The binding of small molecules (e.g., natural ligands, metabolites, and drugs) to proteins governs most biochemical pathways and physiological processes. Here, we use molecular dynamics to investigate the unbinding of dimethyl sulfoxide (DMSO) from two distinct states of a small rotamase enzyme, the FK506-binding protein (FKBP). These states correspond to the FKBP protein relaxed with and without DMSO in the active site. Since the time scale of ligand unbinding (2-20 ns) is faster than protein relaxation (100 ns), a novel methodology is introduced to relax the protein without having to introduce an artificial constraint. The simulation results show that the unbinding time is an order of magnitude longer for dissociation from the DMSO-bound state (holo-relaxed). That is, the actual rate of unbinding depends on the state of the protein, with the protein having a long-lived memory. The rate thus depends on the concentration of the ligand as the apo and holo states reflect low and high concentrations of DMSO, respectively. Moreover, there are multiple binding modes in the apo-relaxed state, while a single binding mode dominates the holo-relaxed state in which DMSO acts as hydrogen bond acceptor from the backbone NH of Ile56, as in the crystal structure of the DMSO/FKBP complex. The solvent relaxes very fast (∼1 ns) close to the NH of Ile56 and with the same time scale of the protein far away from the active site. These results have implications for high-throughput docking, which makes use of a rigid structure of the protein target.