Using the Finite State Projection based Fisher Information Matrix to optimize single-cell experiment designs under different combinations of discrete stochastic models and measurement errors

When combined with discrete stochastic models, single-molecule Fluorescence in situ Hybridization (smFISH) can reveal quantitative insight into gene regulation mechanisms. In principle, infinite smFISH experiment designs are possible (e.g., with different induction levels, measurement times, or observed biological species). Moreover, each experiment can be time consuming or expensive to perform and will result in labeling, imaging, or data processing errors. To find which experiments are best suited to identify a model, we adopt the chemical master equation framework to define likelihood functions, and we calculate the Finite State Projection based Fisher Information Matrix (FSP-FIM) to estimate and compare information for different experiment designs (Fox, 2019, Fox 2020). We extend the FSP-FIM with a probabilistic distortion operator to estimate how errors affect model identification (Vo, 2022). By analyzing different combinations of models, experiment designs, and image distortions, we find practical working principles to optimize smFISH experiments despite inexact imaging. Finally, we validate our FSP-FIM approach using new smFISH data for Dusp1 gene regulation upon Dexamethasone stimulation.