Multiscale Analysis and Simulation of a Signaling Process With Surface Diffusion

Mariya Ptashnyk, Chandrasekhar Venkataraman

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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.
Original languageEnglish
Pages (from-to)851-886
Number of pages36
JournalMultiscale Modeling and Simulation
Volume18
Issue number2
Early online date18 May 2020
DOIs
Publication statusPublished - 2020

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