FHtR卜s|NN1上4k SPE'TROSCO)Y LSI in Nuclear Magnetic Resonance Spectroscopy 32(1998)193-275 Technical aspects of nmr spectroscopy with biological macromolecules and studies of hydration in solution erhard Wider Institut fur Molekularbiologie und Biophysik, Eidgenossische Technische Hochschule, Honggerberg, CH-8093 Zurich, Switzerland Received 1 December 1997 Contents I. Introduction 2. Basic principles 2. 1. Theoretical aspects 2.1. 1. Magnetization, precession and Bloch equations 2.1.2. Operators, coherence, and product operator formalism 2. 1.3. Descriptive representations of experimental schemes 2.1. 4. Relax 2. 1.5. Through-bond correlations 203 2. 1.6. Through-space correlations 204 2.2. Radiofrequency pulses 2.2.1. Rectangular pulse 2.2.2. Amplitude-modulated pulses 2.2.3. Amplitude- and phase-modulated puls 2.3. Magnetic field gradients 210 2.4. Data acquisition 2. 1. Digitizing the signal 2.4.2. Handling the water resonance 2.4.3. Decoupling during acquisition 2.4.4. Oversampling and digital filter 214 5. Multidimensional NMR 215 2.6. Data processing 2.6. 1. Transforming the time domain data into a spectrum 217 2.6.2. Referencing the chemical shift 3. NMR instrumentation 3. 1. Layout of a high-resolution NMR spectrometer 3. 2. Spectrometer configuration for biomolecular NMR 3.3 116333455;fax:+41163315l 0022-2860/98/$19.00@ 1998 Elsevier Science B V. All rights reserved PS0079-6565(98)00014-4
G wider/Progress in Nuclear Magnetic Resonance Spectroscopy 32(1998)193-2 3.3. 1. The transmitting path 3.3. 2. The receiving path 3.3.3. The lock system 3.4. The magnet 3.5. The prol 3.5. 1. The radiofrequency coil 3.5. 2. The magnetic field gradient coil 228 3.5.3. The variable temperature operation 3.6. Stability of the sys stel 4. Basic segments of pulse sequences 230 4. 1. Evolution segments 4.2. Transfer segments 235 4.2. 1. Homonuclear through-bond transfer 4.2.2. Homonuclear through-space transfer 4.2.3. Heteronuclear transfer 43 Decoupling sequences 4.4. Pulsed magnetic field gradients 4.5. Combinations of basic segments 4. 5. 1. The HsQC and the hmQc scheme 4.5.2. Concatenating basic segment: 4. 6. Artefact reduction 5.2. NMR and hydration 5.3. Basic experiments 5.3. 1. NOEs between water and protein protons 53. 2. HYDRA 5.3.,3. Measurement of exchange rates using diffusion filter experiments 5.3. 4. Relaxation dispersion experiments 262 5.4. Artefacts in hydration studies at high magnetic fields 5.4.1. Radiation damping and demagnetizing field effect 5.4.2. Minimizing artefacts in hydration measurements 266 5.4.3. Consequences of radiation damping and demagnetizing field effects Acknowledgements Appendix A: The Bloch equations Appendix B: The product operator formalism 270 References Keywords: Protein NMR: Instrumentation; Hydration; Multidimensional NMR 1. Introduction macromolecules has been a growing field in research and applications [2]. The capability to observe signals The first nuclear magnetic resonance (NMR) from individual atoms in complex biological macro- spectrum of a protein was published some forty molecules in solution makes possible the measure- years ago [l] and ever since, NMR of biological ments of parameters that can be analysed in terms of
in Nuclear Magnetic Resonance Spectroscopy 32(1998)193-275 molecular structure, conformation and dynamics dynamics of biological macromolecules by NMR are Complete assignments of signals in an NMR spectrum established techniques. The rapid expansion of NMr to individual atoms in the molecule are a prerequisite techniques for applications to biological macro- for such studies; a problem that cannot generally be molecules increases the number of interested users solved on the basis of one-dimensional (ID) NMr with little technical background in NMR spectro- spectra. Only the application of two-dimensional scopy. These newcomers find it increasingly difficult (2D)NMR spectroscopy [3, 4], which spreads signals to follow and make use of the myriad of NMR experi into two frequency dimensions, allowed the develop ments available today. The applications and theoreti ment of a general strategy for the assignment of pro- cal foundation of biomolecular NMR are described in on signals in protein spectra using two types of 2D many excellent books, e. g [15-27 however, often petra[5-7 In['H,HJ-COSY spectra [3, 4 protons only a few experimental schemes are discussed and are correlated which are separated by up to three the common features of different pulse sequences are chemical bonds. In [H, HI-NOESY spectra [8, 91 not always made transparent. In addition, important correlations between protons which are closer than technical details of experimental implementations are 0.5 nm through space are detected. The combination either not discussed or may be missed in the over of these two techniques allows the assignment of most whelming amount of information. This review is proton NMR signals to individual protons in small intended to address the need for an introduction to proteins [6, 10,11]. In a further step all distances general technical and methodological aspects of obtainable from NOESY spectra provide the data for modern NMR experiments with biological macro- the calculation of protein structures [12, 13]. These molecules to these newcomers. The basis for this elatively simple techniques allow the determination presentation is not to provide complete experimental of structures of proteins with a molecular weight up to schemes, which change rather rapidly, but instead to 10 kDa whereas for larger proteins extensive signal present the underlying basic technical methods and overlap and increasing resonance linewidths prevent the basic segments from which individual experi complete assignments of all signals, This barrier can ments are constructed and which change much more be overcome with three-dimensional (3D)NMR slowly. The understanding of the basic segments techniques [14] and uniformly"C-and N-labelled should provide the basis for clarifying the functioning proteins. With these methods, systems with molecular of existing and newly developed experiments and weights up to 30 kDa can be studied. However, not assist the reader in making their own adjustments to only overlapping signals limit the size of the macre experiments or even in developing new methods. molecules that can be investigated; in addition faster This review was written with a reader in mind who relaxation of the signals with increasing molecular is interested in technical and methodological aspects weight leads to a substantial sensitivity loss in experi- of NMR with macromolecules in solution, who has ments. The molecular weight limit can be increased to had first contact with spectra of proteins in one and about 50 kDa using deuteration of the protein to two dimensions and knows the principles of their reduce relaxation. Simultaneously with the methodo- analysis. In addition, knowledge of the product logical developments, technical advances revolutio- operator formalism [28] is an advantage since the di nized the design of NMR spectrometers making it cussion of the basic segments requires the application possible to implement the complex experimental of this formalism. This text should help such readers schemes needed for multidimensional NMR experi- to quickly become familiar with the technicalities of ments. The increased complexity of the instrumen- multidimensional NMR experiments ation has been more and more hic om the user The main text starts with Section 2 where some by complex software control theoretical aspects are discussed briefly, followed by selection of all modes of operation from a software an introduction of technical principles starting with interface radiofrequency pulses and ending with multidimen- In parallel to the methodological and technical sional NMR and data processing. Not only in this velopments nmR has become an accepted tool in section but throughout the text, mathematics is kept ructural biology and investigations of structure and to the minimum necessary for the presentation of the
G wider/Progress in Nuclear Magnetic Resonance Spectroscopy 32(1998)193-275 technical aspects of NMR spectroscopy. Section 3 Hertz(Hz) the symbols w or f are used for the former introduces those parts of a modern NMR spectrometer and v for the latter which critically influence the performance of NMR The basis of all NMR experiments is the nuclear experiments. Section 4 concentrates on the basic ich can be interpreted as a magnetic momer experimental segments from which most of the vast A spin i nucleus in this view forms a small number of experiments available today are con- This dipole orients either parallel(a state)or structed. Section 5 discusses hydration studies with allel(B state) to a magnetic field leading to a small NMR and serves two purposes. First, it gives exam- energy difference Ae between the two states ples of experiments using the segments introduced in Section 4 and the les discussed in Section 2. AE=:Bo=hyBo Second, it introduces the technical aspects of a ver interesting application of NMR which allows detaile where Bo is a large externally applied homogeneous studies of individual water molecules in the hydration magnetic field, h is Planck's constant (h h/(2T), shell of a protein. and y the gyromagnetic ratio which is a property of the nucleus and can have a positive or a negative value. Table I lists the gyromagnetic ratio and some 2. Basic principles other properties of nuclei important in NMR of bio- logical macromolecules. from the two states of a L. Th favourable and thus possesses a higher population This section presents some basic theoretical aspects than the p state. Transitions between adjacent energy of nMR which are relevant to a technical discussio levels can be induced by small additional magnetic of the principles and experimental procedures used fields perpendicular to B, which oscillate with a fre- when studying biological macromolecules in solution quency vo fulfilling the resonance condition v,= AE/ by NMR. A rigorous discussion of the theoretical h. The frequency vo typically lies in the radio- foundation of NMR can be found in many textbooks, frequency range and is often referred to as the Larmor e.g. [16, 19, 24, 26, 29]. Only a very limited theoretical frequency. In the equilibrium state the boltzmann foundation is necessary for the technically oriented distribution favours the lower energy states. Thus, discussion of NMR methods in the following sections, the sum of all contributing nuclear magnetic moments The concept of energy levels, the Bloch equations and of the individual nuclei leads to a resulting macro- the product operator formalism are sufficient in most scopic magnetization M along the homogeneous cases. NMR is intimately related with frequencies and external field Bo. In the framework of classical to obtain a clear distinction between angular frequen- physics the behaviour of this magnetization under cies with units rad s and technical frequencies in the action of time-dependent magnetic fields can be Properties of selected nuclei Nucleus y710 Ts Natural abundance/% Relative sensitivit H 99985 H 4.106625 0015 9.65×10 H 6.72828 1.59x10 193378 0.037 ×10-2 10.8394 6.64×10 y, gyromagnetic ratio: 2=1/(2 For an equal number of nuclei to protons
G Wider/Progress in Nuclear Magnetic Resonance Spectroscopy 32(1998)193-275 described by the Bloch equations [30]. Because the In the rotating frame where b becomes static th spin is a quantum mechanical phenomenon this main magnetic field B. vanishes for nuclei with reso- description has a very limited scope, but it proves nance frequency vo. Hence, Eq(2)in this rotating ery useful for the description of single resonance frame contains only a transversecomponent hes under the action of radiofrequency(rf) pulses w=-y(B1, 0,0)with BI chosen along and thus for the characterization of the effect of RF Consequently M precesses by an angle p around the magnetic field B applied as a pulse for the short 2.1. Magnetization, precession and bloch equations In a classical description the macroscopic magneti- zation M created by the spins is described by a vector where B is called the flip angle of the pulse. The fip M parallel to the magnetic field vector Bo M is forced angle is often indicated in degrees, for example during move away from the direction of Bo by an a 90 pulse M can precess from the z axis to the x axis additional linearly polarized magnetic field BI per- The angle B depends on y and is negative for positive pendicular to Bo. BI must fulfil the resonance con- y values such as for protons(Table 1). For positive y ition and oscillate with the resonance frequency vo. values a magnetic field B pointing along the positive The magnetization vector M precesses about the x axis turns M towards the negative y axis. a B, field resulting magnetic field B=B.+BI with an angular along the +y axis turns M towards the +x axis velocity vector w pointing in the opposite direction [16, 31]. When applying an rF pulse with a frequency ind the components as described in Eq (2) differing from vo the action of the rf pulse becomes more complex as described in Appendix A, a situation r(2B, cos(2xv,(+6), 2B, sin(2 vol +o), B,) often referred to as non-ideal behaviour of the RF resonance The oscillating magnetic field 2B, coS(wRFt) used where w=(wr, Wy, Wo), B. is chosen along the z for excitation is linearly polarized in the laboratory ind o describes the angle between the x axis and B frame. The transformation into the rotating frame The magnetic field B is often applied only for short can best be followed when this is thought of as a time periods as RF pulses. The discussion of the superposition of two counter-rotating, circular polar motion of the magnetization vector M in space due zed fields with an amplitude B. When transforming to RF pulses is usually based on a rotating frame of into the rotating frame one component matches the reference which has the same z axis along the static Larmor frequency whereas the other oscillates at magnetic field B as the laboratory frame but rotates twice the Larmor frequency and does not fulfil the around the z axis with a frequency which is often resonance condition. Bloch and Siegert [32] calcu- hosen equal to the resonance frequency vo. In this lated the effect of the non-resonant field and found rotating frame of reference, the relevant component that it slightly shifts the frequency of the observed of the applied oscillating field B, appears static resonance lines away from the disturbing field by making the discussion and visualization much easier the small amount vB=(yB,)/Aw where y=Y/(2T) To fulfil the physical requirement that the magnetiza. and Av stands for twice the resonance frequency tion vector M returns to its equilibrium position in a The Bloch-Siegert shift is small and amounts, for finite period of time after a disturbance, a longitudinal example, to O5 Hz for a frequency of 600 MHz dur elaxation time T,(spin-lattice relaxation)is intro. ing an RF pulse with duration T of 10 us and a fip duced. The loss of coherent precession is described angle of 3(Eq (3)or 90. The shift disappears as by a transverse relaxation time T2(spin-spin relaxa- soon as b is switched off. An effect similar to the tion). The motion of the magnetization vector M Bloch-Siegert shift occurs whenever an RF field is under the action of the magnetic field B and hence applied with a frequency Av off-resonance for the under w can be described by the Bloch equations nuclear spins. Although first described by Ramsey [30]. These equations are presented in Appendix a [33] it is still very often referred to as the bloch- for further reference Siegert effect. To better distinguish it from the effect