SOME APPLICATIONS OF RF- GRADIENTS AND EXCITATION SCULPTING IN NMR SPECTROSCOPY

Transcription

1 SOME APPLICATIONS OF RF- GRADIENTS AND EXCITATION SCULPTING IN NMR SPECTROSCOPY SAMI HEIKKINEN Department of Chemistry OULU 1999

2 SAMI HEIKKINEN SOME APPLICATIONS OF RF- GRADIENTS AND EXCITATION SCULPTING IN NMR SPECTROSCOPY Academic Dissertation to be presented with the assent of the Faculty of Science, University of Oulu, for public discussion in Raahensali (Auditorium L 10), on May 22nd, 1999, at 12 noon. OULUN YLIOPISTO, OULU 1999

3 Copyright 1999 Oulu University Library, 1999 Manuscript received Accepted Communicated by Professor Jukka Jokisaari Professor Jorma Mattinen ISBN (URL: ALSO AVAILABLE IN PRINTED FORMAT ISBN ISSN (URL: OULU UNIVERSITY LIBRARY OULU 1999

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5 3 " So not " (Matti Nykänen, Olympic Winner)

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7 5 Heikkinen, Sami, Some applications of RF-gradients and excitation sculpting in NMR spectroscopy Department ofchemistry, UniversityofOulu, P. O. Box3000, FIN Oulu, Finland 1999 Oulu, Finland (Manuscript received ) Abstract RF-gradients produced utilizing RF-field inhomogenity of conventional receiver/transmitter coil of NMR-probe can be used to mimic the effects of B 0 -gradients. This is done by placing long inhomogenous pulse in between two 90 pulses of appropriate phases (z-rotation cluster). B 0 - gradient based excitation sculpting can be converted into RF-gradient version. Selective onedimensional TOCSY and NOESY using RF-gradient based excitation sculpting are described. In addition, non-selective two-dimensional experiments, TOCSY and NOESY, with RF-gradient based coherence selection are presented. Excitation sculpting using BIRD or BIRD R asinversion element results in isotope filter. Pre-suppression of non- 13 C-bound protons using RF-gradient BIRD priorto HSQC enables recording of spectrumof comparable qualityto B 0 -gradient selected HSQC. This is beneficial for spectrometers lacking B 0 -gradient capabilities. Excitation sculpting using BIRD R can be used efficiently as low-pass filter in HMBC experiment. Furthermore, simultaneous eliminationofprotonsbound to 15 Nand 13 Ccanbeaccomplished with BIRD R based method. Keywords: selective experiments, isotope filters, BIRD, BIRD R

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9 7 Acknowledgements This work has been carried out at the Structural Elucidation Chemistry Division of the Department of Chemistry, University of Oulu and at the NMR Laboratory of the Institute of Biotechnology, University of Helsinki. I would like to express my sincere gratitude to my supervisor, Dean of the Faculty of Science, professor Erkki Rahkamaa for all the support and encouragement during these years as well as for guidance to the world of NMR. I am deeply grateful Docent Ilkka Kilpeläinen for fruitful collaboration. I also want to thank him for his valuable work of reading and commenting the manuscript of this thesis. I thank professor Risto Laitinen, the Head of the Department of Chemistry, University of Oulu, and professor Mart Saarma, the Director of the Institute of Biotechnology, University of Helsinki, for providing me excellent facilities to carry out this work. Professor Jukka Jokisaari and professor Jorma Mattinen are warmly acknowledged for critically reviewing this thesis. My warmest thanks are due to the Heikki, Pasi, Petri, Jorma, Elina, Sampo, Matti, and other friends in the Department of Chemistry for the good time during the years in Oulu. I also want to thank Perttu, Helena, Maarit, Olli, Hanna, Kari, Mari, Tero, Kimmo, Arto, and Tia for creating a homely but efficient atmosphere in Helsinki. I express my warmest thanks to my parents, grandparents, and parents-in-law for love and support. Finally, I am the most grateful to my family, Outi, Ida, and Anni, the most important people in my life, for their endless support and love. This work was supported in part by the Academy of Finland. Helsinki, May 1999 Sami Heikkinen

10 9 Abbreviations 12 C carbon C carbon N nitrogen-15 1D one-dimensional 1 H proton 2D two-dimensional Ala alanine Arg arginine Asn asparagine Asp aspartate B 0 static magnetic field B 1 radio frequency field BIRD bilinear pulse cluster; a method for selective inversion of protons bound to 13 Cand/or 15 N BIRD R BIRD inversion for remote protons. A method for selective inversion of protons not bound to 13 Cand/or 15 N COSY correlated spectroscopy CPD composite pulse decoupling D deuterium DPFGSE EXORCYCLE f 1 f 2 GARP-1 GBIRD GBIRD R Gln Glu Gly double pulsed-field-gradient spin echo a four-step phase-cycle used for elimination of artefacts rising from imperfect 180 pulses. The phase of the 180 pulse is incremented in 90 steps, whereas the phase of the receiver is inverted every second scan. indirectly detected frequency domain in 2D spectroscopy directly detected frequency domain in 2D spectroscopy composite pulse decoupling scheme B 0 -gradient BIRD B 0 -gradient BIRD R glutamine glutamate glycine

11 10 GOESY His HMBC HMQC HSQC Ile Leu LP Lys Met MLEV-17 NOESY PFG PFGSE Phe Pro RF Ser SL t 1 t 1max t 2 T 1 T 2 TnC TnI Thr TOCSY t p TPPI Tyr Val WALTZ-16 γ gradient enhanced nuclear Overhauser effect spectroscopy histidine heteronuclear multiple-bond correlation heteronuclear multiple-quantum correlation heteronuclear single-quantum correlation isoleucine leucine low-pass filter lysine methionine composite pulse isotropic mixing scheme; commonly used in homonuclear TOCSY. nuclear Overhauser enhancement spectroscopy pulsed-field-gradient pulsed-field-gradient spin echo phenylalanine proline radio frequency serine spin-lock incremented delay in 2D-spectroscopy the duration of the last (i.e. longest) time increment directly detected time domain in 2D spectroscopy longitudinal relaxation time transverse relaxation time N-terminal domain of cardiac Troponin C, 93 amino acids Troponin I, 28 amino acids threonine total correlation spectroscopy length of a pulse time-proportional phase-incrementation tyrosine valine composite pulse decoupling scheme gyromagnetic ratio

12 11 List of original papers The present thesis consists of the following original publications: I II Heikkinen S, Rahkamaa E & Kilpeläinen I (1998) Coherence Selection and Excitation Sculpting Using RF-Gradients in Selective 1D Experiments and Nonselective 2D Experiments. J Magn Reson 133: Heikkinen S, Rahkamaa E & Kilpeläinen I (1997) Use of RF Gradients in Excitation Sculpting, with Application to 2D HSQC. J Magn Reson 127: III Heikkinen S & Kilpeläinen I (1999) Gradient BIRD R : A Method to Select Uncoupled Magnetization. J Magn Reson 137: IV Heikkinen S, Permi P & Kilpeläinen I (1999) Gradient-BIRD R and filtration of 15 N, 13 C-bound protons. Manuscript. The papers will be referred to by their Roman numerals in the text.

13 13 Contents Abstract Acknowledgements Abbreviations List of original papers 1. Introduction Basic concepts Coherence selection and RF-gradients RF-gradients Excitation sculpting Isotope filters Applications RF-gradients in some homonuclear 1D- and 2D-experiments Selective one dimensional experiments with RF-gradients Two dimensional TOCSY and NOESY with RF-gradient selection Isotope filtration using excitation sculpting Gradient-BIRD and selection of X-bound magnetization Gradient-BIRD R and selection of non-x-bound magnetization Conclusions References Original papers... 58

14 14 1. Introduction Pulsed field gradient methods in modern NMR spectroscopy [1-4] provide means to improve the quality of the spectra. The performance of the gradient based experiments is quite often superior to classical phase cycled experiments. When applied to multidimensional experiments, gradients significantly shorten the phase cycle thus reducing the needed measurement time, provided that the sample concentration is high enough. Virtually, no phase cycling is needed as gradients can be used to select desired coherences. At the same time the level of artefacts is strongly suppressed. Also many 1D experiments benefit from the use of gradients, especially the selective 1D versions of common 2D experiments. Excitation sculpting based methods produce virtually artefact free spectra and therefore they are widely used to replace conventional selective excitation pulses. In addition, excitation sculpting can be utilized in isotope filtration. Since not all spectrometers are equipped with special pulsed field gradient accessories capable of creating B 0 -gradients, RF-gradients produced utilizing the residual B 1 -field inhomogenity of a normal transmitter/receiver coil can be found useful. Although B 0 -gradients can also be created using shim-coils, these are usually not beneficial, as they are not self-shielded, and thus need long eddy current recovery times. Many of the existing experiments using B 0 -gradients can be converted into RF-gradient versions without virtually any decrease in performance. The topics of current thesis are applications of RF-gradients and excitation sculpting. Chapter 2, Basic concepts, discusses general features of coherence selection (chapter 2.1), RF-gradients (chapter 2.1.1), excitation sculpting (chapter 2.2), and isotope filtering (chapter 2.3). Chapter 3, Applications, contains a discussion based on the work presented in the original articles (I-IV), and describes applications of RF-gradients for some 1D and 2D experiments (chapters 3.1, 3.1.1, and 3.1.2), and applications of excitation sculpting for isotope filtering (chapters 3.2, 3.2.1, and 3.2.2). The conclusions are presented in chapter 4.

15 15 2. Basic concepts 2.1. Coherence selection and RF-gradients When a radio frequency pulse with a flip angle of 90 is applied in an NMR-experiment, equilibrium magnetization is brought to the plane perpendicular to the external magnetic field and superposition of single quantum coherences is created. As only the 1-quantum coherence is detectable, no separate coherence selection is necessarily needed [5a, 6]. The situation is different if the initial pulse is followed by additional propagators which may consist pulses and/or free precession periods. Only pulses can induce coherence transformations and therefore additional coherence pathways can be created [6]. Also misset pulse lengths may serve as a source for additional coherence pathways. However, all the pathways leading to observable signal (-1-quantum coherence) may not be desired. Therefore, a successful multipulse NMR-experiment requires methods to select the desired coherence pathways. The traditional method to select the desired coherences is phase cycling [6, 7]. The phases of the pulses are changed along with the phase of the receiver and thus the selection of desired coherences is based on difference spectroscopy. The number of steps in the phase cycle (and their relative phases) determines which coherences are selected. If the pulse sequence contains several propagators, the total length of the phase cycle needed to select a particular coherence pathway can be very long [6-8]. A detailed description of the design of the phase cycles is given in an article by Bodenhausen et al. [6] Drastic decrease in the measurement time can be achieved with the aid of pulsed field gradients (B 0 -gradients), as the desired coherences can be selected in a single scan [9-14]. Here, a special gradient coil is used to create an additional magnetic field with a variable strength, linearly dependent on position with respect to particular axis in the laboratory frame. The B 0 -gradients dephase the transverse magnetization into a fan of vectors causing destruction of the net magnetization. This dephasing, or phase encoding, is however reversible and can be refocused back to observable magnetization. The magnitude and sign of the accumulated phase encoding is dependent on the coherence order present during the B 0 -gradient pulse, enabling one to utilize B 0 -gradients to select desired coherence pathways. Several review articles describing coherence selection

16 16 using B 0 -gradients can be found in the literature [4, 15-19]. The radio frequency field (RF- or B 1 -field) used to create pulses is not completely homogenous throughout the active sample volume. This inhomogenity of RF-field can be used to select desired coherences in a similar way as that used for B 0 -gradients. The inhomogenity is most pronounced with relatively long pulses. These pulses used to select desired coherence pathways are also called RF-gradients [20-25]. As this work is mostly concentrated on the use of RF-gradients, a more thorough discussion of the subject is presented in the following chapter (2.1.1) RF-gradients A radio frequency (RF) pulse generates magnetic field perpendicular to the direction of the static field with a fixed phase in the rotating frame. The pulse rotates the magnetization, which has a rotating frame phase perpendicular to the phase of the pulse. The magnetization vectors which have a phase parallel to the pulse phase are not rotated, but are in turn spin-locked. The angle (Φ) of rotation is dependent on the length of the pulse (t p ), the strength of RF-field (B 1 ) and gyromagnetic ratio of the nucleus (γ), defined by the relation Φ =-γb 1 t p. Ideally, with a 90 pulse with phase x, all the magnetization vectors aligned along the z-axis (direction of the main field) throughout a sample volume will be rotated in the y-axis [5b]. In practice, however, the B 1 -field is not uniform, and the magnetization vectors will experience different rotation angles, depending on their location within the sample [24, 26]. If the applied pulse is short, the dispersion is not significant, but with a long pulse (a nominal rotation angle several cycles), the magnetization vectors will be dispersed into a fan of vectors in a plane perpendicular to the phase of the pulse. The observable magnetization is now significantly attenuated, and possesses phase encoding [24]. The level of attenuation is dictated by the B 1 - inhomogenity of the transmitter coil producing the pulses [27]. The attenuation of the magnetization as a function of increasing rotation angles is a common performance test for NMR-probes, and can be measured (Fig. 1) by observing the intensity of an onresonance signal with increasing flip angles. Notably (Fig. 1), even with very long pulses, the signal is not completely dephased.

17 17 Fig. 1. The intensity of a signal (on-resonance) monitored as a function of increasing length of the excitation pulse. The length of the excitation pulse was incremented by 2 µs steps starting from an initial value of 2 µs. Intensity ratios 1.00:0.87:0.78:0.66 were obtained for rotation angles 90 (8 µs), 450 (40 µs), 810 (72 µs), and 1170 (104 µs), respectively. Spectra were recorded on a Varian UNITY 500 NMR spectrometer equipped with a Varian tripleresonance probe and z-axis gradient system at 303 K. The sample was 0.5 M sucrose in D 2 O. The displayed signal belongs to the anomeric proton of the sucrose molecule. The dephasing caused by the residual inhomogenity is reversible, and previously phase encoded magnetization can be decoded back to observable magnetization by applying a pulse of same length, but with an opposite phase [28]. The ability of long pulses to phase en- and decode magnetization makes it possible to utilize them for magnetization selection. These long pulses utilizing the inhomogenity of B 1 -field are called RF-gradients and they act on nutation producing space-dependent rotations on nuclear magnetization [24]. If a RF-gradient is produced with a conventional transmitter/receiver coil utilizing the residual inhomogenity of the B 1 -field, the resulting gradient is planar i.e. the amplitude of the RF-field is spatially dependent, whereas the phase is constant [29]. As an example, Eq. 1 presents product operators [30] for the dephasing of z-magnetization with long pulse applied along the x-axis and subsequent rephasing with a pulse of same length but of opposite phase. I z Φ x H I z cosφ I y sinφ H Φ x I z cos 2 Φ +I y cosφsinφ I y sinφcosφ +I z sin 2 Φ =I z (1) The rotation angle Φ is dependent on the spatial localization within the sample. It should be noted that spatial localization with RF-gradients created by normal transmitter/receiver coil is not a simple function of one single axis in the laboratory frame, as is the case with B 0 -gradients [27].

18 18 The disappearance of cosφsinφ and sinφcosφ-terms can be explained by performing integration from Φ = 0toΦ =2π resulting in a zero integral for both cosφ and sinφ, whereas trigonometric terms with even powers result in a non-vanishing integral [24]. Alternatively, refocusing (i.e. rotary echo formation) can be achieved if a 180 pulse is placed between two long pulses with nominal rotation angle Φ. The phases for 180 pulse and Φ-pulses should differ by 90, Φ (x) (y) - Φ (x) [28]. If a long pulse i.e. when a spin-lock pulse (SL) is placed into the so-called z-rotation sandwich with proper phases, 90 (φ) -SL (φ+π/2) -90 (φ+π) (φ = x, y, -x, or y), for instance 90 (y) -SL (-x) -90 (-y), the dephasing and rephasing properties of the RF-gradient can be assumedtobesimilartonormalb 0 -gradients [I-III, 22, 31]. In this case, the RF-gradient acts only on the magnetization that is in the transverse plane, in the same way as the B 0 - gradients. The main advantage of this z-rotation approach is that the defocusing and refocusing follow the same rules as for B 0 -gradients, without any need to consider the relative phases of the SL- and refocusing pulses. Also the polarization of the B 0 -gradient (gradient applied either along +z or -z-axis) is easy to mimic with z-rotation approach, just by changing the phase of the SL-pulse by 180 [22]. RF-gradients can be used in the same way as the conventional B 0 -gradients, to dephase the unwanted coherences [I-III, 27-29, 32, 33], or to use RF-gradients to select the desired ones [I, 23-26, 29]. The RF-gradients have some advantages over conventional B 0 -gradients [24]. The RF-gradients are frequency selective, they do not cause lock disturbances, and there is no need for eddy-current recovery delays. In addition, RF-gradients can be created using a standard coil (usually B 1 -inhomogenity of the normal coil is sufficient), so no extra hardware is needed. RF-gradients are also capable of inducing coherence transformations and phase encoding simultaneously [24, 26, 29, 34-36]. The most important advantage is, however, the fact that there is virtually no chemical shift or coupling evolution during the RF-gradient pulses, provided that the B 1 -field is strong enough [22]. As the RF-gradients act on nutation rather than on precession (B 0 -gradients), off-resonance effects will reduce performance with large bandwidths. With large resonance offsets, some of the magnetization will be spin-locked on the tilted axis of the effective RF-gradient field and will not be properly dephased [27]. Fortunately, if RF-gradients are used on proton frequency, the offset effects are not so dramatic when resonances are within the normal spectral width. Dephasing using RFgradients produced with a normal coil will suffer from the improved B 1 -homogenity of modern probes. In practice, this means that adequate suppression of large signals (i.e. water) is not possible as suppression ratios better than 1:50000 are needed. On the other hand, if the signal to be destroyed is about a few hundredfold larger than the desired signal, the RF-gradients perform well. Special NMR-probes have been constructed, where the normal coil is used for pulses and a separate coil with large B 1 -inhomogenity is used for the RF-gradient generation to improve the suppression ratios [23, 25, 28]. In principle, the RF-gradients could also be used to select coherences in inverse detected heteronuclear experiments. When the magnetization is transferred to the heteronucleus (nucleus X), phase encoding with RF-gradient applied at X-channel can be performed. This phase encoding can be decoded back to observable proton magnetization prior to detection with RF-gradient applied at proton frequency. However, problems are encountered because the spatial distribution of the RF-field is frequency

19 19 dependent [29]. In addition, possible large dispersion of the chemical shifts of the heteronucleus will introduce offset problems for RF-gradient dephasing. The equivalent action on magnetization vectors of B 0 - and RF-gradients arranged in a z-rotation sandwich makes it possible to use most of the homonuclear, B 0 -gradient based experiments with those spectrometers lacking B 0 -gradient capabilities. Also, those heteronuclear experiments where B 0 -gradients are used to dephase proton magnetization are accessible using RF-gradients Excitation sculpting Quite recently Shaka and coworkers introduced the concept of excitation sculpting [37-39]. Basically, it is a pulse sequence element that contains a selective refocusing/inversion propagator embraced by pulsed field gradients (B 0 -gradients). This forms the so-called pulsed field gradient spin echo (PFGSE). Applying this element after a non-selective excitation pulse, all the magnetization that does not experience the inversion is destroyed by the dephasing effect of the gradients. The amplitude of the refocused magnetization depends on the probability of the spin being flipped by the refocusing/inversion propagator, i.e. inversion profile. If the used refocusing/inversion propagator has some frequency dependent phase variation across the excitation bandwidth, these phase errors will also appear in the spectrum. However, if two PFGSEelements are placed in series, the phase properties of the propagator do not affect the resulting spectrum and the excitation profile of the double PFGSE (double pulsed field gradient spin echo, DPFGSE) depends only on the inversion profile of the applied refocusing/inversion pulse [37]. As a single PFGSE cannot eliminate frequencydependent phase errors within the excitation bandwidth, inversion pulses which introduce the aforementioned errors cannot be used as the selective inversion elements in PFGSE. The DPFGSE eliminates this shortcoming and thus frequency-modulated pulses, like hyperbolic secant and other frequency-swept pulses, can be applied reintroducing their tolerance to RF-inhomogenity and miscalibration effects. Due to the superior phase properties of the DPFGSE, the difference between the inversion and refocusing pulses vanishes when they are used in DPFGSE [39]. In principle, the excitation sculpting method does not need any phase cycling because of the use of B 0 -gradients. Frequently, however, EXORCYCLE [40] is applied on the 180 degree pulses to reinforce the echo formation [37]. Basically, EXORCYCLE is equivalent to gradients on both side of the 180 pulse. In practice, if a very strong signal is to be removed, EXORCYCLE alone does not succeed adequately as it relies on subtraction [37]. Excitation sculpting is an efficient substitute for conventional selective excitation, as the phase of the transverse magnetization created by conventional selective excitation pulse is not constant within the whole bandwidth [39]. In addition, the calibration of the 180 selective pulse is easier and there is no phase difference between the hard and soft pulses to be compensated for in the phase cycles [41]. Furthermore, there is no chemical shift or coupling evolution to be taken into account, as 180 pulses are used instead of selective excitation pulses [4, 18]. Today, numerous applications of excitation sculpting have been introduced in the literature. These include solvent

20 20 suppression [37, 42], selective 1D experiments [I, 43-46], multiple excitation [47, 48], multiple solvent suppression [49], multiplication of J-coupling [50, 51], band-filtering in 2D experiments [52], interaction studies [53], and isotope filtering [II-IV, 38, 39, 54], just to mention a few. The original paper of Shaka et al. described the use of DPFGSE utilizing BIRDelement as an inversion propagator for those protons directly bound to 13 C-nucleus [55, 38]. The protons not attached to 13 C are subject to the dephasing action of B 0 -gradients and therefore their intensity is strongly suppressed. Due to the homonuclear J HH - couplings, complete suppression is not possible with double GBIRD. The achievable suppression ratios (50-200) are not enough to eliminate 12 C-bound protons when natural abundance samples are examined [38, 39]. The aforementioned suppression ratios can cope well with mixtures consisting of isotopically enriched and natural abundance molecules, provided that the amount of natural abundance species is not significantly large. Thus, the double GBIRD can be utilized as an isotope filter in various experiments. In practice, however, as there are better ways to select 13 C-bound protons (like HMQC [56-61] or HSQC [61-64]), the applications of double GBIRD may be limited to its original purpose, i.e. to pre-suppress the non 13 C-bound protons prior to phase cycled HMQC/HSQC [56-59, 62, 63]. If the phase of the central 180 pulse of the BIRD propagator is changed from x to y, the resulting BIRD R (BIRD inversion for remote protons) inverts the 12 C-bound protons [55]. The double GBIRD R is very tolerant to J-mismatch effects and can be used as an efficient isotope filter [III, IV]. The excitation sculpting based isotope filtering via BIRD- and BIRD R is discussed in chapter 3.2. Isotope filtering in general is discussed in the chapter Isotope filters The availability of the isotopically enriched samples (especially protein samples, 15 N/ 13 C) has introduced the need for methods which allow selective detection of either protons that are bound to the labeled heteronucleus or that are bound to non-labeled ones. Also when working with natural abundance samples, methods which allow one to suppress the signals arising from the protons directly bound to NMR-active heteronuclei can be very useful, particularly in HMBC-type experiments [60, 65]. The selection, or the elimination, of the magnetization arising from the directly bound protons can be performed using so-called X half-filters. The most usual are so-called in-phase and antiphase filters. The names of the aforementioned filters arise from the state of the heteronuclear magnetization following the filter. Simple in-phase and antiphase filters are presented in Fig. 2 [66-68].

21 21 A) 1 H: XH XH φ1 X: B) 1 H: XH/2 XH/2 φ1 X: Fig. 2. Pulse sequences [66-68] for a simple in-phase (A) and an antiphase X half-filters (B). Narrow white bars and filled black bars indicate 90 and 180 pulses, respectively. All pulses have x-phase unless otherwise indicated. Phases for the pulses: Filtration of X-bound protons, φ 1 = x, -x; receiver = x, x and filtration of non-x-bound protons, φ 1 = x, -x; receiver = x, -x. The delay XH =1/(2 1 J XH ). The implementation of the X half-filters into a variety of pulse sequences is straightforward. The desired filter selects or rejects protons that are coupled to X-spins in the time domain that follows the filter period. The X half-filters are based on special delay periods during which the heteronuclear coupling over one bond 1 J XH is allowed to evolve to create a proton magnetization antiphase with respect to 1 J XH,i.e.H x X z [67]. The time needed to create such a H x X z -magnetization starting from H y is 1/(2 1 J XH ). As there is usually more than one value for 1 J XH in real molecules, the delay XH is set for an average 1 J XH ( for instance 145 Hz for 1 J CH :s) [68]. In order to obtain peaks with good lineshape features, the delay XH should be sufficiently short to prevent extensive evolution of the homonuclear proton-proton couplings. This in turn means for these filters to work properly, that the heteronuclear coupling constant 1 J XH should be significantly larger than the homonuclear coupling constants J HH [2]. This condition is adequately fulfilled with 1 J NH and 1 J CH. In 2D experiments, the half-filter can be applied to either t 1 or t 2 domain. The spectrum can also be acquired with half-filtering in both t 1 and t 2 domains (so-called double half-filtration) [67]. The simplest filter to selectively detect the non-x-bound protons is the low-pass filter commonly used in HMBC-experiment [65, 70]. Because in-phase magnetization during the indirectly or directly detected period is often preferred, the antiphase X half-filters are suitable for elimination of the directly X-bound proton magnetization, if separate refocusing periods are not applied. The in-phase X half-filter presented can in turn be used for both purposes [67]. The PFG z-filter (pulsed field gradient z-filter) is designed only for detection of the non-bound proton magnetization [69]. The sequence for PFG

22 22 (pulsed field gradient) z-filter for elimination of X,Y-bound protons is presented in Fig. 3A. Usually, X and Y represent the 15 Nand 13 C nuclei, respectively. A) 1 H: NH/2 ( NH- CH)/2 CH/2 tg 15 N: 13 C: Grad: G1 G1 G2 B) 1 H: NH/2 ( NH- CH1)/2 CH1/2 tg NH/2 ( NH- CH2)/2 CH2/2 tg 15 N: 13 C: Grad: G1 G1 G2 G3 G3 G4 Fig. 3. Pulse sequences for PFG z-filter to eliminate 15 N, 13 C-attached proton signals [69]. A) Single filter. B) Double filter tuned to two different 1 J CH values. Narrow bars and filled black bars indicate 90 and 180 pulses, respectively. All pulses are applied along the x-axis unless otherwise indicated. The delay t G represents duration of gradient. Gradients are presented with white half-ellipses. The gradient amplitudes G1, G2, G3, and G4 should have different values.

23 23 The total length of the J-evolution period of the filter is determined by the smaller heteronuclear coupling constant, i.e. when the nuclei involved are 15 Nand 13 C, this duration is determined by 1 J NH, NH =1/(2 1 J NH ) [69]. The difference between 1 J NH and 1 J CH can be taken into account if the carbon 180 pulse is shifted by ( NH - CH )/2 from the midpoint of the PFG z-filter element [69]. Similar trick can be applied to other X half-filters as well. Now the evolution times for 1 J NH and 1 J CH are NH and CH, respectively. The magnetization of 15 N- and 13 C-bound protons just before the z-filter element will be in the antiphase form (H N xn z and H C xc z ), whereas the magnetization of the non-bound protons are along the y-axis (H y ). The proton 90 (x) pulse flips the H y - magnetization to z-axis without disturbing H N xn z and H C xc z magnetization, which then will be effectively destroyed by the B 0 -gradient applied during the z-filter delay. The succeeding 90 (x) pulse then flips the z-magnetization of the non-bound protons to observable transverse magnetization. The fact that there is more than just one value for 1 J XH leads to phenomenon called J- leaking [68, 69]. A single X half-filter, tuned to some average value J XH,isusedto eliminate protons bound to nucleus X will pass a small amount of undesired magnetization with an intensity depending on the difference between the actual value of heteronuclear coupling constant, and the value used to tune the filter (so-called J- mismatch) [68]. If the intensity of the leaking signals is comparable to the desired ones, the analysis of the spectrum may lead to erroneous interpretations. As an example, the product operator calculations [30] were performed for the PFG z-filter (Fig. 3A), which filters out X-bound proton magnetization. Results for A- and AX-spin systems are presented in Eq. 2 and Eq. 3. The effects of relaxation are not taken into account in calculations. A-spin system: H z / 2 180x 180 / 2 -H y H 0 90 x 90 x H H z B gradient H x X H y 90 x H -H y (2) AX-spin system: H 90 x B 0 gradient H z / 2 180x 180x / 2 -H y X H y cos(π 1 J XH XH )-H x X z sin(π 1 J XH XH ) H z cos(π 1 J XH XH )-H x X z sin(π 1 J XH XH ) H 90 x -H y cos(π 1 J XH XH ) (3) 90 x H H The desired magnetization component is presented in Eq. 2 and the component due to J-leakage is presented in Eq. 3. Both the leaking and the desired magnetization appear as absorptive, in-phase signals. If the delay XH is correctly matched, the intensity of the leaking magnetization -H y cos(π 1 J XH XH ) will be zero. However, any deviation from the ideal XH -value will introduce leaking. The performance of the filters can be improved by applying two (or more) filter steps with different XH -values in series. The filtering properties of double tuned filters are superior to single stage filters, and therefore these two stage filters have found widespread use in modern NMR-spectroscopy [68, 69]. The pulse sequence for double tuned PFG z-filter is presented in Fig. 3B. The intensity of

24 24 leaking magnetization obtained using double tuned PFG z-filter (tuned with delays XH1 and XH2 )ispresentedineq.4. I leaking(double tuned) -H y cos(π 1 J XH XH1 )cos (π 1 J XH XH2 ) (4) Figure 4 presents theoretical curves for intensity of the leaking magnetization as a function of heteronuclear coupling constant. The intensities of the leaking magnetization for single PFG z-filter and double tuned PFG z-filter were calculated using Eq. 3 and Eq. 4, respectively. The single filter was tuned to 1 J XH =145 Hz whereas values 1 J XH1 =135 Hz and 1 J XH2 =170 Hz were used to tune the double filter. 40% 30% 20% 10% 0% -10% -20% -30% -40% The intensity of leaking signal J XH Fig. 4. Theoretical leaking intensity (percentage of intensity obtained without filtering) as a function of 1 J XH for single PFG z-filter (open rectangles) and double tuned PFG z-filter (filled rectangles) applied to isolated HX-system. The single PFG z-filter was tuned to coupling 145 Hz. Two values, 135 Hz and 170 Hz, were used for the double tuned PFG z- filter. As is the case with all gradient-purged methods with more than one purging step, one must be careful with gradient polarizations, levels and durations to avoid inadvertent refocusing of the previously dephased, unwanted coherences. J-leaking is of major concern when the protons bound to 13 C are to be filtered out. This rises from the fact that the range of 1 J CH is relatively large [1] and thus a filter tuned for a single 1 J CH -value will not usually have acceptable filtering properties [68]. Two filter elements tuned to different 1 J CH -values for example 135 Hz (aliphatic protons) and

25 Hz (aromatic protons) can be applied in succession. This will significantly improve the suppression of the 13 C-bound protons over a considerable range of coupling constant values. The effective elimination of 15 N-bound protons in peptides and proteins (in isotropic solutions) does not require double tuning as the 1 J NH :s fall into a narrow range ( 1 J NH = Hz). If both 15 N- and 13 C-bound protons are to be filtered out simultaneously using the double tuned filter, usually each of the filters are tuned to different 1 J CH :s whereas a single value for 1 J NH is used for both elements (Fig. 3B) [69]. In contrast to filtration of X-bound protons, the mismatches in XH value do not cause J-leaking when X half-filters are used to filter the non-x-bound proton magnetization. The mismatches in the delay XH will only cause a drop in the signal intensities. In addition to the usual X half-filters the selection of the X-bound protons can also be done using HSQC [61-64] and HMQC [56-61] sequences utilizing gradients or phase cycling for coherence selection. It should be noted that phase cycled HMQC without time incrementation is in fact an in-phase X half-filter (Fig. 2A).

26 26 3. Applications 3.1. RF-gradients in some homonuclear 1D- and 2D-experiments The following two chapters present applications of RF-gradients in homonuclear, selective 1D-, and non-selective 2D TOCSY- and NOESY-experiments. The RFgradients in the presented methods are produced using the z-rotation approach discussed in chapter and thus mimic the effect of B 0 -gradients. A similar RF-gradient approach was also applied to isotope filtration (isotope edited) experiments with BIRD and BIRD R, and these are discussed separately in chapters and Selective one dimensional experiments with RF-gradients The simplest way to selectively excite a particular resonance is to apply a frequency selective 90 pulse. The evolution of couplings and chemical shifts during the pulse may easily lead to phase distortions in the resulting spectrum. These problems can be to some extent circumvented with properly shaped excitation pulses which result in pure phase spectra [71-74]. Application of this kind of excitation pulses requires waveform generator which may not be available in older spectrometers. Due to aforementioned fact, and reasons concerning differences between selective 90 and 180 pulses discussed earlier (chapter 2.2), approaches which utilize selective inversion rather than selective excitation are usually recommended. If the capability of the spectrometer in producing selective pulses is restricted to long rectangular pulses or DANTE shaping [75, 76], they are also the only sensible possibility. A selective 180 pulse embraced by two gradients can be used either to destroy all the magnetization not inverted by selective pulse (i.e. excitation sculpting method [37-39]), or to selectively phase encode the inverted magnetization by the gradients [18, 41, 77-81]. In the excitation sculpting approach, the gradients on both side of the selective pulsehavethesamepolarity.iftheb 0 -gradients are replaced with spin-lock pulses arranged in the z-rotation sandwich [22, 31], the concept of equal polarity means that the phases of the spin-lock pulses must be the same. If, in turn, selective phase encoding is

27 27 desired, the phases of the spin-lock pulses in the z-rotation sandwiches on both sides of the selective pulse should differ by 180. Now the inverted magnetization will be labeled by the dephasing action of the both gradients and all other magnetization is not affected. The gradient labeled magnetization can be refocused later in the pulse sequence by applying a gradient with an amplitude equal to the sum of amplitudes of the dephasing gradients. When RF-gradients are used, the most convenient way is to apply a similar RFgradient with duration equal to the sum of the durations of the dephasing gradients. As the evolution of the chemical shifts is not active during the RF-gradients [22], the rephasing can be done without an additional delay and a 180 pulse, which are often needed to compensate for the evolution of the chemical shifts if B 0 -gradients are used [4]. When gradients are used for coherence selection, half of the signal intensity will be lost due to the fact that gradients can select only one of the two coherence pathways [4]. Figures 5A-B present single and double echo excitation sculpting pulse sequence elements. The pulse sequences presented in Fig. 5C-D are based on RF-gradient selection. The white box marked "mixing" can be virtually any mixing element, for example MLEV-17 [82] for a selective 1D TOCSY [I], or 90 -(spoil gradient)-delay-90 for a selective1d NOESY [I]. Selective 1D versions of NOESY [43, 45, 78, 83, 84] and TOCSY [41, 83-85] can be useful for relatively small organic compounds. The selective 1D TOCSY extracts out proton signals of a selected spin system. This can be important when analysis of the proton spectrum is hampered by overlapping signals. The selective 1D TOCSY experiment can be performed using the pulse sequences presented in Fig. 5A-D. Because half of the magnetization is lost in the gradient selected methods (Fig. 5C-D), excitation sculpting based methods are naturally preferred. Figure 6 presents anomeric proton selective 1D TOCSY spectra of sucrose recorded using pulse sequence presented in Fig. 5B (excitation sculpting method) and the corresponding sequence with B 0 -gradients [I]. Both sets of spectra were recorded with 1, 2, and 4 scans. If a single-scan spectrum is needed, the spectrum recorded using the B 0 - gradient method is better but the suppression of the unwanted signals is not complete, though. As two scans are acceptable (the first two steps of EXORCYCLE [40]), both methods work well. Figure 7 presents anomeric proton selective 1D TOCSY using RF-gradient selection approach (pulse sequence presented in Fig. 5C) [I]. The spectrum was recorded with two scans. The quality of the spectrum is the same as for spectrum recorded with the excitation sculpting method utilizing RF-gradients (Fig. 6, two scans)

28 A) y -y- -x - φ1 y -y -x 28 1 H: SL1 SL1 MIXING B) y -y - -x - φ1 y -x -y φ2 y -y -x 1 H: SL1 SL1 + SL2 SL2 MIXING C) y -y- -x - φ1 y -y x y -y x 1 H: SL1 SL1 MIXING 2 SL1 D) y -y- -x - φ1 y x -y φ2 y -y -x y -y x 1 H: SL1 SL1 + SL2 SL2 MIXING 2 SL1+2 SL2 φ3 φ3 φ3 trim MLEV-17 trim :TOCSY MIXING = φ4 y -y x SL3 tmix :NOESY Fig. 5. Selective RF-gradient 1D TOCSY and NOESY using the excitation sculpting approach (single and double echoes, A and B) and gradient selection approach (single and double echo, C and D). Narrow black and white bars indicate 90 hard rectangular pulses in the basic sequences and in RF-gradients using z-rotation approach, respectively. The long spin lock pulses in z-rotation clusters are presented with wide gray bars denoted SL. Selective 180 pulses are presented by dark half ellipses. Wide gray bars denoted trim present low power trim pulses in the TOCSY mixing propagator. All pulses have x-phases unless otherwise indicated. The RF-gradient denoted with SL3 during the NOESY mixing period serves as a spoil-gradient, and t mix represents mixing time. The basic phase cycle is φ 1 =x,y,-x,-y;φ 2 =-x,φ 3 = 4(-y), 4(y), receiver = x, -x, x, -x. Phase φ 4 of NOESY mixing propagator should be set to -x for sequence A, if a single scan spectrum is desired. For other sequences φ 4 =x.

29 29 Fig. 6. The quality of anomeric proton selective 1D TOCSY spectra with 1, 2, and 4 scans. The spectra were recorded using a 0.5 M sucrose sample in D 2 O utilizing the pulse sequence presented in Fig. 5B and the corresponding sequence with B 0 -gradients. The spectra were recorded on a Bruker DRX-500 spectrometer equipped with a triple-resonance probehead incorporating a single shielded gradient coil at 298 K. Relaxation delay = 3.0 s, acquisition time = 1.36 s, selective 180 pulse = 20 ms Gaussian, proton 90 pulse = 5.6 µs, RF-power for trim-pulses and MLEV-17 = 5.48 khz, trim-pulse length = 2.5 ms, isotropic mixing time = ms; an exponential weighting function (0.3 Hz) was applied prior to Fourier transform. RF-gradientmethod:SL1=1.8ms,SL2=2.2ms.B 0 -gradient method: gradient shape = sinusoid, gradient pulse length = 1 ms, recovery delay = 200 µs, gradient amplitudes = 7.2 and 3.0 G/cm. The small signals at 4.05, 3.90, and 3.50 ppm belong to the fructose ring and are due to incomplete suppression by the RF-gradients. Similar residual signals (although smaller) can also be found in B 0 -gradient based experiments [I]. Fig. 7. The anomeric proton selective 1D TOCSY spectrum of sucrose recorded using the RF-gradient selected method presented in Fig. 5C. Number of scans = 2, proton 90 pulse = 16 µs, relaxation delay = 4.0 s, SL1 = 2.8 ms. Other parameters are the same as for spectra in Fig. 6 [I].

30 30 The NOE spectra contain important information about the three dimensional structure of a molecule [86-88]. The classic 1D-method to obtain NOE information is NOE-difference spectroscopy [88]. Although this experiment is very simple to perform, the results can be disappointing. As the experiment is based on the difference of two spectra, the subtraction artefacts may overrun the NOE-enhancement. In principle, a selective 1D NOESY experiment can be performed using either excitation sculpting (Fig. 5A-B), or the gradient selected method (Fig. 5C-D). Although the excitation sculpting preserves both coherence transfer pathways [43-45], and so offers better signal intensity, the relaxation during the NOESY mixing time can lead to spurious peaks [43-45]. After the excitation sculpting step, all the magnetization not inverted by the selective 180 pulse is destroyed by the gradients. The selected magnetization goes through the NOESY step and the resulting spectrum contains the signal of the selected proton (corresponds the diagonal peak in 2D NOESY), and also signals of those protons, which have NOE with the initially selected proton. When the excitation sculpting approach is used, difficulties will be introduced due to relaxation during the NOESY mixing time. The unwanted magnetization dephased by the gradients will relax towards the equilibrium state during the NOESY mixing time. The relaxed magnetization has lost gradient induced phase dispersion and the last pulse of NOESY flips this magnetization into the transverse plane resulting in extra peaks in the spectrum. Elimination of these artefact peaks can be performed by applying EXORCYCLE[40] to the selective pulse. This, however, works only when the intensity of the magnetization responsible for the artefact peaks is not large. When long mixing times are used, almost full intensity of the equilibrium magnetization can be reached and correspondingly successful EXORCYCLE-based difference spectroscopy becomes more difficult [44]. The suppression of the relaxation induced artefact peaks via EXORCYCLE can be improved by adding extra 180 pulse(s) within the mixing time resulting in decrease of the intensity of the forming equilibrium magnetization [44]. In practice the positioning of these 180 pulses can be rather difficult due to the variation in T 1 -relaxation times. A more straightforward way to obtain a selective 1D NOESY is to utilize RFgradient selection [I], as presented in Fig. 5C-D. This method is a modification of the B 0 - gradient based GOESY-experiment [78]. In RF-gradient selected NOESY, the selectively inverted magnetization is phase encoded due to the gradients. This magnetization goes through the NOESY step, during which the phase encoding is transferred to other nuclei via NOE-interaction. The phase encoding is decoded back by the final RF-gradient just before the acquisition. If the first pulse of the mixing propagator has phase x, only the magnetization parallel to y-axis needs to be considered, as the x-magnetization will be further dephased by the spoil-gradient gradient, and therefore is not refocused by the final RF-gradient. The destruction of the x- magnetization leads to the fact that half of the magnetization is lost during the gradient selected methods i.e. only one of the two coherence pathways is selected [43-45]. The gradient labeled y-magnetization has the gradient-induced, spatially dependent phase (cosine function). The 90 pulse prior to the NOESY mixing time creates a longitudinal magnetization, which is aligned along the -z or the +z-axis. Now, an additional signal loss of factor 0.5 is introduced, as only half of the longitudinal magnetization creates NOESY-peaks [I, 44]. Diffusion effects will also cause some decrease in signal

31 31 intensity. This may be problematic for small molecules in non-viscous solvents, when relatively long NOESY mixing times are used [I, 44]. The main advantage of RF-gradient selected 1D NOESY (and GOESY) is that the resulting spectrum contains only the resonances of the target proton and resonances that are formed during mixing time via NOE-interaction. Some spurious small anti-phase signals (i.e. COSY-type signals) can appear in spectrum as a result of terms having coherence order zero during the NOESY mixing time. Zero-quantum coherences and socalled zz terms present during mixing time survive the dephasing caused by the spoilgradient and may be converted into observable signals. Uneven excitation of the target multiplet and imperfect 90 pulses of the NOESY mixing propagator may give rise to these terms [44]. Figure 8 presents anomeric proton selective 1D NOESY spectra of sucrose recorded using the RF-gradient selected method (pulse sequence presented in Fig. 5C) and mixing times of 4 µs, 125 ms, 500 ms, and 1000 ms [I]. For a comparison also anomeric proton slice of 2D NOESY spectrum (mixing time = 1000 ms) is presented. The spectrum in Fig. 8A (mixing time = 4 µs) shows an antiphase J peak at 3.4 ppm due to magnetization components with coherence order zero during the mixing time. As can be seen from the spectra in Fig. 8A-D, the magnitude of J peak remains constant and the developing inphase NOE-peak overruns this J peak when the proper mixing time (1.0 s in this case) is used.

32 32 Fig. 8. Four anomeric proton selective 1D NOESY (pulse sequence in Fig. 5C) spectra with different NOESY mixing times (A-D) and the anomeric proton slice of non-selective 2D NOESY spectrum of 0.5 M sucrose at 298 K. 1D spectra (A-D): Number of scans = 32, relaxation delay = 10 s, acquisition time = 1.36 s, selective 180 pulse = 20 ms Gaussian, SL1 =1.4ms,SL3=1.7ms,t mix =4µs (A), 125 ms (B), 500 ms (C), and 1000 ms (D); an exponential weighting function (0.3 Hz) was applied prior to Fourier transform. 2D phasesensitive NOESY (E): Relaxation delay = 2.0 s, number of transients = 16, number of increments = 256, t mix =1.0s,resolutioninf 2 -dimension 7.82 Hz/pt [I].

33 Two dimensional TOCSY and NOESY with RF-gradient selection The pulse sequences for 2D RF-gradient NOESY and TOCSY are shown in Fig. 9 [I]. No trim-pulses were applied in TOCSY. Again, as the chemical shifts are not active during the RF-gradients, there is no need for extra echo-periods in order to compensate for chemical shift evolution. Phase sensitive spectra can be obtained by applying the echo-antiecho method [89, 90] to the rephasing gradient. The phase of the spin-lock pulse in the z-rotation cluster prior to detection (rephasing gradient) was inverted to record both P- and N-type spectra for the same t 1 -increment value. The RF-gradient versions of these common 2D methods offer good quality spectra in a short time, as there is no need for phase cycling. In practice, a two-step cycle applied to the excitation pulse is preferable to ensure elimination of axial peaks. Figure 10 shows phase-sensitive 2D TOCSY an NOESY spectra of 0.5 M sucrose in D 2 O recorded using pulse sequences presented in Fig. 9 [I]. A two-step cycle was used to avoid axial peaks. A) φ1 y -y φ2 y -y 1 H: t1 -x SL1 MLEV-17 e/ae -x / x SL1 B) 1 H: φ3 y -y -x y -y -x y -y e/ae -x / x t1 SL1 SL2 tmix SL1 Fig. 9. Pulse sequences for phase-sensitive 2D RF-gradient TOCSY (A) and RF-gradient NOESY (B). Notation is the same as in Fig. 5. All pulses are in the x-phase unless otherwise indicated. Phase-sensitive spectra are obtained by inverting the phase of the spin-lock pulse in the z-rotation cluster prior to detection (refocusing RF-gradient) to record both echo- and antiecho-type spectra (denoted by e/ae ) for the same time increment (t 1 ). A) Basic phase cycle is φ 1 =x,-x;φ 2 = x, -x; receiver = x, -x. B) Basic phase cycle φ 3 = x, -x; receiver = x, -x.