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Using finite state projection and Fisher information to improve single-cell experiment design to gain better understanding of DUSP1 transcription dynamics


Many recent studies have combined fluorescent biochemical labels, single-cell microscopy, and discrete stochastic modeling to understand and predict how organisms react to environmental changes to control gene expression. The experimental data used in these studies is often collected using intuitively-designed applications of techniques such as single-cell immunnocytochemistry (ICC) to measure protein expression and transport or single-molecule Fluorescence in situ Hybridization (smFISH) to measure the number and position of transcribed mRNA. Once collected, these single-cell data are then analyzed using discrete stochastic models, often based on the framework of the Chemical Master Equation (CME), which can be solved using the Finite State Projection (FSP) algorithm. Unfortunately, these experiments can be expensive and labor intensive to perform, primarily due to long imaging and image analysis times, and it is not clear how these experiments must be designed to obtain the most information when their results are later analyzed using the FSP techniques. The recently discovered Finite State Projection based Fisher information Matrix (FSP-FIM) provides a potential and practical solution to this experiment design challenge by providing direct estimates for how well any potential experiment should be expected to constrain parameters for a given model or set of models. In this report, we examine this challenge of experiment design in the situation where multiple different types of experiments (i.e., ICC and smFISH) are possible, for different time points, for different numbers of measurements per time point, for different environmental inputs, and for different assumed models and combinations of unknown parameters. We extend the previous FSP-FIM theory to address these multiple challenges, and we introduce new computational tools in the form of advances to the Stochastic System Identification Toolkit (in Mathworks Matlab) that allow users to easily and efficiently compute the FSP and FIM for each of these circumstances. Using experimental smFISH data, we demonstrate the effectiveness of the FSP tools to quantitatively reproduce the single-cell transcription dynamics of the Dual Specific Phosphatase 1 (DUSP1) gene under stimulation by Dexamethasone (Dex), and we show how the FSP-FIM can be used to design optimal combinations of ICC and smFISH to further improve quantification of this gene regulatory process, including predicting the optimal allocation of measurement times to obtain the most amount of information from each experiment. To probe the generality of our results, these FSP and FSP-FIM analyses are conducted for different models, under different assumptions on known and unknown parameters, and under different drug dosage regimens. The approach developed in this work is expected to have substantial impact on how computational models can be employed to improve the selection and design of future single-cell experiments.


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finite state projection
single cell experiment design
Fisher information matrix


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