to ForB indicate transient states in the specification of membrane domains before differentiation into ForB decorated and depleted ones. Annihilation of the patterns by 1 µM of the formin inhibitor SMIFH2 supports the implication of formins in their generation.
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Affiliation(s)
- Mary Ecke
- Max Planck Institute of Biochemistry, D-82152 Martinsried, Munich, Germany
| | - Jana Prassler
- Max Planck Institute of Biochemistry, D-82152 Martinsried, Munich, Germany
| | - Patrick Tanribil
- Max Planck Institute of Biochemistry, D-82152 Martinsried, Munich, Germany
| | - Annette Müller-Taubenberger
- Department of Cell Biology (Anatomy III), Ludwig Maximilian University of Munich, D-82152 Planegg-Martinsried, Munich, Germany
| | - Sarah Körber
- Institute of Biophysical Chemistry, Hannover Medical School, D-30625 Hannover, Germany
| | - Jan Faix
- Institute of Biophysical Chemistry, Hannover Medical School, D-30625 Hannover, Germany
| | - Günther Gerisch
- Max Planck Institute of Biochemistry, D-82152 Martinsried, Munich, Germany
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25
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Yochelis A, Beta C, Gov NS. Excitable solitons: Annihilation, crossover, and nucleation of pulses in mass-conserving activator-inhibitor media. Phys Rev E 2020; 101:022213. [PMID: 32168571 DOI: 10.1103/physreve.101.022213] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2019] [Accepted: 02/05/2020] [Indexed: 11/07/2022]
Abstract
Excitable pulses are among the most widespread dynamical patterns that occur in many different systems, ranging from biological cells to chemical reactions and ecological populations. Traditionally, the mutual annihilation of two colliding pulses is regarded as their prototypical signature. Here we show that colliding excitable pulses may exhibit solitonlike crossover and pulse nucleation if the system obeys a mass conservation constraint. In contrast to previous observations in systems without mass conservation, these alternative collision scenarios are robustly observed over a wide range of parameters. We demonstrate our findings using a model of intracellular actin waves since, on time scales of wave propagations over the cell scale, cells obey conservation of actin monomers. The results provide a key concept to understand the ubiquitous occurrence of actin waves in cells, suggesting why they are so common, and why their dynamics is robust and long-lived.
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Affiliation(s)
- Arik Yochelis
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research (BIDR), Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel.,Department of Physics, Ben-Gurion University of the Negev, Be'er Sheva 8410501, Israel
| | - Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
| | - Nir S Gov
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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26
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Li X, Miao Y, Pal DS, Devreotes PN. Excitable networks controlling cell migration during development and disease. Semin Cell Dev Biol 2019; 100:133-142. [PMID: 31836289 DOI: 10.1016/j.semcdb.2019.11.001] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2019] [Revised: 10/21/2019] [Accepted: 11/01/2019] [Indexed: 12/30/2022]
Abstract
The directed movements of individual, groups, or sheets of cells at specific times in particular locations bring about form and complexity to developing organisms. Cells move by extending protrusions, such as macropinosomes, pseudopods, lamellipods, filopods, or blebs. Although many of the cytoskeletal components within these structures are known, less is known about the mechanisms that determine their location, number, and characteristics. Recent evidence suggests that control may be exerted by a signal transduction excitable network whose components and activities, including Ras, PI3K, TorC2, and phosphoinositides, self-organize on the plasma membrane and propagate in waves. The waves drive the various types of protrusions, which in turn, determine the modes of cell migration. Acute perturbations at specific points in the network produce abrupt shifts in protrusion type, including transitions from pseudopods to filopods or lamellipods. These observations have also contributed to a delineation of the signal transduction network, including candidate fast positive and delayed negative feedback loops. The network contains many oncogenes and tumor suppressors, and other molecules which have recently been implicated in developmental and metabolic abnormalities. Thus, the concept of signal transduction network excitability in cell migration can be used to understand disease states and morphological changes occurring in development.
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Affiliation(s)
- Xiaoguang Li
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD 21205, USA; Department of Biological Chemistry, School of Medicine, Johns Hopkins University, Baltimore, MD 21205, USA
| | - Yuchuan Miao
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD 21205, USA; Department of Biological Chemistry, School of Medicine, Johns Hopkins University, Baltimore, MD 21205, USA
| | - Dhiman Sankar Pal
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD 21205, USA
| | - Peter N Devreotes
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD 21205, USA.
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27
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Abstract
Actin polymerization is essential for cells to migrate, as well as for various cell biological processes such as cytokinesis and vesicle traffic. This brief review describes the mechanisms underlying its different roles and recent advances in our understanding. Actin usually requires "nuclei"-preformed actin filaments-to start polymerizing, but, once initiated, polymerization continues constitutively. The field therefore has a strong focus on nucleators, in particular the Arp2/3 complex and formins. These have different functions, are controlled by contrasting mechanisms, and generate alternate geometries of actin networks. The Arp2/3 complex functions only when activated by nucleation-promoting factors such as WASP, Scar/WAVE, WASH, and WHAMM and when binding to a pre-existing filament. Formins can be individually active but are usually autoinhibited. Each is controlled by different mechanisms and is involved in different biological roles. We also describe the processes leading to actin disassembly and their regulation and conclude with four questions whose answers are important for understanding actin dynamics but are currently unanswered.
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Affiliation(s)
- Simona Buracco
- Institute of Cancer Sciences, University of Glasgow, Bearsden, G61 1BD, UK
| | - Sophie Claydon
- Institute of Cancer Sciences, University of Glasgow, Bearsden, G61 1BD, UK
| | - Robert Insall
- Institute of Cancer Sciences, University of Glasgow, Bearsden, G61 1BD, UK
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28
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Cao Y, Ghabache E, Rappel WJ. Plasticity of cell migration resulting from mechanochemical coupling. eLife 2019; 8:e48478. [PMID: 31625907 PMCID: PMC6799977 DOI: 10.7554/elife.48478] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2019] [Accepted: 10/02/2019] [Indexed: 01/07/2023] Open
Abstract
Eukaryotic cells can migrate using different modes, ranging from amoeboid-like, during which actin filled protrusions come and go, to keratocyte-like, characterized by a stable morphology and persistent motion. How cells can switch between these modes is not well understood but waves of signaling events are thought to play an important role in these transitions. Here we present a simple two-component biochemical reaction-diffusion model based on relaxation oscillators and couple this to a model for the mechanics of cell deformations. Different migration modes, including amoeboid-like and keratocyte-like, naturally emerge through transitions determined by interactions between biochemical traveling waves, cell mechanics and morphology. The model predictions are explicitly verified by systematically reducing the protrusive force of the actin network in experiments using Dictyostelium discoideum cells. Our results indicate the importance of coupling signaling events to cell mechanics and morphology and may be applicable in a wide variety of cell motility systems.
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Affiliation(s)
- Yuansheng Cao
- Department of PhysicsUniversity of California, San DiegoLa JollaUnited States
| | - Elisabeth Ghabache
- Department of PhysicsUniversity of California, San DiegoLa JollaUnited States
| | - Wouter-Jan Rappel
- Department of PhysicsUniversity of California, San DiegoLa JollaUnited States
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29
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Horibe K, Hironaka KI, Matsushita K, Fujimoto K. Curved surface geometry-induced topological change of an excitable planar wavefront. CHAOS (WOODBURY, N.Y.) 2019; 29:093120. [PMID: 31575140 DOI: 10.1063/1.5108838] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Accepted: 08/27/2019] [Indexed: 06/10/2023]
Abstract
On the curved surfaces of living and nonliving materials, planar excitable wavefronts frequently exhibit a directional change and subsequently undergo a discontinuous (topological) change; i.e., a series of wavefront dynamics from collision, annihilation to splitting. Theoretical studies have shown that excitable planar stable waves change their topology significantly depending on the initial conditions on flat surfaces, whereas the directional change of the waves occurs based on the geometry of curved surfaces. However, it is not clear if the geometry of curved surfaces induces this topological change. In this study, we first demonstrated that the curved surface geometry induces bending, collision, and splitting of a planar stable wavefront by numerically solving an excitable reaction-diffusion equation on a bell-shaped surface. We determined two necessary conditions for inducing the topological change: the characteristic length of the curved surface (i.e., the height of the bell-shaped structure) should be greater than the width of the wave, and the ratio of the height to the width of the bell shape should be greater than a threshold. As for the geometrical mechanism of the latter, we found that a bifurcation of the geodesics on the curved surface provides the alternative minimal paths of the wavefront, which circumvent the surface region with a high local curvature, thereby resulting in the topological change. These conditions imply that the topological change of the wavefront can be predicted on the basis of the curved surfaces, whose structures are larger than the wave width.
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Affiliation(s)
- Kazuya Horibe
- Department of Biological Sciences, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Ken-Ichi Hironaka
- Department of Biological Sciences, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Katsuyoshi Matsushita
- Department of Biological Sciences, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Koichi Fujimoto
- Department of Biological Sciences, Osaka University, Toyonaka, Osaka 560-0043, Japan
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30
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Helenius J, Ecke M, Müller DJ, Gerisch G. Oscillatory Switches of Dorso-Ventral Polarity in Cells Confined between Two Surfaces. Biophys J 2019; 115:150-162. [PMID: 29972806 DOI: 10.1016/j.bpj.2018.05.025] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2017] [Revised: 03/23/2018] [Accepted: 05/14/2018] [Indexed: 10/28/2022] Open
Abstract
To maneuver in a three-dimensional space, migrating cells need to accommodate to multiple surfaces. In particular, phagocytes have to explore their environment in the search for particles to be ingested. To examine how cells decide between competing surfaces, we exposed single cells of Dictyostelium to a defined three-dimensional space by confining them between two planar surfaces: those of a cover glass and of a wedged microcantilever. These cells form propagating waves of filamentous actin and PIP3 on their ventral substrate-attached surface. The dynamics of wave formation in the confined cells was explored using two-focus fluorescence imaging. When waves formed on one substrate, wave formation on the other substrate was efficiently suppressed. The propensity for wave formation switched between the opposing cell surfaces with periods of 2-5 min by one of two modes: 1) a rolling mode involving the slipping of a wave along the nonattached plasma membrane and 2) de novo initiation of waves on the previously blank cell surface. These data provide evidence for a cell-autonomous oscillator that switches dorso-ventral polarity in a cell simultaneously exposed to multiple substrate surfaces.
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Affiliation(s)
- Jonne Helenius
- Department of Biosystems Science and Engineering, ETH Zürich, Basel, Switzerland
| | - Mary Ecke
- AG Cell Dynamics, Max Planck Institute of Biochemistry, Martinsried, Germany
| | - Daniel J Müller
- Department of Biosystems Science and Engineering, ETH Zürich, Basel, Switzerland
| | - Günther Gerisch
- AG Cell Dynamics, Max Planck Institute of Biochemistry, Martinsried, Germany.
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31
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Shi Y, Porter CL, Crocker JC, Reich DH. Dissecting fat-tailed fluctuations in the cytoskeleton with active micropost arrays. Proc Natl Acad Sci U S A 2019; 116:13839-13846. [PMID: 31239336 PMCID: PMC6628664 DOI: 10.1073/pnas.1900963116] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The ability of animal cells to crawl, change their shape, and respond to applied force is due to their cytoskeleton: A dynamic, cross-linked network of actin protein filaments and myosin motors. How these building blocks assemble to give rise to cells' mechanics and behavior remains poorly understood. Using active micropost array detectors containing magnetic actuators, we have characterized the mechanics and fluctuations of cells' actomyosin cortex and stress fiber network in detail. Here, we find that both structures display remarkably consistent power law viscoelastic behavior along with highly intermittent fluctuations with fat-tailed distributions of amplitudes. Notably, this motion in the cortex is dominated by occasional large, step-like displacement events, with a spatial extent of several micrometers. Overall, our findings for the cortex appear contrary to the predictions of a recent active gel model, while suggesting that different actomyosin contractile units act in a highly collective and cooperative manner. We hypothesize that cells' actomyosin components robustly self-organize into marginally stable, plastic networks that give cells' their unique biomechanical properties.
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Affiliation(s)
- Yu Shi
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218
| | - Christopher L Porter
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104
| | - John C Crocker
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104
| | - Daniel H Reich
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218;
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32
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The Architecture of Traveling Actin Waves Revealed by Cryo-Electron Tomography. Structure 2019; 27:1211-1223.e5. [PMID: 31230946 DOI: 10.1016/j.str.2019.05.009] [Citation(s) in RCA: 41] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Revised: 04/12/2019] [Accepted: 05/17/2019] [Indexed: 02/06/2023]
Abstract
Actin waves are dynamic supramolecular structures involved in cell migration, cytokinesis, adhesion, and neurogenesis. Although wave-like propagation of actin networks is a widespread phenomenon, the actin architecture underlying wave propagation remained unknown. In situ cryo-electron tomography of Dictyostelium cells unveils the wave architecture and provides evidence for wave progression by de novo actin nucleation. Subtomogram averaging reveals the structure of Arp2/3 complex-mediated branch junctions in their native state, and enables quantitative analysis of the 3D organization of branching within the waves. We find an excess of branches directed toward the substrate-attached membrane, and tent-like structures at sites of branch clustering. Fluorescence imaging shows that Arp2/3 clusters follow accumulation of the elongation factor VASP. We propose that filament growth toward the membrane lifts up the actin network as the wave propagates, until depolymerization of oblique filaments at the back causes the collapse of horizontal filaments into a compact layer.
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33
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Miao Y, Bhattacharya S, Banerjee T, Abubaker-Sharif B, Long Y, Inoue T, Iglesias PA, Devreotes PN. Wave patterns organize cellular protrusions and control cortical dynamics. Mol Syst Biol 2019; 15:e8585. [PMID: 30858181 PMCID: PMC6413885 DOI: 10.15252/msb.20188585] [Citation(s) in RCA: 52] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2018] [Revised: 01/31/2019] [Accepted: 02/04/2019] [Indexed: 02/06/2023] Open
Abstract
Cellular protrusions are typically considered as distinct structures associated with specific regulators. However, we found that these regulators coordinately localize as propagating cortical waves, suggesting a common underlying mechanism. These molecular events fell into two excitable networks, the signal transduction network STEN and the cytoskeletal network CEN with different wave substructures. Computational studies using a coupled-network model reproduced these features and showed that the morphology and kinetics of the waves depended on strengths of feedback loops. Chemically induced dimerization at multiple nodes produced distinct, coordinated alterations in patterns of other network components. Taken together, these studies indicate: STEN positive feedback is mediated by mutual inhibition between Ras/Rap and PIP2, while negative feedback depends on delayed PKB activation; PKBs link STEN to CEN; CEN includes positive feedback between Rac and F-actin, and exerts fast positive and slow negative feedbacks to STEN The alterations produced protrusions resembling filopodia, ruffles, pseudopodia, or lamellipodia, suggesting that these structures arise from a common regulatory mechanism and that the overall state of the STEN-CEN system determines cellular morphology.
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Affiliation(s)
- Yuchuan Miao
- Department of Biological Chemistry, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
| | - Sayak Bhattacharya
- Department of Electrical and Computer Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - Tatsat Banerjee
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
- Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - Bedri Abubaker-Sharif
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
| | - Yu Long
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
| | - Takanari Inoue
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
| | - Pablo A Iglesias
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
- Department of Electrical and Computer Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - Peter N Devreotes
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, MD, USA
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Yang Y, Wu M. Rhythmicity and waves in the cortex of single cells. Philos Trans R Soc Lond B Biol Sci 2019; 373:rstb.2017.0116. [PMID: 29632268 PMCID: PMC5904302 DOI: 10.1098/rstb.2017.0116] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 12/30/2017] [Indexed: 12/15/2022] Open
Abstract
Emergence of dynamic patterns in the form of oscillations and waves on the cortex of single cells is a fascinating and enigmatic phenomenon. Here we outline various theoretical frameworks used to model pattern formation with the goal of reducing complex, heterogeneous patterns into key parameters that are biologically tractable. We also review progress made in recent years on the quantitative and molecular definitions of these terms, which we believe have begun to transform single-cell dynamic patterns from a purely observational and descriptive subject to more mechanistic studies. Specifically, we focus on the nature of local excitable and oscillation events, their spatial couplings leading to propagating waves and the role of active membrane. Instead of arguing for their functional importance, we prefer to consider such patterns as basic properties of dynamic systems. We discuss how knowledge of these patterns could be used to dissect the structure of cellular organization and how the network-centric view could help define cellular functions as transitions between different dynamical states. Last, we speculate on how these patterns could encode temporal and spatial information. This article is part of the theme issue ‘Self-organization in cell biology’.
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Affiliation(s)
- Yang Yang
- Department of Biological Sciences, Centre for Bioimaging Sciences, Mechanobiology Institute, National University of Singapore, Singapore
| | - Min Wu
- Department of Biological Sciences, Centre for Bioimaging Sciences, Mechanobiology Institute, National University of Singapore, Singapore
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Fukushima S, Matsuoka S, Ueda M. Excitable dynamics of Ras triggers spontaneous symmetry breaking of PIP3 signaling in motile cells. J Cell Sci 2019; 132:jcs224121. [PMID: 30745337 PMCID: PMC6432713 DOI: 10.1242/jcs.224121] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2018] [Accepted: 01/31/2019] [Indexed: 12/22/2022] Open
Abstract
Spontaneous cell movement is underpinned by an asymmetric distribution of signaling molecules including small G proteins and phosphoinositides on the cell membrane. However, the molecular network necessary for spontaneous symmetry breaking has not been fully elucidated. Here, we report that, in Dictyostelium discoideum, the spatiotemporal dynamics of GTP bound Ras (Ras-GTP) breaks the symmetry due its intrinsic excitability even in the absence of extracellular spatial cues and downstream signaling activities. A stochastic excitation of local and transient Ras activation induced phosphatidylinositol (3,4,5)-trisphosphate (PIP3) accumulation via direct interaction with Phosphoinositide 3-kinase (PI3K), causing tightly coupled traveling waves that propagated along the membrane. Comprehensive phase analysis of the waves of Ras-GTP and PIP3 metabolism-related molecules revealed the network structure of the excitable system including positive-feedback regulation of Ras-GTP by the downstream PIP3. A mathematical model reconstituted a series of the observed symmetry-breaking phenomena, illustrating the essential involvement of Ras excitability in the cellular decision-making process.
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Affiliation(s)
- Seiya Fukushima
- Department of Biological Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
- RIKEN Center for Biosystems Dynamics Research (BDR), Suita, Osaka 565-0874, Japan
| | - Satomi Matsuoka
- RIKEN Center for Biosystems Dynamics Research (BDR), Suita, Osaka 565-0874, Japan
- Graduate School of Frontier Biosciences, Osaka University, Suita, Osaka 565-0871, Japan
| | - Masahiro Ueda
- Department of Biological Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
- RIKEN Center for Biosystems Dynamics Research (BDR), Suita, Osaka 565-0874, Japan
- Graduate School of Frontier Biosciences, Osaka University, Suita, Osaka 565-0871, Japan
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36
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Hörning M, Shibata T. Three-Dimensional Cell Geometry Controls Excitable Membrane Signaling in Dictyostelium Cells. Biophys J 2019; 116:372-382. [PMID: 30635124 PMCID: PMC6350023 DOI: 10.1016/j.bpj.2018.12.012] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2018] [Revised: 11/16/2018] [Accepted: 12/13/2018] [Indexed: 01/13/2023] Open
Abstract
Phosphatidylinositol (3-5)-trisphosphate (PtdInsP3) is known to propagate as waves on the plasma membrane and is related to the membrane-protrusive activities in Dictyostelium and mammalian cells. Although there have been a few attempts to study the three-dimensional (3D) dynamics of these processes, most studies have focused on the dynamics extracted from single focal planes. However, the relation between the dynamics and 3D cell shape remains elusive because of the lack of signaling information about the unobserved part of the membrane. Here, we show that PtdInsP3 wave dynamics are directly regulated by the 3D geometry (i.e., size and shape) of the plasma membrane. By introducing an analysis method that extracts the 3D spatiotemporal activities on the entire cell membrane, we show that PtdInsP3 waves self-regulate their dynamics within the confined membrane area. This leads to changes in speed, orientation, and pattern evolution, following the underlying excitability of the signal transduction system. Our findings emphasize the role of the plasma membrane topology in reaction-diffusion-driven biological systems and indicate its importance in other mammalian systems.
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Affiliation(s)
- Marcel Hörning
- Laboratory for Physical Biology, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan; Institute of Biomaterials and Biomolecular Systems, University of Stuttgart, Stuttgart, Germany; Institute for Integrated Cell-Material Sciences, Kyoto University, Kyoto, Japan.
| | - Tatsuo Shibata
- Laboratory for Physical Biology, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan.
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37
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Integrating chemical and mechanical signals through dynamic coupling between cellular protrusions and pulsed ERK activation. Nat Commun 2018; 9:4673. [PMID: 30405112 PMCID: PMC6220176 DOI: 10.1038/s41467-018-07150-9] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2018] [Accepted: 10/15/2018] [Indexed: 12/13/2022] Open
Abstract
The Ras-ERK signaling pathway regulates diverse cellular processes in response to environmental stimuli and contains important therapeutic targets for cancer. Recent single cell studies revealed stochastic pulses of ERK activation, the frequency of which determines functional outcomes such as cell proliferation. Here we show that ERK pulses are initiated by localized protrusive activities. Chemically and optogenetically induced protrusions trigger ERK activation through various entry points into the feedback loop involving Ras, PI3K, the cytoskeleton, and cellular adhesion. The excitability of the protrusive signaling network drives stochastic ERK activation in unstimulated cells and oscillations upon growth factor stimulation. Importantly, protrusions allow cells to sense combined signals from substrate stiffness and the growth factor. Thus, by uncovering the basis of ERK pulse generation we demonstrate how signals involved in cell growth and differentiation are regulated by dynamic protrusions that integrate chemical and mechanical inputs from the environment. Cellular ERK activation occurs as discrete pulses but their relationship to upstream Ras signaling is still under debate. Here, the authors show that Ras signaling associated with cellular protrusions triggers pulsed ERK activation, thereby enabling cells to integrate chemical and mechanical stimuli.
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38
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Alonso S, Stange M, Beta C. Modeling random crawling, membrane deformation and intracellular polarity of motile amoeboid cells. PLoS One 2018; 13:e0201977. [PMID: 30138392 PMCID: PMC6107139 DOI: 10.1371/journal.pone.0201977] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2018] [Accepted: 07/25/2018] [Indexed: 11/18/2022] Open
Abstract
Amoeboid movement is one of the most widespread forms of cell motility that plays a key role in numerous biological contexts. While many aspects of this process are well investigated, the large cell-to-cell variability in the motile characteristics of an otherwise uniform population remains an open question that was largely ignored by previous models. In this article, we present a mathematical model of amoeboid motility that combines noisy bistable kinetics with a dynamic phase field for the cell shape. To capture cell-to-cell variability, we introduce a single parameter for tuning the balance between polarity formation and intracellular noise. We compare numerical simulations of our model to experiments with the social amoeba Dictyostelium discoideum. Despite the simple structure of our model, we found close agreement with the experimental results for the center-of-mass motion as well as for the evolution of the cell shape and the overall intracellular patterns. We thus conjecture that the building blocks of our model capture essential features of amoeboid motility and may serve as a starting point for more detailed descriptions of cell motion in chemical gradients and confined environments.
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Affiliation(s)
- Sergio Alonso
- Department of Physics, Universitat Politecnica de Catalunya, Barcelona, Spain
- * E-mail:
| | - Maike Stange
- Institute of Physics and Astronomy, Universität Potsdam, Potsdam, Germany
| | - Carsten Beta
- Institute of Physics and Astronomy, Universität Potsdam, Potsdam, Germany
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39
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The threshold of an excitable system serves as a control mechanism for noise filtering during chemotaxis. PLoS One 2018; 13:e0201283. [PMID: 30059517 PMCID: PMC6066244 DOI: 10.1371/journal.pone.0201283] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2018] [Accepted: 06/18/2018] [Indexed: 01/29/2023] Open
Abstract
Chemotaxis, the migration of cells in the direction of a chemical gradient, is of utmost importance in various biological processes. In recent years, research has demonstrated that the underlying mechanism that controls cell migration is an excitable network. One of the properties that characterizes excitability is the presence of a threshold for activation. Here, we show that excitable systems possess noise filtering capabilities that enable faster and more efficient directed migration compared to other systems that also include a threshold, such as ultrasensitive switches. We demonstrate that this filtering ability is a consequence of the varying responses of excitable systems to step and pulse stimuli. Whereas the response to step inputs is determined solely by the magnitude of the stimulus, for pulse stimuli, the response depends on both the magnitude and duration of the stimulus. We then show that these two forms of threshold behavior can be decoupled from one another, allowing finer control in chemotaxis. Finally, we use a simple model of chemotaxis to demonstrate that cells that rely on an excitable system display faster and more effective directed migration that a hypothetical cell guided by an ultra-sensitive switch.
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40
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The Sealing Zone in Osteoclasts: A Self-Organized Structure on the Bone. Int J Mol Sci 2018; 19:ijms19040984. [PMID: 29587415 PMCID: PMC5979552 DOI: 10.3390/ijms19040984] [Citation(s) in RCA: 67] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2018] [Revised: 03/22/2018] [Accepted: 03/23/2018] [Indexed: 01/08/2023] Open
Abstract
Osteoclasts form a specialized cell-matrix adhesion structure, known as the "sealing zone", during bone resorption. The sealing zone is a dynamic actin-rich structure that defines the resorption area of the bone. The detailed dynamics and fine structure of the sealing zone have been elusive. Osteoclasts plated on glass do not form a sealing zone, but generate a separate supra-molecular structure called the "podosome belt". Podosomes are integrin-based adhesion complexes involved in matrix adhesion, cell migration, matrix degradation, and mechanosensing. Invadopodia, podosome-like protrusions in cancer cells, are involved in cell invasion into other tissues by promoting matrix degradation. Both podosomes and invadopodia exhibit actin pattern transitions during maturation. We previously found that Arp2/3-dependent actin flow occurs in all observed assembly patterns of podosomes in osteoclasts on glass. It is known that the actin wave in Dictyostelium cells exhibits a similar pattern transition in its evolution. Because of significant advances in our understanding regarding the mechanism of podosomes/invadopodia formation over the last decade, we revisited the structure and function of the sealing zone in this review, highlighting the possible involvement of self-organized actin waves in the organogenesis of the sealing zone.
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41
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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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42
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Bruns C, Hauser MJB. Dynamics of scroll waves in a cylinder jacket geometry. Phys Rev E 2018; 96:012203. [PMID: 29347134 DOI: 10.1103/physreve.96.012203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2017] [Indexed: 11/07/2022]
Abstract
The dynamics of scroll waves in a narrow cylinder jacket-shaped reactor is investigated experimentally by optical tomography. The fate of the scroll waves of excitation in the Belousov-Zhabotinsky reaction depends on the thickness of the cylinder jacket. While at sufficiently wide cylinder jackets vertically oriented scroll waves remain stable, the probability that the filament of a scroll hits a lateral wall increases as the cylinder jacket narrows. This may lead to the rupture of the initial filament and pinning of the filament ends at the lateral walls. Filaments that pin to opposite lateral walls shrink and reorient to a horizontal orientation; such a reorientation corresponds to a transition from an intramural to a transmural scroll wave. The kinetics of the reorientation and shrinkage of the scrolls were studied. Furthermore, we find that no new filaments were generated upon collision of excitation waves at the side of the cylinder jacket opposite to the scroll wave. Thus, under the studied conditions, we do not observe any new generation of filaments due to a phenomenon like reentry.
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Affiliation(s)
- Christian Bruns
- Institut für Experimentelle Physik, Abteilung Biophysik, Otto-von-Guericke Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany and Institut für Biometrie und Medizinische Informatik, Otto-von-Guericke Universität Magdeburg, Leipziger Strasse 44, 39120 Magdeburg, Germany
| | - Marcus J B Hauser
- Institut für Experimentelle Physik, Abteilung Biophysik, Otto-von-Guericke Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany and Institut für Biometrie und Medizinische Informatik, Otto-von-Guericke Universität Magdeburg, Leipziger Strasse 44, 39120 Magdeburg, Germany
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43
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Xiao S, Tong C, Yang Y, Wu M. Mitotic Cortical Waves Predict Future Division Sites by Encoding Positional and Size Information. Dev Cell 2017; 43:493-506.e3. [DOI: 10.1016/j.devcel.2017.10.023] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2016] [Revised: 08/02/2017] [Accepted: 10/22/2017] [Indexed: 10/18/2022]
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44
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Hsu HF, Bodenschatz E, Westendorf C, Gholami A, Pumir A, Tarantola M, Beta C. Variability and Order in Cytoskeletal Dynamics of Motile Amoeboid Cells. PHYSICAL REVIEW LETTERS 2017; 119:148101. [PMID: 29053324 DOI: 10.1103/physrevlett.119.148101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2016] [Indexed: 06/07/2023]
Abstract
The chemotactic motion of eukaryotic cells such as leukocytes or metastatic cancer cells relies on membrane protrusions driven by the polymerization and depolymerization of actin. Here we show that the response of the actin system to a receptor stimulus is subject to a threshold value that varies strongly from cell to cell. Above the threshold, we observe pronounced cell-to-cell variability in the response amplitude. The polymerization time, however, is almost constant over the entire range of response amplitudes, while the depolymerization time increases with increasing amplitude. We show that cell-to-cell variability in the response amplitude correlates with the amount of Arp2/3, a protein that enhances actin polymerization. A time-delayed feedback model for the cortical actin concentration is consistent with all our observations and confirms the role of Arp2/3 in the observed cell-to-cell variability. Taken together, our observations highlight robust regulation of the actin response that enables a reliable timing of cell movement.
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Affiliation(s)
- Hsin-Fang Hsu
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
| | - Eberhard Bodenschatz
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
- Institute for Nonlinear Dynamics, University of Göttingen, D-37073 Göttingen, Germany
- Laboratory of Atomic and Solid-State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Christian Westendorf
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
| | - Azam Gholami
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
| | - Alain Pumir
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
- Université Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Marco Tarantola
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
| | - Carsten Beta
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
- Institute of Physics and Astronomy, University of Potsdam, D-14476 Potsdam, Germany
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45
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Actin Waves: Origin of Cell Polarization and Migration? Trends Cell Biol 2017; 27:515-526. [DOI: 10.1016/j.tcb.2017.02.003] [Citation(s) in RCA: 83] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2016] [Revised: 01/26/2017] [Accepted: 02/07/2017] [Indexed: 01/22/2023]
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46
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Abstract
During macropinocytosis, cells remodel their morphologies for the uptake of extracellular matter. This endocytotic mechanism relies on the collapse and closure of precursory structures, which are propagating actin-based, ring-shaped vertical undulations at the dorsal (top) cell membrane, a.k.a. circular dorsal ruffles (CDRs). As such, CDRs are essential to a range of vital and pathogenic processes alike. Here we show, based on both experimental data and theoretical analysis, that CDRs are propagating fronts of actin polymerization in a bistable system. The theory relies on a novel mass-conserving reaction–diffusion model, which associates the expansion and contraction of waves to distinct counter-propagating front solutions. Moreover, the model predicts that under a change in parameters (for example, biochemical conditions) CDRs may be pinned and fluctuate near the cell boundary or exhibit complex spiral wave dynamics due to a wave instability. We observe both phenomena also in our experiments indicating the conditions for which macropinocytosis is suppressed. Circular dorsal ruffles (CDRs) are important for the vesicular uptake of extracellular matter, but the basis of their wave dynamics is not understood. Here, the authors propose and experimentally test a bistable reaction-diffusion system, which they show accounts for the typical CDR expansion and shrinkage and for aberrant formation of pinned waves and spirals.
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Miao Y, Bhattacharya S, Edwards M, Cai H, Inoue T, Iglesias PA, Devreotes PN. Altering the threshold of an excitable signal transduction network changes cell migratory modes. Nat Cell Biol 2017; 19:329-340. [PMID: 28346441 PMCID: PMC5394931 DOI: 10.1038/ncb3495] [Citation(s) in RCA: 84] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2016] [Accepted: 02/22/2017] [Indexed: 12/18/2022]
Abstract
The diverse migratory modes displayed by different cell types are generally believed to be idiosyncratic. Here we show that the migratory behavior of Dictyostelium was switched from amoeboid to keratocyte-like and oscillatory modes by synthetically decreasing PIP2 levels or increasing Ras/Rap-related activities. The perturbations at these key nodes of an excitable signal transduction network initiated a causal chain of events: The threshold for network activation was lowered, the speed and range of propagating waves of signal transduction activity increased, actin driven cellular protrusions expanded and, consequently, the cell migratory mode transitions ensued. Conversely, innately keratocyte-like and oscillatory cells were promptly converted to amoeboid by inhibition of Ras effectors with restoration of directed migration. We use computational analysis to explain how thresholds control cell migration and discuss the architecture of the signal transduction network that gives rise to excitability.
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Affiliation(s)
- Yuchuan Miao
- Department of Biological Chemistry, School of Medicine, Johns Hopkins University, Baltimore, Maryland 21205, USA
| | - Sayak Bhattacharya
- Department of Electrical and Computer Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, Maryland 21205, USA
| | - Marc Edwards
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, Maryland 21205, USA
| | - Huaqing Cai
- State Key Laboratory of Biomacromolecules, Institute of Biophysics, Chinese Academy of Sciences, Beijing 100101, China
| | - Takanari Inoue
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, Maryland 21205, USA
| | - Pablo A Iglesias
- Department of Electrical and Computer Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, Maryland 21205, USA.,Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, Maryland 21205, USA
| | - Peter N Devreotes
- Department of Cell Biology and Center for Cell Dynamics, School of Medicine, Johns Hopkins University, Baltimore, Maryland 21205, USA
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van Haastert PJM, Keizer-Gunnink I, Kortholt A. Coupled excitable Ras and F-actin activation mediates spontaneous pseudopod formation and directed cell movement. Mol Biol Cell 2017; 28:922-934. [PMID: 28148648 PMCID: PMC5385941 DOI: 10.1091/mbc.e16-10-0733] [Citation(s) in RCA: 43] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2016] [Revised: 12/19/2016] [Accepted: 01/26/2017] [Indexed: 11/29/2022] Open
Abstract
Chemotaxis is the mechanism by which cells move in the direction of chemical gradients. The central circuit connecting basal movement and gradient sensing is unknown. Ras activation and F-actin form one coupled excitable system, which is the beating heart of cell movement in both the absence and presence of external cues. Many eukaryotic cells regulate their mobility by external cues. Genetic studies have identified >100 components that participate in chemotaxis, which hinders the identification of the conceptual framework of how cells sense and respond to shallow chemical gradients. The activation of Ras occurs during basal locomotion and is an essential connector between receptor and cytoskeleton during chemotaxis. Using a sensitive assay for activated Ras, we show here that activation of Ras and F-actin forms two excitable systems that are coupled through mutual positive feedback and memory. This coupled excitable system leads to short-lived patches of activated Ras and associated F-actin that precede the extension of protrusions. In buffer, excitability starts frequently with Ras activation in the back/side of the cell or with F-actin in the front of the cell. In a shallow gradient of chemoattractant, local Ras activation triggers full excitation of Ras and subsequently F-actin at the side of the cell facing the chemoattractant, leading to directed pseudopod extension and chemotaxis. A computational model shows that the coupled excitable Ras/F-actin system forms the driving heart for the ordered-stochastic extension of pseudopods in buffer and for efficient directional extension of pseudopods in chemotactic gradients.
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Affiliation(s)
- Peter J M van Haastert
- Department of Cell Biochemistry, University of Groningen, 9747 AG Groningen, Netherlands
| | - Ineke Keizer-Gunnink
- Department of Cell Biochemistry, University of Groningen, 9747 AG Groningen, Netherlands
| | - Arjan Kortholt
- Department of Cell Biochemistry, University of Groningen, 9747 AG Groningen, Netherlands
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Ecke M, Gerisch G. Co-existence of Ras activation in a chemotactic signal transduction pathway and in an autonomous wave - forming system. Small GTPases 2017; 10:72-80. [PMID: 28136018 PMCID: PMC6343538 DOI: 10.1080/21541248.2016.1268666] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
The activation of Ras is common to two activities in cells of Dictyostelium discoideum: the directed movement in a gradient of chemoattractant and the autonomous generation of propagating waves of actin polymerization on the substrate-attached cell surface. We produced large cells by electric-pulse induced fusion to simultaneously study both activities in one cell. For imaging, a fluorescent label for activated Ras was combined with labels for filamentous actin, PIP3, or PTEN. Chemotactic responses were elicited in a diffusion gradient of cyclic AMP. Waves initiated at sites separate from the front of the cell propagated in all directions. Nevertheless, the wave-forming cells were capable of recognizing the attractant gradient and managed to migrate in its direction.
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Affiliation(s)
- Mary Ecke
- a Max Planck Institute of Biochemistry , Martinsried , Germany
| | - Günther Gerisch
- a Max Planck Institute of Biochemistry , Martinsried , Germany
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50
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Bernitt E, Döbereiner HG. Spatiotemporal Patterns of Noise-Driven Confined Actin Waves in Living Cells. PHYSICAL REVIEW LETTERS 2017; 118:048102. [PMID: 28186815 DOI: 10.1103/physrevlett.118.048102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2016] [Indexed: 06/06/2023]
Abstract
Cells utilize waves of polymerizing actin to reshape their morphologies, which is central to physiological and pathological processes alike. Here, we force dorsal actin waves to propagate on one-dimensional domains with periodic boundary conditions, which results in striking spatiotemporal patterns with a clear signature of noise-driven dynamics. We show that these patterns can be very closely reproduced with a noise-driven active medium at coherence resonance.
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Affiliation(s)
- Erik Bernitt
- Institut für Biophysik, Universität Bremen, 28359 Bremen, Germany
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