Closing the loop: a Bayesian approach to targeted experimental design

INTRODUCTION An important factor which complicates the development of mathematical models of biochemical pathways is that data is relatively scarce and consequently the modeller is faced with a situation where multiple parameter sets can adequately describe the measurement data to an acceptable degree. When predictions required to test the hypothesis are insufficiently constrained more data will be required. However, it is often not immediately evident which measurement(s) at which specific time point(s) would be most informative. Although several design criteria exist, many of which aimed at effectively constraining specific parameters we focus on designing experiments specifically targeting the variance of quantities of interest that depend (optionally non-linearly) on model predictions. METHODS In this work we use a Bayesian approach to infer a posterior distribution based on the model and the data, which we subsequently use for simulation. Then self- normalized importance sampling of the Posterior Predictive Distribution (PPD) is performed in order to assess experimental efficacy of specific combinations of experiments. Subsequently this measure is used to perform Optimal Experiment Design (OED). RESULTS We have developed a flexible Bayesian approach to perform hypothesis driven experimental design that enables the modeller to design experiments that target specific predictions of interest whilst considering finite measurement accuracy and model uncertainty. Experiment(s) can be optimized for any quantity that can be expressed in terms of the model simulations and/or model parameters at little additional computational cost. Within this framework, multiple experiments can be taken into account simultaneously and their combinatorial effect evaluated. We present our method by illustrating its use on a model of the JAK-STAT signalling pathway. For this specific model, we show that specific combinations of experiments can greatly outperform others.