Nuclear magnetic resonance (NMR) refers to a broad range of spectroscopic experiments intended to determine and analyze the absorption and emission of radiation by the nuclei of certain atoms. The radiation involved is in the radiofrequency range (RF) of the electromagnetic spectrum, typically between 100 and 1000 MHz; in a strong magnetic field, it produces transitions among the allowed orientational states of nuclear magnetic moments. The exact frequencies are exquisitely sensitive to molecular structure and dynamics. Therefore, NMR experiments can provide information regarding three-dimensional structures, the rates of conformational change, and interactions between molecules. NMR is nondestructive, and samples can be recovered unchanged at the end of an experiment. NMR measurements may be made with samples in any physical state (solid, liquid, gas), although, given the dependence of the NMR phenomenon on molecular mobility, the kinds of experiments done and the information that can be obtained from them are different for different states.
1. Basic NMR
Atomic nuclei must possess a certain property, called angular momentum or "spin," to be observable in an NMR experiment. At least one isotope exists of every known element that has this spin property, although this isotope may not be the most prevalent form of the element. Most experiments with biological materials use so-called spin 1/2 nuclei. Table 1gives some of the characteristics of these nuclei. Notice the low natural abundance of some. Most carbon on the Earth’s surface is the 12 isotope C, but this isotope has zero nuclear spin and is not observable in any NMR experiment.
The isotope C, however, is a spin 1/2 nucleus, and carbon NMR spectroscopy uses this isotope.
There is a 1.1% chance of finding a C nucleus at any given carbon position in a molecule, although the amount of the isotope can be increased to nearly 100% by suitable synthesis using labeled precursors. Similarly, most nitrogen in biological materials is 14N, and the amount of 15N at natural abundance is low but can be increased by synthesis using isotopically enriched precursor molecules.
Table 1. Properties of Spin 1/2 Nuclei
|
Natural Abundance |
NMR Frequ |
ency (MHz) for Strength |
Magnetic Field |
||
|
Isotope |
(%) |
11.75 T |
17.62 T |
21.15 T |
|
|
99.985 |
500.1 |
750.1 |
900.0 |
||
|
13C |
1.108 |
125.8 |
188.7 |
226.32 |
|
|
15n |
0.37 |
50.67 |
76.01 |
91.19 |
|
|
31P |
100.0 |
202.4 |
303.7 |
364.2 |
|
|
19f |
100.0 |
470.5 |
705.7 |
846.6 |
|
When a nucleus that has spin is placed into a magnetic field, its energy depends on its orientation in the field. A quantum mechanical description of a spin 1/2 nucleus in a magnetic field shows that the nucleus must take up one of two possible energy states, and that the difference between the energies of these states depends on the magnitude of the magnetic field. It is the transition from one of these states to the other, concomitant with the absorption or emission of a photon, that is detected in an NMR experiment.
Table 1lists the approximate frequencies for NMR transitions of selected nuclei with various magnetic fields that are used for experiments with biological molecules. The exact frequency for any particular nucleus in a molecule will depend on the molecular structure, as reflected by the chemical shift and any scalar (J) coupling that may be present. The basic goal of an NMR experiment is to determine the frequency or frequencies that can be associated with changes of energy state for the nucleus being studied. (See Chemical Shift, Scalar Coupling.)
A useful, although not completely rigorous, model of spin behavior depicts the spin (angular momentum) of a nucleus as a vector. In the case of spin 1/2 nuclei in a magnetic field, the vector has two possible orientations ("up" and "down"; Fig. 1), corresponding to the two allowed energy states. The spin vectors rotate around the direction of the laboratory magnetic field while keeping constant their angle relative to the field. As the spin vector rotates around the field in this manner, its energy stays constant. This rotation is termed Larmor precession. The frequency of precession is the same as the frequency of the radiation involved in transition of the nuclear spin from one allowed state to the other. If the laboratory field is 17.62 T, the frequency of Larmor precession for the nuclear spin 1 8 vector of the hydrogen ( H) nucleus is 7.5*10 revolutions per second.
Figure 1. The behavior of a spin 1/2 nucleus in a magnetic field (Bo). Such nuclei are allowed to take one of two possible orientations relative to the field. The energies of these are different. In either state, the spin undergoes Larmor precession around the direction of the field.
NMR experiments with biological molecules typically use 20-600 mL of a solution in which the material of interest is present at a concentration of 0.5 to 5.0 mM Under these conditions, a large 18 number (~10 ) of nuclei of any specific type will be present. When the sample is placed into a magnetic field, each nucleus of the sample with the spin property will be sorted into one of the allowed spin energy states and will undergo Larmor precession. The number of nuclei of a given type that is present in each particular allowed spin state is governed by the Boltzmann distribution law. Every molecule in the sample is acted on by seemingly random dynamic processes that exchange energy among the molecules of the sample, driving the system toward equilibrium. These processes are collectively known as relaxation. Any experimental operation that alters the state populations will be counteracted by these relaxation processes, so that the sample eventually returns to the Boltzmann populations that are characteristic of equilibrium.
Another feature of the equilibrium state is a random distribution of spins in their precessional motion. All of the spin-up vectors shown in Fig. 2a have the same component along the direction of the laboratory magnetic field, but their positions around the precessional path are random. (A similar situation holds for the spin-down vectors.)
Figure 2. Precessional behavior of spin 1/2 nuclei in a magnetic field. (a) Noncoherent precessional behavior of a collec precessional behavior of these spins. Nuclei that have the other allowed orientation relative to Bo undergo precession at t motions, at the same time that spins in the orientation illustrated are coherent.
An NMR spectrometer is only able to report the collective behavior of the nuclei of the sample, not the behavior of any single nucleus. It can produce signals only when there is a net macroscopic magnetic field from the sample that is at right angles (transverse) to the direction of the laboratory magnetic field. Although all spins of a particular type have the same Larmor precessional frequency when the sample is placed in the magnetic field, there is no defined starting point for Larmor precession (Fig. 2a). In this case, the individual transverse components of each spin vector collectively cancel, while the longitudinal components of the spins of the sample combine to create a macroscopic magnetic field component that is along the direction of the laboratory field (longitudinal to it). To generate a signal in an NMR spectrometer clearly requires that the equilibrium state of the sample in the laboratory magnetic field be altered.
To change the sample spins away from the equilibrium state requires the absorption or emission of photons, as the nuclei of the sample change spin states. The source of the needed radiation, the transmitter of the NMR instrument, typically is switched on for only a short time (1-20 |is). The energy of this RF pulse can alter the populations of nuclei in the allowed energy states. RF pulses of the appropriate strength and duration can also create coherence in the motions of individual spins (Fig. 2b). The resultant magnetic field produced when sample spins are precessing coherently, as suggested by Fig. 2b, has a macroscopic component in the plane that is transverse to the direction of the magnetic field—precisely what is needed to afford a detectable NMR signal. State populations altered by an RF pulse are eventually restored to their equilibrium values by relaxation processes. These processes also destroy any coherence of spin precession that has been created, and the NMR signal decays back to zero.
Except in special circumstances, RF pulses are nonselective—that is, if the radiofrequency energy source is pulsed on, all spins in the sample that have Larmor frequencies close to that frequency will respond to the pulse. If the RF pulse is at the proton Larmor frequency, all protons of the sample— those in methyl groups, those in aromatic rings, those in water molecules—will be affected by the pulse. If a pulse is designed to create coherence in proton spin motions, all spins in the sample will become coherent and, after the pulse, will contribute to the proton NMR signal detected by the spectrometer.
Spin coherence leads to NMR signals that oscillate at the Larmor frequency of the nuclei. If there are many coherences present (recognizable by their specific Larmor precessional frequencies), the detection system generates a signal that is the sum of the signals created by all coherences present.
The signal is digitized and stored in the instrument computer as a series of 10-10 numbers. Although the signal recorded is a decaying function of time, it is the frequencies present in this signal that is of interest. A Fourier transformation of the numbers representing the signal is performed to obtain these frequencies and their relative intensities.
NMR signals appear at different frequencies because of chemical shifts and the effects of scalar (spin) couplings. The frequency axis of an NMR spectrum is thus usually calibrated in terms of the NMR shielding parameter, using ppm units. Because it is only practical to measure differences in shielding parameters, one shielding parameter (that of a signal chosen as reference) is arbitrarily set to 0. A number on a frequency axis of an NMR spectrum therefore represents the difference between the shielding parameter for the nucleus of interest and that for the reference nucleus.
2. Multidimensional NMR Spectra
Dimension in NMR spectroscopy refers to the number of frequency or chemical shift axes that are needed to represent the results of an experiment. The most basic proton or C spectrum is a one-dimensional (1D) experiment: the intensities of spectral peaks are plotted as a function of one chemical shift axis. Figures 3 and 4 show 1D proton and C NMR spectra of an amino acid derivative. A close correspondence exists between the collections of peaks present in the spectrum and the chemical structure of the molecule examined. An experienced spectroscopist can assign these peaks to specific nuclei (hydrogens and carbons) of the molecule using any of several approaches, including analysis of the fine structure of the peaks due to scalar coupling.
Figure 3. The proton NMR spectrum of -acetyltryptophan obtained under conditions where the proton Larmor frequency is near 500 MHz. The sample was dissolved in d6-dimethylsulfoxide. The signal with the smallest shielding parameter (near 10.8 ppm) is readily assigned to the N-H proton of the indole ring. The signal at 2.5 ppm arises from residual hydrogen atoms in the solvent.
More elaborate NMR experiments can be designed in which observed intensities are dependent on two or more chemical shifts. A spectrum that involves two chemical shift axes is a two-dimensional (2D) spectrum. Reflection will show that a 2D NMR spectrum is actually a three-dimensional object with the two chemical-shift axes defining two dimensions of the object and intensity represented along the third. The most common way that 2D NMR spectra are presented is by use of a contour plot. The two chemical-shift axes appear in the plane of the page, while intensity is represented by a series of contours that correspond to levels of intensity, in the same way that contour lines on a topographic map represent different elevations. Intensity contours in 2D experiments can be either positive or negative and therefore appear above or below the plane. One technique for indicating the sign of the intensity is to plot positive intensities with solid (continuous) lines, whereas negative intensities are plotted with dashed contours. Alternatively, contours corresponding to positive and negative intensity can be plotted in different colors.
Figure 4. A 13C NMR spectrum of N-acetyltryptophan obtained with the same sample used to acquire the proton spectrum shown in Figure 3. A signal exists for each carbon atom in the molecule. The collection of signals at 39.5 ppm is due to the 13C atoms in the solvent.
If both chemical-shift axes of a 2D spectrum refer to the Larmor frequencies of the same nucleus, the spectrum is referred to as a homonuclear 2D experiment. Most commonly, homonuclear 2D experiments are proton-proton. In a heteronuclear 2D spectrum, the shift axes correspond to the Larmor frequencies of different types of nuclei with, perhaps, C frequencies appearing along one axis and proton frequencies along the other.
The essential features of a homonuclear 2D spectrum are abstracted in Figure 5. In this case, the range of frequencies along the axis labeled f is identical to the range of frequencies plotted along the other axis, f 2. There are always features along the 45° diagonal of a 2D map representing a homonuclear experiment. These peaks have the same coordinates (for example, S1,S1) along either axis. The coordinates of a diagonal peak correspond to the chemical shift of a peak or multiplet in the 1D spectrum of the same sample. There could be much fine structure of the diagonal peaks because of scalar coupling, but this might be obscured by the limited resolution of the manner the data are collected and displayed.
Figure 5. Part of a typical homonuclear proton-proton 2D NMR spectrum, using the same N-acetyltryptophan sample and experimental conditions that produced the 1D spectrum shown in Figure 3. This spectrum was produced by a DQF-COSY experiment. The cross peaks show that the aliphatic protons of the amino acid (with shielding parameters 2.98, 3.14, 4.45 ppm) are scalar coupled to each other.
Depending on the nature of the experiment and the structure of the molecule being studied, peaks that are off the diagonal at some coordinate (S1,S2) or (S2,S1) may appear in a 2D spectrum. These are called cross peaks, and their significance depends on the nature of the 2D experiment. Their presence, however, indicates that some relationship exists between the spins characterized by the S1 shift and spins that have the S2 shift. Figure 5 shows part of the homonuclear 2D spectrum that is obtained in a 2D NMR experiment with the same material used to obtain the 1D spectrum in Figure 3. For this particular spectrum (from a proton double quantum filtered Correlation Spectroscopy [DQFCOSY] experiment), cross peaks are present because there is scalar coupling between hydrogen atoms of the molecule. (see COSY Spectrum.)
For heteronuclear experiments, only cross peaks are present in the 2D spectrum. Again, the presence of a cross peak indicates that some structural relationship exists between the spins characterized by the S1 shift along one axis and spins that have the S2 shift along the other.
NMR experiments that provide results of higher dimensionality (for example, 3D, 4D, or 5D) exist and are often applied to structural studies of biological macromolecules. NMR spectra of higher dimensionality than 2D experiments are impossible to represent completely on a single planar surface. These spectra are viewed and analyzed by means of computer displays, which may use color-coding to convey the intensity of an NMR absorption or emission line. Although a few 3D homonuclear experiments are done, most 3D and higher-dimension NMR experiments with biological systems are heteronuclear, usually performed with materials that have carbon or nitrogen positions that are enriched in C and N, respectively. (See Chemical shift, Scalar coupling, COSY spectrum, NOESY spectrum, ROESY spectrum, TOCSY spectrum, Magnetization transfer, Isotope editing, Triple resonance.)
