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From single to collective cell migration: A geometric bulk-surface PDE modelling approach

Anotida Madzwamuse, University of British Columbia
Tuesday January 27, 12-1pm
Zoom Link:
In Person: 550 Sherbrooke, Room 189

Abstract:聽In this talk, I will present a new formalism for modelling single and collective cell migration based on geometric bulk-surface partial differential equations. The cell plasma membrane and the nuclear envelope are modelled as energetic manifolds whose evolution law is based on a force balance equation of each material point on the two closed smooth evolving hypersurfaces (also known as manifolds). The evolution law encodes all forces acting at each material point in the outward pointing normal direction, and these forces include (but are not limited to) cell polarisation, retraction, bending energy, surface tension, pressure, volume or surface area constraint or conservation, mechanics, intra- and extra-cellular, and so forth. Cell polarisation is modelled through bulk-surface reaction-diffusion systems on continuously deforming manifolds. The fully coupled models are solved efficiently by use of the evolving bulk-surface finite element method. To allow for long time simulations, robust adaptive mesh refined and equi-distribution strategies are implemented. To demonstrate the modelling approach, its generality and applicability, several numerical simulations inspired by studies in cell biology will be presented and comparisons to experiments will be illustrated. This approach allows to study how single cells migrate through non-isotropic environment, microchannels of variable width as well as in confinement.