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

Polarizable continuum models provide an effective electrostatic embedding model for fragment-based chemical shift prediction in challenging systems

Ab initio nuclear magnetic resonance chemical shift prediction provides an important tool for interpreting and assigning experimental spectra, but it becomes computationally prohibitive in large systems. The computational costs can be reduced considerably by fragmentation of the large system into a series of contributions from many smaller subsystems. However, the presence of charged functional groups and the need to partition the system across covalent bonds create complications in biomolecules that typically require the use of large fragments and careful descriptions of the electrostatic environment. The present work shows how a model that combines chemical shielding contributions from non-overlapping monomer and dimer fragments embedded in a polarizable continuum model provides a simple, easy-to-implement, and computationally inexpensive approach for predicting chemical shifts in complex systems. The model's performance proves rather insensitive to the continuum dielectric constant, making the selection of the optimal embedding dielectric less critical. The PCM-embedded fragment model is demonstrated to perform well across systems ranging from molecular crystals to proteins.

Protein structure refinement using a quantum mechanics-based chemical shielding predictor

We show that a QM-based predictor of a protein backbone and CB chemical shifts is of comparable accuracy to empirical chemical shift predictors after chemical shift-based structural refinement that removes small structural errors (errors in chemical shifts shown in red).

The accurate prediction of protein chemical shifts using a quantum mechanics (QM)-based method has been the subject of intense research for more than 20 years but so far empirical methods for chemical shift prediction have proven more accurate. In this paper we show that a QM-based predictor of a protein backbone and CB chemical shifts (ProCS15, PeerJ, 2016, 3, e1344) is of comparable accuracy to empirical chemical shift predictors after chemical shift-based structural refinement that removes small structural errors. We present a method by which quantum chemistry based predictions of isotropic chemical shielding values (ProCS15) can be used to refine protein structures using Markov Chain Monte Carlo (MCMC) simulations, relating the chemical shielding values to the experimental chemical shifts probabilistically. Two kinds of MCMC structural refinement simulations were performed using force field geometry optimized X-ray structures as starting points: simulated annealing of the starting structure and constant temperature MCMC simulation followed by simulated annealing of a representative ensemble structure. Annealing of the CHARMM structure changes the CA-RMSD by an average of 0.4 Å but lowers the chemical shift RMSD by 1.0 and 0.7 ppm for CA and N. Conformational averaging has a relatively small effect (0.1–0.2 ppm) on the overall agreement with carbon chemical shifts but lowers the error for nitrogen chemical shifts by 0.4 ppm. If an amino acid specific offset is included the ProCS15 predicted chemical shifts have RMSD values relative to experiments that are comparable to popular empirical chemical shift predictors. The annealed representative ensemble structures differ in CA-RMSD relative to the initial structures by an average of 2.0 Å, with >2.0 Å difference for six proteins. In four of the cases, the largest structural differences arise in structurally flexible regions of the protein as determined by NMR, and in the remaining two cases, the large structural change may be due to force field deficiencies. The overall accuracy of the empirical methods are slightly improved by annealing the CHARMM structure with ProCS15, which may suggest that the minor structural changes introduced by ProCS15-based annealing improves the accuracy of the protein structures. Having established that QM-based chemical shift prediction can deliver the same accuracy as empirical shift predictors we hope this can help increase the accuracy of related approaches such as QM/MM or linear scaling approaches or interpreting protein structural dynamics from QM-derived chemical shift.

Applications of large-scale density functional theory in biology

Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.

Converging nuclear magnetic shielding calculations with respect to basis and system size in protein systems

Ab initio chemical shielding calculations greatly facilitate the interpretation of nuclear magnetic resonance (NMR) chemical shifts in biological systems, but the large sizes of these systems requires approximations in the chemical models used to represent them. Achieving good convergence in the predicted chemical shieldings is necessary before one can unravel how other complex structural and dynamical factors affect the NMR measurements. Here, we investigate how to balance trade-offs between using a better basis set or a larger cluster model for predicting the chemical shieldings of the substrates in two representative examples of protein-substrate systems involving different domains in tryptophan synthase: the N-(4'-trifluoromethoxybenzoyl)-2-aminoethyl phosphate (F9) ligand which binds in the α active site, and the 2-aminophenol quinonoid intermediate formed in the β active site. We first demonstrate that a chemically intuitive three-layer, locally dense basis model that uses a large basis on the substrate, a medium triple-zeta basis to describe its hydrogen-bonding partners and/or surrounding van der Waals cavity, and a crude basis set for more distant atoms provides chemical shieldings in good agreement with much more expensive large basis calculations. Second, long-range quantum mechanical interactions are important, and one can accurately estimate them as a small-basis correction to larger-basis calculations on a smaller cluster. The combination of these approaches enables one to perform density functional theory NMR chemical shift calculations in protein systems that are well-converged with respect to both basis set and cluster size.

Accurate ab initio prediction of NMR chemical shifts of nucleic acids and nucleic acids/protein complexes

NMR chemical shift predictions based on empirical methods are nowadays indispensable tools during resonance assignment and 3D structure calculation of proteins. However, owing to the very limited statistical data basis, such methods are still in their infancy in the field of nucleic acids, especially when non-canonical structures and nucleic acid complexes are considered. Here, we present an ab initio approach for predicting proton chemical shifts of arbitrary nucleic acid structures based on state-of-the-art fragment-based quantum chemical calculations. We tested our prediction method on a diverse set of nucleic acid structures including double-stranded DNA, hairpins, DNA/protein complexes and chemically-modified DNA. Overall, our quantum chemical calculations yield highly/very accurate predictions with mean absolute deviations of 0.3–0.6 ppm and correlation coefficients (r²) usually above 0.9. This will allow for identifying misassignments and validating 3D structures. Furthermore, our calculations reveal that chemical shifts of protons involved in hydrogen bonding are predicted significantly less accurately. This is in part caused by insufficient inclusion of solvation effects. However, it also points toward shortcomings of current force fields used for structure determination of nucleic acids. Our quantum chemical calculations could therefore provide input for force field optimization.

Ab initio nonadiabatic dynamics of multichromophore complexes: a scalable graphical-processing-unit-accelerated exciton framework

Conspectus Although advances in computer hardware and algorithms tuned for novel computer architectures are leading to significant increases in the size and time scale for molecular simulations, it remains true that new methods and algorithms will be needed to address some of the problems in complex chemical systems, such as electrochemistry, excitation energy transport, proton transport, and condensed phase reactivity. Ideally, these new methods would exploit the strengths of emerging architectures. Fragment based approaches for electronic structure theory decompose the problem of solving the electronic Schrodinger equation into a series of much smaller problems. Because each of these smaller problems is largely independent, this strategy is particularly well-suited to parallel architectures. It appears that the most significant advances in computer architectures will be toward increased parallelism, and therefore fragment-based approaches are an ideal match to these trends. When the computational effort involved scales with the third (or higher) power of the molecular size, there is a large benefit to fragment-based approaches even on serial architectures. This is the case for many of the well-known methods for solving the electronic structure theory problem, especially when wave function-based approaches including electron correlation are considered. A major issue in fragment-based approaches is determining or improving their accuracy. Since the Achilles' heel of any such method lies in the approximations used to stitch the smaller problems back together (i.e., in the treatment of the cross-fragment interactions), it can often be important to ensure that the size of the smaller problems is "large enough." Thus, there are two frontiers that need to be extended in order to enable molecular simulations for large systems and long times: the strongly coupled problem of medium sized molecules (100-500 atoms) and the more weakly coupled problem of decomposing ("fragmenting") a molecular system and then stitching it back together. In this Account, we address both of these problems, the first by using graphical processing units (GPUs) and electronic structure algorithms tuned for these architectures and the second by using an exciton model as a framework in which to stitch together the solutions of the smaller problems. The multitiered parallel framework outlined here is aimed at nonadiabatic dynamics simulations on large supramolecular multichromophoric complexes in full atomistic detail. In this framework, the lowest tier of parallelism involves GPU-accelerated electronic structure theory calculations, for which we summarize recent progress in parallelizing the computation and use of electron repulsion integrals (ERIs), which are the major computational bottleneck in both density functional theory (DFT) and time-dependent density functional theory (TDDFT). The topmost tier of parallelism relies on a distributed memory framework, in which we build an exciton model that couples chromophoric units. Combining these multiple levels of parallelism allows access to ground and excited state dynamics for large multichromophoric assemblies. The parallel excitonic framework is in good agreement with much more computationally demanding TDDFT calculations of the full assembly.

QM/MM investigations of organic chemistry oriented questions

About 35 years after its first suggestion, QM/MM became the standard theoretical approach to investigate enzymatic structures and processes. The success is due to the ability of QM/MM to provide an accurate atomistic picture of enzymes and related processes. This picture can even be turned into a movie if nuclei-dynamics is taken into account to describe enzymatic processes. In the field of organic chemistry, QM/MM methods are used to a much lesser extent although almost all relevant processes happen in condensed matter or are influenced by complicated interactions between substrate and catalyst. There is less importance for theoretical organic chemistry since the influence of nonpolar solvents is rather weak and the effect of polar solvents can often be accurately described by continuum approaches. Catalytic processes (homogeneous and heterogeneous) can often be reduced to truncated model systems, which are so small that pure quantum-mechanical approaches can be employed. However, since QM/MM becomes more and more efficient due to the success in software and hardware developments, it is more and more used in theoretical organic chemistry to study effects which result from the molecular nature of the environment. It is shown by many examples discussed in this review that the influence can be tremendous, even for nonpolar reactions. The importance of environmental effects in theoretical spectroscopy was already known. Due to its benefits, QM/MM can be expected to experience ongoing growth for the next decade.In the present chapter we give an overview of QM/MM developments and their importance in theoretical organic chemistry, and review applications which give impressions of the possibilities and the importance of the relevant effects. Since there is already a bunch of excellent reviews dealing with QM/MM, we will discuss fundamental ingredients and developments of QM/MM very briefly with a focus on very recent progress. For the applications we follow a similar strategy.

Conformational Sampling by Ab Initio Molecular Dynamics Simulations Improves NMR Chemical Shift Predictions

Car-Parrinello molecular dynamics simulations were performed for N-methyl acetamide as a small test system for amide groups in protein backbones, and NMR chemical shifts were calculated based on the generated ensemble. If conformational sampling and explicit solvent molecules are taken into account, excellent agreement between the calculated and experimental chemical shifts is obtained. These results represent a landmark improvement over calculations based on classical molecular dynamics (MD) simulations especially for amide protons, which are predicted too high-field shifted based on the latter ensembles. We were able to show that the better results are caused by the solute-solvents interactions forming shorter hydrogen bonds as well as by the internal degrees of freedom of the solute. Inspired by these results, we propose our approach as a new tool for the validation of force fields due to its power of identifying the structural reasons for discrepancies between the experimental and calculated data.

Quantum chemical calculations of amide-15N chemical shift anisotropy tensors for a membrane-bound cytochrome-b5

There is considerable interest in determining amide-(15)N chemical shift anisotropy (CSA) tensors from biomolecules and understanding their variation for structural and dynamics studies using solution and solid-state NMR spectroscopy and also by quantum chemical calculations. Due to the difficulties associated with the measurement of CSA tensors from membrane proteins, NMR-based structural studies heavily relied on the CSA tensors determined from model systems, typically single crystals of model peptides. In the present study, the principal components of backbone amide-(15)N CSA tensors have been determined using density functional theory for a 16.7 kDa membrane-bound paramagnetic heme containing protein, cytochrome-b(5) (cytb(5)). All the calculations were performed by taking residues within 5 Å distance from the backbone amide-(15)N nucleus of interest. The calculated amide-(15)N CSA spans agree less well with our solution NMR data determined for an effective internuclear distance r(N-H) = 1.023 Å and a constant angle β = 18° that the least shielded component (δ(11)) makes with the N-H bond. The variation of amide-(15)N CSA span obtained using quantum chemical calculations is found to be smaller than that obtained from solution NMR measurements, whereas the trends of the variations are found to be in close agreement. We believe that the results reported in this study will be useful in studying the structure and dynamics of membrane proteins and heme-containing proteins, and also membrane-bound protein-protein complexes such as cytochromes-b5-P450.

Electronic Absorption Spectra from MM and ab initio QM/MM Molecular Dynamics: Environmental Effects on the Absorption Spectrum of Photoactive Yellow Protein

We describe a new interface of the GPU parallelized TeraChem electronic structure package and the Amber molecular dynamics package for quantum mechanical (QM) and mixed QM and molecular mechanical (MM) molecular dynamics simulations. This QM/MM interface is used for computation of the absorption spectra of the photoactive yellow protein (PYP) chromophore in vacuum, aqueous solution, and protein environments. The computed excitation energies of PYP require a very large QM region (hundreds of atoms) covalently bonded to the chromophore in order to achieve agreement with calculations that treat the entire protein quantum mechanically. We also show that 40 or more surrounding water molecules must be included in the QM region in order to obtain converged excitation energies of the solvated PYP chromophore. These results indicate that large QM regions (with hundreds of atoms) are a necessity in QM/MM calculations.

Toward the Quantum Chemical Calculation of NMR Chemical Shifts of Proteins. 3. Conformational Sampling and Explicit Solvents Model

Fragment-based quantum chemical calculations are able to accurately calculate NMR chemical shifts even for very large molecules like proteins. But even with systematic optimization of the level of theory and basis sets as well as the use of implicit solvents models, some nuclei like polar protons and nitrogens suffer from poor predictions. Two properties of the real system, strongly influencing the experimental chemical shifts but almost always neglected in the calculations, will be discussed here in great detail: (1) conformational averaging and (2) interactions with first-shell solvent molecules. Classical molecular dynamics simulations in explicit water were carried out for obtaining a representative ensemble including the arrangement of neighboring solvent molecules, which was then subjected to quantum chemical calculations. We could demonstrate with the small test system N-methyl acetamide (NMA) that the calculated chemical shifts show immense variations of up to 6 ppm and 50 ppm for protons and nitrogens, respectively, depending on the snapshot taken from a classical molecular dynamics simulation. Applying the same approach to the HA2 domain of the influenza virus glycoprotein hemagglutinin, a 32-amino-acid-long polypeptide, and comparing averaged values to the experiment, chemical shifts of nonpolar protons and carbon atoms in proteins were calculated with unprecedented accuracy. Additionally, the mean absolute error could be reduced by a factor of 2.43 for polar protons, and reasonable correlations were obtained for nitrogen and carbonyl carbon in contrast to all other studies published so far.

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

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. Proteins2011, 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 H(N) 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.

Toward the quantum chemical calculation of nuclear magnetic resonance chemical shifts of proteins

Despite the many protein structures solved successfully by nuclear magnetic resonance (NMR) spectroscopy, quality control of NMR structures is still by far not as well established and standardized as in crystallography. Therefore, there is still the need for new, independent, and unbiased evaluation tools to identify problematic parts and in the best case also to give guidelines that how to fix them. We present here, quantum chemical calculations of NMR chemical shifts for many proteins based on our fragment-based quantum chemical method: the adjustable density matrix assembler (ADMA). These results show that (13)C chemical shifts of reasonable accuracy can be obtained that can already provide a powerful measure for the structure validation. (1)H and even more (15)N chemical shifts deviate more strongly from experiment due to the insufficient treatment of solvent effects and conformational averaging.