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.
Ptashnyk, M., & Venkataraman, C. (2020). Multiscale Analysis and Simulation of a Signaling Process With Surface Diffusion. Multiscale Modeling and Simulation, 18(2), 851-886. https://doi.org/10.1137/18M1185661