Automated Fragmentation Quantum Mechanical Calculation of 15N and 13C Chemical Shifts in a Membrane Protein

Abstract

In this work, we developed an accurate and cost-effective automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) method to calculate the chemical shifts of ¹⁵N and ¹³C of membrane proteins. The convergence of the AF-QM/MM method was tested using Krokinobacter eikastus rhodopsin 2 as a test case. When the distance threshold of the QM region is equal to or larger than 4.0 Å, the results of the AF-QM/MM calculations are close to convergence. In addition, the effects of selected density functionals, basis sets, and local chemical environment of target atoms on the chemical shift calculations were systematically investigated. Our results demonstrate that the predicted chemical shifts are more accurate when important environmental factors including cross-protomer interactions, lipid molecules, and solvent molecules are taken into consideration, especially for the ¹⁵N chemical shift prediction. Furthermore, with the presence of sodium ions in the environment, the chemical shift of residues, retinal, and retinal Schiff base are affected, which is consistent with the results of the solid-state nuclear magnetic resonance (NMR) experiment. Upon comparing the performance of various density functionals (namely, B3LYP, B3PW91, M06-2X, M06-L, mPW1PW91, OB95, and OPBE), the results show that mPW1PW91 is a suitable functional for the ¹⁵N and ¹³C chemical shift prediction of the membrane proteins. Meanwhile, we find that the improved accuracy of the ¹³C_β chemical shift calculations can be achieved by the employment of the triple-ζ basis set. However, the employment of the triple-ζ basis set does not improve the accuracy of the ¹⁵N and ¹³C_α chemical shift calculations nor does the addition of a diffuse function improve the overall prediction accuracy of the chemical shifts. Our study also underscores that the AF-QM/MM method has significant advantages in predicting the chemical shifts of key ligands and nonstandard residues in membrane proteins than most widely used empirical models; therefore, it could be an accurate computational tool for chemical shift calculations on various types of biological systems.