Macrophage cells that are stimulated by two different ligands which bind to G protein-coupled receptors (GPCRs) usually respond as if the stimulus effects are additive, but for a minority of ligand combinations the response is synergistic. The G protein-coupled receptor system integrates multiple, perhaps conflicting, signaling cues from the environment in order to actuate cell morphology, gene expression, ion homeostasis and other physiological states. We study, in detail, the effects of the two signaling molecules complement factor 5a (C5a) and uridine diphosphate (UDP) on the intracellular second messenger calcium to elucidate principals that govern the mechanism of G protein-coupled signal transduction. We have developed a formal hypothesis, in the form of a kinetic model, for the mechanism of action of this GPCR signal transduction system using data obtained from RAW264.7 macrophage cells. Bayesian statistical methods are employed to formally approach uncertainty and tie the model to experimental data. The model is entertained as a tool in the design of investigative experiments. The model accurately predicts a synergistic region in the calcium peak height dose response that results when cells are simultaneous stimulated by C5a and UDP. Though this model is not a complete representation of the G protein-coupled signal transduction system and contains many approximations, it is consistent with our experimental observations and is a useful substrate for further experimentation. Finally, we address the problem of the design of robust experiments for the G protein-coupled signal transduction model. Classical optimal experiment design methods have not been widely adopted in practice for biological systems, in part because the resulting designs can be very brittle if the nominal parameter estimates for the model are poor, and in part because of computational constraints. We present a method for robust experiment design based on a semidefinite programming relaxation. We present an application of this method to the design of experiments for a complex calcium signal transduction pathway, where we have found that the parameter estimates obtained from the robust design are better than those obtained from an "optimal" design.





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