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In this paper, modeling of the signal transduction process involving G proteins is done with the utilization of genetic algorithm and a weakly nonlinear analysis. Equations which govern the interaction between an inhibitor protein and the ligand-receptor complexes are written and fitted with experimental data of cAMP levels expressed at different elapsed times, in the case that the homogeneous distribution of ligandreceptor complexes is assumed over the surface membrane. The model is then modified to incorporate reaction-diffusion mechanisms whereby the ligand-receptor complexes and the inhibiting agents in the process may diffuse over the cell membrane. We investigate the formation of Turing-type patterns under certain conditions on the system parameters which characterize the formation of stationary symmetry breaking structures; stripes and hexagonal arrays of spots or nets over the cell membrane.