The operation of the proton wire in Green Fluorescent Protein has been simulated by quantum dynamics and considering the coupling to the protein environment by means of a bath of harmonic oscillators. The simulation consists of 36 explicit and fully quantum degrees of freedom: 6 degrees of freedom represent the configuration of the proton wire, which are coupled to 30 bath coordinates. Regimes of weak and strong coupling have been studied. It is found that presence of the bath induces a fast energy transfer from the proton wire to the bath, with characteristic times under 400 fs. This internal vibrational redistribution happens at the expense of the potential energy content of the proton wire, deformed through the interaction to the bath from its uncoupled state. Strong coupling induces a slowing-down of the operation of the wire because it hinders to some extent the approaching of donor and acceptor atoms to distances in which proton transfer can occur. Internal vibrational energy redistribution affects the dynamics, but from our simulations we conclude that it cannot be the only cause responsible for the experimentally reported fluorescence rise times.