Hardware Requirements For Biological

Because of the demands of complexity and linewidth, the highest possible field strength is required. Currently a serious biological NMR group will have an 800 MHz spectrometer and possibly a group of 600s and 800s to accommodate the long experiment times (up to 3.5 days) and large array of experiments required for each sample. Organic chemists are no longer driving the research and development of NMR spectrometers—it is the more demanding experiments and deeper pockets of biological NMR research that is pushing the envelope. Now a few research institutions are investing in 900 MHz spectrometers, which cost many millions of dollars and require construction of an entire building to contain them, all for a 0.5 mL solution of a biological molecule!

The simplest hardware requirement is a probe capable of doing water suppression experiments in 90% H2O samples. "Water suppression" probes have carefully designed shielding on the wires leading up to the proton coil, eliminating the possibility that these wires can "pick up" an NMR signal from the solvent. Any solvent signal needs to be sharp so that it can be effectively suppressed, so this "lead pickup" can be a big problem because it leads to intense, broad solvent signals. Modern probes for biological NMR are

"triple-resonance" inverse probes: the *H coil (also used for 2H lock) is on the inside and the outer coil is double-tuned to 13C and 15N frequencies (1/4 and 1/10 of the *H frequency, respectively). Of course, sensitivity of the probe is critical, and biological researchers will pay a lot of money to get even a 10 or 20% increase in signal-to-noise. Gradients are essential, and in some cases "triple axis" gradients (three gradient channels that produce gradients along the x, y, and z axes) are desirable for optimal water suppression. The engineering limitations of putting three gradient coils in a probe limit the sensitivity a bit, so a single (z) axis gradient probe is usually preferred.

12.3.1 Cryogenic Probes

The latest fad in biological NMR is the cryogenic probe, which has a transmit/receive coil cooled to 25 K. This reduces thermal noise in the coil and leads to an increase of up to 3-4 times in signal-to-noise ratio for XH detection. The *H preamplifier is also cooled to 25 K so that thermal noise is minimized in the first stage of amplification of the FID. The sample is still around room temperature, so the technical challenge of a distance of a millimeter or so between the room temperature solution sample (~25°C) and the receiver coil at 25 K (-248°C) is considerable. This is accomplished by insulation with a high vacuum (~10-8 torr) between the outside of the probe and the cold inner workings, maintained by a turbo vacuum pump that runs continuously. A helium gas refrigerator (two stages of helium compression and expansion) sits away from the magnet and sends cold He gas (~ 10 K) into the probe, returning warmer He gas. A heater block in the probe maintains the desired 25 K temperature and is in thermal contact with the probe coil and the preamplifier. One of the problems with the cryogenic probe is that the advantages are considerably reduced in polar solvents (such as water!) and particularly if salts are present in the solution. For biological NMR the increase in signal-to-noise ratio is typically more like 2-2.5 times rather than 3-4 times, but this is still a major improvement. The main advantage is that we can go considerably lower than the recommended 1 mM concentration of protein. Sometimes a few hundreds of ^M is all the protein you can obtain, or all that will dissolve and remain in the monomeric state.

The spectrometer console has to have at least three separate channels to accommodate triple-resonance experiments in which we detect *H but use pulses on XH, 15N, and 13C. This leads to a problem in terminology because the older two-channel instruments have only two boxes that produce RF energy: the "transmitter" and the "decoupler." Varian uses the term decoupler 2 (dec2) for the additional channel, whereas Bruker sticks to F1, F2, and F3 for naming the three channels (not to be confused with the frequency axes of a 3D experiment: Fi, F2, and F3). Shaped pulse capability on all three channels is desirable. Many spectrometers have a fourth channel for 2H decoupling (dec3 or F4). 2H decoupling is a hardware challenge because the deuterium channel of the spectrometer is busy transmitting and receiving the lock signal in order to stabilize the field strength over time with the lock feedback loop (Chapter 3, Section 3.3). Spectrometers used for biological research often have a "lock switch" that allows rapid switching between transmitting 2H pulses and decoupling sequences and the continuous transmit/receive of the 2H lock feedback loop.

12.3.2 Gradient Shimming

The availability of pulsed-field gradients makes it possible to automatically shim using NMR imaging techniques. In MRI we rely on the dominance of water in the human body to obtain

Figure 12.1

a single, very strong XH NMR signal. By applying a gradient during the acquisition of the FID, the chemical-shift scale is transformed into a scale of physical position because there is only one peak in the normal XH spectrum. Biological NMR samples are similar in that they have one enormous and dominant peak: the H2O peak. In the absence of water suppression techniques, this signal can be used for NMR imaging to "map" the inhomogeneity of the magnetic field along the gradient axis. The software then calculates precisely how much each shim value will have to be changed and applies these changes to remove the inhomogeneity. In principle, this would be the end and you would have perfect homogeneity, but in reality, it takes several rounds of an iterative process: map the inhomogeneity, calculate and apply the shim changes, and repeat. While gradient shimming is not limited to biological samples, it is especially useful because the traditional manual shimming method is especially difficult in D2O or 90% H2O samples. The D2O line in the lock system is broad and the lock level (height of the 2H peak of D2O) does not respond much when shims are changed. Water suppression techniques are sensitive to errors in higher order shims (e.g., Z4, Z5), and these are nearly impossible to shim by hand.

The pulse sequence for gradient shimming is shown in Figure 12.1. This is an imaging experiment, so the gradient is on during the acquisition of the FID. Consider a single-axis (z-axis) gradient and a water signal that is precisely on-resonance. A small-angle pulse creates H2O coherence that is then "twisted" into a coherence helix by the first gradient. During the delay t, water coherence will remain stationary in a perfectly homogeneous field and the phase twist will be preserved exactly as it was at the end of the first gradient. The second gradient, of opposite sign and twice the amplitude as the first, is applied during the acquisition of the FID to "untwist" the helix (Fig. 12.2, left). The water molecules at the top of the tube (z = +8 mm) are experiencing a magnetic field reduced by the gradient so their magnetization vector is moving clockwise in the rotating frame during the recording of the FID. The water molecules at the bottom of the tube (z = -8 mm) are in a region of increased field due to the gradient so their magnetization vector is moving counterclockwise. So the actual frequencies of these vectors are detected in the FID as distinct chemical-shift values, each giving a peak at a different part of the 1H spectrum (Fig. 12.3, top). Water molecules at the center of the tube experience an unaltered Bo field so they give rise to a stationary magnetization vector during the FID, resulting in a peak at the center of the spectral window. The helical phase twist caused by the first gradient unravels during the second gradient and exactly halfway through the second gradient all of the vectors are

Figure 12.2

exactly aligned again (Fig. 12.2, left). At this moment there is an "echo" because the FID signal reaches a maximum when all the vectors align and add together from all levels of the tube. The phase of each peak in the spectrum is determined by the position of the vector at each level in the tube at this moment, halfway through the FID. Because they are all aligned on the y' axis (choosing y' as the phase reference), all of the peaks in the spectrum

are positive absorptive (Fig. 12.3, top). This tells us that during the delay t the Bo field was exactly the same at all levels of the tube and we have perfect field homogeneity.

Consider now what happens if the Bo field is not homogeneous. Let's assume that there is a Z1 shim error, which means a linear gradient in Bo along the z axis. During the t delay the vectors at each level will precess slightly away from the perfect helix created by the first gradient because they are not perfectly on-resonance at each level. Suppose that the linear Z1 gradient leads to an additional 45° rotation for each level, relative to the level above it. This means that at the crucial moment at the center of the FID the H2O magnetization vectors will not be aligned, but rather will have a helical twist of 45° phase change for each 1 mm of vertical distance (Fig. 12.2, right). This twist will lead to phase differences in the peaks in the spectrum. Because each peak represents one of the levels in the NMR tube, we see a progression of phase errors from left to right in the spectrum (Fig. 12.3, bottom): 0° (absorptive positive), 45°, 90° (dispersive), 135°, 180° (absorptive negative), and so on. These phases can be directly "read off" the spectrum as a map of the Bo field along the z axis. We know how long the t delay is, so we can calculate back from the amount of rotation (the phase difference) to obtain the deviation in rotation rate (in hertz) at each level. Assuming that the Z1 shim has been "calibrated" so we know how much field change we get for a given change in the Z1 setting, we could calculate exactly how much and in which direction we have to change the Z1 setting to "erase" the difference in Bo field along the z axis. This is automatic gradient shimming.

If the strength of the gradient used during the acquisition of the FID is 10 gauss/cm (0.001 T/cm), the Bo field is changed by 1 gauss (0.0001 T) for each mm of distance along the z axis. We know that a 500 MHz (*H) NMR instrument has a B0 field of 11.7 T, so 0.0001 T corresponds to (0.0001/11.7) x 500 MHz or 4.27 kHz for protons. The entire height of the NMR receiver coil (16 mm) corresponds to a range of 16 x 4.27 = 68.4 kHz. This is the width of our NMR signal (Fig. 12.3). A typical proton spectral window is 12.5 ppm wide, corresponding to 6.25 kHz on a 500 MHz instrument, so for gradient shimming, we are using a spectral window more than 10 times wider. Note also that it is the length of the receiver coil, not the depth of the water in the sample tube, that determines the width of the NMR signal in frequency domain. The water above and below the receiver coil is not detected so it does not contribute to the spectrum. The amount of "inhomogeneity" at each level can be calculated from the phase difference: if the delay t is set to 3 ms (0.003 s), a 45° phase error corresponds to a difference in Larmor frequency of cycles of rotation = 0.125 = Av (Hz) x t(s) = Av (0.003); Av = 0.125/0.003 = 41.7Hz

Thus we have a linear Bo field difference of 41.7 Hz per mm or 417 Hz/cm along the z axis. We can describe field differences in hertz because we are talking about XH frequencies, just the same way we refer to an 11.7 T magnet as a "500 MHz" magnet. The field differences along the z axis due to field inhomogeneity (bad shims) create phase differences in the signals at each level in the NMR tube as a result of the 3 ms delay time, and the imaging experiment (gradient on during the FID) separates these levels into different frequencies in the spectrum. The phase differences at these different levels can be converted into a precise map of the field strength difference (inhomogeneity) as a function of the z coordinate in the NMR sample.

By now you may have realized that there is a continuum of water molecules in the sample at all levels, not just at the 17 discreet levels we considered above. We can simulate the spectrum we expect by adding together a very large number of NMR peaks, starting at the

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