We studied monosodium glutamate (MSG) in aqueous solution using molecular dynamics simulations and compared the results with recent neutron diffraction with isotope contrast variation/empirical potential structure refinement (EPSR) data obtained on the same system (McLain et al. J. Phys. Chem. B 2006, 110, 21251-21258). We used classical simulations with empirical force fields to study both dilute and more concentrated (1.40 M) solutions. To gauge the importance of polarization and other quantum effects, we carried out first-principles molecular dynamics in the dilute case. The glutamate structure was well reproduced by the OPLS/AA and SPC/E force fields: we found a reasonable agreement between the simulations and the experimental data with respect to the hydration numbers for glutamate carboxylate and amine groups and the observation of significant sodium ion-carboxylate binding. However, none of our simulations could reproduce the dramatic reduction in water-water correlations observed experimentally. Simulations showed a large amount of carboxylate-amine binding, as well as segregation of water and glutamate, at moderately high concentrations of MSG. We attribute this result to the breakdown of currently available classical force fields when applied to concentrated ionic solutions, especially large polyatomic ions. We also did not observe the sharing of a water proton by two carboxylate oxygens simultaneously, and we argue against this interpretation of EPSR data on a variety of physical grounds. We offer several suggestions to resolve these discrepancies between simulation and the current interpretation of neutron diffraction data, which should advance the understanding of aqueous ionic solutions in general.