and infiltration in uncontaminated brain regions. We propose a novel multidisciplinary approach, based on in vivo experiments in Drosophila and mathematical models, for the proteins dynamics at the front of Glioblastoma, with a predictive value of the tumor progression.feedback with an evolutionary mathematical model that predicts behaviors and interactions of these biological agents.GB in Drosophila The most frequent genetic lesions in GB include the constitutive activation of phosphatidylinositol 3-kinase (PI3K) and Epidermal Growth Factor Receptor (EGFR) pathways, which drive cellular proliferation and tumor malignancy (10). Drosophila melanogaster has emerged as one of the most reliable animal models for GB; it is based on equivalent genetic mutations in EGFR and PI3K pathways found in patients (11). Glial cells respond to this oncogenic transformation and reproduce all main features of the disease, including glial expansion and invasion, but in a shorter period of time. This Drosophila model has been used for drug and genetic screenings and the results have been validated in human GB cells (REFs) (12)(13)(14).Agents involved in the battlefield GB growth and migration are driven by specific signaling pathways as well as interactions between the tumor and its extracellular microenvironment. In our study, we include the cell membrane protrusions (TMs) as driving factors of tumor progression, as well as cell response to signaling gradients and the interplay with the Extra Cellular Matrix (ECM). A schematic diagram of the described dynamics is given in Figure 1.The dynamics of tumor cell membrane, including cell protrusions, is fundamental in several processes, among others cell movements, cell transport, and exposure to molecular interactions with substrates during GB progression. Generally, cell protrusions are highly dynamic extensions of the plasma membrane that are involved in cell migration and invasion through the ECM.Different types of protrusions have been identified to contribute to cell spreading, depending on specific contexts, cell types, and microenvironment. In particular, filopodia are thin, finger-like and highly dynamic membrane protrusions that have a significant role in mediating intercellular communication and in modulating cell adhesion. They appear to be required for haptotaxis and chemotaxis (15), i.e., for the cell response to the gradient of insoluble (haptotaxis) and soluble Proteases are enzymes that catalyze the breakdown of proteins into smaller polypeptides or single amino acids. Some type of proteases are localized around the cell membrane and play a key role in promoting tumor invasion and tissue remodeling. They induce proteolysis of ECM components (29) and maintain a microenvironment that facilitates tumor cell survival. Protease profiling studies have indicated that the expression of serine proteases, cysteine proteases and matrix metalloproteases (MMPs), the most prominent family of proteinases associated with tumorigenesis, increase in high-grade astrocytoma compared with nor...