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Mathematical model of mechano-sensing and mechanically induced collective motility of cells on planar elastic substrates

Mathematical model of mechano-sensing and mechanically induced collective motility of cells on planar elastic substrates
Mathematical model of mechano-sensing and mechanically induced collective motility of cells on planar elastic substrates
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.
cell migration, cellular traction force, substrate deformation, strain energy density
1617-7959
Ahmed, Riham K.
417e4e58-9583-48d2-9997-958874c5d1ba
Abdalrahman, Tamer
65d60fa0-5278-4158-9e58-a75854a2c4c1
Davies, Neil H.
e52928b5-b051-443d-87c5-6463fe942865
Vermolen, Fred
91288ff6-2089-4365-8902-8e3a570cffc7
Franz, Thomas
31f508f4-6851-4274-b256-cc01ab321d50
Ahmed, Riham K.
417e4e58-9583-48d2-9997-958874c5d1ba
Abdalrahman, Tamer
65d60fa0-5278-4158-9e58-a75854a2c4c1
Davies, Neil H.
e52928b5-b051-443d-87c5-6463fe942865
Vermolen, Fred
91288ff6-2089-4365-8902-8e3a570cffc7
Franz, Thomas
31f508f4-6851-4274-b256-cc01ab321d50

Ahmed, Riham K., Abdalrahman, Tamer, Davies, Neil H., Vermolen, Fred and Franz, Thomas (2023) Mathematical model of mechano-sensing and mechanically induced collective motility of cells on planar elastic substrates. Biomechanics and Modeling in Mechanobiology. (doi:10.1007/s10237-022-01682-2).

Record type: Article

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.

Text
2 - P086 2D Mechanical model BMMB rev04 clean - Accepted Manuscript
Restricted to Repository staff only until 23 February 2024.

More information

Accepted/In Press date: 28 December 2022
e-pub ahead of print date: 23 February 2023
Published date: 23 February 2023
Keywords: cell migration, cellular traction force, substrate deformation, strain energy density

Identifiers

Local EPrints ID: 476626
URI: http://eprints.soton.ac.uk/id/eprint/476626
ISSN: 1617-7959
PURE UUID: 4154be58-28b4-41e2-9965-99f1e8b5c687

Catalogue record

Date deposited: 10 May 2023 16:41
Last modified: 10 May 2023 17:19

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Contributors

Author: Riham K. Ahmed
Author: Tamer Abdalrahman
Author: Neil H. Davies
Author: Fred Vermolen
Author: Thomas Franz

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