Molecular conformations in a phospholipid bilayer extracted from dipolar couplings: a computer simulation study

This paper describes an analysis of NMR dipolar couplings in a bilayer formed by dimyristoylphosphatidylcholine (DMPC). The couplings are calculated from a trajectory generated in a molecular dynamics (MD) simulation based on a realistic atom-atom interaction potential. The analysis is carried out employing a recently developed approach that focuses on the construction of the conformational distribution function. This approach is a combination of two models, the additive potential (AP) model and the maximum entropy (ME) method, and is therefore called APME. In contrast to the AP model, the APME procedure does not require an intuition-based choice of the functional form of the torsional potential and is, unlike the ME method, applicable to weakly ordered systems. The conformational distribution function for the glycerol moiety of the DMPC molecule derived from the APME analysis of the dipolar couplings is in reasonable agreement with the "true" distributions calculated from the trajectory. Analyses of dipolar couplings derived from MD trajectories can, in general, serve as guidelines for experimental investigations of bilayers and other complex biological systems.     

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.     

The structure and conformation of a mesogenic compound between almost zero and almost complete orientational order

The conformational distributions in molecules that form liquid crystalline phases are predicted to depend strongly on orientational order. Results are presented here to test this hypothesis. The mesogen 4-hexyloxy-4'-cyanobiphenyl (6OCB) has been studied by NMR spectroscopy in the isotropic phase and in the nematic phase. In the isotropic phase the field-induced orientational ordering produces small dipolar couplings between ¹³C and ¹H nuclei, which were determined from the ¹³C spectra. Couplings between ¹H nuclei were also obtained using 2D selective refocusing experiments. In the nematic phase, both ¹H-¹H dipolar couplings and quadrupolar splittings for deuterium nuclei were measured for partially-deuterated samples. Both proton and deuterium spectra were also obtained for 6OCB in an equimolar mixture with 4-(ethoxybenzylidene)-4'-butylaniline (EBBA). This mixture exhibits SmA and SmB phases. The data obtained from these experiments has been analysed to yield the probability distribution of the conformations in this molecule generated by rotations about bonds. It is found that there is a substantial influence of the orientational order of the molecules on these distributions.     

Orientational ordering of liquid crystals containing a difluoro-substituted phenyl ring

The orientational ordering of several liquid crystals containing a difluorosubstituted phenyl ring has been studied through the use of C-13 NMR. The fluorinated phenyl ring of these liquid crystals have C_s symmetry, so three order parameters are required to completely describe the ordering of this ring. All three of these order parameters have been calculated from carbon-fluorine dipolar coupling constants obtained from the carbon-fluorine splittings in the C-13 NMR spectra. Because of the complexity of the fluorine-coupled spectra, variable angle spinning (VAS) was used to resolve the carbon-fluorine splittings. In order to study the orientational ordering over wide ranges of temperature, we have developed an empirical correlation between the order parameter and the value of a carbon-fluorine dipolar coupling constant. This enabled us to study the change in the order parameter with temperature. The results of applying this method to several structurally similar liquid crystals containing the same type of difluorinated phenyl ring are presented. A comparison is made to a similar mono-fluorinated liquid crystal.     

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.     

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.     

Determination of natural abundance 15N-1H and 13C-1H dipolar couplings of molecules in a strongly orienting media using two-dimensional inverse experiments

NMR spectra of molecules oriented in liquid crystals provide homo- and heteronuclear dipolar couplings and thereby the geometry of the molecules. Several inequivalent dilute spins such as 13C and 15N coupled to protons form different coupled spin systems in their natural abundance and appear as satellites in the proton spectra. Identification of transitions belonging to each spin system is essential to determine heteronuclear dipolar couplings, which is a formidable task. In the present study, using 15N-1H and 13C-1H HSQC, and HMQC experiments we have selectively detected spectra of each rare spin coupled to protons. The 15N-1H and 13C-1H dipolar couplings have been determined in the natural abundance of 13C and 15N for the molecules pyrazine, pyrimidine and pyridazine oriented in a thermotropic liquid crystal.     

The 1H NMR spectrum of pyrazole in a nematic phase

The experimental ¹H nuclear magnetic resonance (NMR) spectrum of 1H‐pyrazole was recorded in thermotropic nematic liquid crystal N‐(p‐ethoxybenzylidene)‐p‐butylaniline (EBBA) within the temperature range of 299–308 K. Two of three observable dipolar D_HH‐couplings appeared to be equal at each temperature because of fast prototropic tautomerism. Analysis of the Saupe orientational order parameters using fixed geometry determined by computations and experimental dipolar couplings results in a situation in which the molecular orientation relative to the magnetic field (and the liquid crystal director) can be described exceptionally by a single parameter. Copyright © 2016 John Wiley & Sons, Ltd.     

The structure and conformation of a mesogenic compound between almost zero and almost complete orientational order

The conformational distributions in molecules that form liquid crystalline phases are predicted to depend strongly on orientational order. Results are presented here to test this hypothesis. The mesogen 4‐hexyloxy‐4′‐cyanobiphenyl (6OCB) has been studied by NMR spectroscopy in the isotropic phase and in the nematic phase. In the isotropic phase the field‐induced orientational ordering produces small dipolar couplings between ¹³C and ¹H nuclei, which were determined from the ¹³C spectra. Couplings between ¹H nuclei were also obtained using 2D selective refocusing experiments. In the nematic phase, both ¹H–¹H dipolar couplings and quadrupolar splittings for deuterium nuclei were measured for partially‐deuterated samples. Both proton and deuterium spectra were also obtained for 6OCB in an equimolar mixture with 4‐(ethoxybenzylidene)‐4′‐butylaniline (EBBA). This mixture exhibits SmA and SmB phases. The data obtained from these experiments has been analysed to yield the probability distribution of the conformations in this molecule generated by rotations about bonds. It is found that there is a substantial influence of the orientational order of the molecules on these distributions.     

On the origin of residual dipolar couplings from denatured proteins

Effects of steric obstruction on random flight chains are examined. Spatial probability distributions are elaborated to calculate residual dipolar couplings and residual chemical shift anisotropy, parameters that are acquired by NMR spectroscopy from solutes dissolved in dilute liquid crystals. Calculations yield chain length and residue position-dependent values in good agreement with simulations to provide understanding of recently acquired data from denatured proteins.     

A 2D solid-state NMR experiment to resolve overlapping aromatic resonances of thiophene-based nematogens

In this study, we demonstrate the feasibility of resolving overlapping 13C chemical shift spectral lines of aromatic rings in a thiophene-based nematogen in the mesophase using a 2D PITANSEMA solid-state NMR method. This technique provided the information about chemical shift values as well as dipolar couplings that are used for determining the orientational order parameter. Large C-H dipolar coupling values measured for thiophene in contrast to phenyl rings suggest that the heterocyclic ring is not part of the molecular axis. Using the order parameter, we determined the orientation of C-H vectors of the thiophene ring. We believe that the 2D solid-state NMR can be extended to other types of liquid crystalline materials such as the banana-based mesogens for determining the orientational order and bent angle.     

Ferroelectric liquid crystals derived from isoleucine II. Orientational ordering by carbon-13 separated local field spectroscopy

The orientational ordering of a series of ferroelectric liquid crystals 4'-[(2S, 3S)-3-methyl- 2-halopentanoyloxy]-4-hexyloxybiphenyls (3M2XPHOB, X=F for fluorine, C for chlorine, B for bromine) and their racemates have been studied by two-dimensional carbon-13 separated local field spectroscopy combined with off-magic-angle spinning. All carbons are well-resolved in the carbon-13 NMR spectrum so that carbon-proton dipolar coupling constants for all carbons in the liquid crystal molecule can be determined, giving detailed segmental orienta- tional ordering information. (The order parameters of the biphenyl core segments and each carbon-proton bond in the aliphatic chains were measured as a function of temperature.) The results show that the substitution of different halogens on the chiral chain affects the carbon- proton bond orientational ordering of the entire chiral chain, while the orientational ordering of the rest of the liquid crystal molecule (core and achiral chain) remains unchanged. For the fluoro-substituted liquid crystals, carbon-fluorine dipolar couplings are also observed. At the SmA-to-SmC* transition, there is a discontinuous change in the magnitudes of all C-H bond order parameters. However, the aliphatic ordering relative to the core ordering is unchanged, suggesting that there is a negligible change in the mesogen conformation and the environment of the aliphatic chain at this transition, i.e. there is no evidence for substantial 'chiral interactions' in the SmC* phase.     

Determination of the packing mode of the coiled-coil domain of cGMP-dependent protein kinase Ialpha in solution using charge-predicted dipolar couplings

Coiled-coil motifs are ubiquitous in biology and play essential roles in protein assembly and molecular recognition. Here, we show that the relative orientation and stoichiometry of coiled-coil proteins in solution can be determined by comparison of residual dipolar couplings (RDCs) measured in charged liquid-crystalline medium with values predicted from the three-dimensional charge distribution of the protein. Comparison of charge-predicted RDCs with a small set of one-bond 1DNH dipolar couplings, measured in the negatively charged liquid-crystalline Pf1 bacteriophage medium, identified the coiled-coil region of the cGMP-dependent protein kinase I as a parallel homodimer in solution and ruled out an antiparallel dimeric or monomeric state. The method is very rapid, applicable to a wide variety of liquid crystals used in biological NMR to date, and can be applied to coiled-coil structures and other proteins with higher order assembly.     

An investigation of solute-liquid crystal interaction in hydrogen bonded complexes of palmitic acid and p-octyloxybenzoic acid

The orientational order of a liquid crystalline phase which has a specific solute-liquid crystal interaction was investigated using nuclear magnetic resonance. Three isotopically substituted species of palmitic acid (palmitic acid-d₃₁, 1-¹³C-2.2-H₂-palmitic acid-d₂₉ and 2,2,3,3-H₄-palmitic acid-d₂₇) were dissolved in the liquid crystal p-octyloxybenzoic acid (p-OOBA) and the proton, deuteron and carbon 13 NMR spectra recorded as a function of temperature. ¹H-¹³H dipolar couplings were observed using a spin echo pulse sequence which removes heteronuclear dipolar couplings to the chain deuterons. In the case of the carbon 13 labelled compound, ¹H-¹³C dipolar couplings could be observed by applying an additional refocusing pulse to the ¹³C spins. The dipolar and quadrupolar couplings were used to calculate the complete orientational order matrix of the alpha methylene segment of palmitic acid in p-OOBA. The liquid crystal was shown to largely determine the orientational order of the head group and this was attributed to intermolecular hydrogen bonding. The dipolar and quadrupolar couplings for the rest of the chain were interpreted in terms of a mean field equilibrium statistical model, based on the Samulski Inertial Frame Model. Hydrogen bonding was shown to be of greater importance in the orientational ordering of the solutes in the liquid crystal than are electrostatic interactions in the ordering of the amphiphile in the potassium palmitate/water system.     

Cross-Polarisation Applied to the Study of Liquid Crsytalline Ordering

 Cross polarisation is extensively used in solid state NMR for enhancing signals of nuclei with low gyromagnetic ratio. However, the use of the method for providing quantitative structural and dynamics information is limited. This arises due to the fact that the mechanism which is responsible for cross polarisation namely, the dipolar interaction, has a long range and is also anisotropic. In nematic liquid crystals these limitations are easily overcome since molecules orient in a magnetic field. The uniaxial ordering of the molecules essentially removes problems associated with the angular dependence of the interactions encountered in powdered solids. The molecular motion averages out intermolecular dipolar interaction, while retaining partially averaged intramolecular interaction. In this article the use of cross polarisation for obtaining heteronuclear dipolar couplings and hence the order parameters of liquid crystals is presented. Several modifications to the basic experiment were considered and their utility illustrated. A method for obtaining proton–proton dipolar couplings, by utilizing cross polarisation from the dipolar reservoir, is also presented.     

Determination of the spatial structure of glutathione by residual dipolar coupling analysis

The approach based on analysis of the residual 1H-13C dipolar couplings in molecules partially aligned in a lyotropic liquid crystalline medium was used in the NMR investigation of the reduced glutathione (Glu-Cys-Gly; GSH) structure in a lyotropic medium (cetylpyridinium chloride-n-hexanol). The spatial structure of GSH in solution was established on the basis of the experimental data for observed couplings only.     

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.     

Proton evolved local field solid-state nuclear magnetic resonance using Hadamard encoding: theory and application to membrane proteins

NMR anisotropic parameters such as dipolar couplings and chemical shifts are central to structure and orientation determination of aligned membrane proteins and liquid crystals. Among the separated local field experiments, the proton evolved local field (PELF) scheme is particularly suitable to measure dynamically averaged dipolar couplings and give information on local molecular motions. However, the PELF experiment requires the acquisition of several 2D datasets at different mixing times to optimize the sensitivity for the complete range of dipolar couplings of the resonances in the spectrum. Here, we propose a new PELF experiment that takes the advantage of the Hadamard encoding (HE) to obtain higher sensitivity for a broad range of dipolar couplings using a single 2D experiment. The HE scheme is obtained by selecting the spin operators with phase switching of hard pulses. This approach enables one to detect four spin operators, simultaneously, which can be processed into two 2D spectra covering a broader range of dipolar couplings. The advantages of the new approach are illustrated for a U-(15)N NAL single crystal and the U-(15)N labeled single-pass membrane protein sarcolipin reconstituted in oriented lipid bicelles. The HE-PELF scheme can be implemented in other multidimensional experiments to speed up the characterization of the structure and dynamics of oriented membrane proteins and liquid crystalline samples.