The microtubule-associated protein (MAP) tau plays akey role inthe regulation of microtubule assembly and spatial organization. Tauhyperphosphorylation affects its binding on the tubulin surface andhas been shown to be involved in several pathologies such as Alzheimer'sdisease. As the tau binding site on the microtubule lays close tothe disordered and highly flexible tubulin C-terminal tails (CTTs),these are likely to impact the tau-tubulin interaction. Since thedisordered tubulin CTTs are missing from the available experimentalstructures, we used homology modeling to build two complete modelsof tubulin heterotrimers with different isotypes for the & beta;-tubulinsubunit (& beta;I/& alpha;I/& beta;I and & beta;III/& alpha;I/& beta;III).We then performed long timescale classical Molecular Dynamics simulationsfor the tau-R2/tubulin assembly (in systems with and without CTTs)and analyzed the resulting trajectories to obtain a detailed viewof the protein interface in the complex and the impact of the CTTson the stability of this assembly. Additional analyses of the CTTmobility in the presence, or in the absence, of tau also highlighthow tau might modulate the CTT activity as hooks that are involvedin the recruitment of several MAPs. In particular, we observe a wrapping phenomenon, where the & beta;-tubulin CTTs forma loop over tau-R2, thus stabilizing its interaction with the tubulinsurface and simultaneously reducing the CTT availability for interactionswith other MAPs.