Diffusivity Estimation for Activator–Inhibitor Models: Theory and Application to Intracellular Dynamics of the Actin Cytoskeleton

A theory for diffusivity estimation for spatially extended activator–inhibitor dynamics modeling the evolution of intracellular signaling networks is developed in the mathematical framework of stochastic reaction–diffusion systems. In order to account for model uncertainties, we extend the results for parameter estimation for semilinear stochastic partial differential equations, as developed in Pasemann and Stannat (Electron J Stat 14(1):547–579, 2020), to the problem of joint estimation of diffusivity and parametrized reaction terms. Our theoretical findings are applied to the estimation of effective diffusivity of signaling components contributing to intracellular dynamics of the actin cytoskeleton in the model organism Dictyostelium discoideum.