A coupled bulk-surface model for cell polarisation

Cusseddu, D, Edelstein-Keshet, L, Mackenzie, J A, Portet, S and Madzvamuse, A (2018) A coupled bulk-surface model for cell polarisation. Journal of Theoretical Biology. ISSN 022-5193

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Abstract

Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which cellular symmetry is broken, causing the cell to have a well defined front and back. Recent work on balancing biological complexity with mathematical tractability resulted in the proposal and formulation of a famous minimal model for cell polarisation, known as the wave pinning model. In this study, we present a three-dimensional generalisation of this mathematical framework through the maturing theory of coupled bulk-surface semilinear partial differential equations in which protein compartmentalisation becomes natural. We show how a local perturbation over the surface can trigger propagating reactions, eventually stopped in a stable profile by the interplay with the bulk component. We describe the behaviour of the model through asymptotic and local perturbation analysis, in which the role of the geometry is investigated. The bulk-surface finite element method is used to generate numerical simulations over simple and complex geometries, which confirm our analysis, showing pattern formation due to propagation and pinning dynamics. The generality of our mathematical and computational framework allows to study more complex biochemical reactions and biomechanical properties associated with cell polarisation in multi-dimensions.

Item Type: Article
Keywords: Cell polarisation, bulk-surface wave pinning model, coupled bulk-surface, semilinear partial differential equations, reaction-diffusion systems, bulk-surface finite elements, asymptotic and local perturbation theory
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Mathematics Applied to Biology Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Richard Chambers
Date Deposited: 14 Sep 2018 15:17
Last Modified: 08 Sep 2019 01:00
URI: http://sro.sussex.ac.uk/id/eprint/78785

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Project NameSussex Project NumberFunderFunder Ref
InCeM: Research Training Network on Integrated Component Cycling in Epithelial Cell MotilityG1546EUROPEAN UNION642866 - InCeM