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A moving grid finite element method applied to a mechanobiochemical model for 3D cell migration
Version 2 2023-06-07, 08:49
Version 1 2023-06-07, 07:15
journal contribution
posted on 2023-06-07, 08:49 authored by Laura Murphy, Anotida MadzvamuseAnotida MadzvamuseThis 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.
Funding
Unravelling new mathematics for 3D cell migration; G1438; LEVERHULME TRUST
InCeM: Research Training Network on Integrated Component Cycling in Epithelial Cell Motility; G1546; EUROPEAN UNION
New predictive mathematical and computational models in experimental sciences; G1949; ROYAL SOCIETY; WM160017
History
Publication status
- Published
File Version
- Accepted version
Journal
Applied Numerical MathematicsISSN
0168-9274Publisher
ElsevierExternal DOI
Volume
158Page range
336-359Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes