Assembly of transient and stable signaling platforms in the plasma membrane of cells has been implicated in functions as varied as death and survival, polarity, differentiation, migration, cell-cell communication, virus entry, exocytosis, endocytosis. Naturally, the assembly of signaling microdomains requires the use of most complex molecular mechanisms capable of transducing intrinsic or extrinsic information into the actual making of the domain. Consensus exist that the lateral diffusion and heterogeneity of membrane proteins is absolutely necessary. However, more and more data indicate that the clustering of specific proteins to form a signaling platform involves as well the free lateral diffusion of stable assemblies of sphingoipids and cholesterol (rafts). Despite their fundamental relevance for cell function, the basic events responsible for the formation and dynamics of membrane microdomains is not well understood. Mathematical models are very useful tools for describing diffusion processes in an inhomogeneous medium with some anomalies as well as self-organized systems. Hence, it is my plan to use mathematical models to study the formation of protein-lipid clusters and how normal diffusion on an inhomogeneous membrane can be modified. The formation of protein clusters is a necessary condition for cell polarity and it could be related with the generation of pattern. I will propose a Turing-mechanism model to know if it is possible to generate stable spatial inhomogeneity on the cell surface. In order to formulate the equations it will be needed to make some assumptions about the biological system. Made assumptions will be refused or accepted according to the comparative analysis between theoretical results and experimental data. My background in physics make me feel suitable for undertaking the task of modelling these features. The validation experiments will be performed in the laboratory of Prof. Carlos Dotti where I have chosen to carry out this project.