By providing quantitative insight into signal transduction pathophysiology, systems biology promises to revolutionize the pharmaceutical industry. However, the insight provided to date by current modeling approaches have yet to show substantial impact on real-world industrial and medical applications. We believe that an important contributing factor to this lack of translational impact is the intrinsic difficulty in estimating the parameters for such models uniquely and accurately, since such models typically contain on the order of 100 non-linear ordinary differential equations (ODE) and twice as many unknown parameters. A main difficulty in parameter estimation, in addition to the sheer size of the parameter search space, is that there is no systematic procedure for evaluating parameter identifiability, that is, which parameters can be uniquely estimated from a particular set of experimental data. As a result, there are currently no methods for designing experiments (what to measure and at what time point, using what perturbations) for the purposes of parameter estimation in such models. Addressing these fundamental modeling problems, we present in the current work metrics for evaluating parameter identifiability in signal transduction models, and use these metrics to develop a methodology for optimal experimental design (OED) for parameter estimation in biological signal transduction modeling. We apply this methodology to two well-known models of mammalian signal transduction involving short-term Epidermal Growth Factor (EGF) signaling: the Kholodenko (1999) and Schoeberl (2002) models. First, we show that with the experimental data reported in these studies, the parameters that were estimated are not uniquely identifiable. Second, we propose how these unknown parameter values can be identified using OEDs based on traditional, low-throughput measurements of downstream signaling in response to EGF stimulation, with and without various pharmacological inhibitors. Third, we explore the OEDs when high-throughput, quantitative proteomic measurement of signaling responses are assumed to be readily available, showing that these measurements have the potential to be much more efficient than traditional methods for parameter estimation in this class of models. Overall, our method lays a foundation for effective experimental design and parameter estimation in biological signal transduction modeling, and is generally applicable to high-dimension, non-linear ODE modeling.

References

Kholodenko, B.N., Demin, O.V., Moehren, G. and Hoek, J.B. (1999) Quantification of short term signaling by the epidermal growth factor receptor. J Biol Chem, 274, 30169-30181.

Schoeberl, B., Eichler-Jonsson, C., Gilles, E.D. and Muller, G. (2002) Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nat Biotechnol, 20, 370-375.