Multiscale analysis and simulation of a signalling process with surface diffusion

Ptashnyk, Mariya and Venkataraman, Chandrasekhar (2020) Multiscale analysis and simulation of a signalling process with surface diffusion. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 18 (2). pp. 851-886. ISSN 1540-3459

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Abstract

We present and analyze a model for cell signaling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces and both inter- and intracellular signaling. Using techniques from the theory of two-scale convergence as well the unfolding method, we show convergence of the solutions to the model to solutions of a two-scale macroscopic problem. We also present a two-scale bulk-surface finite element method for the approximation of the macroscopic model. We report on some benchmarking results as well as numerical simulations in a biologically relevant regime that illustrate the influence of cell-scale heterogeneities on macroscopic concentrations.

Item Type: Article
Keywords: Intercellular signalling, receptor-ligand interactions, homogenisation, nonlinear
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 12 Mar 2020 12:13
Last Modified: 26 May 2020 13:45
URI: http://sro.sussex.ac.uk/id/eprint/90376

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