1
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Budde I, Schlichting A, Ing D, Schimmelpfennig S, Kuntze A, Fels B, Romac JMJ, Swain SM, Liddle RA, Stevens A, Schwab A, Pethő Z. Piezo1-induced durotaxis of pancreatic stellate cells depends on TRPC1 and TRPV4 channels. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.12.22.572956. [PMID: 38187663 PMCID: PMC10769407 DOI: 10.1101/2023.12.22.572956] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2024]
Abstract
Pancreatic stellate cells (PSCs) are primarily responsible for producing the stiff tumor tissue in pancreatic ductal adenocarcinoma (PDAC). Thereby, PSCs generate a stiffness gradient between the healthy pancreas and the tumor. This gradient induces durotaxis, a form of directional cell migration driven by differential stiffness. The molecular sensors behind durotaxis are still unclear. To investigate the role of mechanosensitive ion channels in PSC durotaxis, we established a two-dimensional stiffness gradient mimicking PDAC. Using pharmacological and genetic methods, we investigated the role of the ion channels Piezo1, TRPC1, and TRPV4 in PSC durotaxis. We found that PSC migration towards a stiffer substrate is diminished by altering Piezo1 activity. Moreover, disrupting TRPC1 along with TRPV4 abolishes PSC durotaxis even when Piezo1 is functional. Hence, PSC durotaxis is optimal with an intermediary level of mechanosensitive channel activity, which we simulated using a numerically discretized mathematical model. Our findings suggest that mechanosensitive ion channels, particularly Piezo1, detect the mechanical microenvironment to guide PSC migration.
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Affiliation(s)
- Ilka Budde
- Institute of Physiology II, University of Münster, Robert-Koch Str. 27B, 48149, Germany
| | - André Schlichting
- Institute for Analysis and Numerics, University of Münster, Einsteinstr. 62, 48149, Germany
| | - David Ing
- Institute of Physiology II, University of Münster, Robert-Koch Str. 27B, 48149, Germany
| | | | - Anna Kuntze
- Institute of Physiology II, University of Münster, Robert-Koch Str. 27B, 48149, Germany
- Gerhard-Domagk-Institute of Pathology, University of Münster; Münster, Germany
| | - Benedikt Fels
- Institute of Physiology II, University of Münster, Robert-Koch Str. 27B, 48149, Germany
- Institute of Physiology, University of Lübeck; Lübeck, Germany
| | - Joelle M-J Romac
- Department of Medicine, Duke University, Durham, North Carolina, 27708, USA
| | - Sandip M Swain
- Department of Medicine, Duke University, Durham, North Carolina, 27708, USA
| | - Rodger A Liddle
- Department of Medicine, Duke University, Durham, North Carolina, 27708, USA
| | - Angela Stevens
- Institute for Analysis and Numerics, University of Münster, Einsteinstr. 62, 48149, Germany
| | - Albrecht Schwab
- Institute of Physiology II, University of Münster, Robert-Koch Str. 27B, 48149, Germany
| | - Zoltán Pethő
- Institute of Physiology II, University of Münster, Robert-Koch Str. 27B, 48149, Germany
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2
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Marchello R, Colombi A, Preziosi L, Giverso C. A non local model for cell migration in response to mechanical stimuli. Math Biosci 2024; 368:109124. [PMID: 38072125 DOI: 10.1016/j.mbs.2023.109124] [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: 04/07/2023] [Revised: 11/17/2023] [Accepted: 12/05/2023] [Indexed: 12/22/2023]
Abstract
Cell migration is one of the most studied phenomena in biology since it plays a fundamental role in many physiological and pathological processes such as morphogenesis, wound healing and tumorigenesis. In recent years, researchers have performed experiments showing that cells can migrate in response to mechanical stimuli of the substrate they adhere to. Motion towards regions of the substrate with higher stiffness is called durotaxis, while motion guided by the stress or the deformation of the substrate itself is called tensotaxis. Unlike chemotaxis (i.e. the motion in response to a chemical stimulus), these migratory processes are not yet fully understood from a biological point of view. In this respect, we present a mathematical model of single-cell migration in response to mechanical stimuli, in order to simulate these two processes. Specifically, the cell moves by changing its direction of polarization and its motility according to material properties of the substrate (e.g., stiffness) or in response to proper scalar measures of the substrate strain or stress. The equations of motion of the cell are non-local integro-differential equations, with the addition of a stochastic term to account for random Brownian motion. The mechanical stimulus to be integrated in the equations of motion is defined according to experimental measurements found in literature, in the case of durotaxis. Conversely, in the case of tensotaxis, substrate strain and stress are given by the solution of the mechanical problem, assuming that the extracellular matrix behaves as a hyperelastic Yeoh's solid. In both cases, the proposed model is validated through numerical simulations that qualitatively reproduce different experimental scenarios.
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Affiliation(s)
- Roberto Marchello
- Mathematics Area, SISSA (International School for Advanced Studies), Via Bonomea 265, Trieste, 34136, Italy
| | - Annachiara Colombi
- Department of Mathematical Sciences G. L. Lagrange, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, 10129, Italy
| | - Luigi Preziosi
- Department of Mathematical Sciences G. L. Lagrange, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, 10129, Italy
| | - Chiara Giverso
- Department of Mathematical Sciences G. L. Lagrange, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, 10129, Italy.
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3
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Ahmed RK, Abdalrahman T, Davies NH, Vermolen F, Franz T. Mathematical model of mechano-sensing and mechanically induced collective motility of cells on planar elastic substrates. Biomech Model Mechanobiol 2023; 22:809-824. [PMID: 36814004 DOI: 10.1007/s10237-022-01682-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Accepted: 12/28/2022] [Indexed: 02/24/2023]
Abstract
Cells mechanically interact with their environment to sense, for example, topography, elasticity and mechanical cues from other cells. Mechano-sensing has profound effects on cellular behaviour, including motility. The current study aims to develop a mathematical model of cellular mechano-sensing on planar elastic substrates and demonstrate the model's predictive capabilities for the motility of individual cells in a colony. In the model, a cell is assumed to transmit an adhesion force, derived from a dynamic focal adhesion integrin density, that locally deforms a substrate, and to sense substrate deformation originating from neighbouring cells. The substrate deformation from multiple cells is expressed as total strain energy density with a spatially varying gradient. The magnitude and direction of the gradient at the cell location define the cell motion. Cell-substrate friction, partial motion randomness, and cell death and division are included. The substrate deformation by a single cell and the motility of two cells are presented for several substrate elasticities and thicknesses. The collective motility of 25 cells on a uniform substrate mimicking the closure of a circular wound of 200 µm is predicted for deterministic and random motion. Cell motility on substrates with varying elasticity and thickness is explored for four cells and 15 cells, the latter again mimicking wound closure. Wound closure by 45 cells is used to demonstrate the simulation of cell death and division during migration. The mathematical model can adequately simulate the mechanically induced collective cell motility on planar elastic substrates. The model is suitable for extension to other cell and substrates shapes and the inclusion of chemotactic cues, offering the potential to complement in vitro and in vivo studies.
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Affiliation(s)
- Riham K Ahmed
- Division of Biomedical Engineering, Department of Human Biology, Biomedical Engineering Research Centre, University of Cape Town, Observatory, South Africa.
| | - Tamer Abdalrahman
- Division of Biomedical Engineering, Department of Human Biology, Biomedical Engineering Research Centre, University of Cape Town, Observatory, South Africa
- Computational Mechanobiology, Julius Wolff Institute for Biomechanics and Musculoskeletal Regeneration, Charité Universitätsmedizin, Berlin, Germany
| | - Neil H Davies
- Cardiovascular Research Unit, Chris Barnard Division of Cardiothoracic Surgery, MRC IUCHRU, University of Cape Town, Observatory, South Africa
| | - Fred Vermolen
- Computational Mathematics Group, Department of Mathematics and Statistics, University of Hasselt, Diepenbeek, Belgium
| | - Thomas Franz
- Division of Biomedical Engineering, Department of Human Biology, Biomedical Engineering Research Centre, University of Cape Town, Observatory, South Africa
- Bioengineering Science Research Group, Faculty of Engineering and Physical Sciences, University of Southampton, Southampton, UK
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4
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Pramanik D, Jolly MK, Bhat R. Matrix adhesion and remodeling diversifies modes of cancer invasion across spatial scales. J Theor Biol 2021; 524:110733. [PMID: 33933478 DOI: 10.1016/j.jtbi.2021.110733] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2020] [Revised: 04/14/2021] [Accepted: 04/16/2021] [Indexed: 12/14/2022]
Abstract
The metastasis of malignant epithelial tumors begins with the egress of transformed cells from the confines of their basement membrane (BM) to their surrounding collagen-rich stroma. Invasion can be morphologically diverse: when breast cancer cells are separately cultured within BM-like matrix, collagen I (Coll I), or a combination of both, they exhibit collective-, dispersed mesenchymal-, and a mixed collective-dispersed (multimodal)- invasion, respectively. In this paper, we asked how distinct these invasive modes are with respect to the cellular and microenvironmental cues that drive them. A rigorous computational exploration of invasion was performed within an experimentally motivated Cellular Potts-based modeling environment. The model comprised of adhesive interactions between cancer cells, BM- and Coll I-like extracellular matrix (ECM), and reaction-diffusion-based remodeling of ECM. The model outputs were parameters cognate to dispersed- and collective- invasion. A clustering analysis of the output distribution curated through a careful examination of subsumed phenotypes suggested at least four distinct invasive states: dispersed, papillary-collective, bulk-collective, and multimodal, in addition to an indolent/non-invasive state. Mapping input values to specific output clusters suggested that each of these invasive states are specified by distinct input signatures of proliferation, adhesion and ECM remodeling. In addition, specific input perturbations allowed transitions between the clusters and revealed the variation in the robustness between the invasive states. Our systems-level approach proffers quantitative insights into how the diversity in ECM microenvironments may steer invasion into diverse phenotypic modes during early dissemination of breast cancer and contributes to tumor heterogeneity.
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Affiliation(s)
- D Pramanik
- Department of Molecular Reproduction, Development and Genetics, Indian Institute of Science, Bangalore 560012, India; Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India.
| | - M K Jolly
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India.
| | - R Bhat
- Department of Molecular Reproduction, Development and Genetics, Indian Institute of Science, Bangalore 560012, India.
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5
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Enhanced persistence and collective migration in cooperatively aligning cell clusters. Biophys J 2021; 120:1483-1497. [PMID: 33617837 DOI: 10.1016/j.bpj.2021.02.014] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2020] [Revised: 12/21/2020] [Accepted: 02/03/2021] [Indexed: 12/26/2022] Open
Abstract
Most cells possess the capacity to locomote. Alone or collectively, this allows them to adapt, to rearrange, and to explore their surroundings. The biophysical characterization of such motile processes, in health and in disease, has so far focused mostly on two limiting cases: single-cell motility on the one hand and the dynamics of confluent tissues such as the epithelium on the other. The in-between regime of clusters, composed of relatively few cells moving as a coherent unit, has received less attention. Such small clusters are, however, deeply relevant in development but also in cancer metastasis. In this work, we use cellular Potts models and analytical active matter theory to understand how the motility of small cell clusters changes with N, the number of cells in the cluster. Modeling and theory reveal our two main findings: cluster persistence time increases with N, whereas the intrinsic diffusivity decreases with N. We discuss a number of settings in which the motile properties of more complex clusters can be analytically understood, revealing that the focusing effects of small-scale cooperation and cell-cell alignment can overcome the increased bulkiness and internal disorder of multicellular clusters to enhance overall migrational efficacy. We demonstrate this enhancement for small-cluster collective durotaxis, which is shown to proceed more effectively than for single cells. Our results may provide some novel, to our knowledge, insights into the connection between single-cell and large-scale collective motion and may point the way to the biophysical origins of the enhanced metastatic potential of small tumor cell clusters.
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6
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Rens EG, Merks RM. Cell Shape and Durotaxis Explained from Cell-Extracellular Matrix Forces and Focal Adhesion Dynamics. iScience 2020; 23:101488. [PMID: 32896767 PMCID: PMC7482025 DOI: 10.1016/j.isci.2020.101488] [Citation(s) in RCA: 42] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2020] [Revised: 07/13/2020] [Accepted: 08/18/2020] [Indexed: 12/26/2022] Open
Abstract
Many cells are small and rounded on soft extracellular matrices (ECM), elongated on stiffer ECMs, and flattened on hard ECMs. Cells also migrate up stiffness gradients (durotaxis). Using a hybrid cellular Potts and finite-element model extended with ODE-based models of focal adhesion (FA) turnover, we show that the full range of cell shape and durotaxis can be explained in unison from dynamics of FAs, in contrast to previous mathematical models. In our 2D cell-shape model, FAs grow due to cell traction forces. Forces develop faster on stiff ECMs, causing FAs to stabilize and, consequently, cells to spread on stiff ECMs. If ECM stress further stabilizes FAs, cells elongate on substrates of intermediate stiffness. We show that durotaxis follows from the same set of assumptions. Our model contributes to the understanding of the basic responses of cells to ECM stiffness, paving the way for future modeling of more complex cell-ECM interactions.
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Affiliation(s)
- Elisabeth G. Rens
- Scientific Computing, CWI, Science Park 123, 1098 XG Amsterdam, the Netherlands
- Mathematics Department, University of British Columbia, Mathematics Road 1984, Vancouver, BC V6T 1Z2, Canada
| | - Roeland M.H. Merks
- Scientific Computing, CWI, Science Park 123, 1098 XG Amsterdam, the Netherlands
- Mathematical Institute, Leiden University, Niels Bohrweg 1, 2333 CA Leiden, the Netherlands
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7
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Thenard T, Catapano A, Mesnard M, Allena R. A Cellular Potts energy-based approach to analyse the influence of the surface topography on single cell motility. J Theor Biol 2020; 509:110487. [PMID: 32949589 DOI: 10.1016/j.jtbi.2020.110487] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2019] [Revised: 07/23/2020] [Accepted: 09/03/2020] [Indexed: 01/08/2023]
Abstract
The surface shape is an important aspect to take into account to ensure the success of an implant. At the cellular scale level, the cell behaviour, especially its migration, is affected by the specificities of the surface of the substrate, such as the stiffness of the surface and its roughness topography. The latter has been shown to have a great impact on various cell mechanisms, such as the cell adhesion, migration, or proliferation. In fact, the mere presence of micro roughness leads to an improvement of those mechanisms, with a better integration of the implants. However, the phenomena behind those improvements are still not clear. In this paper, we propose a three-dimensional (3D) model of a single cell migration using a Cellular Potts (CP) model to study the influence of the surface topography on cell motility. To do so, various configurations were tested, such as: (i) a substrate with a random roughness, (ii) a substrate with a rectangular groove pattern (parallel and perpendicular to the direction of motion), (ii) a substrate with a sinusoidal groove pattern. To evaluate the influence of the surface topography on cell motility, for each configuration, the cell speed and shape as well as the contact surface between the cell and the substrate have been quantified. Our numerical results demonstrate that, in agreement with the experimental observations of the literature, the substrate topography has an influence on the cell efficiency (i.e. cell speed), orientation and shape. Besides, we also show that the increase of the contact surface alone in presence of roughness is not enough to explain the improvement of cell migration on the various rough surfaces. Finally, we highlight the importance of the roughness dimension on cell motility. This could be a critical aspect to consider for further analyses and applications, such as surface treatments for medical applications.
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Affiliation(s)
- Thomas Thenard
- Arts et Metiers Institute of Technology, Université Paris 13, Sorbonne Paris Cité, IBHGC, HESAM Université, F-75013 Paris, France; Bordeaux INP, Université de Bordeaux, Arts et Métiers Institute of Technology, CNRS, INRA, HESAM Université, I2M UMR 5295, F-33405 Talence, France.
| | - Anita Catapano
- Bordeaux INP, Université de Bordeaux, Arts et Métiers Institute of Technology, CNRS, INRA, HESAM Université, I2M UMR 5295, F-33405 Talence, France
| | - Michel Mesnard
- Arts et Métiers Institute of Technology, Université de Bordeaux, CNRS, INRA, Bordeaux INP, HESAM Université, I2M UMR 5295, F-33405 Talence, France
| | - Rachele Allena
- Arts et Metiers Institute of Technology, Université Paris 13, Sorbonne Paris Cité, IBHGC, HESAM Université, F-75013 Paris, France
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8
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Malik AA, Wennberg B, Gerlee P. The Impact of Elastic Deformations of the Extracellular Matrix on Cell Migration. Bull Math Biol 2020; 82:49. [PMID: 32248312 PMCID: PMC7128007 DOI: 10.1007/s11538-020-00721-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2019] [Accepted: 03/15/2020] [Indexed: 01/06/2023]
Abstract
The mechanical properties of the extracellular matrix, in particular its stiffness, are known to impact cell migration. In this paper, we develop a mathematical model of a single cell migrating on an elastic matrix, which accounts for the deformation of the matrix induced by forces exerted by the cell, and investigate how the stiffness impacts the direction and speed of migration. We model a cell in 1D as a nucleus connected to a number of adhesion sites through elastic springs. The cell migrates by randomly updating the position of its adhesion sites. We start by investigating the case where the cell springs are constant, and then go on to assuming that they depend on the matrix stiffness, on matrices of both uniform stiffness as well as those with a stiffness gradient. We find that the assumption that cell springs depend on the substrate stiffness is necessary and sufficient for an efficient durotactic response. We compare simulations to recent experimental observations of human cancer cells exhibiting durotaxis, which show good qualitative agreement.
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Affiliation(s)
- A A Malik
- Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 412 96, Gothenburg, Sweden.
| | - B Wennberg
- Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 412 96, Gothenburg, Sweden
| | - P Gerlee
- Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 412 96, Gothenburg, Sweden
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9
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General cellular durotaxis induced with cell-scale heterogeneity of matrix-elasticity. Biomaterials 2020; 230:119647. [DOI: 10.1016/j.biomaterials.2019.119647] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2019] [Revised: 11/18/2019] [Accepted: 11/21/2019] [Indexed: 12/12/2022]
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10
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Sugihara K, Sasaki S, Uemura A, Kidoaki S, Miura T. Mechanisms of endothelial cell coverage by pericytes: computational modelling of cell wrapping and in vitro experiments. J R Soc Interface 2020; 17:20190739. [PMID: 31992164 DOI: 10.1098/rsif.2019.0739] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
Pericytes (PCs) wrap around endothelial cells (ECs) and perform diverse functions in physiological and pathological processes. Although molecular interactions between ECs and PCs have been extensively studied, the morphological processes at the cellular level and their underlying mechanisms have remained elusive. In this study, using a simple cellular Potts model, we explored the mechanisms for EC wrapping by PCs. Based on the observed in vitro cell wrapping in three-dimensional PC-EC coculture, the model identified four putative contributing factors: preferential adhesion of PCs to the extracellular matrix (ECM), strong cell-cell adhesion, PC surface softness and larger PC size. While cell-cell adhesion can contribute to the prevention of cell segregation and the degree of cell wrapping, it cannot determine the orientation of cell wrapping alone. While atomic force microscopy revealed that PCs have a larger Young's modulus than ECs, the experimental analyses supported preferential ECM adhesion and size asymmetry. We also formulated the corresponding energy minimization problem and numerically solved this problem for specific cases. These results give biological insights into the role of PC-ECM adhesion in PC coverage. The modelling framework presented here should also be applicable to other cell wrapping phenomena observed in vivo.
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Affiliation(s)
- Kei Sugihara
- Department of Anatomy and Cell Biology, Graduate School of Medical Sciences, Kyushu University, Fukuoka, Japan
| | - Saori Sasaki
- Laboratory of Biomedical and Biophysical Chemistry, Institute for Materials Chemistry and Engineering, Kyushu University, Fukuoka, Japan
| | - Akiyoshi Uemura
- Department of Retinal Vascular Biology, Nagoya City University Graduate School of Medical Sciences, Nagoya, Japan
| | - Satoru Kidoaki
- Laboratory of Biomedical and Biophysical Chemistry, Institute for Materials Chemistry and Engineering, Kyushu University, Fukuoka, Japan
| | - Takashi Miura
- Department of Anatomy and Cell Biology, Graduate School of Medical Sciences, Kyushu University, Fukuoka, Japan.,CREST, Japan Science and Technology Agency, Kawaguchi, Japan
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11
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Márquez S, Reig G, Concha M, Soto R. Cell migration driven by substrate deformation gradients. Phys Biol 2019; 16:066001. [PMID: 31394510 DOI: 10.1088/1478-3975/ab39c7] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Identifying the cues followed by cells is key to understand processes as embryonic development, tissue homeostasis, or several pathological conditions. Based on a durotaxis model, it is shown that cells moving on predeformed thin elastic membrane follow the direction of increasing strain of the substrate. This mechanism, straintaxis, does not distinguish the origin of the strain, but the active stresses produce large strains on cells or tissues being used as substrates. Hence, straintaxis is the natural realization of duratoaxis in vivo. Considering a circular geometry for the substrate cells, it is shown that if the annular component of the active stress component increases with the radial distance, cells migrate toward the substrate cell borders. With appropriate estimation for the different parameters, the migration speeds are similar to those obtained in recent experiments (Reig et al 2017 Nat. Commun. 8 15431). In these, during the annual killifish epiboly, deep cells that move in contact with the epithelial enveloping cell layer (EVL), migrate toward the EVL cell borders with speeds of microns per minute.
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Affiliation(s)
- Susana Márquez
- Departamento de Física, FCFM, Universidad de Chile, Santiago, Chile
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12
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Simsek AN, Braeutigam A, Koch MD, Shaevitz JW, Huang Y, Gompper G, Sabass B. Substrate-rigidity dependent migration of an idealized twitching bacterium. SOFT MATTER 2019; 15:6224-6236. [PMID: 31334524 DOI: 10.1039/c9sm00541b] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Mechanical properties of the extracellular matrix are important determinants of cellular migration in diverse processes, such as immune response, wound healing, and cancer metastasis. Moreover, recent studies indicate that even bacterial surface colonization can depend on the mechanics of the substrate. Here, we focus on physical mechanisms that can give rise to substrate-rigidity dependent migration. We study a "twitcher", a cell driven by extension-retraction cycles, to idealize bacteria and perhaps eukaryotic cells that employ a slip-stick mode of motion. The twitcher is asymmetric and always pulls itself forward at its front. Analytical calculations show that the migration speed of a twitcher depends non-linearly on substrate rigidity. For soft substrates, deformations do not lead to build-up of significant force and the migration speed is therefore determined by stochastic adhesion unbinding. For rigid substrates, forced adhesion rupture determines the migration speed. Depending on the force-sensitivity of front and rear adhesions, forced bond rupture implies an increase or a decrease of the migration speed. A requirement for the occurrence of rigidity-dependent stick-slip migration is a "sticky" substrate, with binding rates being an order of magnitude larger than unbinding rates in absence of force. Computer simulations show that small stall forces of the driving machinery lead to a reduced movement on high rigidities, regardless of force-sensitivities of bonds. The simulations also confirm the occurrence of rigidity-dependent migration speed in a generic model for slip-stick migration of cells on a sticky substrate.
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Affiliation(s)
- Ahmet Nihat Simsek
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Juelich, D-52425 Juelich, Germany.
| | - Andrea Braeutigam
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Juelich, D-52425 Juelich, Germany.
| | - Matthias D Koch
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, NJ 08544, USA
| | - Joshua W Shaevitz
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, NJ 08544, USA
| | - Yunfei Huang
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Juelich, D-52425 Juelich, Germany.
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Juelich, D-52425 Juelich, Germany.
| | - Benedikt Sabass
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Juelich, D-52425 Juelich, Germany.
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13
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Abstract
Cell migration is a fundamental process in biological systems, playing an important role for diverse physiological processes. Cells often exhibit directed migration in a specific direction in response to various types of cues. In particular, cells are able to sense the rigidity of surrounding environments and then migrate toward stiffer regions. To understand this mechanosensitive behavior called durotaxis, several computational models have been developed. However, most of the models employed cell decision making to recapitulate durotactic behaviors, significantly limiting insights provided from these studies. In this study, we developed a computational biomechanical model without any cell decision making to illuminate intrinsic mechanisms of durotactic behaviors of cells migrating on a two-dimensional substrate. The model consists of a simplified cell generating contractile forces and a deformable substrate coarse-grained into an irregular triangulated mesh. Using the model, we demonstrated that durotactic behaviors emerge from purely mechanical interactions between the cell and the underlying substrate. We investigated how durotactic migration is regulated by biophysical properties of the substrate, including elasticity, viscosity, and stiffness profile.
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Affiliation(s)
- Abdel-Rahman Hassan
- Weldon School of Biomedical Engineering, Purdue University, 206 S. Martin Jischke Drive, West Lafayette, Indiana 47907, United States
| | - Thomas Biel
- Weldon School of Biomedical Engineering, Purdue University, 206 S. Martin Jischke Drive, West Lafayette, Indiana 47907, United States
| | - Taeyoon Kim
- Weldon School of Biomedical Engineering, Purdue University, 206 S. Martin Jischke Drive, West Lafayette, Indiana 47907, United States
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14
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Vassaux M, Pieuchot L, Anselme K, Bigerelle M, Milan JL. A Biophysical Model for Curvature-Guided Cell Migration. Biophys J 2019; 117:1136-1144. [PMID: 31400917 DOI: 10.1016/j.bpj.2019.07.022] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2018] [Revised: 06/11/2019] [Accepted: 07/02/2019] [Indexed: 02/06/2023] Open
Abstract
The latest experiments have shown that adherent cells can migrate according to cell-scale curvature variations via a process called curvotaxis. Despite identification of key cellular factors, a clear understanding of the mechanism is lacking. We employ a mechanical model featuring a detailed description of the cytoskeleton filament networks, the viscous cytosol, the cell adhesion dynamics, and the nucleus. We simulate cell adhesion and migration on sinusoidal substrates. We show that cell adhesion on three-dimensional curvatures induces a gradient of pressure inside the cell that triggers the internal motion of the nucleus. We propose that the resulting out-of-equilibrium position of the nucleus alters cell migration directionality, leading to cell motility toward concave regions of the substrate, resulting in lower potential energy states. Altogether, we propose a simple mechanism explaining how intracellular mechanics enable the cells to react to substratum curvature, induce a deterministic cell polarization, and break down cells basic persistent random walk, which correlates with latest experimental evidences.
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Affiliation(s)
- Maxime Vassaux
- Aix Marseille Univ, CNRS, ISM, Marseille, France; Department of Orthopaedics and Traumatology, Institute for Locomotion, APHM, Sainte-Marguerite Hospital, Marseille, France.
| | - Laurent Pieuchot
- Université de Haute-Alsace, CNRS, IS2M, UMR 7361, Mulhouse, France; Université de Strasbourg, Strasbourg, France.
| | - Karine Anselme
- Université de Haute-Alsace, CNRS, IS2M, UMR 7361, Mulhouse, France; Université de Strasbourg, Strasbourg, France
| | - Maxence Bigerelle
- Université de Valenciennes et du Hainaut Cambrésis, Laboratoire d'Automatique, de Mécanique et d'Informatique industrielle et Humaine (LAMIH), UMR-CNRS 8201, Le Mont Houy, Valenciennes, France
| | - Jean-Louis Milan
- Aix Marseille Univ, CNRS, ISM, Marseille, France; Department of Orthopaedics and Traumatology, Institute for Locomotion, APHM, Sainte-Marguerite Hospital, Marseille, France
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15
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Bui J, Conway DE, Heise RL, Weinberg SH. Mechanochemical Coupling and Junctional Forces during Collective Cell Migration. Biophys J 2019; 117:170-183. [PMID: 31200935 DOI: 10.1016/j.bpj.2019.05.020] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2019] [Revised: 05/09/2019] [Accepted: 05/22/2019] [Indexed: 12/31/2022] Open
Abstract
Cell migration, a fundamental physiological process in which cells sense and move through their surrounding physical environment, plays a critical role in development and tissue formation, as well as pathological processes, such as cancer metastasis and wound healing. During cell migration, dynamics are governed by the bidirectional interplay between cell-generated mechanical forces and the activity of Rho GTPases, a family of small GTP-binding proteins that regulate actin cytoskeleton assembly and cellular contractility. These interactions are inherently more complex during the collective migration of mechanically coupled cells because of the additional regulation of cell-cell junctional forces. In this study, we adapted a recent minimal modeling framework to simulate the interactions between mechanochemical signaling in individual cells and interactions with cell-cell junctional forces during collective cell migration. We find that migration of individual cells depends on the feedback between mechanical tension and Rho GTPase activity in a biphasic manner. During collective cell migration, waves of Rho GTPase activity mediate mechanical contraction/extension and thus synchronization throughout the tissue. Further, cell-cell junctional forces exhibit distinct spatial patterns during collective cell migration, with larger forces near the leading edge. Larger junctional force magnitudes are associated with faster collective cell migration and larger tissue size. Simulations of heterogeneous tissue migration exhibit a complex dependence on the properties of both leading and trailing cells. Computational predictions demonstrate that collective cell migration depends on both the emergent dynamics and interactions between cellular-level Rho GTPase activity and contractility and multicellular-level junctional forces.
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Affiliation(s)
- Justin Bui
- Department of Chemical Engineering, University of California Berkeley, Berkeley, California
| | - Daniel E Conway
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, Virginia
| | - Rebecca L Heise
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, Virginia
| | - Seth H Weinberg
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, Virginia.
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16
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Yang HW, Liu XY, Shen ZF, Yao W, Gong XB, Huang HX, Ding GH. An investigation of the distribution and location of mast cells affected by the stiffness of substrates as a mechanical niche. Int J Biol Sci 2018; 14:1142-1152. [PMID: 29989093 PMCID: PMC6036734 DOI: 10.7150/ijbs.26738] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2018] [Accepted: 06/04/2018] [Indexed: 12/27/2022] Open
Abstract
The distribution and location of mast cells are closely related to their physiological and pathological functions, such as allergic responses, immunity, and fibrosis, and are used in acupuncture. In this study, the distribution of mast cells in vivo was observed, and mechanical clues for understanding their distribution based on mechanical niches were explored. By toluidine blue staining and immunohistochemical staining, we examined the distribution and location of mast cells in rat skin and found that mast cells are distributed in a spatially nonuniform manner, preferring to locate at regions in the tissue and extracellular matrix with stiffness changes. In vitro experiments for studying the distribution of rat basophilic leukemia (RBL-2H3) mast cell line on poly-di-methyl-siloxane (PDMS) substrates with stiffness variations were performed. It was found that RBL-2H3 cells migrate and tend to remain in the areas with stiffness variations. The present research suggests that changing the stiffness of local tissues may stimulate mast cell recruitment, which may be the method by which some traditional Chinese medicine treatments, such as acupuncture. On the basis of the origin of mast cells and our experimental results, we predict that mast cells exist in tissues that contain permeable capillaries and prefer regions with stiffness changes. We discussed this prediction using examples of specific tissues from some cases.
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Affiliation(s)
- Hong-Wei Yang
- Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China
| | - Xin-Yue Liu
- Key Laboratory of Hydrodynamics (Ministry of Education), Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Zhou-Feng Shen
- Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China
| | - Wei Yao
- Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China
| | - Xiao-Bo Gong
- Key Laboratory of Hydrodynamics (Ministry of Education), Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Hua-Xiong Huang
- Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada, M3J 1P3
| | - Guang-Hong Ding
- Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China
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17
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A hybrid computational model for collective cell durotaxis. Biomech Model Mechanobiol 2018; 17:1037-1052. [DOI: 10.1007/s10237-018-1010-2] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2017] [Accepted: 02/17/2018] [Indexed: 12/17/2022]
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18
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Marzban B, Yi X, Yuan H. A minimal mechanics model for mechanosensing of substrate rigidity gradient in durotaxis. Biomech Model Mechanobiol 2018; 17:915-922. [PMID: 29354863 DOI: 10.1007/s10237-018-1001-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2017] [Accepted: 01/06/2018] [Indexed: 01/04/2023]
Abstract
Durotaxis refers to the phenomenon in which cells can sense the spatial gradient of the substrate rigidity in the process of cell migration. A conceptual two-part theory consisting of the focal adhesion force generation and mechanotransduction has been proposed previously by Lo et al. to explain the mechanism underlying durotaxis. In the present work, we are concerned with the first part of the theory: how exactly is the larger focal adhesion force generated in the part of the cell adhering to the stiffer region of the substrate? Using a simple elasticity model and by assuming the cell adheres to the substrate continuously underneath the whole cell body, we show that the mechanics principle of static equilibrium alone is sufficient to account for the generation of the larger traction stress on the stiffer region of the substrate. We believe that our model presents a simple mechanistic understanding of mechanosensing of substrate stiffness gradient at the cellular scale, which can be incorporated in more sophisticated mechanobiochemical models to address complex problems in mechanobiology and bioengineering.
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Affiliation(s)
- Bahador Marzban
- Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, Kingston, RI, 02881, USA
| | - Xin Yi
- Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China
| | - Hongyan Yuan
- Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, Kingston, RI, 02881, USA.
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19
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Um E, Oh JM, Granick S, Cho YK. Cell migration in microengineered tumor environments. LAB ON A CHIP 2017; 17:4171-4185. [PMID: 28971203 DOI: 10.1039/c7lc00555e] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Recent advances in microengineered cell migration platforms are discussed critically with a focus on how cell migration is influenced by engineered tumor microenvironments, the medical relevance being to understand how tumor microenvironments may promote or suppress the progression of cancer. We first introduce key findings in cancer cell migration under the influence of the physical environment, which is systematically controlled by microengineering technology, followed by multi-cues of physico-chemical factors, which represent the complexity of the tumor environment. Recognizing that cancer cells constantly communicate not only with each other but also with tumor-associated cells such as vascular, fibroblast, and immune cells, and also with non-cellular components, it follows that cell motility in tumor microenvironments, especially metastasis via the invasion of cancer cells into the extracellular matrix and other tissues, is closely related to the malignancy of cancer-related mortality. Medical relevance of forefront research realized in microfabricated devices, such as single cell sorting based on the analysis of cell migration behavior, may assist personalized theragnostics based on the cell migration phenotype. Furthermore, we urge development of theory and numerical understanding of single or collective cell migration in microengineered platforms to gain new insights in cancer metastasis and in therapeutic strategies.
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Affiliation(s)
- Eujin Um
- Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea
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