Order parameters as well as longitudinal and transverse relaxation rates are calculated for the backbone 15N and 13C alpha nuclei of the basic pancreatic trypsin inhibitor (BPTI) from a 1000 ps molecular dynamics trajectory in explicit water at 277 K using the "model free" approach of Lipari and Szabo. New NMR relaxation data at 277 K are presented, and a comparison is made between NMR relaxation measurements and molecular dynamics relaxation data. It is found that the relaxation processes determining the longitudinal (T1) relaxation rates are inadequately sampled even during this length of simulation. In effect, the calculated relaxation rates are determined almost solely by the order parameters and the overall rotational correlation time of the protein, which appears to be in clear contrast to experimental relaxation rates.