Diffusivity Estimation for Activator\u2013Inhibitor Models: Theory and Application to Intracellular Dynamics of the Actin Cytoskeleton

Gregor Pasemann,Sven Flemming,Sergio Alonso,Carsten Beta,Wilhelm Stannat

doi:10.1007/s00332-021-09714-4

Abstract

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.

Highlights

The purpose of this paper is to develop the mathematical theory for statistical inference methods for the parameter estimation of stochastic reaction–diffusion systems modeling spatially extended signaling networks in cellular systems
While θ02,N works very well on the full domain of 200 × 200 pixels with periodic boundary conditions, it decays rapidly if we just use a square section of 75 × 75 pixels
We have extended the mathematical theory of parameter estimation of stochastic reaction–diffusion system to the joint estimation problem of diffusivity and parametrized reaction terms within the variational theory of stochastic partial differential equations

Summary

Introduction

The purpose of this paper is to develop the mathematical theory for statistical inference methods for the parameter estimation of stochastic reaction–diffusion systems modeling spatially extended signaling networks in cellular systems. Such signaling networks are one of the central topics in cell biology and biophysics as they provide the basis for essential processes including cell division, cell differentiation, and cell motility (Peter 2017). Nonlinearities in these network may cause rich spatiotemporal behavior including the emergence of oscillations and waves (Beta and Kruse 2017). We mainly focus on the estimation of diffusivity, whose precision can be increased by simultaneous calibration of the reaction terms

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