Basic Principles of NMR

Abstract

An NMR spectrometer consists of two components: a high-field-strength superconducting magnet, in which the sample is located, and a console that can generate radio-frequency pulses in any desired combination. Every proton possesses a property known as magnetization, and when a sample is placed in a static magnetic field B 0 , the magnetization lies parallel to B 0 (defined as the z direction). To record a conventional one-dimensional NMR spectrum, a radio-frequency pulse B 1 is applied, which rotates the magnetization away from the z-axis towards the x–y plane. A free-induction decay is recorded immediately after the pulse, and Fourier transformation of this free-induction decay yields the conventional one-dimensional spectrum. To obtain additional information on interactions between spins, double or multiple irradiation experi-ments must be carried out. This requires the use of a second selective radiofrequency pulse B 2 at the position of a particular resonance. As long as there is no reso-nance overlap, the application of such experiments is relatively simple, but in the case of macromolecules, and proteins in particular, there is extensive spectral overlap, rendering this approach unfeasible. The limitations of one-dimensional (1D) NMR can be overcome by extending the measurements into a second dimension. All 2D-NMR experiments use the same basic scheme 15 , consisting of a preparation period, an evolution period (t 1) (during which the spins are labelled according to their chemical shift), a mixing period (during which the spins are correlated with each other), and finally a detection period (t 2). A number of experiments are recorded with successively incremented values of the evolution period t 1 to gen-erate a data matrix, s(t 1 ,t 2). 2D Fourier transformation of s(t 1 ,t 2) then yields the desired 2D frequency spec-trum S(␻ 1 ,␻ 2). In most homonuclear 2D experiments, the diagonal corresponds to the 1D spectrum, and the symmetrically placed cross peaks on either side of the diagonal indicate the existence of an interaction between two spins. The nature of the interaction depends on the type of experiment. Thus, in a corre-lation (COSY) experiment, the cross peaks arise from through-bond scalar correlations, while in a nuclear Overhauser enhancement (NOE) experiment, they arise from through-space correlations. The extension from 2D to 3D and 4D NMR is straightforward and illustrated schematically in Fig. 1 16 . Thus, a 3D experiment is constructed from two 2D experiments by leaving out the detection period of the first 2D experiment and the preparation pulse of the second. This results in a pulse train comprising two independently incremented evolution periods t 1 and t 2 , two corresponding mixing periods M 1 and M 2 , and a detection period t 3 . Similarly, a 4D experi-ment is obtained by combining three 2D experiments in an analogous fashion. The real challenge of 3D and 4D NMR is twofold: first, to ascertain which 2D experiments should be combined to best advantage; and second, to design the pulse sequences in such a way that undesired artifacts, which may severely interfere with the interpretation of the spectra, are removed. The nuclear Overhauser effect The main source of geometric information used in protein-structure determination lies in the nuclear Overhauser effect, which can be used to identify protons separated by less than 5 Å. This distance limit arises from the fact that the NOE (at short mixing times) is proportional to the inverse-sixth power of the distance between the protons. Hence the NOE inten-sity falls off very rapidly with increasing distance between proton pairs. Despite the short-range nature of the observed interactions, the short approximate interproton-distance restraints derived from NOE measurements can be highly conformationally restric-tive, particularly when they involve residues that are far apart in the sequence. The principle of the NOE is relatively simple. Con-sider a simple system with only two protons, between which magnetization is exchanged by a process known as cross relaxation. Because the cross-relaxation rates in both directions are equal, the magnetization of the two protons at equilibrium is equal. The approximate chemical analogy of such a system would be one with two interconverting species with an equilibrium con-stant of 1. The cross-relaxation rate is proportional to two variables: r –6 , where r is the distance between the two protons; and ␶ eff , the effective correlation time of the interproton vector. It follows that, if the magnet-ization of one of the spins is perturbed, the magnet-ization of the second spin will change. In the case of macromolecules, the cross-relaxation rates are positive and the leakage rate from the system is very small; this means that, at a long time following the perturbation event, the magnetization of the two protons would be equalized. The change in magnetization of proton i upon perturbation of the magnetization of proton j is known as the nuclear Overhauser effect. The initial build-up rate of the NOE is equal to the cross-relaxation rate, and hence proportional to r –6 . In 1D NMR, the NOE can be observed in a num-ber of ways, all of which involve the application of a 23