Abstract
This article presents a mathematical and computational model for cell migration that couples a system of reaction-advection-diffusion equations describing the bio-molecular interactions between F-actin and myosin II to a force balance equation describing the structural mechanics of the actin-myosin network. In eukaryotic cells, cell migration is largely powered by a system of actin and myosin dynamics. We formulate the model equations on a two-dimensional cellular migrating evolving domain to take into account the convective and dilution terms for the biochemical reaction-diffusion equations, with hypothetically proposed reaction-kinetics. We employ the evolving finite element method to compute approximate numerical solutions of the coupled biomechanical model in two dimensions. Numerical experiments exhibit cell polarisation through symmetry breaking which driven by the F-actin and myosin II. This conceptual hypothetical proof-of-concept framework set premises for studying experimentally-driven actin-myosin reaction-kinetic network interactions with generalisations to multi-dimensions.
Highlights
Cell migration is fundamental in many biological processes and plays a key role in wound healing, immune response, development of embryos, inflammation, cancer invasion among others [1,2,3,4,5,6]
We model the network of actin filaments in the cell as a viscous gel with active stresses generated from the action of actin and myosin II
We showed that the 2SBDF method used to solve the system of reaction-diffusion equations is a second order
Summary
Cell migration is fundamental in many biological processes and plays a key role in wound healing, immune response, development of embryos, inflammation, cancer invasion among others [1,2,3,4,5,6]. Actin is a polymer that can exist in two forms: F-actin and G-actin forms [1, 5, 6] It converts from inactive state (G-actin) to active state (F-actin) through a process called actin polymerization and from active state to inactive state through actin depolymerization [1, 6, 8]. Actin filaments can assemble structures forming networks and bundles through interaction with motor proteins [9, 10]. These structures produce cell protrusions called lamellipodia [6, 7, 11]. Actin cytoskeleton is the main structure that contributes actively to force generation and drives cell movement [6, 12]
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