Molecular structure extracted from residual dipolar couplings: diphenylmethane dissolved in a nematic liquid crystal

This paper describes an analysis of 1H-1H residual dipolar couplings (RDCs) in diphenylmethane (DPM) dissolved in a nematic liquid crystal, reported by Celebre et al. [J. Chem. Phys. 118, 6417 (2003)]. In that article, the conformational distribution function for DPM was extracted from the RDCs, using the additive potential (AP) model which is based on the molecular-field theory. The AP approach is a powerful, and frequently used, tool for analysis of the nuclear-magnetic-resonance (NMR) parameters in liquid crystals. It requires, however, a priori knowledge of the functional form of the torsional potential, which may even for a simple molecule, such as DPM, be complicated to determine. Here, we analyze the same set of the RDCs using our APME procedure, which is a hybrid model based on the AP approach and maximum entropy (ME) theory. The APME procedure does not require any assumptions about the functional form of the torsional potential and, in contrast with the ME method, is applicable to weakly ordered systems. In the investigation reported in the present study, the results from the APME analysis are in good agreement with the AP interpretation, whereas the ME approach essentially fails in the extraction of the conformational distribution function for DPM.     

NMR studies of molecular conformations in alpha-cyclodextrin

A new approach for analysis of NMR parameters is proposed. The experimental data set includes scalar couplings, NOEs, and residual dipolar couplings. The method, which aims at construction of the conformational distribution function, is applied to alpha-cyclodextrin in isotropic solution and dissolved in a dilute liquid crystal. An attempt to analyze the experimental data using an average molecular conformation resulted in unacceptable errors. Our approach rests on the maximum entropy method (ME), which gives the flattest possible distribution, consistent with the experimental data. Very good agreement between experimental and calculated NMR parameters was observed. In fact, two conformational states were required in order to obtain a satisfactory agreement between calculated and experimental data. In addition, good agreement with Langevin dynamics computer simulations was obtained.     

On the analysis of Liquid Crystal NMR dipolar coupling data via mixed a priori-maximum entropy methods

In this Letter, a general expression is derived for the conformational distribution function of a molecule dissolved in an anisotropic condensed fluid medium by combining an a priori model with the maximum entropy principle applied to treatment of liquid crystalline-NMR data. The recently proposed additive potential maximum entropy (APME) method is recovered as a special case, when the AP is chosen as the a priori model and the orientational order is low.     

Intrinsic information content of NMR dipolar couplings: a conformational investigation of 1,3-butadiene in a nematic phase.

The conformational equilibrium of 1,3-butadiene in a condensed fluid phase is investigated by liquid-crystal NMR spectroscopy. The full set of D(HH) and D(CH) dipolar couplings is determined from the analysis of the (1)H spectra of the three 1,3-butadiene most-abundant isotopomers (i.e. the all (12)C and the two single-labeled (13)C isotopomers) for a total of 21 independent dipolar couplings. A very good starting set of spectral parameters for the analysis of the (1)H spectrum is determined in a semiautomated way by the analysis of the (N-1) (specifically, N=6, the number of 1/2 spin nuclei in the spin system) quantum refocused (5QR), and not (5Q), spectra. As an alternative approach, a Monte Carlo (MC) numerical simulation, capable of predicting the solute ordering, is tested to simulate the 5QR spectrum. The set of D(ij) couplings is very good, proving that the MC method can represent a novel, valid alternative to the existing spectral simplification procedures. The experimentally determined dipolar-coupling data set is fully compatible with the 1,3-butadiene conformational distribution reported in the literature for isolated molecules, indicating the presence of about 99 % of s-trans conformer. With regards to the remaining 1 %, in spite of the direct and very strong dependence of the observables on the molecular structure, it was not possible to discriminate between the planar s-cis and s-gauche forms, both of which produce a very good fit of the dipolar couplings. Vibrational corrections, up to the anharmonic term, were applied; the calculated geometrical parameters are in good- although not exact-agreement with those reported in the literature from experimental and theoretical investigations. This result can be considered as supporting the methodology used for obtaining the structure and conformational distribution of a flexible molecule in a liquid phase.     

Exploring multiple timescale motions in protein GB3 using accelerated molecular dynamics and NMR spectroscopy

Biological function relies on the complex spectrum of conformational dynamics occurring in biomolecules. We have combined Accelerated Molecular Dynamics (AMD) with experimental results derived from NMR to probe multiple time-scale motions in the third IgG-binding domain of Protein G (GB3). AMD is shown to accurately reproduce the amplitude and distribution of slow motional modes characterized using residual dipolar couplings, reporting on dynamics up to the millisecond timescale. In agreement with experiment, larger amplitude slower motions are localized in the beta-strand/loop motif spanning residues 14-24 and in loop 42-44. Principal component analysis shows these fluctuations participating in the primary mode, substantiating the existence of a correlated motion traversing the beta-sheet that culminates in maximum excursions at the active site of the molecule. Fast dynamics were simulated using extensive standard MD simulations and compared to order parameters extracted from 15N relaxation. Notably 60 2-ns fully solvated MD simulations exploring the different conformational substates sampled from AMD resulted in better reproduction of order parameters compared to the same number of simulations starting from the relaxed crystal structure. This illustrates the inherent dependence of protein dynamics on local conformational topology. The results provide rare insight into the complex hierarchy of dynamics present in GB3 and allow us to develop a model of the conformational landscape native to the protein, appearing as a steep sided potential well whose flat bottom comprises multiple similar but discrete conformational substates.     

A high-resolution solid-state NMR approach for the structural studies of bicelles

Bicelles are increasingly being used as membrane mimicking systems in NMR experiments to investigate the structure of membrane proteins. In this study, we demonstrate the effectiveness of a 2D solid-state NMR approach that can be used to measure the structural constraints, such as heteronuclear dipolar couplings between 1H, 13C, and 31P nuclei, in bicelles without the need for isotopic enrichment. This method does not require a high radio frequency power unlike the presently used rotating-frame separated-local-field (SLF) techniques, such as PISEMA. In addition, multiple dipolar couplings can be measured accurately, and the presence of a strong dipolar coupling does not suppress the weak couplings. High-resolution spectra obtained from magnetically aligned DMPC:DHPC bicelles even in the presence of peptides suggest that this approach will be useful in understanding lipid-protein interactions that play a vital role in shaping up the function of membrane proteins.     

Conformational Dynamics of apo‐GlnBP Revealed by Experimental and Computational Analysis

The glutamine binding protein (GlnBP) binds l ‐glutamine and cooperates with its cognate transporters during glutamine uptake. Crystal structure analysis has revealed an open and a closed conformation for apo‐ and holo‐GlnBP, respectively. However, the detailed conformational dynamics have remained unclear. Herein, we combined NMR spectroscopy, MD simulations, and single‐molecule FRET techniques to decipher the conformational dynamics of apo‐GlnBP. The NMR residual dipolar couplings of apo‐GlnBP were in good agreement with a MD‐derived structure ensemble consisting of four metastable states. The open and closed conformations are the two major states. This four‐state model was further validated by smFRET experiments and suggests the conformational selection mechanism in ligand recognition of GlnBP.     

Model-free approach to the dynamic interpretation of residual dipolar couplings in globular proteins.

The effects of internal motions on residual dipolar NMR couplings of proteins partially aligned in a liquid-crystalline environment are analyzed using a 10 ns molecular dynamics (MD) computer simulation of ubiquitin. For a set of alignment tensors with different orientations and rhombicities, MD-averaged dipolar couplings are determined and subsequently interpreted for different scenarios in terms of effective alignment tensors, average orientations of dipolar vectors, and intramolecular reorientational vector distributions. Analytical relationships are derived that reflect similarities and differences between motional scaling of dipolar couplings and scaling of dipolar relaxation data (NMR order parameters). Application of the self-consistent procedure presented here to dipolar coupling measurements of biomolecules aligned in different liquid-crystalline media should allow one to extract in a "model-free" way average orientations of dipolar vectors and specific aspects of their motions.     

Theoretical analysis of residual dipolar coupling patterns in regular secondary structures of proteins

A new approach to the interpretation of residual dipolar couplings for the regular secondary structures of proteins is presented. This paper deals with the analysis of the steric and chiral requirements of protein secondary structures and establishes a quantitative correlation between structure periodicity and the experimental values of the backbone residual dipolar couplings. Building on the recent interpretation of the periodicity of residual dipolar couplings in alpha-helices (i.e., "dipolar waves"), a general parametric equation for fitting the residual dipolar couplings of any regular secondary structure is derived. This equation interprets the modulation of the residual dipolar couplings' periodicity in terms of the secondary structure orientation with respect to an arbitrary reference frame, laying the groundwork for using backbone residual dipolar couplings as a fast tool for determining protein folding by NMR spectroscopy.     

An alternative method for pucker determination in carbohydrates from residual dipolar couplings: a solution NMR study of the fructofuranosyl ring of sucrose

A simple solution NMR method is presented for pucker determination of five-membered rings using only residual dipolar couplings obtained in a single liquid crystalline medium, DMPC/DHPC bicelles (DMPC = dimyristoylphosphatidylcholine; DHPC = dihexanoylphosphatidylcholine). The method was applied to determine the pucker of the fructofuranosyl ring of sucrose. The results indicate a fructofuranosyl pucker phase in the 20 degrees - 70 degrees range. The pucker phases are in agreement with those from previous NMR and optical spectroscopic studies and, importantly, do not rely on empirically parametrized Karplus curves. Furthermore, the analysis implies more than one stable pucker phase and rapid ring interconversion in this range. The present results suggest that using residual dipolar couplings alone can reveal multiple conformations present in solution. Hence, when a sufficient number of residual dipolar coupling constants is measured, the outcome is a robust, reliable, and independent route for determining carbohydrate and nucleic acid structure by NMR spectroscopy.     

Structures in solutions from joint experimental-computational analysis: applications to cyclic molecules and studies of noncovalent interactions

The potential of an approach combining nuclear magnetic resonance (NMR) spectroscopy, molecular dynamics (MD) simulations, and quantum mechanical (QM) calculations for full structural characterizations in solution is assessed using cyclic organic compounds, namely, benzazocinone derivatives 1-3 with fused five- and eight-membered aliphatic rings, camphoric anhydride 4, and bullvalene 5. Various MD simulations were considered, using force field and semiempirical QM treatments, implicit and explicit solvation, and high-temperature MD calculations for selecting plausible molecular geometries for subsequent QM geometry optimizations using mainly B3LYP, M062X, and MP2 methods. The QM-predicted values of NMR parameters were compared to their experimental values for verification of the final structures derived from the MD/QM analysis. From these comparisons, initial estimates of quality thresholds (calculated as rms deviations) were 0.7-0.9 Hz for (3)J(HH) couplings, 0.07-0.11 ? for interproton distances, 0.05-0.08 ppm for (1)H chemical shifts, and 1.0-2.1 ppm for (13)C chemical shifts. The obtained results suggest that the accuracy of the MD analysis in predicting geometries and relative conformational energies is not critical and that the final geometry refinements of the structures selected from the MD simulations using QM methods are sufficient for correcting for the expected inaccuracy of the MD analysis. A unique example of C(sp(3))-H···N(sp(3)) intramolecular noncovalent interaction is also identified using the NMR/MD/QM and the natural bond orbital analyses. As the NMR/MD/QM approach relies on the final QM geometry optimization, comparisons of geometric characteristics predicted by different QM methods and those from X-ray and neutron diffraction measurements were undertaken using rigid and flexible cyclic systems. The joint analysis shows that intermolecular noncovalent interactions present in the solid state alter molecular geometries significantly compared to the geometries of isolated molecules from QM calculations.     

Dynamic effects on j-couplings across hydrogen bonds in proteins

We combine molecular dynamics simulation (MD) with density functional theory (DFT)/finite perturbation theory (FPT) to obtain the Fermi contact contributions to the 3hJNC' couplings in the SMN Tudor domain. Our results show that the effect of conformational motion needs to be considered for the accurate prediction of these scalar couplings. For hydrogen bonds in the beta-sheet regions, the calculated cumulative J-coupling averages remain constant after the first 200 ps. In the more flexible regions at the edges of the beta-sheets, the cumulative J-coupling averages vary over the 500-ps trajectory, providing a qualitative insight into the degree of conformational motion in different regions of the protein.     

Orientation and conformational preference of leucine-enkephalin at the surface of a hydrated dimyristoylphosphatidylcholine bilayer: NMR and MD simulation

The morphogenic opiate pentapeptide leucine-enkephalin (lenk) in a hydrated dimyristoylphosphatidylcholine (DMPC) bilayer is studied using NMR spectroscopy and molecular dynamics simulation. Contrary to the frequent assumption that the peptide attains a single fixed conformation in the presence of membranes, we find that the lenk molecule is flexible, switching between specific bent conformations. The constraints to the orientation of the aromatic rings that are identified by the NMR experiment are found by the MD simulation to be related to the depth of the peptide in the bilayer. The motion of the N-H vectors of the peptide bonds with respect to the magnetic field direction as observed by MD largely explain the magnitude of the observed residual dipolar coupling (RDC), which are much reduced over the static (15)N-(1)H coupling. The measured RDCs are nevertheless significantly larger than the predicted ones, possibly due the absence of long-time motions in the simulations. The conformational behavior of lenk at the DMPC surface is compared to that in the aqueous solution, both in the neutral and in the zwitterionic forms.     

Nuclear magnetic resonance study of alkane conformational statistics

NMR spectra of ethane, propane, and n-butane as solutes in the nematic liquid crystals 4-n-pentyl-4(')-cyanobiphenyl (5CB) and Merck ZLI 1132 (1132) are investigated over a wide temperature range. The ratios of dipolar couplings of ethane to propane are constant over the entire temperature range. Assuming that this constancy applies to the butane conformers facilitates the separation of probability from order parameter. This separation allows the investigation of conformational distribution without the need of invoking any model for the anisotropic intermolecular potential. The results give an order matrix that is consistent with that predicted from model potentials that describe the orientational potential in terms of short-range size and shape effects. The isotropic intermolecular potential contribution to the trans-gauche energy difference E(tg) is found to be temperature dependent with the values and variation in agreement with that found when the same results are analyzed using the chord model for anisotropic interactions [A. C. J. Weber and E. E. Burnell, Chem. Phys. Lett. 506, 196 (2011)]. The fit obtained for 9 spectra in 5CB (63 dipolar couplings) has an RMS difference between experimental and calculated dipolar couplings of 2.7 Hz, while that for the 16 spectra in 1132 (112 couplings) is 6.2 Hz; this excellent fit with nine adjustable parameters suggests that the assumption of equal temperature dependencies of the order parameters for ethane, propane, and each conformer of butane is correct. Also the fit parameters (E(tg) and the methyl angle increase) obtained for 1132 and 5CB agree. The results indicate that the chord model, which was designed to treat hydrocarbon chains, is indeed the model of choice for these chains. The temperature variation of E(tg) provides a challenge for theoreticians. Finally, even better fits to the experimental dipolar couplings are obtained when the energy in the Boltzmann factor is used for scaling ethane to butane results. However, in this case the values obtained for E(tg) differ between 1132 and 5CB.     

Measurement of Large Dipolar Couplings of a Liquid Crystal with Terminal Phenyl Rings and Estimation of the Order Parameters

NMR spectroscopy is a powerful means of studying liquid‐crystalline systems at atomic resolutions. Of the many parameters that can provide information on the dynamics and order of the systems, ¹H–¹³C dipolar couplings are an important means of obtaining such information. Depending on the details of the molecular structure and the magnitude of the order parameters, the dipolar couplings can vary over a wide range of values. Thus the method employed to estimate the dipolar couplings should be capable of estimating both large and small dipolar couplings at the same time. For this purpose, we consider here a two‐dimensional NMR experiment that works similar to the insensitive nuclei enhanced by polarization transfer (INEPT) experiment in solution. With the incorporation of a modification proposed earlier for experiments with low radio frequency power, the scheme is observed to enable a wide range of dipolar couplings to be estimated at the same time. We utilized this approach to obtain dipolar couplings in a liquid crystal with phenyl rings attached to either end of the molecule, and estimated its local order parameters.     

Torsion sensitivity in NMR of aligned molecules: study on various substituted biphenyls

To estimate the torsion sensitivity of dipolar coupling, biphenylic molecules were chosen as probes due to their relatively simple structure and the surprisingly high ambiguity of the only flexible parameter-the interring torsion angle. Solution structures of 4,4'-dibromobiphenyl and 4,4'-diiodobiphenyl are reported for the first time in two liquid crystals I52 and ZLI 1695. The comparison of NMR structures of various para-substituted biphenyls (BPs), calculated by the additive potential maximum entropy (APME) approach, shows that the small spread of torsion angle values in case of different solvents and para-substituents is in good agreement with theoretical expectations from hybrid density functional theory (DFT) methods. Furthermore, the real structural changes of interring torsion and the prevalence of solvent effects over para-halosubstitution can be correctly revealed from these small fluctuations.     

Parameterization and validation of Gromos force field to use in conformational analysis of epoxidic systems

In order to study the conformational space of new natural products derivatives using molecular mechanics (MM) and molecular dynamics (MD), the Gromos force field has been expanded to include epoxidic systems. The parameterization and validation of Gromos were done to simulate 22, 23 epoxides in brassinosteroids analogs. The parameters were derived with an emphasis on the dependence between energy and dihedral angle due to its relevance in the conformational analysis. Molecular dynamics simulations of two model systems similar to those of interest were performed to validate the force field with the proposed parameters. Excellent agreement has been obtained between the MD simulation and the results of a potential energy surface (PES) calculated at B3LYP/6-31G^** level.     

High-resolution 2D NMR spectroscopy of bicelles to measure the membrane interaction of ligands

Magnetically aligned bicelles are increasingly being used as model membranes in solution- and solid-state NMR studies of the structure, dynamics, topology, and interaction of membrane-associated peptides and proteins. These studies commonly utilize the PISEMA pulse sequence to measure dipolar coupling and chemical shift, the two key parameters used in subsequent structural analysis. In the present study, we demonstrate that the PISEMA and other rotating-frame pulse sequences are not suitable for the measurement of long-range heteronuclear dipolar couplings, and that they provide inaccurate values when multiple protons are coupled to a 13C nucleus. Furthermore, we demonstrate that a laboratory-frame separated-local-field experiment is capable of overcoming these difficulties in magnetically aligned bicelles. An extension of this approach to accurately measure 13C-31P and 1H-31P couplings from phospholipids, which are useful to understand the interaction of molecules with the membrane, is also described. In these 2D experiments, natural abundance 13C was observed from bicelles containing DMPC and DHPC lipid molecules. As a first application, these solid-state NMR approaches were utilized to probe the membrane interaction of an antidepressant molecule, desipramine, and its location in the membrane.