Chemical Shifts in Proteins: A Shielding Trajectory Analysis of the Fluorine Nuclear Magnetic Resonance Spectrum of the Escherichia coli Galactose Binding Protein Using a Multipole Shielding Polarizability-Local Reaction Field-Molecular Dynamics Approach

We report the first successful calculation of the fluorine nuclear magnetic resonance spectrum of a protein, the galactose binding protein from Escherichia coli, labeled with [5-¹⁹F]tryptophan. Our results indicate that the experimental ¹⁹F chemical shifts are dominated by weak, or long-range, electrical interactions, which can be calculated by using the responses of the shielding tensor elements to the uniform field components (∂σ_αβ/∂E_x) and the nonuniform or gradient terms (∂σ_αβ/∂V_ii), together with the average values of the fields (E_x) and field gradients (V_ii) obtained from molecular dynamics (MD) trajectories. A series of “shielding trajectories”, Δσ(E_x, V_xx, V_yy, V_zz)f(τ), are obtained, and the mean values, [formula omitted], correlate well with the actual shift pattern and overall shift range observed experimentally (Luck, L. A.; Falke, J. J. Biochemistry 1991, 30, 4248–4256). The computed ¹⁹F NMR shielding of the pentapeptide Gly-Gly-[5-F]Trp-Gly-Gly in H₂O is close to, but somewhat more shielded than, that of the denatured protein. Almost all computed ¹⁹F chemical shifts are upfield of the field-free value, in accord with the results of ab initio calculations. The chemical shifts calculated are sensitive to the charge chosen for F in the LRF-MD trajectories, and best agreement with experiment is obtained with q^F = −0.25. Calculations on the Salmonella typhimurium galactose binding protein yield extremely similar chemical shift spectra, consistent with the ~7% difference in amino acid composition. The uniform field components make the largest contributions to the shielding patterns observed, presumably because the gradient terms fall off more rapidly with distance. The exposed residue, Trp 284, has the largest amplitude of fluctuation associated with its shielding trajectory, possibly due to the rapid and random movement of neighboring water molecules. Trp 284 is highly shielded due to interaction with water, although other buried residues (e.g. Trp 133) may also be highly shielded, due to electric field effects within the protein. Our results imply that van der Waals interactions do not play a major role for fluorine shielding nonequivalence in proteins, since the experimental results can be reproduced by using solely the computed field and field gradient terms. The ability to predict protein NMR shielding patterns and ranges offers promise for structural analysis and also provides a way of validating different methods of computing protein electrostatics. In this respect, it is instructive to note that the charge fields from ionized surface groups are found to be largely shielded by the dielectric response of the solvent and the protein.