Toward the Quantum Chemical Calculation of NMR Chemical Shifts of Proteins. 2. Level of Theory, Basis Set, and Solvents Model Dependence

Abstract

It has been demonstrated that the fragmentation scheme of our adjustable density matrix assembler (ADMA) approach for the quantum chemical calculations of very large systems is well-suited to calculate NMR chemical shifts of proteins [Frank et al. Proteins 2011, 79, 2189–2202]. The systematic investigation performed here on the influences of the level of theory, basis set size, inclusion or exclusion of an implicit solvent model, and the use of partial charges to describe additional parts of the macromolecule on the accuracy of NMR chemical shifts demonstrates that using a valence triple-ζ basis set leads to large improvement compared to the results given in the previous publication. Additionally, moving from the B3LYP to the mPW1PW91 density functional and including partial charges and implicit solvents gave the best results with mean absolute errors of 0.44 ppm for hydrogen atoms excluding HN atoms and between 1.53 and 3.44 ppm for carbon atoms depending on the size and also on the accuracy of the protein structure. Polar hydrogen and nitrogen atoms are more difficult to predict. For the first, explicit hydrogen bonds to the solvents need to be included and, for the latter, going beyond DFT to post-Hartree–Fock methods like MP2 is probably required. Even if empirical methods like SHIFTX+ show similar performance, our calculations give for the first time very reliable chemical shifts that can also be used for complexes of proteins with small-molecule ligands or DNA/RNA. Therefore, taking advantage of its ab initio nature, our approach opens new fields of application that would otherwise be largely inaccessible due to insufficient availability of data for empirical parametrization.

Assessing and refining molecular dynamics simulations of proteins with nuclear magnetic resonance data

“…In principle, Q can be calculated from r using quantum-chemical methods (Oldfield 2002;Bühl and van Mourik 2011), but the accuracy that can currently be reached is rather low because a number of approximations must be made due to the expense of the calculations (Mulder and Filatov 2010;Frank et al 2012). This also renders such calculations too expensive to carry out "on the fly" during an MD simulation.…”

“…There is no simple analytical relationship linking chemical shifts to protein structure. Methods for calculating chemical shifts using quantum mechanics are improving, but remain too slow to be applicable during simulations (Mulder and Filatov 2010;Frank et al 2012). A number of fast empirical methods for calculating chemical shifts approximately have been developed (Xu and Case 2001;Neal et al 2003;Meiler 2003;Shen and Bax 2007;Kohlhoff et al 2009;Shen and Bax 2010;Han et al 2011;Nielsen et al 2012), although even these state-ofthe-art programs often result in errors much larger than the deviation between back-calculated and experimental chemical shifts (Kjaergaard and Poulsen 2012), and so should be used with caution.…”

Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

“…[18][19][20][21] The linearscaling QM algorithms [22][23][24][25] have primarily been developed for energy and gradient evaluations; the efficiency of Hessian computations has also been improved. [26][27][28] Some fragment based approaches [29][30][31][32][33][34][35][36][37][38][39][40] feature analytic second derivatives. [41][42][43][44][45][46] The fragment molecular orbital (FMO) method [47][48][49][50][51] is a fragment-based approach.…”

GIAO/DFT studies on 1,2,4‐triazole‐5‐thiones and their propargyl derivatives

“…[14] Quantum chemical and density functional theory (DFT) calculation packages available now are capable of providing very good estimation of NMR shielding parameters. [15][16][17] The observed NMR chemical shifts are statistical averages of various dynamic events such as conformational, tautomeric or rotameric equilibria present in the system. On the contrary, the theoretical values of chemical shifts can be computed for molecules in every possible conformation, tautomeric or rotameric forms.…”