A theoretical approach to G-protein modulation of cellular responsiveness

Structure and function of cells often depend critically on molecular signals arriving at their surface. There are universal mechanisms of signal transduction and signal processing across cell membranes. In this paper the mechanisms involving guanine-nucleotide regulatory proteins ("G-proteins") and certain receptor-kinases are considered. On the basis of recent findings in molecular biology a mathematical model is developed taking into account all essential components in the biochemical network between first and second messenger. There are two coupled feedback loops inherent in this process. The model finally consists of three nonlinear equations, which are obtained from a system of originally ten equations by using conservation laws and quasi-steady state conditions. The second part of the paper contains a mathematical analysis of the model. Solutions describing the temporal development of the involved biochemical species are shown to be bounded, more specifically to remain, independent of the size of the input signal, in a bounded domain of the state space. For the situation of stationary input signals existence, uniqueness and asymptotic stability of steady states are derived. We also demonstrate biologically relevant stimulus-response properties like monotonicity and saturation effects. For temporally non-constant input signals we show numerically that the model is able to produce phenomena of hypersensitivity and desensitization which are important characteristics of cellular responsiveness.