Optimal Design of Experiments for Simulation-Based Inference of Mechanistic Acyclic Biological Networks

Abstract: Biological signaling pathways based upon proteins binding to one another to relay a signal for genetic expression, such as the Bone Morphogenetic Protein (BMP) signaling pathway, can be modeled by mass action kinetics and conservation laws that result in non-closed form polynomial equations. Accurately determining parameters of biological pathways that represent physically relevant features, such as binding affinity of proteins and their associated uncertainty, presents a challenge for biological models lacking an explicit likelihood function. Additionally, parameterizing non-closed form biological models requires copious amounts of data from expensive perturbation-response experiments to fit model parameters. We present an algorithm (SBIDOEMAN) for determining optimal experiments and parameters of systems biology models with implicit likelihoods. We evaluate our algorithm using simulations of held-out true parameter values and demonstrate an improvement in the rate of accurate parameter inference over random and equidistant experimental designs when evaluated on two simple models of the BMP signaling pathway with an implicit likelihood function.