Sequential design of single-cell experiments to identify discrete stochastic models for gene expression

Control of gene regulation requires quantitatively accurate predictions of heterogeneous cellular responses. When inferred from single-cell experiments, discrete stochastic models can enable such predictions, but such experiments are highly adjustable, allowing for almost infinitely many potential designs (e.g., at different induction levels, for different measurement times, or considering different observed biological species). Not all experiments are equally informative, experiments are time-consuming or expensive to perform, and research begins with limited prior information with which to construct models. To address these concerns, we developed a sequential experiment design strategy that starts with simple preliminary experiments and then integrates chemical master equations to compute the likelihood of single-cell data, a Bayesian inference procedure to sample posterior parameter distributions, and a finite state projection based Fisher information matrix to estimate the expected information for different designs for subsequent experiments. Using simulated then real single-cell data, we determined practical working principles to reduce the overall number of experiments needed to achieve predictive, quantitative understanding of single-cell responses.