Constant-time variable-delay

In 2000, Krishnamurthy et al. have presented the 2/,3/-HMBC experiment (Figure 20), that affords for the first time the means of unequivocally differentiating between 2/ch from 3Jch correlations.59 Their approach is based on a further derivative of the constant-time variable delay introduced in the IMPEACH-MBC experiment. The user-definable /-scaling factor of the CIGAR-HMBC is used in the new experiment, the 2J,3J-HMBC experiment, to differentiate between 2/CH from 3Jch correlations. This new pulse sequence element has been given the acronym STAR (Selectively Tailored Accordion F1 Refocused) operator. 

The first step in optimizing the ACCORD-HMBC sequence and removing the tilt of the correlation peaks, is the IMPEACH experiment [5.173] which utilizes a constanttime variable delay element to remove the skewed shape of the correlation peaks. The constant-time variable delay element discriminates between IH-IH and DC-lH coupling... 

The Constant Time Variable Delay Element = 1/(2 nJj n(C,H)) for the CIGAR experiment. 

In contrast to the IMPEACH-HMBC experiment, the CIGAR experiment incorporates into the constant-time variable delay incrementation of dO, the f 1 increment. A further development is the STARR operator whereby in a 2J, 3J-HMBC experiment it is possible to label the 2J(C, H) correlation peaks by a tilt due to 3J(H, H). A pre-requisite for this labelling is that the I3c nucleus is neither a quaternary atom or completely substituted. The STARR operator is shown below and it is left as an exercise for the reader [5.175]. 

In an effort to address the essentially uncontrolled F skew inherent to the ACCORD-HMBC, the author and co-workers next reported the development of the IMPEACH-MBC experiment, the pulse sequence for which is shown in Fig, 14. Recognizing that F skew arises due to homonuclear scalar coupling modulation for which the variable duration accordion-optimized delay serves as an evolution time, the variable delay, vd, was modified in the IMPEACH-MBC experiment. The variable delay can be made into a constant time delay for homonuclear components of magnetization by adding a new segment to the overall delay centered about a 180° X pulse to refocus heteronuclear magnetization. The thus modified constant time variable delay is given by... 

Fig. 14. IMPEACH-MBC (IMproved PErformance ACcordion-optimized Heteionucicar multiple bond correlation) pulse sequence developed by Martin and co-workers. The experiment is a further modification of the ACCORD-HMBC experiment that utilizes a constant time variable delay in lieu of a simple variable delay. The con.stant time variable delay introduces the interval, D/2 — 180° "C — D/2, which precedes the variable delay interval, vd. As the evolution lime ti is incremented, the interval vd is decremented in the usual fashion. However, at the same time, the Dll (ct A) intervals are incremented in a manner to keep the overall duration of the period D + vd a constant time interval. Hence, homonuclear modulation, which plagues ACCORD-HMBC experiments, is suppressed by the constant time of the intcrv al D + vd. In contrast, evolving heteronuclear couplings arc refocused at time D by the 180° - C pulse located at DU. These couplings then evolve during the variable interval vd to be sampled in the usual, accordion manner. By using this approach, the constant time variable delay pulse sequence element is of constant duration for homonuclear components of magnetization while serving as a variable delay for heteronuclear components.

Retrospectively, after demonstrating in the implementation of the IMPEACH-MBC experiment that it is possible to suppress F skew, it was evident that the skew of responses in F, while a nuisance if uncontrolled, could serve as a useful means of response authentication if Fi skew was under user control. The CIGAR-HMBC experiment aeeomplishes this task. While the constant time variable delay of the IMPEACH-MBC experiment (see Eq. (8)) renders the duration of the variable delay constant, the CIGAR-HMBC pulse sequence modifies the variable delay interval of the experiment still further, as shown below the complete puLse sequence is shown in Fig. 17. 

Fig. 19. Pulse sequence for the J, J-HMBC experiment described by Krishnamurthy ei This experiment represents the most refined version of the accordion-optimized experiments to be developed thus far and allows the differentiation of Jxh from Jxh long-range correlations to protonated heteroatoms ( - C and N). The experiment further modifies the concept of the constant time variable delay used in the IMPEACH-MBC and CIGAR-HMBC experiments to even more selectively manipulate various components of magnetization. This is done using the pulse sequence operator given the acronym STAR (Selectively Tailored Accordion F Refocusing) (.see also Fig. 20). Differentiation of various components of heteronuclear long-range magnetization is accomplished within the STAR operator, with the balance of the pulse sequence similar to that of the IMPEACH-MBC and CIGAR-HMBC experiments.

Homonuclear coupling modulation during the variable delay in the ACCORD-HMBC experiment prompted the development of a constant time variable delay... 

While uncontrolled F response skew of the type encountered in the ACCORD-HMBC experiment is undesirable [145], user-defined Fj skew can be a useful determinant of response authenticity. A further generation accordion-optimized long-range experiment, CIGAR-HMBC, was developed to provide this flexibility. The constant time variable delay from the IMPEACH-MBC experiment was further modified as follows ... 

A new element for simultaneous indirect detection of C and signals in labelled proteins was proposed by Uhrin et The CT- CHs, VT- N-HSQC sequence combines constant-time carbon evolution with variable delay nitrogen evolution. This is achieved by the variation of the position of a 90° pulse creating transverse coherence within the C constant-time period. The maximum indirect acquisition time for both nuclei is determined by constant-time period set to l/ /(C,C) = 28.6 ms. The method is best suited for detection of CH3 signals due to their slower relaxation. The proposed element was incorporated into NOESY-based experiments resulting in 3D NOESY-CH3NH and 3D HSQC-NOESY-CH3NH sequences. The experiments... 

Left two-pulse [(a) primary ESEEM] and three-pulse [(b) stimulated echo ESEEM] sequences t is the (fixed) delay time between pulses one and two and T is a variable delay time. Right frequency domain and time domain (inset) of the two-pulse EESEM spectrum of VO - vanabin, recorded at the m = — 1 /2 line, at 77 K and a pulse width of 20 ns.P l The superhyperfine coupling constant = 4.5 MHz (obtained from the N double-quantum lines at 3.9 and 7.1 MHz) is in accord with amine nitrogen provided by lysines of the vanadium-binding protein. The spin echo due to proton coupling, at 13.7 MHz, was also observed. Reproduced from K. Eukui et al., J. Am. Chem. Soc. 125, 6352-6353. Copyright (2003), with permission from the American Chemical Society. 

Interpulse Low-pass Constant time Evolution Constant time Low-pass delay J filter variable delay variable delay J filter... 

The STAR operator used in the J, J-HMBC sequence is shown in Fig. 20. The STAR operator utilizes four variable delays, D, which are incremented from zero in concert with the decrementation of vd, A1 and A2, the sum of which is held constant, and vd, which is decremented as a function of the accordion-optimization range selected in the usual fashion from 7i ax to Tmin- Hence, the overall duration of the variable delay interval is constant. Within the STAR operator, the first variable delay, Al, is incremented from zero to y caic x fi ax in steps of Jsc-,x c x ti, while conversely A2 is decremented from a starting value of Vsciiie X fimax to zero in steps of Jscaie X t. Thus, while the sum of A1 -1- A2 is constant, each of the delays are variable and a function of the evolution time, t. ... 

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