1
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Leech V, Kenny FN, Marcotti S, Shaw TJ, Stramer BM, Manhart A. Derivation and simulation of a computational model of active cell populations: How overlap avoidance, deformability, cell-cell junctions and cytoskeletal forces affect alignment. PLoS Comput Biol 2024; 20:e1011879. [PMID: 39074138 DOI: 10.1371/journal.pcbi.1011879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Accepted: 07/13/2024] [Indexed: 07/31/2024] Open
Abstract
Collective alignment of cell populations is a commonly observed phenomena in biology. An important example are aligning fibroblasts in healthy or scar tissue. In this work we derive and simulate a mechanistic agent-based model of the collective behaviour of actively moving and interacting cells, with a focus on understanding collective alignment. The derivation strategy is based on energy minimisation. The model ingredients are motivated by data on the behaviour of different populations of aligning fibroblasts and include: Self-propulsion, overlap avoidance, deformability, cell-cell junctions and cytoskeletal forces. We find that there is an optimal ratio of self-propulsion speed and overlap avoidance that maximises collective alignment. Further we find that deformability aids alignment, and that cell-cell junctions by themselves hinder alignment. However, if cytoskeletal forces are transmitted via cell-cell junctions we observe strong collective alignment over large spatial scales.
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Affiliation(s)
- Vivienne Leech
- Department of Mathematics, University College London, London, United Kingdom
| | - Fiona N Kenny
- Randall Centre for Cell and Molecular Biophysics, King's College London, London, United Kingdom
| | - Stefania Marcotti
- Randall Centre for Cell and Molecular Biophysics, King's College London, London, United Kingdom
| | - Tanya J Shaw
- Randall Centre for Cell and Molecular Biophysics, King's College London, London, United Kingdom
| | - Brian M Stramer
- Randall Centre for Cell and Molecular Biophysics, King's College London, London, United Kingdom
| | - Angelika Manhart
- Department of Mathematics, University College London, London, United Kingdom
- Faculty of Mathematics, University of Vienna, Vienna, Austria
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2
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Wang W, Law RA, Perez Ipiña E, Konstantopoulos K, Camley BA. Confinement, jamming, and adhesion in cancer cells dissociating from a collectively invading strand. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.06.28.601053. [PMID: 38979161 PMCID: PMC11230418 DOI: 10.1101/2024.06.28.601053] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
When cells in a primary tumor work together to invade into nearby tissue, this can lead to cell dissociations-cancer cells breaking off from the invading front-leading to metastasis. What controls the dissociation of cells, and whether they break off singly or in small groups? Can this be determined by cell-cell adhesion or chemotactic cues given to cells? We develop a physical model for this question, based on experiments that mimic aspects of cancer cell invasion using microfluidic devices with microchannels of different widths. Experimentally, most dissociation events ("ruptures") involve single cells breaking off, but we observe some ruptures of large groups ( ∼ 20 cells) in wider channels. The rupture probability is nearly independent of channel width. We recapitulate the experimental results with a phase field cell motility model by introducing three different cell states (follower, guided, and high-motility metabolically active leader cells) based on their spatial position. These leader cells may explain why single-cell rupture is the universal most probable outcome. Our simulation results show that cell-channel adhesion is necessary for cells in narrow channels to invade, and strong cell-cell adhesion leads to fewer but larger ruptures. Chemotaxis also influences the rupture behavior: Strong chemotaxis strength leads to larger and faster ruptures. Finally, we study the relationship between biological jamming transitions and cell dissociations. Our results suggest unjamming is necessary but not sufficient to create ruptures.
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3
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Chojowski R, Schwarz US, Ziebert F. The role of the nucleus for cell mechanics: an elastic phase field approach. SOFT MATTER 2024; 20:4488-4503. [PMID: 38804018 DOI: 10.1039/d4sm00345d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2024]
Abstract
The nucleus of eukaryotic cells typically makes up around 30% of the cell volume and has significantly different mechanics, which can make it effectively up to ten times stiffer than the surrounding cytoplasm. Therefore it is an important element for cell mechanics, but a quantitative understanding of its mechanical role during whole cell dynamics is largely missing. Here we demonstrate that elastic phase fields can be used to describe dynamical cell processes in adhesive or confining environments in which the nucleus acts as a stiff inclusion in an elastic cytoplasm. We first introduce and verify our computational method and then study several prevalent cell-mechanical measurement methods. For cells on adhesive patterns, we find that nuclear stress is shielded by the adhesive pattern. For cell compression between two parallel plates, we obtain force-compression curves that allow us to extract an effective modulus for the cell-nucleus composite. For micropipette aspiration, the effect of the nucleus on the effective modulus is found to be much weaker, highlighting the complicated interplay between extracellular geometry and cell mechanics that is captured by our approach. We also show that our phase field approach can be used to investigate the effects of Kelvin-Voigt-type viscoelasticity and cortical tension.
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Affiliation(s)
- Robert Chojowski
- Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, 69120 Heidelberg, Germany.
- BioQuant, Heidelberg University, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany
| | - Ulrich S Schwarz
- Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, 69120 Heidelberg, Germany.
- BioQuant, Heidelberg University, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany
| | - Falko Ziebert
- Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, 69120 Heidelberg, Germany.
- BioQuant, Heidelberg University, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany
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4
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Perez Ipiña E, d’Alessandro J, Ladoux B, Camley BA. Deposited footprints let cells switch between confined, oscillatory, and exploratory migration. Proc Natl Acad Sci U S A 2024; 121:e2318248121. [PMID: 38787878 PMCID: PMC11145245 DOI: 10.1073/pnas.2318248121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Accepted: 04/08/2024] [Indexed: 05/26/2024] Open
Abstract
For eukaryotic cells to heal wounds, respond to immune signals, or metastasize, they must migrate, often by adhering to extracellular matrix (ECM). Cells may also deposit ECM components, leaving behind a footprint that influences their crawling. Recent experiments showed that some epithelial cell lines on micropatterned adhesive stripes move persistently in regions they have previously crawled over, where footprints have been formed, but barely advance into unexplored regions, creating an oscillatory migration of increasing amplitude. Here, we explore through mathematical modeling how footprint deposition and cell responses to footprint combine to allow cells to develop oscillation and other complex migratory motions. We simulate cell crawling with a phase field model coupled to a biochemical model of cell polarity, assuming local contact with the deposited footprint activates Rac1, a protein that establishes the cell's front. Depending on footprint deposition rate and response to the footprint, cells on micropatterned lines can display many types of motility, including confined, oscillatory, and persistent motion. On two-dimensional (2D) substrates, we predict a transition between cells undergoing circular motion and cells developing an exploratory phenotype. Small quantitative changes in a cell's interaction with its footprint can completely alter exploration, allowing cells to tightly regulate their motion, leading to different motility phenotypes (confined vs. exploratory) in different cells when deposition or sensing is variable from cell to cell. Consistent with our computational predictions, we find in earlier experimental data evidence of cells undergoing both circular and exploratory motion.
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Affiliation(s)
- Emiliano Perez Ipiña
- William H. Miller III Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD21218
| | | | - Benoît Ladoux
- Université Paris Cité, CNRS, Institut Jacques Monod, F-75013Paris, France
| | - Brian A. Camley
- William H. Miller III Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD21218
- Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD21218
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5
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Perez Ipiña E, D'Alessandro J, Ladoux B, Camley BA. Deposited footprints let cells switch between confined, oscillatory, and exploratory migration. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.09.14.557437. [PMID: 37745526 PMCID: PMC10515912 DOI: 10.1101/2023.09.14.557437] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/26/2023]
Abstract
For eukaryotic cells to heal wounds, respond to immune signals, or metastasize, they must migrate, often by adhering to extracellular matrix. Cells may also deposit extracellular matrix components, leaving behind a footprint that influences their crawling. Recent experiments showed that some epithelial cells on micropatterned adhesive stripes move persistently in regions they have previously crawled over, where footprints have been formed, but barely advance into unexplored regions, creating an oscillatory migration of increasing amplitude. Here, we explore through mathematical modeling how footprint deposition and cell responses to footprint combine to allow cells to develop oscillation and other complex migratory motions. We simulate cell crawling with a phase field model coupled to a biochemical model of cell polarity, assuming local contact with the deposited footprint activates Rac1, a protein that establishes the cell's front. Depending on footprint deposition rate and response to the footprint, cells on micropatterned lines can display many types of motility, including confined, oscillatory, and persistent motion. On two-dimensional substrates, we predict a transition between cells undergoing circular motion and cells developing an exploratory phenotype. Small quantitative changes in a cell's interaction with its footprint can completely alter exploration, allowing cells to tightly regulate their motion, leading to different motility phenotypes (confined vs exploratory) in different cells when deposition or sensing is variable from cell to cell. Consistent with our computational predictions, we find in earlier experimental data evidence of cells undergoing both circular and exploratory motion.
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6
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Brückner DB, Broedersz CP. Learning dynamical models of single and collective cell migration: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:056601. [PMID: 38518358 DOI: 10.1088/1361-6633/ad36d2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2023] [Accepted: 03/22/2024] [Indexed: 03/24/2024]
Abstract
Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.
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Affiliation(s)
- David B Brückner
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Chase P Broedersz
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilian-University Munich, Theresienstr. 37, D-80333 Munich, Germany
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7
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Schindler D, Moldenhawer T, Beta C, Huisinga W, Holschneider M. Three-component contour dynamics model to simulate and analyze amoeboid cell motility in two dimensions. PLoS One 2024; 19:e0297511. [PMID: 38277351 PMCID: PMC10817190 DOI: 10.1371/journal.pone.0297511] [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: 08/27/2023] [Accepted: 01/07/2024] [Indexed: 01/28/2024] Open
Abstract
Amoeboid cell motility is relevant in a wide variety of biomedical processes such as wound healing, cancer metastasis, and embryonic morphogenesis. It is characterized by pronounced changes of the cell shape associated with expansions and retractions of the cell membrane, which result in a crawling kind of locomotion. Despite existing computational models of amoeboid motion, the inference of expansion and retraction components of individual cells, the corresponding classification of cells, and the a priori specification of the parameter regime to achieve a specific motility behavior remain challenging open problems. We propose a novel model of the spatio-temporal evolution of two-dimensional cell contours comprising three biophysiologically motivated components: a stochastic term accounting for membrane protrusions and two deterministic terms accounting for membrane retractions by regularizing the shape and area of the contour. Mathematically, these correspond to the intensity of a self-exciting Poisson point process, the area-preserving curve-shortening flow, and an area adjustment flow. The model is used to generate contour data for a variety of qualitatively different, e.g., polarized and non-polarized, cell tracks that visually resemble experimental data very closely. In application to experimental cell tracks, we inferred the protrusion component and examined its correlation to common biomarkers: the F-actin density close to the membrane and its local motion. Due to the low model complexity, parameter estimation is fast, straightforward, and offers a simple way to classify contour dynamics based on two locomotion types: the amoeboid and a so-called fan-shaped type. For both types, we use cell tracks segmented from fluorescence imaging data of the model organism Dictyostelium discoideum. An implementation of the model is provided within the open-source software package AmoePy, a Python-based toolbox for analyzing and simulating amoeboid cell motility.
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Affiliation(s)
- Daniel Schindler
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| | - Ted Moldenhawer
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| | - Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| | - Wilhelm Huisinga
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| | - Matthias Holschneider
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
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8
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Giverso C, Jankowiak G, Preziosi L, Schmeiser C. The Influence of Nucleus Mechanics in Modelling Adhesion-independent Cell Migration in Structured and Confined Environments. Bull Math Biol 2023; 85:88. [PMID: 37626216 PMCID: PMC10457269 DOI: 10.1007/s11538-023-01187-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2022] [Accepted: 07/17/2023] [Indexed: 08/27/2023]
Abstract
Recent biological experiments (Lämmermann et al. in Nature 453(7191):51-55, 2008; Reversat et al. in Nature 7813:582-585, 2020; Balzer et al. in ASEB J Off Publ Fed Am Soc Exp Biol 26(10):4045-4056, 2012) have shown that certain types of cells are able to move in structured and confined environments even without the activation of focal adhesion. Focusing on this particular phenomenon and based on previous works (Jankowiak et al. in Math Models Methods Appl Sci 30(03):513-537, 2020), we derive a novel two-dimensional mechanical model, which relies on the following physical ingredients: the asymmetrical renewal of the actin cortex supporting the membrane, resulting in a backward flow of material; the mechanical description of the nuclear membrane and the inner nuclear material; the microtubule network guiding nucleus location; the contact interactions between the cell and the external environment. The resulting fourth order system of partial differential equations is then solved numerically to conduct a study of the qualitative effects of the model parameters, mainly those governing the mechanical properties of the nucleus and the geometry of the confining structure. Coherently with biological observations, we find that cells characterized by a stiff nucleus are unable to migrate in channels that can be crossed by cells with a softer nucleus. Regarding the geometry, cell velocity and ability to migrate are influenced by the width of the channel and the wavelength of the external structure. Even though still preliminary, these results may be potentially useful in determining the physical limit of cell migration in confined environments and in designing scaffolds for tissue engineering.
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Affiliation(s)
- Chiara Giverso
- Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Gaspard Jankowiak
- Department of Mathematics and Statistics, University of Konstanz, 78457 Constance, Germany
| | - Luigi Preziosi
- Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Christian Schmeiser
- Faculty of Mathematics, University of Vienna, Oskar-Morgenstern Platz 1, 1090 Wien, Austria
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9
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Nagayama M, Monobe H, Sakakibara K, Nakamura KI, Kobayashi Y, Kitahata H. On the reaction-diffusion type modelling of the self-propelled object motion. Sci Rep 2023; 13:12633. [PMID: 37537247 PMCID: PMC10400585 DOI: 10.1038/s41598-023-39395-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 07/25/2023] [Indexed: 08/05/2023] Open
Abstract
In this study, we propose a mathematical model of self-propelled objects based on the Allen-Cahn type phase-field equation. We combine it with the equation for the concentration of surfactant used in previous studies to construct a model that can handle self-propelled object motion with shape change. A distinctive feature of our mathematical model is that it can represent both deformable self-propelled objects, such as droplets, and solid objects, such as camphor disks, by controlling a single parameter. Furthermore, we demonstrate that, by taking the singular limit, this phase-field based model can be reduced to a free boundary model, which is equivalent to the [Formula: see text]-gradient flow model of self-propelled objects derived by the variational principle from the interfacial energy, which gives a physical interpretation to the phase-field model.
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Affiliation(s)
- Masaharu Nagayama
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Hokkaido, 060-0812, Japan.
| | - Harunori Monobe
- Department of Mathematics, Graduate School of Science, Osaka Metropolitan University, Osaka, 599-8531, Japan
| | - Koya Sakakibara
- Institute of Science and Engineering, Kanazawa University, Ishikawa, 920-1192, Japan
- RIKEN iTHEMS, Saitama, 351-0198, Japan
| | - Ken-Ichi Nakamura
- Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, 164-8525, Japan
| | - Yasuaki Kobayashi
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Hokkaido, 060-0812, Japan
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10
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Feng L, Zhao T, Xu H, Shi X, Li C, Hsia KJ, Zhang S. Physical forces guide curvature sensing and cell migration mode bifurcating. PNAS NEXUS 2023; 2:pgad237. [PMID: 37680491 PMCID: PMC10482382 DOI: 10.1093/pnasnexus/pgad237] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Accepted: 07/11/2023] [Indexed: 09/09/2023]
Abstract
The ability of cells to sense and adapt to curvy topographical features has been implicated in organ morphogenesis, tissue repair, and tumor metastasis. However, how individual cells or multicellular assemblies sense and differentiate curvatures remains elusive. Here, we reveal a curvature sensing mechanism in which surface tension can selectively activate either actin or integrin flows, leading to bifurcating cell migration modes: focal adhesion formation that enables cell crawling at convex front edges and actin cable assembly that pulls cells forward at concave front edges. The molecular flows and curved front morphogenesis are sustained by coordinated cellular tension generation and transmission. We track the molecular flows and mechanical force transduction pathways by a phase-field model, which predicts that multicellular curvature sensing is more efficient than individual cells, suggesting collective intelligence of cells. The unique ability of cells in curvature sensing and migration mode bifurcating may offer insights into emergent collective patterns and functions of living active systems at different length scales.
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Affiliation(s)
- Luyi Feng
- Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802, USA
| | - Tiankai Zhao
- Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802, USA
| | - Hongmei Xu
- School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore
| | - Xuechen Shi
- Department of Biomedical Engineering, Pennsylvania State University, University Park, PA 16802, USA
| | - Changhao Li
- Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802, USA
| | - K Jimmy Hsia
- School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore
- School of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University, Singapore 639798, Singapore
| | - Sulin Zhang
- Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802, USA
- Department of Biomedical Engineering, Pennsylvania State University, University Park, PA 16802, USA
- Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802, USA
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11
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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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12
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Copperman J, Gross SM, Chang YH, Heiser LM, Zuckerman DM. Morphodynamical cell state description via live-cell imaging trajectory embedding. Commun Biol 2023; 6:484. [PMID: 37142678 PMCID: PMC10160022 DOI: 10.1038/s42003-023-04837-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 04/10/2023] [Indexed: 05/06/2023] Open
Abstract
Time-lapse imaging is a powerful approach to gain insight into the dynamic responses of cells, but the quantitative analysis of morphological changes over time remains challenging. Here, we exploit the concept of "trajectory embedding" to analyze cellular behavior using morphological feature trajectory histories-that is, multiple time points simultaneously, rather than the more common practice of examining morphological feature time courses in single timepoint (snapshot) morphological features. We apply this approach to analyze live-cell images of MCF10A mammary epithelial cells after treatment with a panel of microenvironmental perturbagens that strongly modulate cell motility, morphology, and cell cycle behavior. Our morphodynamical trajectory embedding analysis constructs a shared cell state landscape revealing ligand-specific regulation of cell state transitions and enables quantitative and descriptive models of single-cell trajectories. Additionally, we show that incorporation of trajectories into single-cell morphological analysis enables (i) systematic characterization of cell state trajectories, (ii) better separation of phenotypes, and (iii) more descriptive models of ligand-induced differences as compared to snapshot-based analysis. This morphodynamical trajectory embedding is broadly applicable to the quantitative analysis of cell responses via live-cell imaging across many biological and biomedical applications.
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Affiliation(s)
- Jeremy Copperman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR, 97239, USA.
| | - Sean M Gross
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR, 97239, USA
| | - Young Hwan Chang
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR, 97239, USA
- Knight Cancer Institute, Oregon Health and Science University, Portland, OR, 97239, USA
| | - Laura M Heiser
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR, 97239, USA.
- Knight Cancer Institute, Oregon Health and Science University, Portland, OR, 97239, USA.
| | - Daniel M Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR, 97239, USA.
- Knight Cancer Institute, Oregon Health and Science University, Portland, OR, 97239, USA.
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13
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Kuang X, Guan G, Tang C, Zhang L. MorphoSim: an efficient and scalable phase-field framework for accurately simulating multicellular morphologies. NPJ Syst Biol Appl 2023; 9:6. [PMID: 36806172 PMCID: PMC9938209 DOI: 10.1038/s41540-023-00265-w] [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: 04/16/2022] [Accepted: 01/04/2023] [Indexed: 02/19/2023] Open
Abstract
The phase field model can accurately simulate the evolution of microstructures with complex morphologies, and it has been widely used for cell modeling in the last two decades. However, compared to other cellular models such as the coarse-grained model and the vertex model, its high computational cost caused by three-dimensional spatial discretization hampered its application and scalability, especially for multicellular organisms. Recently, we built a phase field model coupled with in vivo imaging data to accurately reconstruct the embryonic morphogenesis of Caenorhabditis elegans from 1- to 8-cell stages. In this work, we propose an improved phase field model by using the stabilized numerical scheme and modified volume constriction. Then we present a scalable phase-field framework, MorphoSim, which is 100 times more efficient than the previous one and can simulate over 100 mechanically interacting cells. Finally, we demonstrate how MorphoSim can be successfully applied to reproduce the assembly, self-repairing, and dissociation of a synthetic artificial multicellular system - the synNotch system.
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Affiliation(s)
- Xiangyu Kuang
- grid.11135.370000 0001 2256 9319Center for Quantitative Biology, Peking University, Beijing, 100871 China
| | - Guoye Guan
- grid.11135.370000 0001 2256 9319Center for Quantitative Biology, Peking University, Beijing, 100871 China
| | - Chao Tang
- Center for Quantitative Biology, Peking University, Beijing, 100871, China. .,Peking-Tsinghua Center for Life Sciences, Peking University, Beijing, 100871, China. .,School of Physics, Peking University, Beijing, 100871, China.
| | - Lei Zhang
- Center for Quantitative Biology, Peking University, Beijing, 100871, China. .,Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China. .,Center for Machine Learning Research, Peking University, Beijing, 100871, China.
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14
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Urdeitx P, Mousavi SJ, Avril S, Doweidar MH. Computational modeling of multiple myeloma interactions with resident bone marrow cells. Comput Biol Med 2023; 153:106458. [PMID: 36599211 DOI: 10.1016/j.compbiomed.2022.106458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Revised: 12/08/2022] [Accepted: 12/19/2022] [Indexed: 12/27/2022]
Abstract
The interaction of multiple myeloma with bone marrow resident cells plays a key role in tumor progression and the development of drug resistance. The tumor cell response involves contact-mediated and paracrine interactions. The heterogeneity of myeloma cells and bone marrow cells makes it difficult to reproduce this environment in in-vitro experiments. The use of in-silico established tools can help to understand these complex problems. In this article, we present a computational model based on the finite element method to define the interactions of multiple myeloma cells with resident bone marrow cells. This model includes cell migration, which is controlled by stress-strain equilibrium, and cell processes such as proliferation, differentiation, and apoptosis. A series of computational experiments were performed to validate the proposed model. Cell proliferation by the growth factor IGF-1 is studied for different concentrations ranging from 0-10 ng/mL. Cell motility is studied for different concentrations of VEGF and fibronectin in the range of 0-100 ng/mL. Finally, cells were simulated under a combination of IGF-1 and VEGF stimuli whose concentrations are considered to be dependent on the cancer-associated fibroblasts in the extracellular matrix. Results show a good agreement with previous in-vitro results. Multiple myeloma growth and migration are shown to correlate linearly to the IGF-1 stimuli. These stimuli are coupled with the mechanical environment, which also improves cell growth. Moreover, cell migration depends on the fiber and VEGF concentration in the extracellular matrix. Finally, our computational model shows myeloma cells trigger mesenchymal stem cells to differentiate into cancer-associated fibroblasts, in a dose-dependent manner.
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Affiliation(s)
- Pau Urdeitx
- School of Engineering and Architecture (EINA), University of Zaragoza, Zaragoza, 50018, Spain; Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, 50018, Spain; Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Zaragoza, 50018, Spain
| | - S Jamaleddin Mousavi
- Mines Saint-Étienne, University of Lyon, University of Jean Monnet, INSERM, Saint-Etienne, 42023, France
| | - Stephane Avril
- Mines Saint-Étienne, University of Lyon, University of Jean Monnet, INSERM, Saint-Etienne, 42023, France; Institute for Mechanics of Materials and Structures, TU Wien-Vienna University of Technology, Vienna, 1040, Austria
| | - Mohamed H Doweidar
- School of Engineering and Architecture (EINA), University of Zaragoza, Zaragoza, 50018, Spain; Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, 50018, Spain; Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Zaragoza, 50018, Spain.
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15
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Kemeth FP, Alonso S, Echebarria B, Moldenhawer T, Beta C, Kevrekidis IG. Black and gray box learning of amplitude equations: Application to phase field systems. Phys Rev E 2023; 107:025305. [PMID: 36932491 DOI: 10.1103/physreve.107.025305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2022] [Accepted: 01/26/2023] [Indexed: 06/18/2023]
Abstract
We present a data-driven approach to learning surrogate models for amplitude equations and illustrate its application to interfacial dynamics of phase field systems. In particular, we demonstrate learning effective partial differential equations describing the evolution of phase field interfaces from full phase field data. We illustrate this on a model phase field system, where analytical approximate equations for the dynamics of the phase field interface (a higher-order eikonal equation and its approximation, the Kardar-Parisi-Zhang equation) are known. For this system, we discuss data-driven approaches for the identification of equations that accurately describe the front interface dynamics. When the analytical approximate models mentioned above become inaccurate, as we move beyond the region of validity of the underlying assumptions, the data-driven equations outperform them. In these regimes, going beyond black box identification, we explore different approaches to learning data-driven corrections to the analytically approximate models, leading to effective gray box partial differential equations.
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Affiliation(s)
- Felix P Kemeth
- Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
| | - Sergio Alonso
- Department of Physics, Universitat Politècnica de Catalunya, Carrer de Jordi Girona 1-3, 08034 Barcelona, Spain
| | - Blas Echebarria
- Department of Physics, Universitat Politècnica de Catalunya, Carrer de Jordi Girona 1-3, 08034 Barcelona, Spain
| | - Ted Moldenhawer
- Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany
| | - Carsten Beta
- Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany
| | - Ioannis G Kevrekidis
- Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
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16
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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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17
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Fuji K, Tanida S, Sano M, Nonomura M, Riveline D, Honda H, Hiraiwa T. Computational approaches for simulating luminogenesis. Semin Cell Dev Biol 2022; 131:173-185. [PMID: 35773151 DOI: 10.1016/j.semcdb.2022.05.021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Revised: 05/24/2022] [Accepted: 05/24/2022] [Indexed: 12/14/2022]
Abstract
Lumens, liquid-filled cavities surrounded by polarized tissue cells, are elementary units involved in the morphogenesis of organs. Theoretical modeling and computations, which can integrate various factors involved in biophysics of morphogenesis of cell assembly and lumens, may play significant roles to elucidate the mechanisms in formation of such complex tissue with lumens. However, up to present, it has not been documented well what computational approaches or frameworks can be applied for this purpose and how we can choose the appropriate approach for each problem. In this review, we report some typical lumen morphologies and basic mechanisms for the development of lumens, focusing on three keywords - mechanics, hydraulics and geometry - while outlining pros and cons of the current main computational strategies. We also describe brief guidance of readouts, i.e., what we should measure in experiments to make the comparison with the model's assumptions and predictions.
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Affiliation(s)
- Kana Fuji
- Universal Biology Institute, Graduate School of Science, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Sakurako Tanida
- Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo, Japan
| | - Masaki Sano
- Institute of Natural Sciences, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Makiko Nonomura
- Department of Mathematical Information Engineering, College of Industrial Technology, Nihon University, 1-2-1 Izumicho, Narashino-shi, Chiba 275-8575, Japan
| | - Daniel Riveline
- Laboratory of Cell Physics IGBMC, CNRS, INSERM and Université de Strasbourg, Strasbourg, France
| | - Hisao Honda
- Division of Cell Physiology, Department of Physiology and Cell Biology, Graduate School of Medicine Kobe University, Kobe, Hyogo, Japan
| | - Tetsuya Hiraiwa
- Mechanobiology Institute, Singapore, National University of Singapore, 117411, Singapore.
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18
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Effects of solution conductivity on macropore size dynamics in electroporated lipid vesicle membranes. Bioelectrochemistry 2022; 147:108222. [PMID: 35944467 DOI: 10.1016/j.bioelechem.2022.108222] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Revised: 07/29/2022] [Accepted: 08/01/2022] [Indexed: 11/21/2022]
Abstract
Using fast imaging microscopy, we investigate in detail the expansion of micron-sized pores occurring in individual electroporated giant unilamellar vesicles composed of the phospholipid 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC). To infer pore dynamics on the electrodeformed and electropermeabilized vesicles, we develop a computational approach and provide for the first time a direct evidence of quantitative agreement between experimental data and the well-established theoretical prediction of Smith, Neu and Krassowska (SNK). The analysis we describe also provides an extension to the current theoretical literature on how the conductivity ratio of the internal and the external vesicle solution plays a determinant role in the definition of the electrical force driving pore expansion kinetics.
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19
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Moldenhawer T, Moreno E, Schindler D, Flemming S, Holschneider M, Huisinga W, Alonso S, Beta C. Spontaneous transitions between amoeboid and keratocyte-like modes of migration. Front Cell Dev Biol 2022; 10:898351. [PMID: 36247011 PMCID: PMC9563996 DOI: 10.3389/fcell.2022.898351] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 07/18/2022] [Indexed: 01/17/2023] Open
Abstract
The motility of adherent eukaryotic cells is driven by the dynamics of the actin cytoskeleton. Despite the common force-generating actin machinery, different cell types often show diverse modes of locomotion that differ in their shape dynamics, speed, and persistence of motion. Recently, experiments in Dictyostelium discoideum have revealed that different motility modes can be induced in this model organism, depending on genetic modifications, developmental conditions, and synthetic changes of intracellular signaling. Here, we report experimental evidence that in a mutated D. discoideum cell line with increased Ras activity, switches between two distinct migratory modes, the amoeboid and fan-shaped type of locomotion, can even spontaneously occur within the same cell. We observed and characterized repeated and reversible switchings between the two modes of locomotion, suggesting that they are distinct behavioral traits that coexist within the same cell. We adapted an established phenomenological motility model that combines a reaction-diffusion system for the intracellular dynamics with a dynamic phase field to account for our experimental findings.
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Affiliation(s)
- Ted Moldenhawer
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
| | - Eduardo Moreno
- Department of Physics, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Daniel Schindler
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
| | - Sven Flemming
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
| | | | - Wilhelm Huisinga
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
| | - Sergio Alonso
- Department of Physics, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
- *Correspondence: Carsten Beta,
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20
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Force Estimation during Cell Migration Using Mathematical Modelling. J Imaging 2022; 8:jimaging8070199. [PMID: 35877643 PMCID: PMC9320649 DOI: 10.3390/jimaging8070199] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Revised: 07/06/2022] [Accepted: 07/12/2022] [Indexed: 11/29/2022] Open
Abstract
Cell migration is essential for physiological, pathological and biomedical processes such as, in embryogenesis, wound healing, immune response, cancer metastasis, tumour invasion and inflammation. In light of this, quantifying mechanical properties during the process of cell migration is of great interest in experimental sciences, yet few theoretical approaches in this direction have been studied. In this work, we propose a theoretical and computational approach based on the optimal control of geometric partial differential equations to estimate cell membrane forces associated with cell polarisation during migration. Specifically, cell membrane forces are inferred or estimated by fitting a mathematical model to a sequence of images, allowing us to capture dynamics of the cell migration. Our approach offers a robust and accurate framework to compute geometric mechanical membrane forces associated with cell polarisation during migration and also yields geometric information of independent interest, we illustrate one such example that involves quantifying cell proliferation levels which are associated with cell division, cell fusion or cell death.
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21
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Stepien TL, Secomb TW. Spreading mechanics and differentiation of astrocytes during retinal development. J Theor Biol 2022; 549:111208. [DOI: 10.1016/j.jtbi.2022.111208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Revised: 05/27/2022] [Accepted: 06/21/2022] [Indexed: 11/30/2022]
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22
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Ardaševa A, Mueller R, Doostmohammadi A. Bridging microscopic cell dynamics to nematohydrodynamics of cell monolayers. SOFT MATTER 2022; 18:4737-4746. [PMID: 35703313 DOI: 10.1039/d2sm00537a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
It is increasingly being realized that liquid-crystalline features can play an important role in the properties and dynamics of cell monolayers. Here, we present a cell-based model of cell layers, based on the phase-field formulation, that connects cell-cell interactions specified at the single cell level to large-scale nematic and hydrodynamic properties of the tissue. In particular, we present a minimal formulation that reproduces the well-known bend and splay hydrodynamic instabilities of the continuum nemato-hydrodynamic formulation of active matter, together with an analytical description of the instability threshold in terms of activity and elasticity of the cells. Furthermore, we provide a quantitative characterisation and comparison of flows and topological defects for extensile and contractile stress generation mechanisms, and demonstrate activity-induced heterogeneity and spontaneous formation of gaps within a confluent monolayer. Together, these results contribute to bridging the gap between cell-scale dynamics and tissue-scale collective cellular organisation.
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Affiliation(s)
| | - Romain Mueller
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, UK
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23
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Seirin-Lee S, Yamamoto K, Kimura A. The extra-embryonic space and the local contour are crucial geometric constraints regulating cell arrangement. Development 2022; 149:275369. [PMID: 35552395 PMCID: PMC9148568 DOI: 10.1242/dev.200401] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 03/23/2022] [Indexed: 12/29/2022]
Abstract
In multicellular systems, cells communicate with adjacent cells to determine their positions and fates, an arrangement important for cellular development. Orientation of cell division, cell-cell interactions (i.e. attraction and repulsion) and geometric constraints are three major factors that define cell arrangement. In particular, geometric constraints are difficult to reveal in experiments, and the contribution of the local contour of the boundary has remained elusive. In this study, we developed a multicellular morphology model based on the phase-field method so that precise geometric constraints can be incorporated. Our application of the model to nematode embryos predicted that the amount of extra-embryonic space, the empty space within the eggshell that is not occupied by embryonic cells, affects cell arrangement in a manner dependent on the local contour and other factors. The prediction was validated experimentally by increasing the extra-embryonic space in the Caenorhabditis elegans embryo. Overall, our analyses characterized the roles of geometrical contributors, specifically the amount of extra-embryonic space and the local contour, on cell arrangements. These factors should be considered for multicellular systems. Summary: The local contour and the extra-embryonic space, the empty space within the eggshell not occupied by embryonic cells, are important geometric constraints in cell arrangement of nematode embryos.
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Affiliation(s)
- Sungrim Seirin-Lee
- Institute for the Advanced Study of Human Biology (ASHBi), Kyoto University Institute for Advanced Study, Kyoto University, Kyoto 606-8315, Japan.,JST CREST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
| | - Kazunori Yamamoto
- Department of Applied Bioscience, Faculty of Applied Bioscience, Kanagawa Institute of Technology, Atsugi 243-0292, Japan
| | - Akatsuki Kimura
- Cell Architecture Laboratory, Department of Chromosome Science, National Institute of Genetics, Mishima 411-8540, Japan.,Department of Genetics, The Graduate University for Advanced Studies, Sokendai, Mishima 411-8540, Japan
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24
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Kuang X, Guan G, Wong MK, Chan LY, Zhao Z, Tang C, Zhang L. Computable early Caenorhabditis elegans embryo with a phase field model. PLoS Comput Biol 2022; 18:e1009755. [PMID: 35030161 PMCID: PMC8794267 DOI: 10.1371/journal.pcbi.1009755] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Revised: 01/27/2022] [Accepted: 12/14/2021] [Indexed: 01/11/2023] Open
Abstract
Morphogenesis is a precise and robust dynamic process during metazoan embryogenesis, consisting of both cell proliferation and cell migration. Despite the fact that much is known about specific regulations at molecular level, how cell proliferation and migration together drive the morphogenesis at cellular and organismic levels is not well understood. Using Caenorhabditis elegans as the model animal, we present a phase field model to compute early embryonic morphogenesis within a confined eggshell. With physical information about cell division obtained from three-dimensional time-lapse cellular imaging experiments, the model can precisely reproduce the early morphogenesis process as seen in vivo, including time evolution of location and morphology of each cell. Furthermore, the model can be used to reveal key cell-cell attractions critical to the development of C. elegans embryo. Our work demonstrates how genetic programming and physical forces collaborate to drive morphogenesis and provides a predictive model to decipher the underlying mechanism. Embryonic development is a precise process involving cell division, cell-cell interaction, and cell migration. During the process, how each cell reaches its supposed location and be in contact with the right neighbors, and what roles genetic factors and physical forces play are important and fascinating questions. Using the worm Caenorhabditis elegans as a model system, we build a phase field model to simulate early morphogenesis. With a few physical inputs, the model can precisely reproduce the early morphological development of the worm. Such an accurate simulator can not only teach us how physical forces work together with genetic factors to shape up the complex process of development, but also make predictions, such as key cell-cell attractions critical in the process.
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Affiliation(s)
- Xiangyu Kuang
- Center for Quantitative Biology, Peking University, Beijing, China
| | - Guoye Guan
- Center for Quantitative Biology, Peking University, Beijing, China
| | - Ming-Kin Wong
- Department of Biology, Hong Kong Baptist University, Hong Kong, China
| | - Lu-Yan Chan
- Department of Biology, Hong Kong Baptist University, Hong Kong, China
| | - Zhongying Zhao
- Department of Biology, Hong Kong Baptist University, Hong Kong, China
- State Key Laboratory of Environmental and Biological Analysis, Hong Kong Baptist University, Hong Kong, China
| | - Chao Tang
- Center for Quantitative Biology, Peking University, Beijing, China
- Peking-Tsinghua Center for Life Sciences, Peking University, Beijing, China
- School of Physics, Peking University, Beijing, China
- * E-mail: (CT); (LZ)
| | - Lei Zhang
- Center for Quantitative Biology, Peking University, Beijing, China
- Beijing International Center for Mathematical Research, Peking University, Beijing, China
- * E-mail: (CT); (LZ)
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25
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Ghabache E, Cao Y, Miao Y, Groisman A, Devreotes PN, Rappel W. Coupling traction force patterns and actomyosin wave dynamics reveals mechanics of cell motion. Mol Syst Biol 2021; 17:e10505. [PMID: 34898015 PMCID: PMC8666840 DOI: 10.15252/msb.202110505] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Revised: 11/18/2021] [Accepted: 11/19/2021] [Indexed: 11/13/2022] Open
Abstract
Motile cells can use and switch between different modes of migration. Here, we use traction force microscopy and fluorescent labeling of actin and myosin to quantify and correlate traction force patterns and cytoskeletal distributions in Dictyostelium discoideum cells that move and switch between keratocyte-like fan-shaped, oscillatory, and amoeboid modes. We find that the wave dynamics of the cytoskeletal components critically determine the traction force pattern, cell morphology, and migration mode. Furthermore, we find that fan-shaped cells can exhibit two different propulsion mechanisms, each with a distinct traction force pattern. Finally, the traction force patterns can be recapitulated using a computational model, which uses the experimentally determined spatiotemporal distributions of actin and myosin forces and a viscous cytoskeletal network. Our results suggest that cell motion can be generated by friction between the flow of this network and the substrate.
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Affiliation(s)
| | - Yuansheng Cao
- Department of PhysicsUniversity of California, San DiegoLa JollaCAUSA
| | - Yuchuan Miao
- Department of Cell BiologySchool of MedicineJohns Hopkins UniversityBaltimoreMDUSA
| | - Alex Groisman
- Department of PhysicsUniversity of California, San DiegoLa JollaCAUSA
| | - Peter N Devreotes
- Department of Cell BiologySchool of MedicineJohns Hopkins UniversityBaltimoreMDUSA
| | - Wouter‐Jan Rappel
- Department of PhysicsUniversity of California, San DiegoLa JollaCAUSA
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26
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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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27
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Imoto D, Saito N, Nakajima A, Honda G, Ishida M, Sugita T, Ishihara S, Katagiri K, Okimura C, Iwadate Y, Sawai S. Comparative mapping of crawling-cell morphodynamics in deep learning-based feature space. PLoS Comput Biol 2021; 17:e1009237. [PMID: 34383753 PMCID: PMC8360578 DOI: 10.1371/journal.pcbi.1009237] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2020] [Accepted: 07/03/2021] [Indexed: 12/13/2022] Open
Abstract
Navigation of fast migrating cells such as amoeba Dictyostelium and immune cells are tightly associated with their morphologies that range from steady polarized forms that support high directionality to those more complex and variable when making frequent turns. Model simulations are essential for quantitative understanding of these features and their origins, however systematic comparisons with real data are underdeveloped. Here, by employing deep-learning-based feature extraction combined with phase-field modeling framework, we show that a low dimensional feature space for 2D migrating cell morphologies obtained from the shape stereotype of keratocytes, Dictyostelium and neutrophils can be fully mapped by an interlinked signaling network of cell-polarization and protrusion dynamics. Our analysis links the data-driven shape analysis to the underlying causalities by identifying key parameters critical for migratory morphologies both normal and aberrant under genetic and pharmacological perturbations. The results underscore the importance of deciphering self-organizing states and their interplay when characterizing morphological phenotypes. Migratory cells that move by crawling do so by extending and retracting their plasma membrane. When and where these events take place determine the cell shape, and this is directly linked to the movement patterns. Understanding how the highly plastic and interconvertible morphologies appear from their underlying dynamics remains a challenge partly because their inherent complexity makes quantitatively comparison against the outputs of mathematical models difficult. To this end, we employed machine-learning based classification to extract features that characterize the basic migrating morphologies. The obtained features were then used to compare real cell data with outputs of a conceptual model that we introduced which describes coupling via feedback between local protrusive dynamics and polarity. The feature mapping showed that the model successfully recapitulates the shape dynamics that were not covered by previous related models and also hints at the critical parameters underlying state transitions. The ability of the present approach to compare model outputs with real cell data systematically and objectively is important as it allows outputs of future mathematical models to be quantitatively tested in an accessible and common reference frame.
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Affiliation(s)
- Daisuke Imoto
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan
| | - Nen Saito
- Universal Biological Institute, University of Tokyo, Tokyo, Japan
- Exploratory Research Center on Life and Living Systems, National Institutes of Natural Sciences, Okazaki, Japan
| | - Akihiko Nakajima
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan
- Research Center for Complex Systems Biology, Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan
| | - Gen Honda
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan
| | - Motohiko Ishida
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan
| | - Toyoko Sugita
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan
| | - Sayaka Ishihara
- Department of Biosciences, School of Science, Kitasato University, Sagamihara, Japan
| | - Koko Katagiri
- Department of Biosciences, School of Science, Kitasato University, Sagamihara, Japan
| | - Chika Okimura
- Faculty of Science, Yamaguchi University, Yamaguchi, Japan
| | | | - Satoshi Sawai
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan
- Universal Biological Institute, University of Tokyo, Tokyo, Japan
- Research Center for Complex Systems Biology, Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan
- Department of Biology, Graduate School of Science, University of Tokyo, Tokyo, Japan
- * E-mail:
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28
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A Perfect Plastic Material for Studies on Self-Propelled Motion on the Water Surface. Molecules 2021; 26:molecules26113116. [PMID: 34071048 PMCID: PMC8197156 DOI: 10.3390/molecules26113116] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2021] [Revised: 04/22/2021] [Accepted: 05/17/2021] [Indexed: 11/17/2022] Open
Abstract
We describe a novel plastic material composed of camphene, camphor, and polypropylene that seems perfectly suited for studies on self-propelled objects on the water surface. Self-motion is one of the attributes of life, and chemically propelled objects show numerous similarities with animated motion. One of important questions is the relationship between the object shape and its motility. In our paper published in 2019, we presented a novel hybrid material, obtained from the solution of camphor in camphene, that allowed making objects of various shapes. This hybrid material has wax-like mechanical properties, but it has a very high tackiness. Here, we report that a small amount of polypropylene removed this undesirable feature. We investigated the properties of camphor–camphene–polypropylene plastic by performing the statistical analysis of a pill trajectory inside a Petri dish and compared them with those of camphor-camphene wax. The plastic showed the stable character of motion for over an hour-long experiment. The surface activity of objects made of plastic did not significantly depend on the weight ratios of the compounds. Such a significant increase in usefulness came from the polypropylene, which controlled the dissipation of camphor and camphene molecules.
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29
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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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30
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Urdeitx P, Doweidar MH. Enhanced Piezoelectric Fibered Extracellular Matrix to Promote Cardiomyocyte Maturation and Tissue Formation: A 3D Computational Model. BIOLOGY 2021; 10:biology10020135. [PMID: 33572184 PMCID: PMC7914718 DOI: 10.3390/biology10020135] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Revised: 02/03/2021] [Accepted: 02/04/2021] [Indexed: 12/26/2022]
Abstract
Mechanical and electrical stimuli play a key role in tissue formation, guiding cell processes such as cell migration, differentiation, maturation, and apoptosis. Monitoring and controlling these stimuli on in vitro experiments is not straightforward due to the coupling of these different stimuli. In addition, active and reciprocal cell-cell and cell-extracellular matrix interactions are essential to be considered during formation of complex tissue such as myocardial tissue. In this sense, computational models can offer new perspectives and key information on the cell microenvironment. Thus, we present a new computational 3D model, based on the Finite Element Method, where a complex extracellular matrix with piezoelectric properties interacts with cardiac muscle cells during the first steps of tissue formation. This model includes collective behavior and cell processes such as cell migration, maturation, differentiation, proliferation, and apoptosis. The model has employed to study the initial stages of in vitro cardiac aggregate formation, considering cell-cell junctions, under different extracellular matrix configurations. Three different cases have been purposed to evaluate cell behavior in fibered, mechanically stimulated fibered, and mechanically stimulated piezoelectric fibered extra-cellular matrix. In this last case, the cells are guided by the coupling of mechanical and electrical stimuli. Accordingly, the obtained results show the formation of more elongated groups and enhancement in cell proliferation.
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Affiliation(s)
- Pau Urdeitx
- Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, 50018 Zaragoza, Spain;
- Aragon Institute of Engineering Research (I3A), University of Zaragoza, 50018 Zaragoza, Spain
- Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), 50018 Zaragoza, Spain
| | - Mohamed H. Doweidar
- Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, 50018 Zaragoza, Spain;
- Aragon Institute of Engineering Research (I3A), University of Zaragoza, 50018 Zaragoza, Spain
- Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), 50018 Zaragoza, Spain
- Correspondence:
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31
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Ecker N, Kruse K. Excitable actin dynamics and amoeboid cell migration. PLoS One 2021; 16:e0246311. [PMID: 33524055 PMCID: PMC7850500 DOI: 10.1371/journal.pone.0246311] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Accepted: 01/15/2021] [Indexed: 11/23/2022] Open
Abstract
Amoeboid cell migration is characterized by frequent changes of the direction of motion and resembles a persistent random walk on long time scales. Although it is well known that cell migration is typically driven by the actin cytoskeleton, the cause of this migratory behavior remains poorly understood. We analyze the spontaneous dynamics of actin assembly due to nucleation promoting factors, where actin filaments lead to an inactivation of these factors. We show that this system exhibits excitable dynamics and can spontaneously generate waves, which we analyze in detail. By using a phase-field approach, we show that these waves can generate cellular random walks. We explore how the characteristics of these persistent random walks depend on the parameters governing the actin-nucleator dynamics. In particular, we find that the effective diffusion constant and the persistence time depend strongly on the speed of filament assembly and the rate of nucleator inactivation. Our findings point to a deterministic origin of the random walk behavior and suggest that cells could adapt their migration pattern by modifying the pool of available actin.
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Affiliation(s)
- Nicolas Ecker
- Department of Biochemistry, University of Geneva, Geneva, Switzerland
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
| | - Karsten Kruse
- Department of Biochemistry, University of Geneva, Geneva, Switzerland
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
- NCCR Chemical Biology, University of Geneva, Geneva, Switzerland
- * E-mail:
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32
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Karmakar R, Tang MH, Yue H, Lombardo D, Karanam A, Camley BA, Groisman A, Rappel WJ. Cellular memory in eukaryotic chemotaxis depends on the background chemoattractant concentration. Phys Rev E 2021; 103:012402. [PMID: 33601617 DOI: 10.1103/physreve.103.012402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2020] [Accepted: 12/16/2020] [Indexed: 01/17/2023]
Abstract
Cells of the social amoeba Dictyostelium discoideum migrate to a source of periodic traveling waves of chemoattractant as part of a self-organized aggregation process. An important part of this process is cellular memory, which enables cells to respond to the front of the wave and ignore the downward gradient in the back of the wave. During this aggregation, the background concentration of the chemoattractant gradually rises. In our microfluidic experiments, we exogenously applied periodic waves of chemoattractant with various background levels. We find that increasing background does not make detection of the wave more difficult, as would be naively expected. Instead, we see that the chemotactic efficiency significantly increases for intermediate values of the background concentration but decreases to almost zero for large values in a switch-like manner. These results are consistent with a computational model that contains a bistable memory module, along with a nonadaptive component. Within this model, an intermediate background level helps preserve directed migration by keeping the memory activated, but when the background level is higher, the directional stimulus from the wave is no longer sufficient to activate the bistable memory, suppressing directed migration. These results suggest that raising levels of chemoattractant background may facilitate the self-organized aggregation in Dictyostelium colonies.
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Affiliation(s)
- Richa Karmakar
- Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
| | - Man-Ho Tang
- Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
| | - Haicen Yue
- Courant Institute for Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Daniel Lombardo
- Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
| | - Aravind Karanam
- Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
| | - Brian A Camley
- Department of Physics & Astronomy, Department of Biophysics, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Alex Groisman
- Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
| | - Wouter-Jan Rappel
- Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
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33
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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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34
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Buttenschön A, Edelstein-Keshet L. Bridging from single to collective cell migration: A review of models and links to experiments. PLoS Comput Biol 2020; 16:e1008411. [PMID: 33301528 PMCID: PMC7728230 DOI: 10.1371/journal.pcbi.1008411] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.
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Affiliation(s)
- Andreas Buttenschön
- Department of Mathematics, University of British Columbia, Vancouver, Canada
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35
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Bolle N, Mizuhara MS. Dynamics of a cell motility model near the sharp interface limit. J Theor Biol 2020; 505:110420. [PMID: 32739242 DOI: 10.1016/j.jtbi.2020.110420] [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: 03/31/2020] [Revised: 07/14/2020] [Accepted: 07/20/2020] [Indexed: 10/23/2022]
Abstract
Phase-field models have recently had great success in describing the dynamic morphologies and motility of eukaryotic cells. In this work we investigate the minimal phase-field model introduced in Berlyand et al. (2017). Rigorous analysis of its sharp interface limit dynamics was completed in Mizuhara et al. (2016) and Mizuhara et al. (2019), where it was observed that persistent cell motion was not stable. In this work we numerically study the pre-limiting phase-field model near the sharp interface limit, to better understand this lack of persistent motion. We find that immobile, persistent, and rotating states are all exhibited in this minimal model, and investigate the loss of persistent motion in the sharp interface limit.
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Affiliation(s)
- Nicolas Bolle
- Department of Mathematics and Statistics, The College of New Jersey Ewing Township, NJ, United States.
| | - Matthew S Mizuhara
- Department of Mathematics and Statistics, The College of New Jersey Ewing Township, NJ, United States.
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36
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Zheng Y, Fan Q, Eddy CZ, Wang X, Sun B, Ye F, Jiao Y. Modeling multicellular dynamics regulated by extracellular-matrix-mediated mechanical communication via active particles with polarized effective attraction. Phys Rev E 2020; 102:052409. [PMID: 33327171 DOI: 10.1103/physreve.102.052409] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2020] [Accepted: 11/02/2020] [Indexed: 01/23/2023]
Abstract
Collective cell migration is crucial to many physiological and pathological processes such as embryo development, wound healing, and cancer invasion. Recent experimental studies have indicated that the active traction forces generated by migrating cells in a fibrous extracellular matrix (ECM) can mechanically remodel the ECM, giving rise to bundlelike mesostructures bridging individual cells. Such fiber bundles also enable long-range propagation of cellular forces, leading to correlated migration dynamics regulated by the mechanical communication among the cells. Motivated by these experimental discoveries, we develop an active-particle model with polarized effective attractions (APPA) to investigate emergent multicellular migration dynamics resulting from ECM-mediated mechanical communications. In particular, the APPA model generalizes the classic active-Brownian-particle (ABP) model by imposing a pairwise polarized attractive force between the particles, which depends on the instantaneous dynamic states of the particles and mimics the effective mutual pulling between the cells via the fiber bundle bridge. The APPA system exhibits enhanced aggregation behaviors compared to the classic ABP system, and the contrast is more apparent at lower particle densities and higher rotational diffusivities. Importantly, in contrast to the classic ABP system where the particle velocities are not correlated for all particle densities, the high-density phase of the APPA system exhibits strong dynamic correlations, which are characterized by the slowly decaying velocity correlation functions with a correlation length comparable to the linear size of the high-density phase domain (i.e., the cluster of particles). The strongly correlated multicellular dynamics predicted by the APPA model is subsequently verified in in vitro experiments using MCF-10A cells. Our studies indicate the importance of incorporating ECM-mediated mechanical coupling among the migrating cells for appropriately modeling emergent multicellular dynamics in complex microenvironments.
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Affiliation(s)
- Yu Zheng
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
| | - Qihui Fan
- Beijing National Laboratory for Condensed Matte Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Christopher Z Eddy
- Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA
| | - Xiaochen Wang
- Beijing National Laboratory for Condensed Matte Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Bo Sun
- Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA
| | - Fangfu Ye
- Beijing National Laboratory for Condensed Matte Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325001, China
| | - Yang Jiao
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
- Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA
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37
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Toyota T, Sugiyama H, Hiroi S, Ito H, Kitahata H. Chemically artificial rovers based on self-propelled droplets in micrometer-scale environment. Curr Opin Colloid Interface Sci 2020. [DOI: 10.1016/j.cocis.2020.04.003] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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38
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Chojowski R, Schwarz US, Ziebert F. Reversible elastic phase field approach and application to cell monolayers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2020; 43:63. [PMID: 33009970 DOI: 10.1140/epje/i2020-11988-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2020] [Accepted: 09/16/2020] [Indexed: 06/11/2023]
Abstract
Motion and generation of forces by single cells and cell collectives are essential elements of many biological processes, including development, wound healing and cancer cell migration. Quantitative wound healing assays have demonstrated that cell monolayers can be both dynamic and elastic at the same time. However, it is very challenging to model this combination with conventional approaches. Here we introduce an elastic phase field approach that allows us to predict the dynamics of elastic sheets under the action of active stresses and localized forces, e.g. from leader cells. Our method ensures elastic reversibility after release of forces. We demonstrate its potential by studying several paradigmatic situations and geometries relevant for single cells and cell monolayers, including elastic bars, contractile discs and expanding monolayers with leader cells.
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Affiliation(s)
- Robert Chojowski
- Institute for Theoretical Physics, Heidelberg University, D-69120, Heidelberg, Germany
- BioQuant, Heidelberg University, D-69120, Heidelberg, Germany
| | - Ulrich S Schwarz
- Institute for Theoretical Physics, Heidelberg University, D-69120, Heidelberg, Germany
- BioQuant, Heidelberg University, D-69120, Heidelberg, Germany
| | - Falko Ziebert
- Institute for Theoretical Physics, Heidelberg University, D-69120, Heidelberg, Germany.
- BioQuant, Heidelberg University, D-69120, Heidelberg, Germany.
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39
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A Stochastic Modelling Framework for Single Cell Migration: Coupling Contractility and Focal Adhesions. Symmetry (Basel) 2020. [DOI: 10.3390/sym12081348] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
The interaction of the actin cytoskeleton with cell–substrate adhesions is necessary for cell migration. While the trajectories of motile cells have a stochastic character, investigations of cell motility mechanisms rarely elaborate on the origins of the observed randomness. Here, guided by a few fundamental attributes of cell motility, I construct a minimal stochastic cell migration model from ground-up. The resulting model couples a deterministic actomyosin contractility mechanism with stochastic cell–substrate adhesion kinetics, and yields a well-defined piecewise deterministic process. Numerical simulations reproduce several experimentally observed results, including anomalous diffusion, tactic migration and contact guidance. This work provides a basis for the development of cell–cell collision and population migration models.
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40
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41
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Qin B, Fei C, Bridges AA, Mashruwala AA, Stone HA, Wingreen NS, Bassler BL. Cell position fates and collective fountain flow in bacterial biofilms revealed by light-sheet microscopy. Science 2020; 369:71-77. [PMID: 32527924 DOI: 10.1126/science.abb8501] [Citation(s) in RCA: 74] [Impact Index Per Article: 18.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2020] [Accepted: 05/19/2020] [Indexed: 12/17/2022]
Abstract
Bacterial biofilms represent a basic form of multicellular organization that confers survival advantages to constituent cells. The sequential stages of cell ordering during biofilm development have been studied in the pathogen and model biofilm-former Vibrio cholerae It is unknown how spatial trajectories of individual cells and the collective motions of many cells drive biofilm expansion. We developed dual-view light-sheet microscopy to investigate the dynamics of biofilm development from a founder cell to a mature three-dimensional community. Tracking of individual cells revealed two distinct fates: one set of biofilm cells expanded ballistically outward, while the other became trapped at the substrate. A collective fountain-like flow transported cells to the biofilm front, bypassing members trapped at the substrate and facilitating lateral biofilm expansion. This collective flow pattern was quantitatively captured by a continuum model of biofilm growth against substrate friction. Coordinated cell movement required the matrix protein RbmA, without which cells expanded erratically. Thus, tracking cell lineages and trajectories in space and time revealed how multicellular structures form from a single founder cell.
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Affiliation(s)
- Boyang Qin
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, USA.,Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Chenyi Fei
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, USA.,Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA
| | - Andrew A Bridges
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, USA.,The Howard Hughes Medical Institute, Chevy Chase, MD 20815, USA
| | - Ameya A Mashruwala
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, USA.,The Howard Hughes Medical Institute, Chevy Chase, MD 20815, USA
| | - Howard A Stone
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Ned S Wingreen
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, USA.,Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA.,Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, USA
| | - Bonnie L Bassler
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, USA. .,The Howard Hughes Medical Institute, Chevy Chase, MD 20815, USA
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42
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Tuning Cell Motility via Cell Tension with a Mechanochemical Cell Migration Model. Biophys J 2020; 118:2894-2904. [PMID: 32416081 DOI: 10.1016/j.bpj.2020.04.030] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2019] [Revised: 04/24/2020] [Accepted: 04/29/2020] [Indexed: 12/17/2022] Open
Abstract
Cell migration is orchestrated by a complicated mechanochemical system. However, few cell migration models take into account the coupling between the biochemical network and mechanical factors. Here, we construct a mechanochemical cell migration model to study the cell tension effect on cell migration. Our model incorporates the interactions between Rac-GTP, Rac-GDP, F-actin, myosin, and cell tension, and it is very convenient in capturing the change of cell shape by taking the phase field approach. This model captures the characteristic features of cell polarization, cell shape change, and cell migration modes. It shows that cell tension inhibits migration ability monotonically when cells are applied with persistent external stimuli. On the other hand, if random internal noise is significant, the regulation of cell tension exerts a nonmonotonic effect on cell migration. Because the increase of cell tension hinders the formation of multiple protrusions, migration ability could be maximized at intermediate cell tension under random internal noise. These model predictions are consistent with our single-cell experiments and other experimental results.
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43
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Zheng Y, Nan H, Liu Y, Fan Q, Wang X, Liu R, Liu L, Ye F, Sun B, Jiao Y. Modeling cell migration regulated by cell extracellular-matrix micromechanical coupling. Phys Rev E 2020; 100:043303. [PMID: 31770879 DOI: 10.1103/physreve.100.043303] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2019] [Indexed: 01/24/2023]
Abstract
Cell migration in fibrous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response, and cancer progression. During migration, individual cells can generate active pulling forces via actomyosin contraction, which are transmitted to the ECM fibers through focal adhesion complexes, remodel the ECM, and eventually propagate to and can be sensed by other cells in the system. The microstructure and physical properties of the ECM can also significantly influence cell migration, e.g., via durotaxis and contact guidance. Here, we develop a computational model for two-dimensional cell migration regulated by cell-ECM micromechanical coupling. Our model explicitly takes into account a variety of cellular-level processes, including focal adhesion formation and disassembly, active traction force generation and cell locomotion due to actin filament contraction, transmission and propagation of tensile forces in the ECM, as well as the resulting ECM remodeling. We validate our model by accurately reproducing single-cell dynamics of MCF-10A breast cancer cells migrating on collagen gels and show that the durotaxis and contact guidance effects naturally arise as a consequence of the cell-ECM micromechanical interactions considered in the model. Moreover, our model predicts strongly correlated multicellular migration dynamics, which are resulted from the ECM-mediated mechanical coupling among the migrating cell and are subsequently verified in in vitro experiments using MCF-10A cells. Our computational model provides a robust tool to investigate emergent collective dynamics of multicellular systems in complex in vivo microenvironment and can be utilized to design in vitro microenvironments to guide collective behaviors and self-organization of cells.
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Affiliation(s)
- Yu Zheng
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
| | - Hanqing Nan
- Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Yanping Liu
- College of Physics, Chongqing University, Chongqing 401331, China
| | - Qihui Fan
- Beijing National Laboratory for Condensed Matte Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.,School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Xiaochen Wang
- Beijing National Laboratory for Condensed Matte Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.,School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Ruchuan Liu
- College of Physics, Chongqing University, Chongqing 401331, China
| | - Liyu Liu
- College of Physics, Chongqing University, Chongqing 401331, China
| | - Fangfu Ye
- Beijing National Laboratory for Condensed Matte Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.,School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Bo Sun
- Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA
| | - Yang Jiao
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA.,Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA
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44
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Loisy A, Eggers J, Liverpool TB. How many ways a cell can move: the modes of self-propulsion of an active drop. SOFT MATTER 2020; 16:3106-3124. [PMID: 32154549 DOI: 10.1039/d0sm00070a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Numerous physical models have been proposed to explain how cell motility emerges from internal activity, mostly focused on how crawling motion arises from internal processes. Here we offer a classification of self-propulsion mechanisms based on general physical principles, showing that crawling is not the only way for cells to move on a substrate. We consider a thin drop of active matter on a planar substrate and fully characterize its autonomous motion for all three possible sources of driving: (i) the stresses induced in the bulk by active components, which allow in particular tractionless motion, (ii) the self-propulsion of active components at the substrate, which gives rise to crawling motion, and (iii) a net capillary force, possibly self-generated, and coupled to internal activity. We determine travelling-wave solutions to the lubrication equations as a function of a dimensionless activity parameter for each mode of motion. Numerical simulations are used to characterize the drop motion over a wide range of activity magnitudes, and explicit analytical solutions in excellent agreement with the simulations are derived in the weak-activity regime.
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Affiliation(s)
- Aurore Loisy
- School of Mathematics, University of Bristol, Bristol BS8 1UG, UK.
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45
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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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Recho P, Putelat T, Truskinovsky L. Active gel segment behaving as an active particle. Phys Rev E 2020; 100:062403. [PMID: 31962422 DOI: 10.1103/physreve.100.062403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2019] [Indexed: 12/14/2022]
Abstract
We reduce a one-dimensional model of an active segment (AS), which is used, for instance, in the description of contraction-driven cell motility, to a zero-dimensional model of an active particle (AP) characterized by two internal degrees of freedom: position and polarity. Both models give rise to hysteretic force-velocity relations showing that an active agent can support two opposite polarities under the same external force and that it can maintain the same polarity while being dragged by external forces with opposite orientations. This double bistability results in a rich dynamic repertoire which we illustrate by studying static, stalled, motile, and periodically repolarizing regimes displayed by an active agent confined in a viscoelastic environment. We show that the AS and AP models can be calibrated to generate quantitatively similar dynamic responses.
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Affiliation(s)
- P Recho
- LIPhy, CNRS-UMR 5588, Université Grenoble Alpes, F-38000 Grenoble, France
| | - T Putelat
- SAS, Rothamsted Research, Harpenden, AL5 2JQ, United Kingdom.,DEM, Queen's School of Engineering, University of Bristol, Bristol, BS8 1TR, United Kingdom
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Xiong L, Cao Y, Cooper R, Rappel WJ, Hasty J, Tsimring L. Flower-like patterns in multi-species bacterial colonies. eLife 2020; 9:e48885. [PMID: 31933477 PMCID: PMC6959979 DOI: 10.7554/elife.48885] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2019] [Accepted: 11/16/2019] [Indexed: 11/13/2022] Open
Abstract
Diverse interactions among species within bacterial colonies lead to intricate spatiotemporal dynamics, which can affect their growth and survival. Here, we describe the emergence of complex structures in a colony grown from mixtures of motile and non-motile bacterial species on a soft agar surface. Time-lapse imaging shows that non-motile bacteria 'hitchhike' on the motile bacteria as the latter migrate outward. The non-motile bacteria accumulate at the boundary of the colony and trigger an instability that leaves behind striking flower-like patterns. The mechanism of the front instability governing this pattern formation is elucidated by a mathematical model for the frictional motion of the colony interface, with friction depending on the local concentration of the non-motile species. A more elaborate two-dimensional phase-field model that explicitly accounts for the interplay between growth, mechanical stress from the motile species, and friction provided by the non-motile species, fully reproduces the observed flower-like patterns.
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Affiliation(s)
- Liyang Xiong
- Department of PhysicsUniversity of California, San DiegoLa JollaUnited States
- BioCircuits InstituteUniversity of California, San DiegoLa JollaUnited States
| | - Yuansheng Cao
- Department of PhysicsUniversity of California, San DiegoLa JollaUnited States
| | - Robert Cooper
- BioCircuits InstituteUniversity of California, San DiegoLa JollaUnited States
| | - Wouter-Jan Rappel
- Department of PhysicsUniversity of California, San DiegoLa JollaUnited States
| | - Jeff Hasty
- BioCircuits InstituteUniversity of California, San DiegoLa JollaUnited States
- The San Diego Center for Systems BiologySan DiegoUnited States
- Molecular Biology Section, Division of Biological SciencesUniversity of California, San DiegoLa JollaUnited States
- Department of BioengineeringUniversity of California, San DiegoLa JollaUnited States
| | - Lev Tsimring
- BioCircuits InstituteUniversity of California, San DiegoLa JollaUnited States
- The San Diego Center for Systems BiologySan DiegoUnited States
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48
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Cao Y, Ghabache E, Miao Y, Niman C, Hakozaki H, Reck-Peterson SL, Devreotes PN, Rappel WJ. A minimal computational model for three-dimensional cell migration. J R Soc Interface 2019; 16:20190619. [PMID: 31847757 DOI: 10.1098/rsif.2019.0619] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
During migration, eukaryotic cells can continuously change their three-dimensional morphology, resulting in a highly dynamic and complex process. Further complicating this process is the observation that the same cell type can rapidly switch between different modes of migration. Modelling this complexity necessitates models that are able to track deforming membranes and that can capture the intracellular dynamics responsible for changes in migration modes. Here we develop an efficient three-dimensional computational model for cell migration, which couples cell mechanics to a simple intracellular activator-inhibitor signalling system. We compare the computational results to quantitative experiments using the social amoeba Dictyostelium discoideum. The model can reproduce the observed migration modes generated by varying either mechanical or biochemical model parameters and suggests a coupling between the substrate and the biomechanics of the cell.
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Affiliation(s)
- Yuansheng Cao
- Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA
| | - Elisabeth Ghabache
- Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA
| | - Yuchuan Miao
- Department of Biological Chemistry, School of Medicine, Johns Hopkins University, Baltimore, MD 21205, USA
| | - Cassandra Niman
- Department of Cellular and Molecular Medicine, University of California, San Diego, La Jolla, CA 92093, USA
| | - Hiroyuki Hakozaki
- National Center for Microscopy and Imaging Research, University of California, San Diego, La Jolla, CA 92093, USA
| | - Samara L Reck-Peterson
- Department of Cellular and Molecular Medicine, Division of Biological Sciences, University of California, San Diego, La Jolla, CA 92093, USA.,Howard Hughes Medical Institute, Chevy Chase, MD 20815, USA
| | - Peter N Devreotes
- Department of Cell Biology, Johns Hopkins University, Baltimore, MD, USA
| | - Wouter-Jan Rappel
- Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA
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Thüroff F, Goychuk A, Reiter M, Frey E. Bridging the gap between single-cell migration and collective dynamics. eLife 2019; 8:e46842. [PMID: 31808744 PMCID: PMC6992385 DOI: 10.7554/elife.46842] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2019] [Accepted: 12/06/2019] [Indexed: 11/13/2022] Open
Abstract
Motivated by the wealth of experimental data recently available, we present a cellular-automaton-based modeling framework focussing on high-level cell functions and their concerted effect on cellular migration patterns. Specifically, we formulate a coarse-grained description of cell polarity through self-regulated actin organization and its response to mechanical cues. Furthermore, we address the impact of cell adhesion on collective migration in cell cohorts. The model faithfully reproduces typical cell shapes and movements down to the level of single cells, yet allows for the efficient simulation of confluent tissues. In confined circular geometries, we find that specific properties of individual cells (polarizability; contractility) influence the emerging collective motion of small cell cohorts. Finally, we study the properties of expanding cellular monolayers (front morphology; stress and velocity distributions) at the level of extended tissues.
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Affiliation(s)
- Florian Thüroff
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of PhysicsLudwig-Maximilians-Universität MünchenMunichGermany
| | - Andriy Goychuk
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of PhysicsLudwig-Maximilians-Universität MünchenMunichGermany
| | - Matthias Reiter
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of PhysicsLudwig-Maximilians-Universität MünchenMunichGermany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of PhysicsLudwig-Maximilians-Universität MünchenMunichGermany
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Löffler RJG, Hanczyc MM, Gorecki J. A hybrid camphor-camphene wax material for studies on self-propelled motion. Phys Chem Chem Phys 2019; 21:24852-24856. [PMID: 31702747 DOI: 10.1039/c9cp04722k] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
A new material that combines the self-propelling properties of camphor with the malleability of camphene is reported. It has wax-like mechanical properties at room temperature and can be formed into required shapes. The speed of the self-propelled objects and the trajectory depend on the shape and camphor-camphene weight ratio.
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Affiliation(s)
- Richard J G Löffler
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, Warsaw 01-224, Poland.
| | - Martin M Hanczyc
- Laboratory for Artificial Biology, Department of Cellular, Computational and Integrative Biology (CIBIO), University of Trento, Polo Scientifico e Tecnologico Fabio Ferrari, Polo B, Via Sommarive 9, 38123 Povo, TN, Italy and Chemical and Biological Engineering, University of New Mexico, Albuquerque, NM, USA
| | - Jerzy Gorecki
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, Warsaw 01-224, Poland.
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