Mathematical modeling and application of genetic algorithm to parameter estimation in signal transduction: trafficking and promiscuous coupling of G-protein coupled receptors.

G-protein-coupled receptors (GPCRs) constitute a large and diverse family of proteins whose primary function is to transduce extracellular stimuli into intracellular signals. These receptors play a critical role in signal transduction, and are among the most important pharmacological drug targets. Upon binding of extracellular ligands, these receptor molecules couple to one or several subtypes of G-protein which reside at the intracellular side of the plasma membrane to trigger intracellular signaling events. The question of how GPCRs select and activate a single or multiple G-protein subtype(s) has been the topic of intense investigations. Evidence is also accumulating; however, that certain GPCRs can be internalized via lipid rafts and caveolae. In many cases, the mechanisms responsible for this still remain to be elucidated. In this work, we extend the mathematical model proposed by Chen et al. [Modelling of signalling via G-protein coupled receptors: pathway-dependent agonist potency and efficacy, Bull. Math. Biol. 65 (5) (2003) 933-958] to take into account internalization, recycling, degradation and synthesis of the receptors. In constructing the model, we assume that the receptors can exist in multiple conformational states allowing for a multiple effecter pathways. As data on kinetic reaction rates in the signalling processes measured in reliable in vivo and in vitro experiments is currently limited to a small number of known values. In this paper, we also apply a genetic algorithm (GA) to estimate the parameter values in our model.