2.2.5. Relaxation-Edited NMR Spectroscopy
Relaxation in NMR is a phenomenon describing the time dependence involved in signal intensity after an induced RF (radiofrequency) pulse is applied [153]. After application of a 90° RF pulse, the bulk magnetization will move to the transverse (xy) plane and will gradually return to its original equilibrium position along the longitudinal (z) axis [154]. This process is described in Figure 4, and is termed T1 relaxation. The details are beyond the scope of the manuscript and interested readers are directed to [155] and references therein. Relaxation times for NMR are even more complicated and exist in two categories: T1 and T2. T1 refers to the rate of longitudinal (or spin-lattice) Z-axis relaxation as the system returns to equilibrium. A second component also contributes, i.e., T2 relaxation and refers to the rate of transverse (or spin-spin) relaxation [154] which occurs in the XY plane. T2 is independent of the longitudinal relaxation (T1) and represents the loss of coherence in the precessing spins. Therefore NMR relaxation spectroscopy can be based on T1 and/or T2 [156], and is collectively referred to as “relaxation edited NMR” [157].
T1-based methods typically measure and compare the T1 times of the free and bound ligands. A common way to measure the T1 value of a small molecule is the inversion recovery experiment [158,159], although other experiments are also available such as ultrafast NMR T1 [160] and saturation inversion recovery [161]. In general, the shorter T1 the relaxation time the less intense the peak signal will be and the broader the signal linewidth [162]. The T1 values of free and bound ligand will differ depending on how strongly the ligand binds because molecular interactions with the target will influence the ligand’s molecular motion, and hence, its longitudinal relaxation [156]. Bound ligands will have smaller T1 values than in their free form because, overall, they will experience slower molecular motion upon interacting with a target [163] therefore behaving like a much larger molecule. They can (depending on molecule size) also display a negative NOE difference spectrum (transferred NOE) [164], whereas non-binding ligands normally show small-positive NOEs [156]. For binding ligands to display negative NOEs, their T1 values must be comparatively longer than the 1/koff value of the target [156].
T1 relaxation times can be easily used to screen small molecules as ligands for DNA [165] and serve as a basis for HTS experiments [166]. An experiment related to drug design that utilized 1D and 2D relaxation edited NMR was done by Hajduk et al. [167] in which he and others used 1D and 2D relaxation edited NMR techniques to detect ligands that bind to FK506 binding protein and stromelysin. One year earlier, Liu et al. [157] used relaxation edited one-and two-dimensional 1H-NMR spectroscopy to characterize biological fluids. Tang et al. [168] extended this by applying relaxation edited NMR Spectroscopy to improve the detection of metabolites in blood plasma. More recently, Jaremko et al. commented on available models used to interpret 15N protein relaxation data [169], and even used deficient 15N relaxation data to rapidly calculate the dynamics of proteins [170].
The T2 relaxation experiment relies on so-called Carr–Purcell–Meiboom–Gill (CPMG) building blocks (Figure 5).
This pulse sequence is explained with the following steps: First, application of a 90° RF pulse creates a transverse (xy plane) magnetization. Second, a spin-echo period (delay-180°-delay block) is responsible for Mx/y magnetization decay. This period is repeated “n’’ times (CPMG building blocks). It is essential to point out that every NMR experiment involving a large number of pulses (e. g. due to the repeating building blocks) is likely to be sensitive to hardware restrictions and small miscalibrations of the duration of the applied pulses. To attenuate the unwanted effects of miscalibrations, Meiboom and Gill modified the previously used Carr–Purcell sequence [171] by changing the phase of the applied 180° pulses from x to y [172]. This procedure can be used to measure T2 relaxation times of any type of nuclei. For instance, in the case of 13C, all pulses and acquisitions are applied on 13C channel, while broadband proton decoupling is applied during all pulse sequences. It works analogically for different NMR-active nuclei [173].
In a typical CPMG experiment, the effective transverse relaxation rate, R2,eff, is typically measured by fitting the signal decay as a function of a variable number of CPMG blocks [174]. The experimental half-height linewidth (d) of a given resonance signal is directly related to T2* (also called as ‘effective’ or “observed’’) by the following equation:(1) d=1π T2*
T2 represents the transverse relaxation times, and additional broadening comes from the magnetic field inhomogeneities (T2inh), which must be taken into account. (2) 1T2*=1T2+1T2inh
T2 measurements of ligands are also useful for determining the binding nature of a small molecule. The T2 values of small molecules are quite large compared to those of bigger molecules (i.e., proteins) mostly because macromolecules have more spin-spin diffusion [175]. Bound ligands will, therefore, display shorter T2 values than non-binding ligands because they interact with the target (i.e., protein), adopting similar vibrational and rotational energies to the target [176]. This interaction is represented by the resonance line broadening in the binding ligand’s spectrum when a receptor is introduced into the sample [156]. Given the sizable difference of T2 values of binding and non-binding ligands, one can utilize 1D relaxation-edited experiments to distinguish the binding ligands from the non-binding ligands efficiently and effectively based on the differences in the T2 values [167]. These and other related relaxation edited experiments prove useful in drug design.
Relaxation edited NMR spectroscopy takes advantage of an inherent atomic property (i.e., the return of bulk magnetization back to equilibrium [177]), so no molecular enrichment (e.g., 15N isotopic enrichment of protein targets) is required [167]. Furthermore, the slow time scale of NMR relaxation allows the user to manipulate the external conditions (i.e., length and power of pulse) to increase the resolution of targets and potential drugs [155] in NMR drug design experiments. However, this slow timescale also sets the lower limit at which NMR drug design experiments can be performed [155], meaning that any external manipulations cannot decrease experimental time below a certain threshold. This varies based on the drugs and targets used in the experiment. Low drug solubility is also a challenge, as the ligands must be at a sufficiently high concentration to allow detection via NMR, although the use of organic solvents has helped to attenuate this effect in relaxation edited NMR spectroscopy [156]. For examples of experiments that use different NMR techniques mentioned above, see Table 1.