Optimal Experimental Design for a Bistable Gene Regulatory Network

Abstract

Accurate model calibration is essential for model-based design of synthetic gene regulatory networks. Optimal experimental design (OED) techniques can be used to efficiently decrease parameter uncertainty. However, many biological networks of interest exhibit multi-modal response functions due to multistability. These models are incompatible with traditional OED approaches that have been developed for models with mono-modal error distributions. In this work we propose an OED approach for a gene expression model that exhibits bistability via a saddle-node bifurcation with respect to an experimental input. We demonstrate construction of an approximate likelihood and derive the corresponding Fisher information across the monostable and bistable regimes. We use the linear noise approximation for the local error model and apply logistic regression to capture the switching probabilities between the stable equilibria. We then use this Fisher information matrix to generate locally optimal experimental designs for this system. This leads to a simple, qualitative approach to optimal experimental design based on experimental detection of bimodality.