Stochastic Reaction-Diffusion Systems in Biophysics: Towards a Toolbox for Quantitative Model Evaluation

TL;DR

This paper introduces a statistical toolbox for evaluating stochastic reaction-diffusion models of intracellular processes, focusing on parameter estimation, error analysis, and application to microscopy data of actin in amoebae.

Contribution

It develops new statistical inference methods tailored for stochastic reaction-diffusion systems and demonstrates their application to real biological data.

Findings

Effective parameter estimation methods for reaction-diffusion models.

Analysis of estimation errors related to spatial measurement resolution.

Insights into model misspecification impacts on inference accuracy.

Abstract

We develop a statistical toolbox for a quantitative model evaluation of stochastic reaction-diffusion systems modeling space-time evolution of biophysical quantities on the intracellular level. Starting from space-time data $X_N(t,x)$, as, e.g., provided in fluorescence microscopy recordings, we discuss basic modelling principles for conditional mean trend and fluctuations in the class of stochastic reaction-diffusion systems, and subsequently develop statistical inference methods for parameter estimation. With a view towards application to real data, we discuss estimation errors and confidence intervals, in particular in dependence of spatial resolution of measurements, and investigate the impact of misspecified reaction terms and noise coefficients. We also briefly touch implementation issues of the statistical estimators. As a proof of concept we apply our toolbox to the statistical inference on intracellular actin concentration in the social amoeba Dictyostelium discoideum.