Plasma membranes, or cytoplasmatic membranes, are the reaction fields of many biological reactions involved in diseases, and an active barrier for the transportation of information and materials between the inside and outside compartments of cells. Lipid bilayers are the fundamental structure of cell membranes. Examining the functional behavior of lipids and proteins and their ensemble by using artificial lipid bilayers integrated in biosensors is important in order to determine the physical and chemical processes involved in cell membrane reactions, that are relevant in a wide range of biomedical applications. By using supported lipid bilayers (SLBs) on graphene-based substrates, it is possible to develop novel biosensors able to obtain molecular information from membrane proteins embedded in lipid bilayers: the graphene acts as the transducer of the electrical signals and the phospholipidic bilayers with embedded molecular proteins form the receptor layer. The main objectives of this thesis are the design and optimization of the interactions between graphene and lipid bilayers, through the analysis of the fabrication process of graphene, its surface treatments and how these affects the formation of supported lipid membranes. These are essential steps aiming at manufacturing a novel properly designed biosensing platform with integrated membrane proteins. Nanomaterials can play a very significant role in the development of the next generation of biosensors, since they can help to address some of the key issues in the development of biosensors. Graphene is a carbon-based nanomaterial that has recently attracted most interest due to its unique electronic properties, arising from its crystal structure, which result in a extremely low noise level and an increased signal-to-noise ratio. The fabrication of biosensors based on SLBs on graphene requires the study and optimization of the building blocks of the sensor and of the interface between them. The formation of SLBs is strongly influenced by the physical and chemical properties of the underlying substrates. Then, in order to induce the formation of lipid bilayers possessing a sufficient stability for practical biosensing applications, the wetting properties of the supporting layer should be investigated. Since graphene is a hydrophobic material, the introduction of defects on the surface both by heat treatments or functionalization have been investigated.