Mathematical Modeling of K-Ras Nanocluster Formation on the Plasma Membrane

K-Ras functions as a critical node in the mitogen-activated protein kinase (MARK) pathway that regulates key cellular functions including proliferation, differentiation, and apoptosis. Following growth factor receptor activation K-Ras.GTP forms nanoclusters on the plasma membrane through interaction with the scaffold protein galectin-3. The generation of nanoclusters is essential for high fidelity signal transduction via the MARK pathway. To explore the mechanisms underlying K-Ras.GTP nanocluster formation, we developed a mathematical model of K-Ras-galectin-3 interactions. We designed a computational method to calculate protein collision rates based on experimentally determined protein diffusion rates and diffusion mechanisms and used a genetic algorithm to search the values of key model parameters. The optimal estimated model parameters were validated using experimental data. The resulting model accurately replicates critical features of K-Ras nanoclustering, including a fixed ratio of clustered K-Ras.GTP to monomeric K-Ras.GTP that is independent of the concentration of K-Ras.GTP. The model reproduces experimental results showing that the cytosolic level of galectin-3 determines the magnitude of the K-Ras.GTP clustered fraction and illustrates that nanoclustering is regulated by key nonequilibrium processes. Our kinetic model identifies a potential biophysical mechanism for K-Ras nanoclustering and suggests general principles that may be relevant for other plasma-membrane-localized proteins.