Simulation of oriented NMR spectra: Combining molecular dynamics and chemical shift tensor calculations

Solid state NMR is widely used to study the orientation and other structural features of proteins and peptides in lipid bilayers. Using data obtained by PISEMA (Polarization Inversion Spin Exchange at Magic Angle) experiments, periodic spectral patterns arise from well-aligned α-helical molecules. Significant problems in the interpretation of PISEMA spectra may arise for systems that do not form perfectly defined secondary structures, like α-helices, or the signal pattern is disturbed by molecular motion. Here, we present a new method that combines molecular dynamics simulation with tensorial orientational constraints (MDOC) and chemical shift tensor calculations for the simulation and interpretation of PISEMA-like spectra. The calculations include the spectra arising from non α-helical molecules and molecules with non-uniform intrinsic mobility. In a first step, dipolar or quadrupolar interaction tensors drive molecular rotations and reorientations to obtain the proper mean values as observed in corresponding NMR experiments. In a second step, the coordinate snapshots of the MDOC simulations are geometry optimized with the isotropic 15 N chemical shifts as constraints using Bond Polarization Theory (BPT) to provide reliable 15 N CS tensor data. The averaged dipolar 1 H-15 N couplings and the δzz tensor components can then be combined to simulate PISEMA patterns. We apply this method to the ß-helical peptide gramicidin A (gA) and demonstrate that this method enables the assignment of most PISEMA resonances. In addition, MDOC simulations provide local order parameters for the calculated sites. These local order parameters reveal large differences in backbone mobility between L- and D-amino acids of gA.

Energetics and J-coupling constants for Ala, Gly, and Val peptides demonstrated using ABEEM polarizable force field in vacuo and an aqueous solution

The development of an atom-bond electronegativity equalisation method at the σπ-level (ABEEM) polarisable force field (PFF) for peptides is presented. ABEEM PFF utilises a fluctuating charge model to explicitly describe...

Investigation of backbone dynamics and local geometry of bio-molecules using calculated NMR chemical shifts and anisotropies

Prerequisite for chemical shift (CS) and CS tensor calculations are highly refined structures defining the molecular surroundings of the nuclei under study. Here, we present geometry optimizations with ¹³C and ¹⁵N CS constraints for large bio-molecules like peptides and proteins. The method discussed here provides both, refined structures and chemical shift tensors. Furthermore, since the experimental resonances of aligned systems are related to CS tensors, they strongly depend on the orientation and motion of molecules, their fragments, functional groups and moieties. For efficient CS calculations we apply a semi-empirical approach-the bond polarization theory (BPT). The BPT relies on linear bond polarization parameters and we present a new set of parameters based on ab initio second-order Møller-Plesset perturbation theory calculations. The new parametrization extends the applicability of the BPT approach to a wide range of organic molecules and bio-polymers. Here, the method has been applied to the protein ubiquitin and the membrane-active peptide gramicidin A (dimer) in oriented bilayers. The calculated ¹³C and ¹⁵N CS values of best-refined structures published until now gave a large scatter with respect to the experiment. It will be shown that BPT CS optimizations can reduce these errors to values near the experimental uncertainty. In combination with molecular dynamics with orientational constraints it is possible to study motional dynamics and BPT calculations can provide residual chemical shift anisotropies.

Configuration determination by residual dipolar couplings: accessing the full conformational space by molecular dynamics with tensorial constraints

Residual dipolar couplings (RDCs) and other residual anisotropic NMR parameters provide valuable structural information of high quality and quantity, bringing detailed structural models of flexible molecules in solution in reach. The corresponding data interpretation so far is directly or indirectly based on the concept of a molecular alignment tensor, which, however, is ill-defined for flexible molecules. The concept is typically applied to a single or a small set of lowest energy structures, ignoring the effect of vibrational averaging. Here, we introduce an entirely different approach based on time averaged molecular dynamics with dipolar couplings as tensorial orientational restraints that can be used to solve structural problems in molecules of any size without the need of introducing an explicit molecular alignment tensor into the computation. RDC restraints are represented by their full 3D interaction tensor in the laboratory frame, for which pseudo forces are calculated using a secular dipolar Hamiltonian as the target. The resulting rotational averaging of each individual tensorial restraint leads to structural ensembles that best fulfil the experimental data. Using one-bond RDCs, the approach has been implemented in the force field procedures of the program COSMOS and extensively tested. A concise theoretical introduction, including the special treatment of force fields for stable and fast MD simulations, as well as applications regarding configurational analyses of small to medium-sized organic molecules with different degrees of flexibility, is given. The observed results are discussed in detail.

Insight into the chromophore of rhodopsin and its Meta-II photointermediate by 19F solid-state NMR and chemical shift tensor calculations

19F nuclei are useful labels in solid-state NMR studies, since their chemical shift and tensor elements are very sensitive to the electrostatic and space-filling properties of their local environment. In this study we have exploited a fluorine substituent, strategically placed at the C-12-position of 11-cis retinal, the chromophore of visual rhodopsins. This label was used to explore the local environment of the chromophore in the ground state of bovine rhodopsin and its active photo-intermediate Meta II. In addition, the chemical shift and tensor elements of the chromophore in the free state in a membrane environment and the bound state in the protein were determined. Upon binding of the chromophore into rhodopsin and Meta II, the isotropic chemical shift changes in the opposite direction by +9.7 and -8.4 ppm, respectively. An unusually large isotropic shift difference of 35.9 ppm was observed between rhodopsin and Meta II. This partly originates in the light-triggered 11-cis to all-trans isomerization of the chromophore. The other part reflects the local conformational rearrangements in the chromophore and the binding pocket. These NMR data were correlated with the available X-ray structures of rhodopsin and Meta II using bond polarization theory. For this purpose hydrogen atoms have to be inserted and hereto a family of structures were derived that best correlated with the well-established 13C chemical shifts. Based upon these structures, a 12-F derivative was obtained that best corresponded with the experimentally determined 19F chemical shifts and tensor elements. The combined data indicate strong changes in the local environment of the C-12 position and a substantially different interaction pattern with the protein in Meta II as compared to rhodopsin.

1H line width dependence on MAS speed in solid state NMR - Comparison of experiment and simulation

Recent developments in magic angle spinning (MAS) technology permit spinning frequencies of ≥100 kHz. We examine the effect of such fast MAS rates upon nuclear magnetic resonance proton line widths in the multi-spin system of β-Asp-Ala crystal. We perform powder pattern simulations employing Fokker-Plank approach with periodic boundary conditions and ¹H-chemical shift tensors calculated using the bond polarization theory. The theoretical predictions mirror well the experimental results. Both approaches demonstrate that homogeneous broadening has a linear-quadratic dependency on the inverse of the MAS spinning frequency and that, at the faster end of the spinning frequencies, the residual spectral line broadening becomes dominated by chemical shift distributions and susceptibility effects even for crystalline systems.

Fast Atomic Charge Calculation for Implementation into a Polarizable Force Field and Application to an Ion Channel Protein

Polarization of atoms plays a substantial role in molecular interactions. Class I and II force fields mostly calculate with fixed atomic charges which can cause inadequate descriptions for highly charged molecules, for example, ion channels or metalloproteins. Changes in charge distributions can be included into molecular mechanics calculations by various methods. Here, we present a very fast computational quantum mechanical method, the Bond Polarization Theory (BPT). Atomic charges are obtained via a charge calculation method that depend on the 3D structure of the system in a similar way as atomic charges ofab initiocalculations. Different methods of population analysis and charge calculation methods and their dependence on the basis set were investigated. A refined parameterization yielded excellent correlation ofR=0.9967. The method was implemented in the force field COSMOS-NMR and applied to the histidine-tryptophan-complex of the transmembrane domain of the M2 protein channel of influenza A virus. Our calculations show that moderate changes of side chain torsion angleχ1and small variations ofχ2of Trp-41 are necessary to switch from the inactivated into the activated state; and a rough two-side jump model of His-37 is supported for proton gating in accordance with a flipping mechanism.

An overview of tools for the validation of protein NMR structures

Biomolecular structures at atomic resolution present a valuable resource for the understanding of biology. NMR spectroscopy accounts for 11% of all structures in the PDB repository. In response to serious problems with the accuracy of some of the NMR-derived structures and in order to facilitate proper analysis of the experimental models, a number of program suites are available. We discuss nine of these tools in this review: PROCHECK-NMR, PSVS, GLM-RMSD, CING, Molprobity, Vivaldi, ResProx, NMR constraints analyzer and QMEAN. We evaluate these programs for their ability to assess the structural quality, restraints and their violations, chemical shifts, peaks and the handling of multi-model NMR ensembles. We document both the input required by the programs and output they generate. To discuss their relative merits we have applied the tools to two representative examples from the PDB: a small, globular monomeric protein (Staphylococcal nuclease from S. aureus, PDB entry 2kq3) and a small, symmetric homodimeric protein (a region of human myosin-X, PDB entry 2lw9).

Prediction of RNA 1H and 13C chemical shifts: a structure based approach

The use of NMR-derived chemical shifts in protein structure determination and prediction has received much attention, and, as such, many methods have been developed to predict protein chemical shifts from three-dimensional (3D) coordinates. In contrast, little attention has been paid to predicting chemical shifts from RNA coordinates. Using the random forest machine learning approach, we developed RAMSEY, which is capable of predicting both (1)H and protonated (13)C chemical shifts from RNA coordinates. In this report, we introduce RAMSEY, assess its accuracy, and demonstrate the sensitivity of RAMSEY-predicted chemical shifts to RNA 3D structure.

Structural characterization of a peptoid with lysine-like side chains and biological activity using NMR and computational methods

N-substituted glycine oligomers or peptoids with charged side chains are a novel class of cell penetrating peptide mimetics and have been shown to serve as drug delivery agents. Here, we investigated by NMR spectroscopy and quantum chemical calculations whether a Rhodamine B labelled peptoid [RhoB(Spiro)-Ahx]-[But](6A)NH(2) with lysine-like side chains adopts structural motifs similar to regular peptides. Due to a low chemical shift dispersion, high resolution structure determination with conventional NMR-derived distance restraints and J-couplings was not possible. Instead, a combined assignment and structure refinement strategy using the QM/MM force field COSMOS-NMR was developed to interpret the highly ambiguous chemical shift and distance constraints and obtain a medium resolution three-dimensional structural model. This allowed us to select for the all cis-amide conformation of the peptide with a pseudo-helical arrangement of extended side chains as a faithful representative structure of [RhoB(Spiro)-Ahx]-[But](6A)NH(2). We tested the biological activity of the peptoid by live-cell imaging, which showed that the cellular uptake of the peptoid was comparable to conventional cell-penetrating peptides.