A moving grid finite element method applied to a mechanobiochemical model for 3D cell migration

Murphy, Laura and Madzvamuse, Anotida (2020) A moving grid finite element method applied to a mechanobiochemical model for 3D cell migration. Applied Numerical Mathematics, 158. pp. 336-359. ISSN 0168-9274

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Abstract

This work presents the development, analysis and numerical simulations of a biophysical model for 3D cell deformation and movement, which couples biochemical reactions and biomechanical forces. We propose a mechanobiochemical model which considers the actin filament network as a viscoelastic and contractile gel. The mechanical properties are modelled by a force balancing equation for the displacements, the pressure and contractile forces are driven by actin and myosin dynamics, and these are in turn modelled by a system of reaction-diffusion equations on a moving cell domain. The biophysical model consists of highly non-linear partial differential equations whose analytical solutions are intractable. To obtain approximate solutions to the model system, we employ the moving grid finite element method. The numerical results are supported by linear stability theoretical results close to bifurcation points during the early stages of cell migration. Numerical simulations exhibited show both simple and complex cell deformations in 3-dimensions that include cell expansion, cell protrusion and cell contraction. The computational framework presented here sets a strong foundation that allows to study more complex and experimentally driven reaction-kinetics involving actin, myosin and other molecular species that play an important role in cell movement and deformation.

Item Type: Article
Keywords: Mechanobiochemical model, Viscoelastic, Force balance equation, Cell motility, Moving grid finite elements, Reaction-diffusion equations, Partial differential equations, Moving boundary problem
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 27 Aug 2020 15:40
Last Modified: 01 Sep 2020 07:01
URI: http://sro.sussex.ac.uk/id/eprint/91891

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