Abstract:
In this work, we present a mechanobiochemical model for two-dimensional cell migration which couples
mechanical properties of the cell cytosol with biochemical processes taking place near or on the cell plasma
membrane. The modelling approach is based on a recently developed mathematical formalism of evolving bulksurface
partial differential equations of reaction–diffusion type. We solve these equations using finite element
methods within a moving-mesh framework derived from the weak formulation of the evolving bulk-surface
PDEs. In the present work, the cell cytosol interior (bulk) dynamics are coupled to the cell membrane (surface)
dynamics through non-homogeneous Dirichlet boundary conditions. The modelling approach exhibits both
directed cell migration in response to chemical cues as well as spontaneous migration in the absence of such
cues. As a by-product, the approach shows fundamental characteristics associated with single cell migration
such as: (i) cytosolic and membrane polarisation, (ii) actin dependent protrusions, and (iii) continuous shape
deformation of the cell during migration.
Cell migration is an ubiquitous process in life that is mainly triggered by the dynamics of the actin
cytoskeleton and therefore is driven by both mechanical and biochemical processes. It is a multistep process
essential for mammalian organisms and is closely linked to a vast diversity of processes; from embryonic
development to cancer invasion. Experimental, theoretical and computational studies have been key to
elucidate the mechanisms underlying cell migration. On one hand, rapid advances in experimental techniques
allow for detailed experimental measurements of cell migration pathways, while, on the other, computational
approaches allow for the modelling, analysis and understanding of such observations. The bulk-surface
mechanobiochemical modelling approach presented in this work, set premises to study single cell migration
through complex non-isotropic environments in two- and three-space dimensions.
