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.

Structures Controlled by Entropy: The Flexibility of Strychnine as Example

To study the flexibility of strychnine, we performed molecular dynamics simulations with orientational tensorial constraints (MDOC). Tensorial constraints are derived from nuclear magnetic resonance (NMR) interaction tensors, for instance, from residual dipolar couplings (RDCs). Used as orientational constraints, they rotate the whole molecule and molecular parts with low rotational barriers. Since the NMR parameters are measured at ambient temperatures, orientational constraints generate conformers that populate the whole landscape of Gibbs free energy. In MDOC, structures are populated that are not only controlled by energy but by the entropy term TΔS of the Gibbs free energy. In the case of strychnine, it is shown that ring conformers are populated, which has not been discussed in former investigations. These conformer populations are not only in accordance with RDCs but fulfill nuclear Overhauser effect (NOE)-derived distance constraints and ³J_HH couplings as well.

Conformational Investigations in Flexible Molecules Using Orientational NMR Constraints in Combination with 3J-Couplings and NOE Distances

The downscaling of NMR tensorial interactions, such as dipolar couplings, from tens of kilohertz to a few hertz in low-order media is the result of dynamics spanning several orders of magnitudes, including vibrational modes (~ns-fs), whole-molecule reorientation (~ns) and higher barrier internal conformational exchange (<ms). In this work, we propose to employ these dynamically averaged interactions to drive an “alignment-tensor-free” molecular dynamic simulation with orientation constraints (MDOC) in order to efficiently access the conformational space sampled by flexible small molecules such as natural products. Key to this approach is the application of tensorial pseudo-force restraints which simultaneously guide the overall reorientation and conformational fluctuations based on defined memory function over the running trajectory. With the molecular mechanics force-field, which includes bond polarization theory (BPT), and complemented with other available NMR parameters such as NOEs and scalar J-couplings, MDOC efficiently arrives at dynamic ensembles that reproduce the entire NMR dataset with exquisite accuracy and theoretically reveal the systems conformational space and equilibrium. The method as well as its potential towards configurational elucidation is presented on diastereomeric pairs of flexible molecules: a small 1,4-diketone 1 with a single rotatable bond as well as a 24-ring macrolide related to the natural product mandelalide A 2.

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.

Molecular dynamics simulations on PGLa using NMR orientational constraints

NMR data obtained by solid state NMR from anisotropic samples are used as orientational constraints in molecular dynamics simulations for determining the structure and dynamics of the PGLa peptide within a membrane environment. For the simulation the recently developed molecular dynamics with orientational constraints technique (MDOC) is used. This method introduces orientation dependent pseudo-forces into the COSMOS-NMR force field. Acting during a molecular dynamics simulation these forces drive molecular rotations, re-orientations and folding in such a way that the motional time-averages of the tensorial NMR properties are consistent with the experimentally measured NMR parameters. This MDOC strategy does not depend on the initial choice of atomic coordinates, and is in principle suitable for any flexible and mobile kind of molecule; and it is of course possible to account for flexible parts of peptides or their side-chains. MDOC has been applied to the antimicrobial peptide PGLa and a related dimer model. With these simulations it was possible to reproduce most NMR parameters within the experimental error bounds. The alignment, conformation and order parameters of the membrane-bound molecule and its dimer were directly derived with MDOC from the NMR data. Furthermore, this new approach yielded for the first time the distribution of segmental orientations with respect to the membrane and the order parameter tensors of the dimer systems. It was demonstrated the deuterium splittings measured at the peptide to lipid ratio of 1/50 are consistent with a membrane spanning orientation of the peptide.