Optimal variational perturbations for the inference of stochastic reaction dynamics

Although single-cell techniques are advancing rapidly, quantitative assessment of kinetic parameters is still characterized by ill-posedness and a large degree of uncertainty. In many standard experiments, where transcriptional activation is recorded upon application of a step-like external perturbation, cells almost instantaneously adapt such that only a few informative measurements can be obtained. Consequently, the information gain between subsequent experiments or time points is comparably low, which is reflected in a hardly decreasing parameter uncertainty. However, novel microfluidic techniques can be applied to synthesize more sophisticated perturbations to increase the informativeness of such time-course experiments. Here we introduce a mathematical framework to design optimal perturbations for the inference of stochastic reaction dynamics. Based on Bayesian statistics, we formulate a variational problem to find optimal temporal perturbations and solve it using a stochastic approximation algorithm. Simulations are provided for the realistic scenario of noisy and discrete-time measurements using two simple reaction networks.