Analysis and Simulations of Coupled Bulk-surface Reaction-Diffusion Systems on Exponentially Evolving Volumes

Madzvamuse, Anotida; Chung, Andy H.W.

doi:10.1051/mmnp/201611502

Cited by 4 publications

(3 citation statements)

References 43 publications

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“…In [26] the same analysis was done for the model (1)-(3) where a and b are defined on the same unidimensional spatial domain. They derive a well mixed and LPA system which is a special case of our models (28)- (27) and (30)- (32) when ω = 1. They initially use a sharp switch approximation for the reaction (7) (passing to the limit as n → ∞) in order to be able to calculate the steady states analytically.…”

Section: Local Perturbation Analysismentioning

confidence: 99%

“…We present new three-dimensional results on regular and irregular geometries, exhibiting the wave pinning process on complex geometries. A key part of our study involves the numerical simulation of the BSWP model in three-dimensional geometries using a recently developed bulk-surface finite element method (BS-FEM) [10,12,31,32,33,34]. This numerical framework allows to compute the solutions of the BSWP model on complex convex and non-convex geometries.…”

Section: Introductionmentioning

confidence: 99%

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A coupled bulk-surface model for cell polarisation

Cusseddu

Edelstein‐Keshet

Mackenzie

et al. 2019

Journal of Theoretical Biology

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117

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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 behavior 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.

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Section: Local Perturbation Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A coupled bulk-surface model for cell polarisation

Cusseddu

Edelstein‐Keshet

Mackenzie

et al. 2019

Journal of Theoretical Biology

Self Cite

117

View full text Add to dashboard Cite

show abstract

“…In this issue the pattern formation for reaction-diffusion systems defined on evolving domains is presented by A. Madzvamuse and A.H. Chung [11]. A coupling between bulk and surface dynamics induces an interesting and important aspect of the analysis.…”

mentioning

confidence: 99%