The Spin Lock

A spin lock is a relatively long (1 100 ms), low-power (usually 12-33% ofthefli amplitude of a hard pulse) radio frequency pulse applied on the same axis as the desired sample 

SHAPED PULSES, PULSED FIELD GRADIENTS, AND SPIN LOCKS 

In the rotating frame of reference for an on-resonance peak, the B0 field is exactly canceled by a fictitious field created by the rotation of the axes, so that for nuclei that are on-resonance the only field present is the B field during the spin lock (Z eff =B i). If we place the sample magnetization on the y axis of the rotating frame with a 90° hard pulse (phase —jc), the spin lock can be placed on the y axis (phase y). While the spin lock is on, the sample magnetization is locked on the y axis and will not undergo precession, as the only field present is the B field and the sample magnetization is on the same axis as the B field (Fig. 8.37). 

2 Fate of Magnetization Perpendicular to the Spin Lock Purge Pulses 

At this point, a purge spin lock on the y axis would preserve the antiphase term 2IySz and destroy the in-phase term I. We then proceed to the coherence transfer step (simultaneous 90° pulses on 13C and lH) with pure antiphase lH coherence. 

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Parhcular care has to be taken when implementing ROESY experiments. The spin-lock, which holds the spins along a defined axis perpendicular to the stahc magnetic field, can be realized in many different ways and is shU an achve field of research [18, 20]. In most spin-lock sequences the conditions for undesired TOCSY transfer are parhally fulfilled and especially cross-peaks close to the diagonal or anhdiagonal might not be accurately interpretable. Since in most cases the effechveness of the spin-lock also depends on the chemical shift offset, an offset-dependent correction has to be applied to the measured cross-peak intensities [20]. 

The spin-locking and CP behavior of the most commonly used SQ coherence (CT) in quadrupolar nuclei under static and MAS conditions has been described in detail by Vega using the fictitious spin-1/2 approximation [223]. In a static sample, the Hartmann-Hahn matching condition requires that co = nut where co ut is one of the nutation frequencies associated with the SQ coherence of the quadrupolar S spin (see Sect. 2.3.4). In the simple case of on-resonance SQ-CP this translates to [224]... 

Under MAS the quadrupole splitting becomes time dependent, Qg = Qg (f) (see Sect. 2.3.4). This influences both the spin-locking behavior [223] and the polarization transfer [224], with the latter being further affected by the periodic modulation of the IS dipolar interaction. The effect of MAS on spin-locking of the S magnetization depends on the magnitude of the so-called adiabaticity parameter ... 

The CP can also be used for polarization transfer to MQ coherences of half-integer quadrupolar nuclei [222, 223, 228-231]. This type of transfer is mainly used in the context of MQMAS [228,229,231], although the spin-locking of MQ coherences is also featured in experiments involving homonuclear dipolar recoupling experiments [232]. 

Total correlation spectroscopy (TOCSY) is similar to the COSY sequence in that it allows observation of contiguous spin systems [35]. However, the TOCSY experiment additionally will allow observation of up to about six coupled spins simultaneously (contiguous spin system). The basic sequence is similar to the COSY sequence with the exception of the last pulse, which is a spin-lock pulse train. The spin lock can be thought of as a number of homonuclear spin echoes placed very close to one another. The number of spin echoes is dependent on the amount of time one wants to apply the spin lock (typically 60 msec for small molecules). This sequence is extremely useful in the identification of spin systems. The TOCSY sequence can also be coupled to a hetero-nuclear correlation experiment as described later in this chapter. 

One can further increase the amount of transferred polarization if one carries out the cross polarization in an adiabatic fashion. In this experiment, the amplitude of one of the spin-lock fields is usually varied in a tangential shape [33-35]. In addition to the compensation of instabilities in the amplitude and rf field inhomogeneities, one can also obtain a gain in signal by a up to a factor of two. The concept of adiabatic polarization transfer will be discussed in more detail in Sect. 11.3.1. 

The spin lock period is used to translate broad lines into less intense lines... 

The simplest double tuned filter can be constructed by a concatenation of two X-half filters and removal of redundant 180° pulse pairs (Fig. 17.4d) [22]. Alternatively, it can also be realized by keeping the 180° pulse pairs and adding short spin-lock periods (to dephase the 1H-13C magnetization which is orthogonal to the spin-lock axis, Fig. 17.4e) [23], or it is based on the gradient-purging scheme of Fig. 17.4b, resulting in the double filter shown in Fig. 17.4f [18]. 

Jonas et al. measured the proton rotating frame spin-lattice relaxation time (Tip) at pressures from 1 bar to 5000 bar and at temperatures of 50 to 70 °C for DPPC and at 5 to 35 °C for POPC. If intermolecular dipolar interactions modulated by translational motion contribute significantly to the proton relaxation, the rotating frame spin-lattice relaxation rate (1/Tip) is a function of the square root of the spin-locking field angular frequency... 

Fig. 5. Principle of a spin-lock experiment leading to the determination of the relaxation time in the rotating frame (Tip). (SL)y stands for the spin-lock period which corresponds to the application of a rf field along the y axis of the rotating frame.

Figure 6. The proton(I)-carbon(S) dipolar coupling during a C-13 T,p and decoupled Tj experiment are compared. The relaxation rate is determined by the molecular fluctuation at the spin lock frequency u>,c or decoupling frequency a,a-...

In a ID TOCSY-NOESY experiment [39], the proton magnetization is aligned along the spin-lock axis after the initial selective TOCSY step. The... 

Fig. 8. ID ROESY-TOCSY. (a) H spectrum of the oligosaccharide 3 (5 mg/0.5 ml D2O). (b) ID ROESY spectrum of 3 acquired using the pulse sequence of fig. 7(a) with selective excitation of the H-lb proton. Duration of the 270° Gaussian pulse and the spin-lock pulse ( yBi/ K = 2.8 kHz) was 49.2 ms and 0.5 s, respectively. The spin-lock pulse was applied 333.3 Hz downfield from the H-lb resonance. The time used for the frequency change was 3 ms. (c) ID ROESY-TOCSY spectrum acquired using the pulse sequence of fig. 7(c) and the selective ROESY transfer from H-lb followed by a selective TOCSY transfer from H-4c. Parameters for the ROESY part were the same as in (b). A 49.2 ms Gaussian pulse was used at the beginning of the 29.07 ms TOCSY spin lock. 256 scans were accumulated. A partial structure of 3 is given in the inset. Solid and dotted lines represent TOCSY and ROESY...

Concatenation of two TOCSY steps in a ID TOCSY-TOCSY experiment [72] is a straightforward matter (fig. 10(a)). After the initial TOCSY transfer, the magnetization is returned to the 2 axis by a nonselective 90° pulse applied perpendicularly to the spin-lock axis. The carrier frequency is changed and the second 90° selective pulse applied to a different proton followed by the second TOCSY spin-lock period. 

Fig. 1. Pulse sequence of the C HSQC experiment with a spin-lock pulse for the suppression of signals from protons not bound to C. Narrow and wide bars denote 90° and 180° pulses, respectively. The spin-lock pulse is labeled SL. r is set to 1/[2J( C, H)]. The detection period is symbolized by a triangle. Phase cycle ] = 8(y) 4>2 = 2 x,x,y,y) 03 = 4 = 4n = 8(x) 05 =4(x,—x) 05 = 4(x),4(—x) acquisition = 2(x,—x,—x,x). The phases of the C pulses before U (03 and 0.5) are subjected to the States-TPPI scheme [38].

The magnetization from C-bound protons is suppressed by the spin-lock purge pulse. Denoting the operators of a proton 2-spin system as and Hb, the product operator calculation yields... 

Averaging over all possible flip angles / which result from the spin-lock pulse, all signals from eq. (2) cancel. It can be shown that this holds for... 

In practice, the suppression of the signals from C-bound protons is not complete. In part, this arises from imperfections of the 180°(if) pulse in the delay r. If the chemical shift evolution is not refocused, pure proton terms are generated which pass the spin-lock purge pulse. Therefore, the suppression of the signals from C-bound protons is improved by applying the Excorcycle [11] phase cycle to this 180°(if) pulse [10]. To keep the phase cycle short, only the first two steps of Excorcycle can be used. The selection of the correlations is further improved by phase cycling... 

Since water protons are not bound to or nuclei, the water signal is also suppressed by the spin-lock purge pulse. In practice, the suppression of the water signal is sufficient to record HSQC spectra of protein samples dissolved in mixtures of 95% H20/5% D2O without any further water suppression scheme [12]. For optimum water suppression the carrier frequency must be at the frequency of the water resonance. On resonance, the phase of the water magnetization is not affected by imperfections of the first 180°(ff) pulse, so that no solvent magnetization ends up along the axis of the spin-lock purge pulse. 

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