G-protein-coupled receptors (GPCRs) 2 are the largest family of cell membrane receptors. An estimated 50% of current pharmaceuticals target GPCRs (1), suggesting that further increases in our understanding of GPCRs and the signaling pathways they initiate will lead to new drug targets. Mathematical and computational modeling (here, simply "modeling") has a substantial history in modern biology and pharmacology (2, 3) and offers a powerful tool for examining GPCR pathways. Such models can be used to better understand hypothesized mechanisms, run virtual (in silico) experiments, interpret data, suggest new drug targets, motivate experiments, and offer new explanations for observed phenomena.
Many Simultaneous Kinetic ProcessesThe more we learn about GPCRs and the pathways they activate, the more complicated our picture of GPCR signaling becomes. At the subsecond to minute time scale, ligand binding, interactions of receptors with G-proteins, G-protein activation/deactivation, and the action of RGS (regulator of G-protein signaling) proteins in GAP or non-GAP roles occur. Depending on the particular G-protein subunit, many downstream signaling molecules (e.g. adenylyl cyclase, cAMP, phospholipase C, Ca 2ϩ , membrane channels) are transiently modulated, locally or over the entire cell. At a slightly longer time scale, receptor phosphorylation, arrestin binding, and activation of non-G-protein-dependent signaling pathways occur (4, 5). Receptor trafficking events, i.e. internalization, recycling, routing to lysosomes, and up-regulation, as well as new receptor synthesis and regulation of gene expression, also occur over the time scale of minutes to hours. Many of the receptor and membrane level events are shown schematically in Fig. 1A. Noble attempts to consolidate information on intracellular signaling pathways initiated by GPCR binding are available (and evolving) (e.g. Database of Science Signaling) (6, 7).Put simply, it is difficult to intuit the net result of so many simultaneous kinetic processes. Add nonlinearities such as feedback, time-varying sequestering of molecules via scaffolds and other mechanisms, and multiple receptor and G-protein species to the temporal and spatial variations already mentioned, and it is virtually impossible. Modeling helps: putting in hypothesized mechanisms and numbers (rates, concentrations) allows both qualitative and quantitative insights. With models one can ask questions such as, which of several simultaneous pathways plays a larger role? Do these events happen fast enough to be important in signaling? What mechanisms might allow modulation of signaling, desensitization, or receptor cross-talk? What factors influence ligand efficacy? Interruption of processes at which points (i.e. drug targets) is most effective? Which experimental protocol is most likely to emphasize a particular mechanism?
Model DevelopmentHow do you create a model? Mathematical/computational modeling that is mechanistic (as opposed to empirical models, which approximate the shape of a relationship with...