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.

翻译：我们开发了一个统计工具箱，用于对描述细胞内生物物理量时空演化的随机反应-扩散系统进行定量模型评估。从时空数据$X_N(t,x)$（例如荧光显微镜记录中提供的数据）出发，我们讨论了随机反应-扩散系统类别中条件均值趋势和波动的基本建模原则，进而发展了用于参数估计的统计推断方法。着眼于实际数据的应用，我们讨论了估计误差和置信区间，特别是与测量空间分辨率相关的部分，并研究了错误设定的反应项和噪声系数的影响。我们还简要涉及了统计估计器的实现问题。作为概念验证，我们将这个工具箱应用于对盘基网柄菌（Dictyostelium discoideum）细胞内肌动蛋白浓度的统计推断。