Convergence of calculated nuclear magnetic resonance chemical shifts in a protein with respect to quantum mechanical model size

An important aspect of mixed quantum mechanics and molecular mechanics (QM/MM) calculation of nuclear magnetic resonance chemical shifts in proteins is the choice of a sufficiently large QM region. This region must be large enough that the electronic structure of the chromophore in the QM/MM model is essentially the same as in the complete system. In this work, we calculate the chemical shifts for a single glycine residue in a 46 amino acid, fungal dockerin domain using QM/MM partitions of increasing size. The QM region is defined as all amino acids within a given radius of the gly39 amino acid and the MM region is defined as the remaining atoms in the protein. The atoms in the MM region are represented as point charges. We find that convergence of the chemical shifts is very slow with respect to system size due to significant charge transfer within the protein. All amino acids lying within 6 Å of gly39 must be included in the QM region to obtain chemical shifts that are reasonably close to the limiting, full protein values. We also show that the chromophore Mulliken atomic charges display the same behaviour as a function of QM region size as do the chemical shifts and thus may serve as a generally useful indicator of convergence in the calculated chemical shifts.