Modeling and analysis of the signal transduction process with delays involving G protein coupled receptors as a drug target

Abstract

Mathematical modeling has played a significant role in modern biology and pharmacology and has become a powerful tool for examining GPCR pathways. Modeling can be used to validate hypothesized mechanisms, and identify relevant data. More importantly, it can suggest new drug targets, designs of experiments, and new explanations for observed phenomena. G protein coupled receptors (GPCRs) constitute the largest family of cell membrane receptors which are subject to being targeted by an estimated 50% of current pharmaceuticals. Thus, better understanding of GPCRs and the signal transduction pathways they mediate will lead to new drug targets. Signal transduction is the process by which a cell recognizes and extracellular signal and converts that signal into an intracellular response. Subjected to transient stimuli, biological systems can exhibit early responses and/or late responses. In this study, we use mathematical modelling and analysis to study dynamical mechanisms of biological memory and delayed response to external stimuli. A delay model of signaling pathways involving G-proteins is analyzed to show that the model admits positive solutions and is uniformly persistent. Global stability of the system is shown to be attainable under certain conditions on the system's parametric values. It is found that the delays τ I in response to inhibition and τ R in G protein mediated response to external stimuli of the receptors do not appear to impact on the persistent and stability characteristics of this system.