Proton-detected local-field (PDLF) NMR spectroscopy, using magic-angle spinning and dipolar recoupling, is presently the most powerful experimental technique for obtaining atomistic structural information from small molecules undergoing anisotropic motion. Common examples include peptides, drugs, or lipids in model membranes and molecules that form liquid crystals. The measurements on complex systems are however compromised by the larger number of transients required. Retaining sufficient spectral quality in the direct dimension requires that the indirect time-domain modulation becomes too short for yielding dipolar splittings in the frequency domain. In such cases, the dipolar couplings can be obtained by fitting the experimental data; however ideal models often fail to fit PDLF data properly due to effects of radiofrequency field (RF) spatial inhomogeneity. Here, we demonstrate that by accounting for RF spatial inhomogeneity in the modeling of R-symmetry-based PDLF NMR experiments, the fitting accuracy is improved, facilitating the analysis of the experimental data. In comparison to the analysis of dipolar splittings without any fitting procedure, the accurate modeling of PDLF measurements makes possible three important improvements: the use of shorter experiments that enable the investigation of samples with a higher level of complexity, the measurement of C–H bond order parameters with smaller magnitudes

The methodology for characterizing molecular structure in biological systems has been advancing rapidly over recent years

Of these techniques, researchers have consistently used

A number of PDLF pulse sequences have been implemented to investigate lipid membranes and other systems

In general, the strategy for developing better dipolar recoupling methods has been to minimize the sensitivity to RF spatial inhomogeneity, by using/designing dipolar recoupling sequences that are less sensitive to RF imperfections and reducing the sample studied to a narrow volume, and using recoupling pulse sequences with a high scaling factor that enable the measurement of smaller dipolar couplings

PDLF experiments have been mostly analyzed by “reading off” the dipolar splittings obtained in the indirect frequency domain of the 2D spectra. In contrast to the standard analysis of REDOR or DIPSHIFT dipolar evolutions

Here, we present an analysis procedure that enables one to increase the accuracy and applicability of R-symmetry-based PDLF NMR (R-PDLF) through R-PDLF numerical simulations that take into account the RF spatial inhomogeneity of the probe used explicitly, i.e., rather than trying to minimize the effect of RF spatial inhomogeneity, we include it in the NMR simulations used to fit the experimental measurements. The use of RF inhomogeneity for data analysis has been done recently for investigating protein molecular structure

The typical approach for determining C–H bond order parameter magnitudes with PDLF dipolar recoupling NMR is by performing a Fourier transform,

For a dipolar modulation corresponding to a single C–H bond order parameter and acquired under optimal experimental conditions, the use of Eq. (

The effect of using a limited number of time-domain points to describe a superposition of two Pake patterns with distinct splittings.

Numerical simulations of the R-PDLF pulse sequence for a fixed dipolar coupling displaying the effects of RF nutation frequency deviation from ideal settings

Analyzing the measured data with a fitting model (in either the time or frequency domains) can be used to circumvent the limitations outlined above. The practical bottleneck for such an analysis is the RF inhomogeneity across the sample, intrinsic to the majority of experimental setups

The outcome of an experiment is always the sum over all the detectable spatially distributed sample volumes. Therefore, the experimental data measured with an R-PDLF experiment are a sum over dipolar modulations, each modulation with a characteristic lineshape that depends on the local RF field. To simulate realistic R-PDLF experiments accounting for RF inhomogeneity, we first measured the RF inhomogeneity in the probe used in this work by the method suggested by

Simulation of the effect of RF spatial inhomogeneity on R-PDLF dipolar modulation and illustration of the advantage of time-domain analysis of the data over reading-off the dipolar splitting(s) in the frequency domain.

The result of accounting for RF inhomogeneity in the R-PDLF simulations is exemplified in Fig.

From the description shown in the preceding section, it is clear that RF spatial inhomogeneity affects the dipolar modulation in R-PDLF experiments. Therefore, for accurate fits of experimental data, this effect needs to be taken into account. In this and the following section we demonstrate that accounting for the effect of RF inhomogeneity in time-domain fits of experimental data indeed leads to highly accurate fits of the experimental data and consequently to a considerable improvement of the accuracy of the C–H bond order parameters determined. Instead of in the time domain, the fitting could also be performed in the frequency domain, i.e., by performing the Fourier transform of the experimental data in the indirect dimension and by then fitting these data with the Fourier transform of the numerical simulations. Here, we simply use time-domain fits and avoid performing the additional step of the Fourier transform which is unnecessary and has an extra computational time cost.

Figure

The proposed method applied to a sample of POPE MLVs.

The proposed methodology applied to a sample of a DMPC/DMPCd54 liquid crystalline system.

To further test the accuracy of using a model of R-PDLF experiments that includes RF inhomogeneity, we used a water/DMPC/DMPCd54 liquid crystalline system (

Comparison of the order parameter magnitudes,

The

The agreement between the

For determining the numbers shown in Table

Phospholipid headgroup C–H bond order parameter magnitudes determined from a brain lipid extract using time-domain fits accounting for B

To showcase the applicability of the presented methodology, we investigated the molecular structure of a complex membrane system composed of a brain lipid extract with several lipid types present. The lipid mixture consists of the chloroform

Figure

Order parameter magnitudes determined from a brain lipid extract using the methodology proposed in this work as shown in Fig.

Figure

The headgroup order parameters determined from the set of different phospholipid types in the brain lipid extract are very much in line with what is observed in corresponding lipid model membranes. The only exception is the PS

In summary, we have described a PDLF NMR methodology that consists of performing time-domain fits of the dipolar modulation with numerical simulations that account for the RF spatial inhomogeneity of the probe used. The RF inhomogeneity is experimentally measured and is an a priori constraint. A dipolar modulation of a single component is therefore fitted with only two parameters, the dipolar coupling and a phenomenological relaxation time to account for exponential relaxation. The proposed methodology enables one to determine C–H bond order parameters from simple model systems with a much higher accuracy than previously and enables the investigation of complex lipid membrane systems that were so far inaccessible using the conventional read-off PDLF NMR methodology. We believe that the method presented will be extremely useful in the future concerning molecular structural investigations of complex systems such as multi-component models, lipid extracts, and lipid membranes with drugs, peptides, or other molecules incorporated. Moreover, the higher accuracy and farther reach of the method will also be fundamental to validate molecular dynamics simulations for which structural experimental data were not accessible so far.

The simulation data and code used for the publication can be found at

The supplement related to this article is available online at:

TMF conceived the project. TMF and AW developed the code. TMF and AW performed experiments and processed the experimental data. TMF, AW, and KS analyzed and discussed the results and the paper. TMF wrote the paper.

At least one of the (co-)authors is a member of the editorial board of

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Tiago Mendes Ferreira greatly acknowledges Alexey Krushelnitsky for invaluable support and discussions. This research study was funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG; project no. 189853844, TRR 102, Tiago Mendes Ferreira and Anika Wurl).

This research has been supported by the Deutsche Forschungsgemeinschaft (project no. 189853844, TRR 102).

This paper was edited by Beat Meier and reviewed by two anonymous referees.