Modeling Signal Transduction Involving G Protein Coupled Receptors by Genetic Algorithm and Nonlinear Spatiotemporal Analysis CHONTITA RATTANAKUL 1,2 , MEECHOKE CHUDOUNG 1 , YONGWIMON LENBURY 1,2,* , VARANUJ CHATSUDTHIPONG 3 , WANNAPONG TRIAMPO 4 , BORIBOON NOVAPRATEEP 1,2 , TITIWAT SUNGKAWORN 3 1 Deparment of Mathematics, Faculty of Science, Mahidol University, Bangkok, THAILAND 2 National Centre of Excellence in Mathematics, PERDO, Bangkok, THAILAND 3 Department of Physiology, Mahidol University, Bangkok, THAILAND 4 Department of Physics, Mahidol University, Bangkok, THAILAND *Corresponding author: scylb@mahidol.ac.th Abstract: - 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 ligand- receptor 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. Key-Words: - Nonlinear analysis, signal transduction, Turing patterns, ligand-receptor complexes diffusion. 1 Introduction Signal transduction at the cellular level refers to the movement of signals or flow of information from outside the cell to the inside. The movement of signals can be simple, such as that which involves the receptor molecules of the acetylcholine class. More complex signal transduction involves the coupling of ligand-receptor interaction to various intracellular events. Thus, external stimuli are relayed to a series of internal reactants, which in turn trigger key cellular functions. A healthy functioning cell signaling mechanism is therefore essential for the well-being of the life form. Abnormalities of signal transduction pathways have been linked to the development of many serious disorders, such as Alzheimer’s disease and cancer. In an earlier work, Rattanakul et al. [1] studied a model of the signal transduction pathway which involves G protein coupled receptors (GPCR), based on earlier investigations and modeling efforts [2, 3]. The reference model considered in the work of Rattanakul et al. [1] consists of a system of two reaction diffusion equations which govern the interaction between an inhibitor protein (I) and the ligand-receptor complexes (R). In their model, only the ligand coupled receptors are allowed to diffuse over the extra-cellular membrane surface in two dimensions, while some transport of molecules across cell membrane (internalization) may take place to a certain extent. However, according to several studies [4-6] lateral diffusion coefficient of the inhibiting units of G protein in the cytosol has been observed to be significantly higher than that of the membrane receptor complexes. Lamb [5] reported that the diffusion coefficient of G protein is in the range of 1-2, while the lateral diffusion coefficients of ligand-receptor complexes are reported [7] to be in the range of 2 2 2 1.5 10 8 10 / m s μ − − × − × . Here, the model equations proposed in [3] are investigated in terms of experimental data we have collected. It is then modified to model the signal transduction pathway in which both reactants that take the major roles in the interactions, namely the inhibitor component and the ligand-receptor (LR) complexes, are allowed to diffuse over the two dimensional cell membrane surface and the plasmalemma. The fact that the diffusion rate of the inhibitor is significantly greater than that of the activator in our system permits the weakly nonlinear stability analysis of the model to be carried out to classify the dynamics and steady-state properties of model solutions. We show that Turing-type patterns will be formed robustly under different conditions imposed on the system parameters. RECENT ADVANCES IN APPLIED MATHEMATICS AND COMPUTATIONAL AND INFORMATION SCIENCES - Volume I ISBN: 978-960-474-071-0 ISSN: 1790-5117 39