1
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Quintanilla MA, Patel H, Wu H, Sochacki KA, Chandrasekar S, Akamatsu M, Rotty JD, Korobova F, Bear JE, Taraska JW, Oakes PW, Beach JR. Local monomer levels and established filaments potentiate non-muscle myosin 2 assembly. J Cell Biol 2024; 223:e202305023. [PMID: 38353656 PMCID: PMC10866686 DOI: 10.1083/jcb.202305023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Revised: 01/02/2024] [Accepted: 01/26/2024] [Indexed: 02/16/2024] Open
Abstract
The ability to dynamically assemble contractile networks is required throughout cell physiology, yet direct biophysical mechanisms regulating non-muscle myosin 2 filament assembly in living cells are lacking. Here, we use a suite of dynamic, quantitative imaging approaches to identify deterministic factors that drive myosin filament appearance and amplification. We find that actin dynamics regulate myosin assembly, but that the static actin architecture plays a less clear role. Instead, remodeling of actin networks modulates the local myosin monomer levels and facilitates assembly through myosin:myosin-driven interactions. Using optogenetically controlled myosin, we demonstrate that locally concentrating myosin is sufficient to both form filaments and jump-start filament amplification and partitioning. By counting myosin monomers within filaments, we demonstrate a myosin-facilitated assembly process that establishes filament stacks prior to partitioning into clusters that feed higher-order networks. Together, these findings establish the biophysical mechanisms regulating the assembly of non-muscle contractile structures that are ubiquitous throughout cell biology.
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Affiliation(s)
- Melissa A. Quintanilla
- Department of Cell and Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, USA
| | - Hiral Patel
- Department of Cell and Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, USA
| | - Huini Wu
- Department of Cell and Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, USA
| | - Kem A. Sochacki
- Laboratory of Molecular Biophysics, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, MD, USA
| | - Shreya Chandrasekar
- Department of Cell and Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, USA
| | - Matthew Akamatsu
- Department of Biology, University of Washington, Seattle, WA, USA
| | - Jeremy D. Rotty
- Department of Biochemistry, Uniformed Services University of the Health Sciences, Bethesda, MD, USA
| | - Farida Korobova
- Feinberg School of Medicine, Northwestern University, Chicago, IL, USA
| | - James E. Bear
- Department of Cell Biology and Physiology, University of North Carolina-Chapel Hill, Chapel Hill, NC, USA
| | - Justin W. Taraska
- Laboratory of Molecular Biophysics, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, MD, USA
| | - Patrick W. Oakes
- Department of Cell and Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, USA
| | - Jordan R. Beach
- Department of Cell and Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, USA
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2
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Moreno E, Alonso S. Generation of a Virtual Cell using a Phase Field Approach to Model Amoeboid Crawling. Methods Mol Biol 2024; 2828:205-220. [PMID: 39147979 DOI: 10.1007/978-1-0716-4023-4_15] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/17/2024]
Abstract
The process of chemotaxis of living cells is complex. Cells follow gradients of an external signal because the interior of the cells gets polarized. The description of the exterior and the interior of the cell together with its motion for the convenient realization of the computational modeling of the whole process is a complex technical problem. Here, we employ a phase field model to characterize the interior of the cell, permitting the integration of stochastic partial differential equations, responsible for the polarization in the interior of the cell, and simultaneously, the calculation of the shape deformations of the cell, including its locomotion. We detail the mathematical description of the process and the procedure to calculate numerically the phase field with a simple reaction-diffusion equation for a single concentration.
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Affiliation(s)
- Eduardo Moreno
- Department of Physics, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Sergio Alonso
- Department of Physics, Universitat Politècnica de Catalunya, Barcelona, Spain.
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3
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Sakuta H, Nakatani N, Torisawa T, Sumino Y, Tsumoto K, Oiwa K, Yoshikawa K. Self-emergent vortex flow of microtubule and kinesin in cell-sized droplets under water/water phase separation. Commun Chem 2023; 6:80. [PMID: 37100870 PMCID: PMC10133263 DOI: 10.1038/s42004-023-00879-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Accepted: 04/11/2023] [Indexed: 04/28/2023] Open
Abstract
By facilitating a water/water phase separation (w/wPS), crowded biopolymers in cells form droplets that contribute to the spatial localization of biological components and their biochemical reactions. However, their influence on mechanical processes driven by protein motors has not been well studied. Here, we show that the w/wPS droplet spontaneously entraps kinesins as well as microtubules (MTs) and generates a micrometre-scale vortex flow inside the droplet. Active droplets with a size of 10-100 µm are generated through w/wPS of dextran and polyethylene glycol mixed with MTs, molecular-engineered chimeric four-headed kinesins and ATP after mechanical mixing. MTs and kinesin rapidly created contractile network accumulated at the interface of the droplet and gradually generated vortical flow, which can drive translational motion of a droplet. Our work reveals that the interface of w/wPS contributes not only to chemical processes but also produces mechanical motion by assembling species of protein motors in a functioning manner.
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Affiliation(s)
- Hiroki Sakuta
- Faculty of Life and Medical Sciences, Doshisha University, Kyotanabe, Kyoto, 610-0394, Japan
- Organization for Research Initiatives and Development, Doshisha University, Kyotanabe, Kyoto, 610-0394, Japan
- Center for Complex Systems Biology, Universal Biology Institute, The University of Tokyo, Meguro, Tokyo, 153-8902, Japan
- Graduate School of Arts and Sciences, The University of Tokyo, Meguro, Tokyo, 153-8902, Japan
| | - Naoki Nakatani
- Faculty of Life and Medical Sciences, Doshisha University, Kyotanabe, Kyoto, 610-0394, Japan
| | - Takayuki Torisawa
- Cell Architecture Laboratory, Structural Biology Center, National Institute of Genetics, Mishima, Shizuoka, 411-8540, Japan
| | - Yutaka Sumino
- Department of Applied Physics, Faculty of Advanced Engineering, WaTUS and DCIS, Tokyo University of Science, Katsushika, Tokyo, 125-8585, Japan.
| | - Kanta Tsumoto
- Division of Chemistry for Materials, Graduate School of Engineering, Mie University, Tsu, Mie, 514-8507, Japan
| | - Kazuhiro Oiwa
- Advanced ICT Research Institute, National Institute of Information and Communications Technology, Kobe, Hyogo, 651-2492, Japan.
- Department of Life Science, Graduate School of Science, University of Hyogo, Ako, Hyogo, 678-1297, Japan.
| | - Kenichi Yoshikawa
- Faculty of Life and Medical Sciences, Doshisha University, Kyotanabe, Kyoto, 610-0394, Japan
- Center for Integrative Medicine and Physics, Institute for Advanced Study, Kyoto University, Kyoto, Kyoto, 606-8501, Japan
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4
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Nwogbaga I, Camley BA. Coupling cell shape and velocity leads to oscillation and circling in keratocyte galvanotaxis. Biophys J 2023; 122:130-142. [PMID: 36397670 PMCID: PMC9822803 DOI: 10.1016/j.bpj.2022.11.021] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2022] [Revised: 10/03/2022] [Accepted: 11/11/2022] [Indexed: 11/18/2022] Open
Abstract
During wound healing, fish keratocyte cells undergo galvanotaxis where they follow a wound-induced electric field. In addition to their stereotypical persistent motion, keratocytes can develop circular motion without a field or oscillate while crawling in the field direction. We developed a coarse-grained phenomenological model that captures these keratocyte behaviors. We fit this model to experimental data on keratocyte response to an electric field being turned on. A critical element of our model is a tendency for cells to turn toward their long axis, arising from a coupling between cell shape and velocity, which gives rise to oscillatory and circular motion. Galvanotaxis is influenced not only by the field-dependent responses, but also cell speed and cell shape relaxation rate. When the cell reacts to an electric field being turned on, our model predicts that stiff, slow cells react slowly but follow the signal reliably. Cells that polarize and align to the field at a faster rate react more quickly and follow the signal more reliably. When cells are exposed to a field that switches direction rapidly, cells follow the average of field directions, while if the field is switched more slowly, cells follow a "staircase" pattern. Our study indicated that a simple phenomenological model coupling cell speed and shape is sufficient to reproduce a broad variety of different keratocyte behaviors, ranging from circling to oscillation to galvanotactic response, by only varying a few parameters.
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Affiliation(s)
- Ifunanya Nwogbaga
- Department of Biophysics, Johns Hopkins University, Baltimore, Maryland
| | - Brian A Camley
- Department of Biophysics, Johns Hopkins University, Baltimore, Maryland; William H. Miller III Department of Physics & Astronomy, Johns Hopkins University, Baltimore, Maryland.
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5
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Safsten CA, Rybalko V, Berlyand L. Asymptotic stability of contraction-driven cell motion. Phys Rev E 2022; 105:024403. [PMID: 35291081 DOI: 10.1103/physreve.105.024403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Accepted: 12/24/2021] [Indexed: 06/14/2023]
Abstract
We study the onset of motion of a living cell (e.g., a keratocyte) driven by myosin contraction with focus on a transition from unstable radial stationary states to stable asymmetric moving states. We introduce a two- dimensional free-boundary model that generalizes a previous one-dimensional model [P. Recho, T. Putelat, and L. Truskinovsky, Phys. Rev. Lett. 111, 108102 (2013)10.1103/PhysRevLett.111.108102] by combining a Keller-Segel model, a Hele-Shaw boundary condition, and the Young-Laplace law with a regularizing term which precludes blowup or collapse by ensuring that membrane-cortex interaction is sufficiently strong. We find a family of asymmetric traveling solutions bifurcating from stationary solutions. Our main result is nonlinear asymptotic stability of traveling solutions that model observable steady cell motion. We derive an explicit asymptotic formula for the stability-determining eigenvalue via asymptotic expansions in small speed. This formula greatly simplifies computation of this eigenvalue and shows that stability is determined by the change in total myosin mass when stationary solutions bifurcate to traveling solutions. Our spectral analysis reveals the physical mechanisms of stability.
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Affiliation(s)
- C Alex Safsten
- Department of Mathematics, The Pennsylvania State University, Pennsylvania, USA
| | - Volodmyr Rybalko
- B. Verkin Institute for Low Temperature Physics and Engineering, Kharkiv, Ukraine
| | - Leonid Berlyand
- Department of Mathematics and Huck Institute for Life Sciences, The Pennsylvania State University, Pennsylvania, USA
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6
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Chandra A, Butler MT, Bear JE, Haugh JM. Modeling cell protrusion predicts how myosin II and actin turnover affect adhesion-based signaling. Biophys J 2022; 121:102-118. [PMID: 34861242 PMCID: PMC8758409 DOI: 10.1016/j.bpj.2021.11.2889] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Revised: 11/03/2021] [Accepted: 11/29/2021] [Indexed: 01/07/2023] Open
Abstract
Orchestration of cell migration is essential for development, tissue regeneration, and the immune response. This dynamic process integrates adhesion, signaling, and cytoskeletal subprocesses across spatial and temporal scales. In mesenchymal cells, adhesion complexes bound to extracellular matrix mediate both biochemical signal transduction and physical interaction with the F-actin cytoskeleton. Here, we present a mathematical model that offers insight into both aspects, considering spatiotemporal dynamics of nascent adhesions, active signaling molecules, mechanical clutching, actin treadmilling, and nonmuscle myosin II contractility. At the core of the model is a positive feedback loop, whereby adhesion-based signaling promotes generation of barbed ends at, and protrusion of, the cell's leading edge, which in turn promotes formation and stabilization of nascent adhesions. The model predicts a switch-like transition and optimality of membrane protrusion, determined by the balance of actin polymerization and retrograde flow, with respect to extracellular matrix density. The model, together with new experimental measurements, explains how protrusion can be modulated by mechanical effects (nonmuscle myosin II contractility and adhesive bond stiffness) and F-actin turnover.
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Affiliation(s)
- Ankit Chandra
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina
| | - Mitchell T Butler
- Department of Cell Biology and Physiology, UNC Lineberger Comprehensive Cancer Center, University of North Carolina School of Medicine, Chapel Hill, North Carolina
| | - James E Bear
- Department of Cell Biology and Physiology, UNC Lineberger Comprehensive Cancer Center, University of North Carolina School of Medicine, Chapel Hill, North Carolina
| | - Jason M Haugh
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina.
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7
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Wortel IMN, Niculescu I, Kolijn PM, Gov NS, de Boer RJ, Textor J. Local actin dynamics couple speed and persistence in a cellular Potts model of cell migration. Biophys J 2021; 120:2609-2622. [PMID: 34022237 PMCID: PMC8390880 DOI: 10.1016/j.bpj.2021.04.036] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Revised: 03/24/2021] [Accepted: 04/14/2021] [Indexed: 12/28/2022] Open
Abstract
Cell migration is astoundingly diverse. Molecular signatures, cell-cell interactions, and environmental structures each play their part in shaping cell motion, yielding numerous morphologies and migration modes. Nevertheless, in recent years, a simple unifying law was found to describe cell migration across many different cell types and contexts: faster cells turn less frequently. This universal coupling between speed and persistence (UCSP) was explained by retrograde actin flow from front to back, but it remains unclear how this mechanism generalizes to cells with complex shapes and cells migrating in structured environments, which may not have a well-defined front-to-back orientation. Here, we present an in-depth characterization of an existing cellular Potts model, in which cells polarize dynamically from a combination of local actin dynamics (stimulating protrusions) and global membrane tension along the perimeter (inhibiting protrusions). We first show that the UCSP emerges spontaneously in this model through a cross talk of intracellular mechanisms, cell shape, and environmental constraints, resembling the dynamic nature of cell migration in vivo. Importantly, we find that local protrusion dynamics suffice to reproduce the UCSP-even in cases in which no clear global, front-to-back polarity exists. We then harness the spatial nature of the cellular Potts model to show how cell shape dynamics limit both the speed and persistence a cell can reach and how a rigid environment such as the skin can restrict cell motility even further. Our results broaden the range of potential mechanisms underlying the speed-persistence coupling that has emerged as a fundamental property of migrating cells.
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Affiliation(s)
- Inge M N Wortel
- Department of Tumor Immunology, Radboud Institute for Molecular Life Sciences, Nijmegen, the Netherlands; Data Science, Institute for Computing and Information Sciences, Radboud University, Nijmegen, the Netherlands.
| | - Ioana Niculescu
- Theoretical Biology and Bioinformatics, Department of Biology, Utrecht University, Utrecht, the Netherlands
| | - P Martijn Kolijn
- Theoretical Biology and Bioinformatics, Department of Biology, Utrecht University, Utrecht, the Netherlands
| | - Nir S Gov
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Rob J de Boer
- Theoretical Biology and Bioinformatics, Department of Biology, Utrecht University, Utrecht, the Netherlands
| | - Johannes Textor
- Department of Tumor Immunology, Radboud Institute for Molecular Life Sciences, Nijmegen, the Netherlands; Data Science, Institute for Computing and Information Sciences, Radboud University, Nijmegen, the Netherlands.
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8
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de Guinea M, Estrada A, Janmaat KR, Nekaris KAI, Van Belle S. Disentangling the importance of social and ecological information in goal-directed movements in a wild primate. Anim Behav 2021. [DOI: 10.1016/j.anbehav.2020.12.017] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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9
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Johnson ME, Chen A, Faeder JR, Henning P, Moraru II, Meier-Schellersheim M, Murphy RF, Prüstel T, Theriot JA, Uhrmacher AM. Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry. Mol Biol Cell 2021; 32:186-210. [PMID: 33237849 PMCID: PMC8120688 DOI: 10.1091/mbc.e20-08-0530] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 10/13/2020] [Accepted: 11/17/2020] [Indexed: 12/29/2022] Open
Abstract
Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multimolecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases, we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.
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Affiliation(s)
- M. E. Johnson
- Thomas C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD, 21218
| | - A. Chen
- Thomas C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD, 21218
| | - J. R. Faeder
- Department of Computational and Systems Biology, University of Pittsburgh School of Medicine, Pittsburgh, PA, 15260
| | - P. Henning
- Institute for Visual and Analytic Computing, University of Rostock, 18055 Rostock, Germany
| | - I. I. Moraru
- Department of Cell Biology, Center for Cell Analysis and Modeling, University of Connecticut Health Center, Farmington, CT 06030
| | - M. Meier-Schellersheim
- Laboratory of Immune System Biology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, MD 20892
| | - R. F. Murphy
- Computational Biology Department, Department of Biological Sciences, Department of Biomedical Engineering, Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA 15289
| | - T. Prüstel
- Laboratory of Immune System Biology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, MD 20892
| | - J. A. Theriot
- Department of Biology and Howard Hughes Medical Institute, University of Washington, Seattle, WA 98195
| | - A. M. Uhrmacher
- Institute for Visual and Analytic Computing, University of Rostock, 18055 Rostock, Germany
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10
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DiNapoli KT, Robinson DN, Iglesias PA. Tools for computational analysis of moving boundary problems in cellular mechanobiology. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2020; 13:e1514. [PMID: 33305503 DOI: 10.1002/wsbm.1514] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Revised: 10/08/2020] [Accepted: 10/20/2020] [Indexed: 12/29/2022]
Abstract
A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.
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Affiliation(s)
- Kathleen T DiNapoli
- Department of Cell Biology, Johns Hopkins School of Medicine, Baltimore, Maryland, USA
| | - Douglas N Robinson
- Department of Cell Biology, Johns Hopkins School of Medicine, Baltimore, Maryland, USA
| | - Pablo A Iglesias
- Department of Cell Biology, Johns Hopkins School of Medicine, Baltimore, Maryland, USA
- Department of Electrical & Computer Engineering, Johns Hopkins University, Baltimore, Maryland, USA
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11
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Zmurchok C, Collette J, Rajagopal V, Holmes WR. Membrane Tension Can Enhance Adaptation to Maintain Polarity of Migrating Cells. Biophys J 2020; 119:1617-1629. [PMID: 32976760 PMCID: PMC7642449 DOI: 10.1016/j.bpj.2020.08.035] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Revised: 08/20/2020] [Accepted: 08/25/2020] [Indexed: 12/31/2022] Open
Abstract
Migratory cells are known to adapt to environments that contain wide-ranging levels of chemoattractant. Although biochemical models of adaptation have been previously proposed, here, we discuss a different mechanism based on mechanosensing, in which the interaction between biochemical signaling and cell tension facilitates adaptation. We describe and analyze a model of mechanochemical-based adaptation coupling a mechanics-based physical model of cell tension coupled with the wave-pinning reaction-diffusion model for Rac GTPase activity. The mathematical analysis of this model, simulations of a simplified one-dimensional cell geometry, and two-dimensional finite element simulations of deforming cells reveal that as a cell protrudes under the influence of high stimulation levels, tension-mediated inhibition of Rac signaling causes the cell to polarize even when initially overstimulated. Specifically, tension-mediated inhibition of Rac activation, which has been experimentally observed in recent years, facilitates this adaptation by countering the high levels of environmental stimulation. These results demonstrate how tension-related mechanosensing may provide an alternative (and potentially complementary) mechanism for cell adaptation.
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Affiliation(s)
- Cole Zmurchok
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee
| | - Jared Collette
- Department of Biomedical Engineering, University of Melbourne, Melbourne, Australia
| | - Vijay Rajagopal
- Department of Biomedical Engineering, University of Melbourne, Melbourne, Australia
| | - William R Holmes
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee; Department of Mathematics, Vanderbilt University, Nashville, Tennessee; Quantitative Systems Biology Center, Vanderbilt University, Nashville, Tennessee.
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12
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Allen GM, Lee KC, Barnhart EL, Tsuchida MA, Wilson CA, Gutierrez E, Groisman A, Theriot JA, Mogilner A. Cell Mechanics at the Rear Act to Steer the Direction of Cell Migration. Cell Syst 2020; 11:286-299.e4. [PMID: 32916096 PMCID: PMC7530145 DOI: 10.1016/j.cels.2020.08.008] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Revised: 06/17/2020] [Accepted: 08/10/2020] [Indexed: 01/18/2023]
Abstract
Motile cells navigate complex environments by changing their direction of travel, generating left-right asymmetries in their mechanical subsystems to physically turn. Currently, little is known about how external directional cues are propagated along the length scale of the whole cell and integrated with its force-generating apparatus to steer migration mechanically. We examine the mechanics of spontaneous cell turning in fish epidermal keratocytes and find that the mechanical asymmetries responsible for turning behavior predominate at the rear of the cell, where there is asymmetric centripetal actin flow. Using experimental perturbations, we identify two linked feedback loops connecting myosin II contractility, adhesion strength and actin network flow in turning cells that are sufficient to explain the observed cell shapes and trajectories. Notably, asymmetries in actin polymerization at the cell leading edge play only a minor role in the mechanics of cell turning-that is, cells steer from the rear.
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Affiliation(s)
- Greg M Allen
- Department of Biochemistry and Howard Hughes Medical Institute, Stanford University School of Medicine, Stanford, CA 94305, USA
| | - Kun Chun Lee
- Department of Neurobiology, Physiology and Behavior, University of California, Davis, Davis, CA 95616, USA
| | - Erin L Barnhart
- Department of Biochemistry and Howard Hughes Medical Institute, Stanford University School of Medicine, Stanford, CA 94305, USA
| | - Mark A Tsuchida
- Department of Biochemistry and Howard Hughes Medical Institute, Stanford University School of Medicine, Stanford, CA 94305, USA
| | - Cyrus A Wilson
- Department of Biochemistry and Howard Hughes Medical Institute, Stanford University School of Medicine, Stanford, CA 94305, USA
| | - Edgar Gutierrez
- Department of Physics, University of California, San Diego, San Diego, CA 92023, USA
| | - Alexander Groisman
- Department of Physics, University of California, San Diego, San Diego, CA 92023, USA
| | - Julie A Theriot
- Department of Biology and Howard Hughes Medical Institute, University of Washington, Seattle, WA 98195, USA.
| | - Alex Mogilner
- Courant Institute of Mathematical Sciences and Department of Biology, New York University, New York, NY 10012, USA.
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13
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Le Goff T, Liebchen B, Marenduzzo D. Actomyosin Contraction Induces In-Bulk Motility of Cells and Droplets. Biophys J 2020; 119:1025-1032. [PMID: 32795395 DOI: 10.1016/j.bpj.2020.06.029] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Revised: 04/29/2020] [Accepted: 06/01/2020] [Indexed: 01/07/2023] Open
Abstract
Cell crawling on two-dimensional surfaces is a relatively well-understood phenomenon that is based on actin polymerization at a cell's front edge and anchoring on a substrate, allowing the cell to pull itself forward. However, some cells, such as cancer cells invading a three-dimensional matrigel, can also swim in the bulk, where surface adhesion is impossible. Although there is strong evidence that the self-organized engine that drives cells forward in the bulk involves myosin, the specific propulsion mechanism remains largely unclear. Here, we propose a minimal model for in-bulk self-motility of a droplet containing an isotropic and compressible contractile gel, representing a cell extract containing a disordered actomyosin network. In our model, contraction mediates a feedback loop between myosin-induced flow and advection-induced myosin accumulation, which leads to clustering and locally enhanced flow. The symmetry of such flow is then spontaneously broken through actomyosin-membrane interactions, leading to self-organized droplet motility relative to the underlying solvent. Depending on the balance between contraction, diffusion, detachment rate of myosin, and effective surface tension, this motion can be either straight or circular. Our simulations and analytical results shed new light on in-bulk myosin-driven cell motility in living cells and provide a framework to design a novel type of synthetic active matter droplet potentially resembling the motility mechanism of biological cells.
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Affiliation(s)
| | - Benno Liebchen
- Institute of Condensed Matter Physics, Technische Universität Darmstadt, Darmstadt, Germany
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom.
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14
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Moure A, Gomez H. Influence of myosin activity and mechanical impact on keratocyte polarization. SOFT MATTER 2020; 16:5177-5194. [PMID: 32459252 DOI: 10.1039/d0sm00473a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In cell migration, polarization is the process by which a stationary cell breaks symmetry and initiates motion. Although a lot is known about the mechanisms involved in cell polarization, the role played by myosin contraction remains unclear. In addition, cell polarization by mechanical impact has received little attention. Here, we study the influence of myosin activity on cell polarization and the initiation of motion induced by mechanical cues using a computational model for keratocytes. The model accounts for cell deformation, the dynamics of myosin and the signaling protein RhoA (a member of the Rho GTPases family), as well as the forces acting on the actomyosin network. Our results show that the attainment of a steady polarized state depends on the strength of myosin down- or up-regulation and that myosin upregulation favors cell polarization. Our results also confirm the existence of a threshold level for cell polarization, which is determined by the level of polarization of the Rho GTPases at the time the external stimuli vanish. In all, this paper shows that capturing the interactions between the signaling proteins (Rho GTPases for keratocytes) and the compounds of the motile machinery in a moving cell is crucial to study cell polarization.
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Affiliation(s)
- Adrian Moure
- School of Mechanical Engineering, Purdue University, West Lafayette, 47907 IN, USA.
| | - Hector Gomez
- School of Mechanical Engineering, Purdue University, West Lafayette, 47907 IN, USA. and Weldon School of Biomedical Engineering, Purdue University, West Lafayette, 47907 IN, USA and Purdue University Center for Cancer Research, Purdue University, West Lafayette, 47906 IN, USA
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15
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Mogilner A, Barnhart EL, Keren K. Experiment, theory, and the keratocyte: An ode to a simple model for cell motility. Semin Cell Dev Biol 2020; 100:143-151. [DOI: 10.1016/j.semcdb.2019.10.019] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Revised: 09/27/2019] [Accepted: 10/31/2019] [Indexed: 01/20/2023]
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16
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Zmurchok C, Holmes WR. Simple Rho GTPase Dynamics Generate a Complex Regulatory Landscape Associated with Cell Shape. Biophys J 2020; 118:1438-1454. [PMID: 32084329 DOI: 10.1016/j.bpj.2020.01.035] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2019] [Revised: 01/27/2020] [Accepted: 01/30/2020] [Indexed: 02/08/2023] Open
Abstract
Migratory cells exhibit a variety of morphologically distinct responses to their environments that manifest in their cell shape. Some protrude uniformly to increase substrate contacts, others are broadly contractile, some polarize to facilitate migration, and yet others exhibit mixtures of these responses. Prior studies have identified a discrete collection of shapes that the majority of cells display and demonstrated that activity levels of the cytoskeletal regulators Rac1 and RhoA GTPase regulate those shapes. Here, we use computational modeling to assess whether known GTPase dynamics can give rise to a sufficient diversity of spatial signaling states to explain the observed shapes. Results show that the combination of autoactivation and mutually antagonistic cross talk between GTPases, along with the conservative membrane binding, generates a wide array of distinct homogeneous and polarized regulatory phenotypes that arise for fixed model parameters. From a theoretical perspective, these results demonstrate that simple GTPase dynamics can generate complex multistability in which six distinct stable steady states (three homogeneous and three polarized) coexist for a fixed set of parameters, each of which naturally maps to an observed morphology. From a biological perspective, although we do not explicitly model the cytoskeleton or resulting cell morphologies, these results, along with prior literature linking GTPase activity to cell morphology, support the hypothesis that GTPase signaling dynamics can generate the broad morphological characteristics observed in many migratory cell populations. Further, the observed diversity may be the result of cells populating a complex morphological landscape generated by GTPase regulation rather than being the result of intrinsic cell-cell variation. These results demonstrate that Rho GTPases may have a central role in regulating the broad characteristics of cell shape (e.g., expansive, contractile, polarized, etc.) and that shape heterogeneity may be (at least partly) a reflection of the rich signaling dynamics regulating the cytoskeleton rather than intrinsic cell heterogeneity.
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Affiliation(s)
- Cole Zmurchok
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee
| | - William R Holmes
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee; Department of Mathematics, Vanderbilt University, Nashville, Tennessee; Quantitative Systems Biology Center, Vanderbilt University, Nashville, Tennessee.
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17
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Moure A, Gomez H. Dual role of the nucleus in cell migration on planar substrates. Biomech Model Mechanobiol 2020; 19:1491-1508. [PMID: 31907682 DOI: 10.1007/s10237-019-01283-6] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2019] [Accepted: 12/21/2019] [Indexed: 01/09/2023]
Abstract
Cell migration is essential to sustain life. There have been significant advances in the understanding of the mechanisms that control cell crawling, but the role of the nucleus remains poorly understood. The nucleus exerts a tight control of cell migration in 3D environments, but its influence in 2D migration on planar substrates remains unclear. Here, we study the role of the cell nucleus in 2D cell migration using a computational model of fish keratocytes. Our results indicate that the apparently minor role played by the nucleus emerges from two antagonist effects: While the nucleus modifies the spatial distributions of actin and myosin in a way that reduces cell velocity (e.g., the nucleus displaces myosin to the sides and front of the cell), its mechanical connection with the cytoskeleton alters the intracellular stresses promoting cell migration. Overall, the favorable effect of the nucleus-cytoskeleton connection prevails, which may explain why regular cells usually move faster than enucleated cells.
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Affiliation(s)
- Adrian Moure
- School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47907, USA.
| | - Hector Gomez
- School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47907, USA.,Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, 47907, USA.,Purdue University Center for Cancer Research, Purdue University, West Lafayette, IN, 47906, USA
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18
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Active poroelastic two-phase model for the motion of physarum microplasmodia. PLoS One 2019; 14:e0217447. [PMID: 31398215 PMCID: PMC6688797 DOI: 10.1371/journal.pone.0217447] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2019] [Accepted: 07/24/2019] [Indexed: 01/05/2023] Open
Abstract
The onset of self-organized motion is studied in a poroelastic two-phase model with free boundaries for Physarum microplasmodia (MP). In the model, an active gel phase is assumed to be interpenetrated by a passive fluid phase on small length scales. A feedback loop between calcium kinetics, mechanical deformations, and induced fluid flow gives rise to pattern formation and the establishment of an axis of polarity. Altogether, we find that the calcium kinetics that breaks the conservation of the total calcium concentration in the model and a nonlinear friction between MP and substrate are both necessary ingredients to obtain an oscillatory movement with net motion of the MP. By numerical simulations in one spatial dimension, we find two different types of oscillations with net motion as well as modes with time-periodic or irregular switching of the axis of polarity. The more frequent type of net motion is characterized by mechano-chemical waves traveling from the front towards the rear. The second type is characterized by mechano-chemical waves that appear alternating from the front and the back. While both types exhibit oscillatory forward and backward movement with net motion in each cycle, the trajectory and gel flow pattern of the second type are also similar to recent experimental measurements of peristaltic MP motion. We found moving MPs in extended regions of experimentally accessible parameters, such as length, period and substrate friction strength. Simulations of the model show that the net speed increases with the length, provided that MPs are longer than a critical length of ≈ 120 μm. Both predictions are in line with recent experimental observations.
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19
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Nickaeen M, Berro J, Pollard TD, Slepchenko BM. Actin assembly produces sufficient forces for endocytosis in yeast. Mol Biol Cell 2019; 30:2014-2024. [PMID: 31242058 PMCID: PMC6727779 DOI: 10.1091/mbc.e19-01-0059] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
We formulated a spatially resolved model to estimate forces exerted by a polymerizing actin meshwork on an invagination of the plasma membrane during endocytosis in yeast cells. The model, which approximates the actin meshwork as a visco-active gel exerting forces on a rigid spherocylinder representing the endocytic invagination, is tightly constrained by experimental data. Simulations of the model produce forces that can overcome resistance of turgor pressure in yeast cells. Strong forces emerge due to the high density of polymerized actin in the vicinity of the invagination and because of entanglement of the meshwork due to its dendritic structure and cross-linking. The model predicts forces orthogonal to the invagination that are consistent with formation of a flask shape, which would diminish the net force due to turgor pressure. Simulations of the model with either two rings of nucleation-promoting factors (NPFs) as in fission yeast or a single ring of NPFs as in budding yeast produce enough force to elongate the invagination against the turgor pressure.
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Affiliation(s)
- Masoud Nickaeen
- Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, CT 06030
| | - Julien Berro
- Departments of Molecular Biophysics and Biochemistry and of Cell Biology.,Nanobiology Institute, Yale University, New Haven, CT 06520
| | - Thomas D Pollard
- Departments of Molecular Biophysics and Biochemistry and of Cell Biology.,Department of Molecular Cellular and Developmental Biology, Yale University, New Haven, CT 06520
| | - Boris M Slepchenko
- Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, CT 06030
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20
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Matsiaka OM, Baker RE, Shah ET, Simpson MJ. Mechanistic and experimental models of cell migration reveal the importance of cell-to-cell pushing in cell invasion. Biomed Phys Eng Express 2019. [DOI: 10.1088/2057-1976/ab1b01] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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21
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Manhart A, Icheva TA, Guerin C, Klar T, Boujemaa-Paterski R, Thery M, Blanchoin L, Mogilner A. Quantitative regulation of the dynamic steady state of actin networks. eLife 2019; 8:42413. [PMID: 30869077 PMCID: PMC6417862 DOI: 10.7554/elife.42413] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2018] [Accepted: 02/26/2019] [Indexed: 12/30/2022] Open
Abstract
Principles of regulation of actin network dimensions are fundamentally important for cell functions, yet remain unclear. Using both in vitro and in silico approaches, we studied the effect of key parameters, such as actin density, ADF/Cofilin concentration and network width on the network length. In the presence of ADF/Cofilin, networks reached equilibrium and became treadmilling. At the trailing edge, the network disintegrated into large fragments. A mathematical model predicts the network length as a function of width, actin and ADF/Cofilin concentrations. Local depletion of ADF/Cofilin by binding to actin is significant, leading to wider networks growing longer. A single rate of breaking network nodes, proportional to ADF/Cofilin density and inversely proportional to the square of the actin density, can account for the disassembly dynamics. Selective disassembly of heterogeneous networks by ADF/Cofilin controls steering during motility. Our results establish general principles on how the dynamic steady state of actin network emerges from biochemical and structural feedbacks.
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Affiliation(s)
- Angelika Manhart
- Courant Institute of Mathematical Sciences, New York University, New York, United States.,Department of Biology, New York University, New York, United States
| | - Téa Aleksandra Icheva
- CytomorphoLab, Biosciences & Biotechnology Institute of Grenoble, Laboratoire de Physiologie Cellulaire & Végétale, Université Grenoble-Alpes/CEA/CNRS/INRA, Grenoble, France
| | - Christophe Guerin
- CytomorphoLab, Biosciences & Biotechnology Institute of Grenoble, Laboratoire de Physiologie Cellulaire & Végétale, Université Grenoble-Alpes/CEA/CNRS/INRA, Grenoble, France
| | - Tobbias Klar
- CytomorphoLab, Biosciences & Biotechnology Institute of Grenoble, Laboratoire de Physiologie Cellulaire & Végétale, Université Grenoble-Alpes/CEA/CNRS/INRA, Grenoble, France
| | - Rajaa Boujemaa-Paterski
- CytomorphoLab, Biosciences & Biotechnology Institute of Grenoble, Laboratoire de Physiologie Cellulaire & Végétale, Université Grenoble-Alpes/CEA/CNRS/INRA, Grenoble, France
| | - Manuel Thery
- CytomorphoLab, Biosciences & Biotechnology Institute of Grenoble, Laboratoire de Physiologie Cellulaire & Végétale, Université Grenoble-Alpes/CEA/CNRS/INRA, Grenoble, France.,CytomorphoLab, Hôpital Saint Louis, Institut Universitaire d'Hematologie, UMRS1160, INSERM/AP-HP/Université Paris Diderot, Paris, France
| | - Laurent Blanchoin
- CytomorphoLab, Biosciences & Biotechnology Institute of Grenoble, Laboratoire de Physiologie Cellulaire & Végétale, Université Grenoble-Alpes/CEA/CNRS/INRA, Grenoble, France.,CytomorphoLab, Hôpital Saint Louis, Institut Universitaire d'Hematologie, UMRS1160, INSERM/AP-HP/Université Paris Diderot, Paris, France
| | - Alex Mogilner
- Courant Institute of Mathematical Sciences, New York University, New York, United States.,Department of Biology, New York University, New York, United States
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22
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Metzcar J, Wang Y, Heiland R, Macklin P. A Review of Cell-Based Computational Modeling in Cancer Biology. JCO Clin Cancer Inform 2019; 3:1-13. [PMID: 30715927 PMCID: PMC6584763 DOI: 10.1200/cci.18.00069] [Citation(s) in RCA: 175] [Impact Index Per Article: 35.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/28/2018] [Indexed: 12/14/2022] Open
Abstract
Cancer biology involves complex, dynamic interactions between cancer cells and their tissue microenvironments. Single-cell effects are critical drivers of clinical progression. Chemical and mechanical communication between tumor and stromal cells can co-opt normal physiologic processes to promote growth and invasion. Cancer cell heterogeneity increases cancer's ability to test strategies to adapt to microenvironmental stresses. Hypoxia and treatment can select for cancer stem cells and drive invasion and resistance. Cell-based computational models (also known as discrete models, agent-based models, or individual-based models) simulate individual cells as they interact in virtual tissues, which allows us to explore how single-cell behaviors lead to the dynamics we observe and work to control in cancer systems. In this review, we introduce the broad range of techniques available for cell-based computational modeling. The approaches can range from highly detailed models of just a few cells and their morphologies to millions of simpler cells in three-dimensional tissues. Modeling individual cells allows us to directly translate biologic observations into simulation rules. In many cases, individual cell agents include molecular-scale models. Most models also simulate the transport of oxygen, drugs, and growth factors, which allow us to link cancer development to microenvironmental conditions. We illustrate these methods with examples drawn from cancer hypoxia, angiogenesis, invasion, stem cells, and immunosurveillance. An ecosystem of interoperable cell-based simulation tools is emerging at a time when cloud computing resources make software easier to access and supercomputing resources make large-scale simulation studies possible. As the field develops, we anticipate that high-throughput simulation studies will allow us to rapidly explore the space of biologic possibilities, prescreen new therapeutic strategies, and even re-engineer tumor and stromal cells to bring cancer systems under control.
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23
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Goodhill GJ. Theoretical Models of Neural Development. iScience 2018; 8:183-199. [PMID: 30321813 PMCID: PMC6197653 DOI: 10.1016/j.isci.2018.09.017] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2018] [Revised: 08/06/2018] [Accepted: 09/19/2018] [Indexed: 12/22/2022] Open
Abstract
Constructing a functioning nervous system requires the precise orchestration of a vast array of mechanical, molecular, and neural-activity-dependent cues. Theoretical models can play a vital role in helping to frame quantitative issues, reveal mathematical commonalities between apparently diverse systems, identify what is and what is not possible in principle, and test the abilities of specific mechanisms to explain the data. This review focuses on the progress that has been made over the last decade in our theoretical understanding of neural development.
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Affiliation(s)
- Geoffrey J Goodhill
- Queensland Brain Institute and School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072, Australia.
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24
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Sfakianakis N, Brunk A. Stability, Convergence, and Sensitivity Analysis of the FBLM and the Corresponding FEM. Bull Math Biol 2018; 80:2789-2827. [PMID: 30159856 DOI: 10.1007/s11538-018-0460-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2017] [Accepted: 06/29/2018] [Indexed: 10/28/2022]
Abstract
We study in this paper the filament-based lamellipodium model (FBLM) and the corresponding finite element method (FEM) used to solve it. We investigate fundamental numerical properties of the FEM and justify its further use with the FBLM. We show that the FEM satisfies a time step stability condition that is consistent with the nature of the problem and propose a particular strategy to automatically adapt the time step of the method. We show that the FEM converges with respect to the (two-dimensional) space discretization in a series of characteristic and representative chemotaxis and haptotaxis experiments. We embed and couple the FBLM with a complex and adaptive extracellular environment comprised of chemical and adhesion components that are described by their macroscopic density and study their combined time evolution. With this combination, we study the sensitivity of the FBLM on several of its controlling parameters and discuss their influence in the dynamics of the model and its future evolution. We finally perform a number of numerical experiments that reproduce biological cases and compare the results with the ones reported in the literature.
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Affiliation(s)
- N Sfakianakis
- Institute of Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 205, 69120, Heidelberg, Germany.
| | - A Brunk
- Institute of Mathematics, Johannes Gutenberg-University, Staudingerweg 9, 55128, Mainz, Germany
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25
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Dolati S, Kage F, Mueller J, Müsken M, Kirchner M, Dittmar G, Sixt M, Rottner K, Falcke M. On the relation between filament density, force generation, and protrusion rate in mesenchymal cell motility. Mol Biol Cell 2018; 29:2674-2686. [PMID: 30156465 PMCID: PMC6249830 DOI: 10.1091/mbc.e18-02-0082] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Lamellipodia are flat membrane protrusions formed during mesenchymal motion. Polymerization at the leading edge assembles the actin filament network and generates protrusion force. How this force is supported by the network and how the assembly rate is shared between protrusion and network retrograde flow determines the protrusion rate. We use mathematical modeling to understand experiments changing the F-actin density in lamellipodia of B16-F1 melanoma cells by modulation of Arp2/3 complex activity or knockout of the formins FMNL2 and FMNL3. Cells respond to a reduction of density with a decrease of protrusion velocity, an increase in the ratio of force to filament number, but constant network assembly rate. The relation between protrusion force and tension gradient in the F-actin network and the density dependency of friction, elasticity, and viscosity of the network explain the experimental observations. The formins act as filament nucleators and elongators with differential rates. Modulation of their activity suggests an effect on network assembly rate. Contrary to these expectations, the effect of changes in elongator composition is much weaker than the consequences of the density change. We conclude that the force acting on the leading edge membrane is the force required to drive F-actin network retrograde flow.
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Affiliation(s)
- Setareh Dolati
- Max Delbrück Center for Molecular Medicine, 13125 Berlin, Germany
| | - Frieda Kage
- Division of Molecular Cell Biology, Zoological Institute, Technische Universität Braunschweig, 38106 Braunschweig, Germany.,Department of Cell Biology, Helmholtz Centre for Infection Research, 38124 Braunschweig, Germany
| | - Jan Mueller
- Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria
| | - Mathias Müsken
- Central Facility for Microscopy, Helmholtz Centre for Infection Research, 38124 Braunschweig, Germany
| | | | - Gunnar Dittmar
- Department of Oncology, Luxembourg Institute of Health, L-1445 Strassen, Luxembourg
| | - Michael Sixt
- Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria
| | - Klemens Rottner
- Division of Molecular Cell Biology, Zoological Institute, Technische Universität Braunschweig, 38106 Braunschweig, Germany.,Department of Cell Biology, Helmholtz Centre for Infection Research, 38124 Braunschweig, Germany
| | - Martin Falcke
- Max Delbrück Center for Molecular Medicine, 13125 Berlin, Germany.,Department of Physics, Humboldt Universität, 12489 Berlin, Germany
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