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Singh J, Imran Alsous J, Garikipati K, Shvartsman SY. Mechanics of stabilized intercellular bridges. Biophys J 2022; 121:3162-3171. [PMID: 35778841 PMCID: PMC9463629 DOI: 10.1016/j.bpj.2022.06.033] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Revised: 06/04/2022] [Accepted: 06/27/2022] [Indexed: 11/02/2022] Open
Abstract
Numerous engineered and natural systems form through reinforcement and stabilization of a deformed configuration that was generated by a transient force. An important class of such structures arises during gametogenesis, when a dividing cell undergoes incomplete cytokinesis, giving rise to daughter cells that remain connected through a stabilized intercellular bridge (ICB). ICBs can form through arrest of the contractile cytokinetic furrow and its subsequent stabilization. Despite knowledge of the molecular components, the mechanics underlying robust ICB assembly and the interplay between ring contractility and stiffening are poorly understood. Here, we report joint experimental and theoretical work that explores the physics underlying robust ICB assembly. We develop a continuum mechanics model that reveals the minimal requirements for the formation of stable ICBs, and validate the model's equilibrium predictions through a tabletop experimental analog. With insight into the equilibrium states, we turn to the dynamics: we demonstrate that contractility and stiffening are in dynamic competition and that the time intervals of their action must overlap to ensure assembly of ICBs of biologically observed proportions. Our results highlight a mechanism in which deformation and remodeling are tightly coordinated-one that is applicable to several mechanics-based applications and is a common theme in biological systems spanning several length scales.
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Affiliation(s)
- Jaspreet Singh
- Center for Computational Biology, Flatiron Institute, New York, New York
| | | | - Krishna Garikipati
- Departments of Mechanical Engineering, and Mathematics, Michigan Institute for Computational Discovery & Engineering, University of Michigan, Ann Arbor, Michigan.
| | - Stanislav Y Shvartsman
- Department of Molecular Biology, Princeton University, Princeton, New Jersey; The Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey.
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2
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DiNapoli KT, Robinson DN, Iglesias PA. A mesoscale mechanical model of cellular interactions. Biophys J 2021; 120:4905-4917. [PMID: 34687718 PMCID: PMC8633826 DOI: 10.1016/j.bpj.2021.10.021] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Revised: 08/25/2021] [Accepted: 10/18/2021] [Indexed: 01/16/2023] Open
Abstract
Computational models of cell mechanics allow the precise interrogation of cell shape change. These morphological changes are required for cells to survive in diverse tissue environments. Here, we present a mesoscale mechanical model of cell-substrate interactions using the level set method based on experimentally measured parameters. By implementing a viscoelastic mechanical equivalent circuit, we accurately model whole-cell deformations that are important for a variety of cellular processes. To effectively model shape changes as a cell interacts with a substrate, we have included receptor-mediated adhesion, which is governed by catch-slip bond behavior. The effect of adhesion was explored by subjecting cells to a variety of different substrates including flat, curved, and deformable surfaces. Finally, we increased the accuracy of our simulations by including a deformable nucleus in our cells. This model sets the foundation for further exploration into computational analyses of multicellular interactions.
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Affiliation(s)
- Kathleen T DiNapoli
- Department of Cell Biology, Johns Hopkins University School of Medicine, Baltimore, Maryland
| | - Douglas N Robinson
- Department of Cell Biology, Johns Hopkins University School of Medicine, Baltimore, Maryland
| | - Pablo A Iglesias
- Department of Cell Biology, Johns Hopkins University School of Medicine, Baltimore, Maryland; Department of Electrical & Computer Engineering, Johns Hopkins University Whiting School of Engineering, Baltimore, Maryland.
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3
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Frey F, Idema T. More than just a barrier: using physical models to couple membrane shape to cell function. SOFT MATTER 2021; 17:3533-3549. [PMID: 33503097 DOI: 10.1039/d0sm01758b] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The correct execution of many cellular processes, such as division and motility, requires the cell to adopt a specific shape. Physically, these shapes are determined by the interplay of the plasma membrane and internal cellular driving factors. While the plasma membrane defines the boundary of the cell, processes inside the cell can result in the generation of forces that deform the membrane. These processes include protein binding, the assembly of protein superstructures, and the growth and contraction of cytoskeletal networks. Due to the complexity of the cell, relating observed membrane deformations back to internal processes is a challenging problem. Here, we review cell shape changes in endocytosis, cell adhesion, cell migration and cell division and discuss how by modeling membrane deformations we can investigate the inner working principles of the cell.
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Affiliation(s)
- Felix Frey
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.
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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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5
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Verma V, Mogilner A, Maresca TJ. Classical and Emerging Regulatory Mechanisms of Cytokinesis in Animal Cells. BIOLOGY 2019; 8:biology8030055. [PMID: 31357447 PMCID: PMC6784142 DOI: 10.3390/biology8030055] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/29/2019] [Revised: 07/05/2019] [Accepted: 07/23/2019] [Indexed: 12/12/2022]
Abstract
The primary goal of cytokinesis is to produce two daughter cells, each having a full set of chromosomes. To achieve this, cells assemble a dynamic structure between segregated sister chromatids called the contractile ring, which is made up of filamentous actin, myosin-II, and other regulatory proteins. Constriction of the actomyosin ring generates a cleavage furrow that divides the cytoplasm to produce two daughter cells. Decades of research have identified key regulators and underlying molecular mechanisms; however, many fundamental questions remain unanswered and are still being actively investigated. This review summarizes the key findings, computational modeling, and recent advances in understanding of the molecular mechanisms that control the formation of the cleavage furrow and cytokinesis.
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Affiliation(s)
- Vikash Verma
- Biology Department, University of Massachusetts, Amherst, MA 01003, USA.
| | - Alex Mogilner
- Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
- Department of Biology, New York University, New York, NY 10012, USA
| | - Thomas J Maresca
- Biology Department, University of Massachusetts, Amherst, MA 01003, USA
- Molecular and Cellular Biology Graduate Program, University of Massachusetts, Amherst, MA 01003, USA
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6
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Bächer C, Gekle S. Computational modeling of active deformable membranes embedded in three-dimensional flows. Phys Rev E 2019; 99:062418. [PMID: 31330647 DOI: 10.1103/physreve.99.062418] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2019] [Indexed: 06/10/2023]
Abstract
Active gel theory has recently been very successful in describing biologically active materials such as actin filaments or moving bacteria in temporally fixed and simple geometries such as cubes or spheres. Here we develop a computational algorithm to compute the dynamic evolution of an arbitrarily shaped, deformable thin membrane of active material embedded in a three-dimensional flowing liquid. For this, our algorithm combines active gel theory with the classical theory of thin elastic shells. To compute the actual forces resulting from active stresses, we apply a parabolic fitting procedure to the triangulated membrane surface. Active forces are then dynamically coupled via an immersed-boundary method to the surrounding fluid whose dynamics can be solved by any standard, e.g., Lattice-Boltzmann, flow solver. We validate our algorithm using the Green's functions of Berthoumieux et al. [New J. Phys. 16, 065005 (2014)10.1088/1367-2630/16/6/065005] for an active cylindrical membrane subjected (i) to a locally increased active stress and (ii) to a homogeneous active stress. For the latter scenario, we predict in addition a nonaxisymmetric instability. We highlight the versatility of our method by analyzing the flow field inside an actively deforming cell embedded in external shear flow. Further applications may be cytoplasmic streaming or active membranes in blood flows.
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Affiliation(s)
- Christian Bächer
- Biofluid Simulation and Modeling, Theoretische Physik VI, Universität Bayreuth, Universitätsstrasse 30, Bayreuth, Germany
| | - Stephan Gekle
- Biofluid Simulation and Modeling, Theoretische Physik VI, Universität Bayreuth, Universitätsstrasse 30, Bayreuth, Germany
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Yang X, Gong Y, Li J, Eisenberg RS, Wang Q. Quasi-incompressible multi-species ionic fluid models. J Mol Liq 2019. [DOI: 10.1016/j.molliq.2018.10.033] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Cortes DB, Dawes A, Liu J, Nickaeen M, Strychalski W, Maddox AS. Unite to divide - how models and biological experimentation have come together to reveal mechanisms of cytokinesis. J Cell Sci 2018; 131:131/24/jcs203570. [PMID: 30563924 DOI: 10.1242/jcs.203570] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
Cytokinesis is the fundamental and ancient cellular process by which one cell physically divides into two. Cytokinesis in animal and fungal cells is achieved by contraction of an actomyosin cytoskeletal ring assembled in the cell cortex, typically at the cell equator. Cytokinesis is essential for the development of fertilized eggs into multicellular organisms and for homeostatic replenishment of cells. Correct execution of cytokinesis is also necessary for genome stability and the evasion of diseases including cancer. Cytokinesis has fascinated scientists for well over a century, but its speed and dynamics make experiments challenging to perform and interpret. The presence of redundant mechanisms is also a challenge to understand cytokinesis, leaving many fundamental questions unresolved. For example, how does a disordered cytoskeletal network transform into a coherent ring? What are the long-distance effects of localized contractility? Here, we provide a general introduction to 'modeling for biologists', and review how agent-based modeling and continuum mechanics modeling have helped to address these questions.
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Affiliation(s)
- Daniel B Cortes
- Department of Biology, University of North Carolina at Chapel Hill, 407 Fordham Hall, Chapel Hill, NC 27599, USA
| | - Adriana Dawes
- Departments of Mathematics and of Molecular Genetics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, OH 43210, USA
| | - Jian Liu
- National Heart, Lung and Blood Institute, Biochemistry and Biophysics Center, 50 South Drive, NIH, Bethesda, MD 20892, USA
| | - Masoud Nickaeen
- Richard D. Berlin Center for Cell Analysis and Modeling, University of Connecticut Health Center, Department of Cell Biology, 263 Farmington Avenue, Farmington, CT 06030-6406, USA
| | - Wanda Strychalski
- Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA
| | - Amy Shaub Maddox
- Department of Biology, University of North Carolina at Chapel Hill, 407 Fordham Hall, Chapel Hill, NC 27599, USA
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9
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Lee S. Mathematical Model of Contractile Ring-Driven Cytokinesis in a Three-Dimensional Domain. Bull Math Biol 2018; 80:583-597. [PMID: 29344759 DOI: 10.1007/s11538-018-0390-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2017] [Accepted: 01/05/2018] [Indexed: 12/22/2022]
Abstract
In this paper, a mathematical model of contractile ring-driven cytokinesis is presented by using both phase-field and immersed-boundary methods in a three-dimensional domain. It is one of the powerful hypotheses that cytokinesis happens driven by the contractile ring; however, there are only few mathematical models following the hypothesis, to the author's knowledge. I consider a hybrid method to model the phenomenon. First, a cell membrane is represented by a zero-contour of a phase-field implicitly because of its topological change. Otherwise, immersed-boundary particles represent a contractile ring explicitly based on the author's previous work. Here, the multi-component (or vector-valued) phase-field equation is considered to avoid the emerging of each cell membrane right after their divisions. Using a convex splitting scheme, the governing equation of the phase-field method has unique solvability. The numerical convergence of contractile ring to cell membrane is proved. Several numerical simulations are performed to validate the proposed model.
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Affiliation(s)
- Seunggyu Lee
- National Institute for Mathematical Sciences, Daejeon, 34047, Republic of Korea.
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Zhao J, Seeluangsawat P, Wang Q. Modeling antimicrobial tolerance and treatment of heterogeneous biofilms. Math Biosci 2016; 282:1-15. [DOI: 10.1016/j.mbs.2016.09.005] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2016] [Revised: 07/23/2016] [Accepted: 09/06/2016] [Indexed: 11/25/2022]
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Abstract
Cytokinesis is essential for development and survival of all organisms by increasing cell number and diversity. It is a highly regulated process that requires spatiotemporal coordination of hundreds of proteins functioning in the assembly, constriction, and disassembly of a contractile actomyosin ring, targeted vesicle fusion, and localized extracellular matrix remodeling. Cytokinesis has been studied in multiple systems with a wide range of technologies to learn the common principles. In this chapter, we describe the analysis of protein dynamics during cytokinesis in the budding yeast Saccharomyces cerevisiae by several live-cell imaging methods. This, in combination with the power of yeast genetics, has yielded novel insights into the mechanism of cytokinesis. Similar approaches are increasingly used to study this fundamental process in more complex systems.
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Affiliation(s)
- S Okada
- University of Pennsylvania, Philadelphia, PA, United States; Kyushu University, Fukuoka, Japan
| | - C Wloka
- University of Pennsylvania, Philadelphia, PA, United States; University of Groningen, Groningen, The Netherlands
| | - E Bi
- University of Pennsylvania, Philadelphia, PA, United States
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