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In solid-state NMR exphydrated samples biopolymers are susceptible to radio-frequency heating and have a significant impact on probe tuning frequency and performance parameters such as sensitivity. These considerations are increasingly important as magnetic field strengths increase with improved magnet technology. Recent developments in the design, construction, and performance of probes for solid-state NMR experiments on stationary lossy biological samples at high magnetic fields are reviewed.
Most proteins express their biological function as constituents of supramolecular assemblies immersed in a salt-containing aqueous environment. Since the individual protein subunits are immobilized within the assemblies, both high magnetic fields and high power radiofrequency (RF) irradiations are needed to obtain high-resolution spectra on stationary, aligned samples. However, these electrically lossy samples are problematic for the performance of NMR probes tuned for the high resonance frequencies. As a result, it has been necessary to rethink the design and construction of the multiple-resonance probes used for solids-state NMR studies of proteins.
In NMR spectroscopy, the term “solid-state” does not describe the physical state of the sample. Rather, it refers to the instrumentation and experimental methods that deal with un-averaged, anisotropic (static) nuclear spin interactions present in molecules that are immobile on timescales that are long compared to the inverse of the frequency spans of these interactions. In a typical sample of a membrane protein suitable for solid-state NMR experiments, the polypeptides are associated with liquid crystalline phospholipid bilayers in excess water, and such samples will have the appearance of a clear solution at room temperature. However, solution NMR spectra of these samples contain no or very weak, broad resonances because of the lack of sufficient motional averaging. Only the high power radiofrequency irradiations of multiple-pulse and double-resonance solid-state NMR experiments are capable of averaging the spin interactions and yielding high-resolution NMR spectra.
There are two basic classes of designs for probes capable of performing solid-state NMR experiments. Either a single sample resonator, such as a solenoid coil, tuned to multiple frequencies, or multiple sample resonators nested in a cross-coil  configuration, each of which is tuned to one or two frequencies, are used. The tradeoffs between these two designs are complex and the better choice depends upon the specific requirements of the samples and experiments. At high fields, there are large frequency differences between the 1H and the low gamma (13C and 15N) nuclei, which makes the compromises inherent in double- or triple- tuned single coils more costly, and the use of multiple resonators more attractive, since individual resonators can be optimized for their frequency of operation, and complexity of the tuning circuits is reduced by relying in-part on physical separation rather than solely on circuit elements, such as traps and filters, to provide the requisite isolation of the frequencies. An extreme example of the multiple resonator probe concept is represented by Electron Paramagnetic Resonance (EPR) probes designed to perform Electron Nuclear Double Resonance (ENDOR) experiments where the only feasible choice is to use individual resonators optimized for the gigahertz electron resonance and the megahertz nuclear resonances frequencies . The drawbacks of using multiple resonator probes are chiefly geometric, because of the necessity of generating orthogonal fields with cross coils and the unavoidable reduction of the filling factor for the outer resonator in a nested configuration. In solid-state NMR, traditional probe designs relied on a single solenoid coil tuned to multiple frequencies, which works well for relatively low frequencies and crystalline samples. However, as the frequency disparity increases in high field magnets, the trade-offs associated with any given value of solenoid coil inductance become more pronounced, especially for lossy aqueous samples of biopolymers.
The interactions between an electrically lossy sample and the electrical fields generated in the tuned resonator by high frequency RF irradiations result in sample heating and dramatic changes in the performance of the probe, especially a loss of sensitivity [3; 4]. Two general strategies have been pursued to mitigate the deleterious effects of the lossy sample upon probe performance, both of which reduce the undesirable electrical effects and the sample heating that originate mostly in the conservative electric fields generated by a solenoid coil. The conservative electric field generated within the sample volume is proportional to the coil inductance, or with all other parameters held constant, the number of turns of the solenoid coil. A scroll coil provides a reduced electric field at the sample by virtue of its design, which features a built-in capacitance as well as a relatively low inductance [5; 6]. We have described a 1H/31P double-resonance scroll coil probe that takes advantages of the favorable high frequency performance of this design. Other types of resonators have been introduced that reduce RF heating by minimizing the electric fields within the sample volume [7; 8]. We recently described an approach that enables solenoid coils to be used with lossy samples; based on the principles of a Faraday shield , a strip-shield insert , placed between the sample and the coil, localizes the undesirable conservative electric fields outside the sample volume, effectively shielding the sample from the heating effects of the RF irradiations [11; 12]. An alternative approach uses a low inductance resonator tuned to the high 1H frequency while employing a solenoid coil for the low frequency channels in a cross-coil configuration [13; 14; 15; 16; 17]. We have described a cross-coil double-resonance probe that uses an outer Modified Alderman-Grant Coil (MAGC) tuned to the 1H frequency and an inner solenoid coil tuned to the low gamma 15N frequency . Other groups have recently described a number of other promising approaches to probes for solid-state NMR of lossy samples at high fields [8; 19; 20]. In this review we summarize recent progress in probe development and compare the various designs.
As the interface between the sample and the weak magnetic fields generated by the RF irradiations, the probe is the spectrometer component with the strongest influence on the overall performance of the experiments. Besides providing a mechanical platform for positioning or rotating the sample and controlling its temperature, the probe consists of one or more resonators located concentrically around the sample that are tuned by capacitors and other circuit elements to the resonance frequencies of the nuclei of interest. Superconducting magnets are now capable of generating homogeneous, stable magnetic fields at strengths (23T) that correspond to 1H resonance frequencies (1 GHz) in the middle of the Ultra High Frequency (UHF) (300 MHz – 3 GHz) band, and higher fields are in the offing as magnet technology continues to develop. At these field strengths, solid-state NMR experiments on stationary samples are extremely demanding because of the high RF fields needed to perform homo- and hetero-nuclear decoupling across broad bandwidths for the entire duration of an experiment without the assistance of averaging due to mechanical rotation of the sample at the magic angle.
Probes must meet the conflicting demands presented by electrically lossy samples and irradiations with intense radiofrequency fields at high frequencies. Two aspects of the problem are illustrated in Figure 1. The insertion of a lossy sample that mimics the properties of protein-containing phospholipid bilayers into an empty solenoid coil tuned to 800 MHz induces a significant (41 MHz) downward shift of the tuning frequency. By itself, this shift presents a challenge in circuit design. The relative breadth of the signals in Figure 1 shows that the introduction of a lossy sample lowers the quality (Q) factor of the circuit from 160 to 27, which results in a dramatic loss of probe efficiency and sensitivity. Moreover, the frequency shift and Q reduction are accompanied by substantial sample heating from the RF irradiations which interact strongly with the conductive sample , particularly at the high 1H resonance frequency but also at the lower 13C frequency. Taken together, these factors preclude the use of conventional solenoid coils at 1H resonance frequencies.
In early contributions , Gadian and others attributed these effects to dielectric loss as well as the conductivity of the sample. They showed that the interaction of the scalar (conservative) electric field was the dominant mechanism of the deleterious interactions between the coil and the conductive sample. Notably, Alderman and Grant  recognized that the scalar portion of the electric field is proportional to the voltage drop across the leads of the coil, and thus proportional to the inductance of the coil, and this led to the substitution of low inductance resonators for solenoid coils in NMR probes.
The construction of probes capable of withstanding prolonged high power RF irradiations was an integral part of the development of the field of high-resolution solid-state NMR spectroscopy. The probes used in the initial double-resonance experiments had two single-tuned resonators in a cross-coil configuration, typically an outer Helmholtz coil tuned to the 1H frequency and an inner solenoid coil tuned to the 13C frequency as a mean of simplifying the overall circuit design . For the next 25 – 30 years, most probes utilized a single, double- or triple-tuned solenoid coil in recognition of the elegance of such an approach, and the availability of circuits that offered simple and effective ways to electrically isolate the tuning frequencies. In the past few years, the necessity of dealing with lossy samples at high frequencies has resulted in a resurgence of interest in cross-coil probes, since it is possible to reduce the amount of sample heating from the 1H resonator in this configuration by using a low inductance coil with a concomitantly low conservative electric field heating effect. The main disadvantage of cross-coil designs results from the low filling factor for the outer coil, which limits its ability to generate strong B1 fields and reduces its sensitivity, although the reduced filling factor does contribute indirectly to a reduction of sample heating. Our conceptualization of coil selection is illustrated in Figure 2, which plots probe performance on a lossy sample as a function of sample coil inductance, or if all other parameters remain constant, the number of turns in the coil. At high frequencies, the performance of the coil improves significantly for lossy samples as the inductance is decreased. Similarly, the sensitivity of the low frequency coil improves with increasing inductance within certain limits; wire resistance generally diminishes the advantage of 5 mm solenoid coils with more than 8 or 9 turns. For double or triple tuned solenoid coils, Figure 2 suggests that it is feasible to select a coil with an inductance that is a compromise between low frequency sensitivity and high frequency performance. For example, we have found that a 5 mm ID, 5 turn solenoid coil can be double-tuned to 1H at 700 MHz and 15N at 70 MHz, and give reasonable performance, albeit with sample heating and somewhat reduced 15N sensitivity, in double-resonance experiments on lossy samples.
RF heating is a well-characterized phenomenon that plagues all NMR experiments on lossy aqueous samples. Efforts to minimize sample heating have focused primarily on the resonator tuned to the 1H frequency. However, significant heating can also result from irradiations at 13C resonance frequencies at high fields, and this will become an increasingly important factor in the design and construction of probes for 1H/13C/15N triple-resonance experiments in the future.
In this review, in order to make these considerations more concrete, we describe three probe designs that we have constructed and tested in the past few years as part of our solid-state NMR studies of proteins in supramolecular assemblies, such as virus particles and membranes. They should be equally applicable to other types of proteins that are immobile and hydrated. These designs include probes that incorporate a strip-shield solenoid coil, a scroll coil, and a modified Alderman-Grant coil. In the summary we make comparisons to alternative probe designs for biological solid-state NMR experiments.
In the past, most solid-state NMR probes utilized a solenoid coil that was double- or triple- tuned using a Cross-Waugh type of circuit [23; 24; 25; 26; 27] or a variation that employed transmission lines as tuning elements [28; 29]. The contemporary version of a Cross-Waugh circuit shown in Figure 3A can be used to double tune a solenoid sample coil of inductance Ls. The circuit utilizes capacitors C1 and C4 for scaling; variable capacitor C2 tunes the 1H circuit and variable capacitor C3 matches the 1H circuit. Capacitor C5 and transmission line L1 together constitute the “quarter wave” element, which resonates at the 1H frequency, and provides a ground for the low frequency channel, effectively isolating it from the 1H tuning elements. An optional band stop filter utilizing capacitor C7 and inductor L2 may be used to isolate the 1H channel from the low frequency X channel. Capacitor C6 serves as a voltage divider, variable capacitor C8 tunes the low frequency circuit, and fixed capacitor C9 shifts the low frequency resonance to the desired frequency. Variable capacitor C10 is the low frequency match capacitor, and inductor L3 and capacitor C11 form an LC trap resonating at the 1H frequency to provide isolation at the 1H frequency. Historically, the inductance of solenoid sample coils (Ls) with between 4 and 7 turns provided a reasonable compromise as described in Figure 2 - high enough for the low frequency nuclei (13C and 15N) and low enough to accommodate tuning to the high frequency nucleus (1H). A solenoid coil probe and a typical aqueous sample of a membrane protein in phospholipid bilayers are shown in Figure 3. This design worked well in many chemical and biochemical applications, and only became problematic when the combination of high magnetic fields and lossy biological samples resulted in the substantial frequency shifts and Q reduction illustrated in Figure 1 and the severe sample heating that denatured samples.
It is possible to work around the sample-induced frequency shifts shown in Figure 1 by extending the tuning range of the circuit, although in many cases this necessitates the replacement of fixed capacitors when samples are changed to allow for tuning to samples with a wide range of conductivities. However, desoldering and soldering delicate capacitors every time the sample is changed is not a practical approach. The problem of Q reduction also illustrated in Figure 1 can be partially overcome by using higher RF power and longer signal averaging. However, the sample heating can be intractable, even with the use of long recycle delays that exacerbate the sensitivity problems. Although all three effects are linked, sample heating has received the most attention because of its devastating effects on the samples. The most direct way to reduce the RF heating is to reduce the inductance of the coil and, therefore, the scalar electrical field generated within the sample. While a low inductance coil is desirable for the 1H resonance frequency, at high field strengths, the large gap between the frequencies of 1H and 13C and especially 15N place competing demands on the choice of inductance of solenoid coils in double or triple tuned configurations. At moderate 1H resonance frequencies (< 700 MHz), it is possible to work with a coil with a somewhat reduced coil inductance that results in acceptable performance for 13C and 15N and tolerable sample heating that can be managed with long recycle delays. This enables the flexibility of solenoid coils to be available for specific experiments. For example, we have constructed double-resonance probes with relatively large “flat” solenoid coils  in order to optimize the filling factor for mechanically-oriented samples of membrane proteins on glass plates as well as a platform for tilted coil experiments .
Although a double- or triple-tuned solenoid coil can perform well with non-lossy samples, such as anhydrous crystalline materials, in high magnetic fields, the effects of lossy aqueous samples on tuning, quality factor, and sample heating are limiting. A strip-shield  combats these effects while preserving the favorable characteristics of the solenoid coil. As shown in Figures 4 and and5,5, a strip-shield is a thin tube inserted between the sample and the solenoid coil; it locates thin copper strips along the long axis of the coil, parallel to the B1 field generated by the RF irradiation. The copper strips are encapsulated in a dielectric material (polytetrafluoroethylene (PTFE) ) to prevent arcing. The shield, in effect, sequesters the undesirable electric fields into the region of the conductive copper strips, and away from the sample.
Figure 4 illustrates the principal features of a strip-shield. Since the strips and the dielectric material reduce the filling factor of the coil by requiring a somewhat larger inner diameter (5.6 mm) than required by the outer diameter of the sample (5 mm), it is desirable to utilize the thinnest shield that is practical. Following standard practice, the single solenoid coil is double- or triple- tuned to the resonance frequencies of interest. A complete double-resonance probe based on a modified version of the Cross-Waugh circuit is shown in Figure 5. Unlike many cross-coil designs [13; 14] where the electric field reduction only affects the 1H channel, in this design all channels benefit. At the higher 1H and 13C resonance frequencies, the improvement in Q for a lossy sample more than compensates for the loss in filling factor in terms of the magnitudes of the B1 fields generated at a specified power level, and sensitivity, and the strip-shield reduces RF heating by a factor of 5 – 7. At the 15N frequency, the performance of the strip-shield containing coil is similar to that of a stand-alone solenoid coil.
With lossy samples a scroll coil offers several advantages over a solenoid coil of similar size. Foremost are the increased efficiency and sensitivity, and reduced sample heating at the high 1H resonance frequency. In addition, the B1 homogeneity is very high without the need for a sophisticated radiofrequency circuit, making circuit design straightforward. It is an excellent choice for 1H-detected experiments where high frequency 1H performance is of paramount importance. The most significant drawback to the scroll coil is the markedly reduced efficiency and sensitivity at the lower 13C and 15N resonance frequencies.
A scroll coil consists of a single sheet of copper wrapped concentrically with a non-conducting dielectric material, such as PTFE, as shown in Figure 6. Because of the small electric field generated within the sample volume of a scroll coil, sample heating is minimal, and probe tuning is not significantly perturbed by lossy samples. As a result, the probe has sufficient flexibility to be used to test pulse sequences on single crystal or powder samples, and then to be used to study aqueous protein samples without replacing fixed capacitors or other tuning elements.
A scroll coil has lower sensitivity than a solenoid coil for directly-detected 13C or 15N experiments because of its marginal low frequency performance; however, we have found that for higher frequency operations in a 1H/31P double-resonance probe, the scroll coil is truly outstanding. Most applications of the scroll coil in NMR probes have been for 1H/13C/15N triple-resonance magic angle sample spinning experiments, where it has been suggested that the high B1 homogeneity of the scroll coil leads to more effective cross-polarization which may somewhat offset the low sensitivity for directly-detected 15N and 13C experiments [5; 6].
The compromises inherent in double- or triple- tuned solenoid or scroll coils, can be largely avoided in cross-coil probes with two separate resonators and tuning circuits. With this approach, one resonator is optimized for the high frequency of 1H and the other for the lower frequencies of 15N and/or 13C. This results in a probe that generates little RF heating because the outer resonator tuned to the high 1H frequency has low inductance and a small filling factor. High efficiency and sensitivity for the 15N and 13C frequencies result from the high inductance and filling factor of the inner solenoid coil holding the sample, although the 13C channel retains the sample heating properties of a solenoid coil.
In the early versions of cross-coil probes, the outer 1H resonator was a Helmholtz coil , however, this resonator is obsolete because of its poor performance at high frequencies and marginal RF homogeneity. A modified Alderman-Grant coil has much better performance characteristics. Its low inductance ensures a minimal voltage drop across the resonator, and thus the sample. The MAGC shown in Figure 7 was machined from a solid rod of oxygen free copper, which enabled its geometry to be optimized to create a homogenous B1 field in the central region where a 5mm ID solenoid coil is located in the assembled probe. With the capacitors in place, the resonator produces a B1 field orthogonal to its long axis, through the window [32; 33], and the inner solenoid coil produces its B1 field along the long axis of the solenoid/MAGC pair. The simplified tuning circuit and inductance optimized for its frequencies of operation ensure excellent sensitivity in 13C and 15N direct-detection experiments. It is essential to balance  the circuit in order for the MAGC to exhibit optimal efficiency, homogeneity, and power handling capabilities, but this is a straightforward process for a single resonance circuit.
Overall, using a MAGC as the outer coil in a cross-coil probe offers several advantages. The low inductance of the MAGC coil is very effective at reducing RF heating due to irradiation at the high 1H frequency (Figure 8). The simple tuning circuit utilizes a minimum number of tuning elements for the inner coil and provides the flexibility to choose an inner coil of optimal inductance for the low frequency detection channel. This contributes to good sensitivity in direct detection experiments. The outer MAGC is relatively compact, which improves the performance of the 1H channel, and results in a compact overall resonator structure that fits inside narrow bore magnets. The main disadvantage of this design (and present in all cross-coil designs) results from the very same properties of the MAGC resonator that minimize the RF heating, namely the low inductance of the MAGC and its relatively low filling factor, which render the coil insensitive for direct observation of 1H signals. However, the design could be reversed, and cross-coil designs with an inner 1H resonator and outer low frequency resonator have been described , which would sacrifice low frequency sensitivity for increased 1H performance while still retaining the favorable RF heating properties of a low inductance 1H resonator. Taken together, the advantages resulting from the compact cross-coil design and the optimization of the respective high and low frequency coils make this a good choice for many studies of lossy biology samples by solid-state NMR.
Reducing the RF heating of samples is important not only because of the potential for denaturing the proteins, but also because RF heating is not uniform across the sample volume, and even modest temperature gradients can broaden resonances and effectively reduce both resolution and sensitivity . The RF heating data for the strip-shield and MAGC probe designs are compared in Figure 8. Sample temperature is plotted as a function of the average RF field deposition, calculated as the product of the square of B1 and the duty cycle factor. The duty cycle is the ratio of the time that the RF irradiation is on to the total duration of the pulse sequence, and average RF field deposition values for 1H range from 4 – 10 for typical double-resonance multidimensional solid-state NMR experiments, and up to about 2.5 for the low frequency channels. For the 1H channel, RF heating is reduced 5-fold and 20-fold for the Strip-Shield and MAGC, respectively. The MAGC results in minimal sample heating due to the shielding effects provided by the inner coil in addition to the relatively small filling factor for the outer resonator. The strip-shield also offers a 7-fold reduction in 13C RF heating over a conventional solenoid coil, such as that employed in the MAGC, which may be significant in triple resonance experiments that incorporate 13C decoupling during signal acquisition. The scroll coil was shown to have favorable heating characteristics for a very wide range of sample ionic strengths . In our implementation on a 1H/31P probe, we found that it provided a 6.5-fold reduction in 1H RF heating ,
Optimal resolution and sensitivity in solid-state NMR experiments on proteins are obtained at high magnetic fields. A conventional solenoid coil has excellent performance characteristics and can be tuned to multiple frequencies. However, the insertion of a lossy aqueous sample impairs its performance in several ways. These effects are strongest at frequencies >700 MHz, but can also impact the performance at lower frequencies. The most noticeable effects are a large change in the center frequency and reduction of the Q of the circuit (Figure 1). While tuning the probe for lossy samples rather than an empty coil can compensate for this, it limits the ability to switch between lossy and non-lossy samples to tune and set up the spectrometer system for complex experiments. Increasing the tuning range to accommodate both lossy and non-lossy samples often results in unstable tuning. Equally deleterious effects result from the lowering of the Q of the circuit, which decreases the efficiency of the RF irradiations and the sensitivity of the probe. A complicating factor is that the individual high (1H) and low (15N, 13C) frequency channels in double- or triple- tuned probes are differentially affected by lossy samples at high fields, with a stronger effect on the higher frequency channels. The severe heating of lossy samples by high frequency RF irradiation can destroy samples, and this has been addressed by several recent developments, principally through the use of alternative coil geometries in the probes [8; 13; 35].
The strengths and weaknesses of the various coils used in probes for solid-state NMR of proteins are compared in Figure 9. In general, for samples that are not lossy, the solenoid coil offers the best overall performance but would be the worst choice for analysis of lossy samples. Cross-coil probes have sensitivity advantages, since the inductance and filling factor of the inner resonator are optimized for the lower frequency resonances that are detected, and because of the simplified single resonance circuits that are employed to the individual coils. The scroll coil would likely be the best choice for 1H detected experiments in situations where the reduced B1 capabilities and sensitivity of the lower frequency channels can be tolerated. The strip-shield-containing solenoid coil offers excellent RF heating characteristics, and provides a significant improvement in overall 1H and 13C performance with lossy samples at a small cost of 15N performance. Moreover, the strip shield reduces RF heating at the 13C frequency, which may will become an increasingly important factor as higher field magnets are developed.
The probe designs compared in Figure 9 are all aimed at improving performance characteristics for the study of lossy samples at high magnetic fields, where RF heating and the effects of lossy samples on probe sensitivity can be overwhelmingly for conventional solenoid coils. For the most part, these are relatively recent developments built upon principals that have been discussed in the literature and informally among spectroscopists for decades. There is no single optimal probe configuration for solid-state NMR of lossy biological samples. However, the design, construction, and testing of probes is an active area of research and the pace of improvements is increasing to match the unrivalled potential of solid-state NMR to study proteins under physiological conditions.
The ideas and their practical implementations described in this review were informed by valuable discussions with student and postdoctoral researchers at UCSD, and with colleagues at other universities and the vendors of commercial instrumentation. The daunting challenges in the design and construction of probes for solid-state NMR encourage the exchange of ideas and information in the field, which have benefited our own efforts and the writing of this review. This research was performed at the Biomedical Technology Resource for NMR Molecular Imaging of Proteins at the University of California, San Diego, which is supported by NIH grant P41EB002031.
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