  Quantitatively predictive models of biomolecular circuits are important tools
for the design of synthetic biology and molecular communication circuits. The
information content of typical time-lapse single-cell data for the inference of
kinetic parameters is not only limited by measurement uncertainty and intrinsic
stochasticity, but also by the employed perturbations. Novel microfluidic
devices enable the synthesis of temporal chemical concentration profiles. The
informativeness of a perturbation can be quantified based on mutual
information. We propose an approximate method to perform optimal experimental
design of such perturbation profiles. To estimate the mutual information we
perform a multivariate log-normal approximation of the joint distribution over
parameters and observations and scan the design space using Metropolis-Hastings
sampling. The method is demonstrated by finding optimal perturbation sequences
for synthetic case studies on a gene expression model with varying reporter
characteristics.
