Optimal Experimental Design for Parameter Estimation of a Cell Signaling Model

Differential equation models that describe the dynamic changes of biochemical signaling states are important tools to understand cellular behavior. An essential task in building such representations is to infer the affinities, rate constants, and other parameters of a model from actual measurement data. However, intuitive measurement protocols often fail to generate data that restrict the range of possible parameter values. Here we utilized a numerical method to iteratively design optimal live-cell fluorescence microscopy experiments in order to reveal pharmacological and kinetic parameters of a phosphatidylinositol 3,4,5-trisphosphate (PIP3) second messenger signaling process that is deregulated in many tumors. The experimental approach included the activation of endogenous phosphoinositide 3-kinase (PI3K) by chemically induced recruitment of a regulatory peptide, reversible inhibition of PI3K using a kinase inhibitor, and monitoring of the PI3K-mediated production of PIP3 lipids using the pleckstrin homology (PH) domain of Akt. We found that an intuitively planned and established experimental protocol did not yield data from which relevant parameters could be inferred. Starting from a set of poorly defined model parameters derived from the intuitively planned experiment, we calculated concentration-time profiles for both the inducing and the inhibitory compound that would minimize the predicted uncertainty of parameter estimates. Two cycles of optimization and experimentation were sufficient to narrowly confine the model parameters, with the mean variance of estimates dropping more than sixty-fold. Thus, optimal experimental design proved to be a powerful strategy to minimize the number of experiments needed to infer biological parameters from a cell signaling assay.Author Summary: Differential equation models of signaling processes are useful to gain a molecular and quantitative understanding of cellular information flow. Although these models are typically based on simple kinetic rules, they can often qualitatively describe the behavior of biological systems. However, in the quest to transform biomedical research into an engineering discipline, biologists face the challenge of estimating important parameters of such models from laboratory data. Measurement noise as well as the robust architecture of biological circuits are causes for large uncertainty of parameter estimates. This makes it difficult to plan informative experiments. Here, we used a computational method to predict and minimize the uncertainty of parameter estimates we would obtain from prospective experiments given a cancer-relevant signaling model. This was achieved by optimizing the concentrations and time points for adding drugs in a live-cell microscopy experiment. Our experimental results demonstrated that the advice given by this algorithm resulted in many-fold more informative data than we would obtain by repeating an intuitively planned experiment. Our study shows that significant experimental effort and time can be saved by adopting an optimal experimental design strategy for inferring relevant parameters from biomedical experiments.