Quantum mechanics (QM) calculations are applied to examine 1H, 13C, 15N, and 31P chemical shifts of two phosphorylation sites in an intrinsically disordered protein region. The QM calculations employ a combination of (1) structural ensembles generated by molecular dynamics, (2) a fragmentation technique based on the adjustable density matrix assembler, and (3) density functional methods. The combined computational approach is used to obtain chemical shifts (i) in the S19 and S40 residues of the nonphosphorylated and (ii) in the pS19 and pS40 residues of the doubly phosphorylated human tyrosine hydroxylase 1 as the system of interest. We study the effects of conformational averaging and explicit solvent sampling as well as the effects of phosphorylation on the computed chemical shifts. Good to great quantitative agreement with the experiment is achieved for all nuclei, provided that the systematic error cancellation is optimized by the choice of a suitable NMR standard. The effect of the standard reference on the computed 15N and 31P chemical shifts is demonstrated by employing three different referencing methods. Error bars associated with the statistical averaging of the computed 31P chemical shifts are larger than the difference between the 31P chemical shift of pS19 and pS40. The sequence trend of 31P shifts therefore could not be reliably reproduced. On the contrary, the calculations correctly predict the change of the 13C chemical shift for CB induced by the phosphorylation of the serine residues. The present work demonstrates that QM calculations coupled with molecular dynamics simulations and fragmentation techniques can be used as an alternative to empirical prediction tools in the structure characterization of intrinsically disordered proteins.

Faculty of Pharmacy in Hradec Králové Charles University Akademika Heyrovského 1203 500 05 Hradec Králové Czech Republic

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