2.2. Multi-Dimensional NMR Spectroscopy
NMR experiments are not limited to one-dimensional direct acquisition; they can be extended to multidimensional methods including 2D, 3D, 4D, and even higher dimensionality. The focus of this section is common 2D NMR experiments that have been used in drug design and drug development. A brief description of Correlation Spectroscopy (COSY), Total Correlation Spectroscopy (TOCSY), and Heteronuclear Multiple Bond Correlation (HMBC), along with their uses in drug design and discovery will be presented.

2.2.1. 2D 1H,1H-COSY
COSY is one of the simplest and most frequently used 2D NMR experiment [123]. It shows the homonuclear coupling of nuclei (i.e., 1H-1H) separated by up to several covalent bonds. The pulse sequence consists of a 90° excitation pulse followed by a specific evolution time (t1), a second pulse, and finally a measurement period (t2, not to be confused with relaxation rates or times). The second pulse can be 90° or 45° or 135°, depending upon the specific requirements, and respectively yield COSY [124], COSY-45 or COSY-135 functionality (see [125,126,127]). A two-dimensional Fourier Transform (FT) yields the final spectra and shows the frequencies for proton (1H) or carbon (in the case of carbon detection) along both axes. There are two types of peaks; (I) Diagonal peaks, which represent the peaks of the conventional 1D spectra, and (II) cross-peaks, which have different values in the two frequency axes and are therefore off the diagonal. These off diagonal cross-peaks are the most important pieces of information as they mark correlations between pairs of nuclei due to through bond magnetization transfer. This helps in identifying which atoms are connected [128], critical for structural elucidation of both known molecules and unknown molecules in solution [129]. By implementing phase-cycling [130,131], it is also possible to distinguish different types of coupling and yields further helpful information about the chemical structure of a molecule [132]. As an example, the use of the COSY experiment was presented in the work of Zheng et al. [88]. The main goal of their work was to investigate potential biological differences and compare the pharmacological effects between Danggui (an herbal drug used in traditional Chinese medicine) and European Danggui. For that, Zheng et al. treated blood deficiency rats with Danggui and European Danggui and collected samples of their serum and urine. The samples were later measured using 1H-CPMG-NMR, 1H-NOESYPRESAT-1D, 1H,1H-COSY, and 1H,13C-HSQC, and then compared to equivalent spectra from untreated rats. The results showed that exposure to Danggui and European Danggui altered the levels of 18 different metabolites, such as lactate, nicotinamide, glycerol and formate, which were involved in a total of seven different metabolism pathways. Additionally, it was proven that Danggui and European Danggui have different chemical compositions, with Danggui having better blood-enriching effects than European Danggui.

2.2.2. 2D 1H,1H-TOCSY
Total Correlation Spectroscopy (TOCSY) also originally known as the Homonuclear Hartmann Hahn (HOHAHA) experiment can be considered an extension of the 2D 1H,1H-COSY experiment. The difference between the two experiments is that a TOCSY experiment will show multiple cross-peaks including indirectly coupled nuclei (i.e., longer range via scalar coupling) throughout the J-coupled spin system of a chemical compound. The basic pulse sequence of the TOCSY consists of excitation by a 90° pulse, followed by a free variable evolution period which encodes the indirect dimension. This is normally followed by an isotropic mixing sequence to transfer magnetization between spins via the strong scalar coupling. The mixing generates in-phase magnetization throughout a spin coupled network of the associated nuclei during the mixing time. Lastly, a direct detection is performed. A major advantage of the TOCSY experiment is that it detects in-phase magnetization (i.e., pure absorptive line-shape) which is far easier to analyze compared to the anti-phase information in the phase sensitivity COSY-type experiment. The isotropic mixing is usually performed using a composite pulse scheme such as WALTZ, MLEV or DIPSI [133,134] pulse train, and can be sandwiched between two z-filters [135] where isotropic mixing is performed on the longitudinal magnetization. The most obvious advantage of TOCSY is that all cross-peaks of the same spin system can be observed for whole spin system at once. This is useful for identifying the complete network of spins and reducing the ambiguity of any spectral overlap. The TOCSY experiment can be produced as 1D with a relatively shorter time and easier analysis compared to 2D but lacks the benefit of multi-dimensional resolution. The 2D TOCSY is usually done to resolve spectra overlap [50] when first identifying molecules [136,137,138]. For example, Jiang et al. used this to predict the response to gemcitabine-carboplatin (GC) chemotherapy in patients with metastatic breast cancer who were previously exposed to treatment with both anthracyclines and taxanes [137]. For that, researchers collected serum samples from 29 patients prior to treatment and measured them using 1D 1H-NMR. Additionally, they conducted 2D NMR experiments such as the 1H,1H-COSY, 1,1H-TOCSY, 1H,13C-HSQC, and 1H,13C-HMBC to help assign serum metabolites. After receiving the treatment with gemcitabine-carboplatin, patients were divided into four groups based on the results from the computed tomography: complete response (CR), partial response (PR), stable disease (SD), or progressive disease (PD). After comparing NMR results prior to the treatment with the outcome of chemotherapy, the researchers observed lower baseline levels of serum format and acetate in breast cancer patients who progressed with the disease than in those who achieved a clinical benefit from therapy, indicating that those two biomarkers could be used to distinguish between patients who will benefit from GC treatment from those who do not [137].

2.2.3. 2D 1H,13C-HSQC
2D- Heteronuclear Single Quantum Coherence (HSQC) experiments are commonly used to help resolve spectral overlap [139] while providing 13C information without the inherent sensitivity losses involved in 13C direct detection (see below). HSQC shows the correlations between directly coupled nuclei [140], e.g., 1H-13C or 1H-15N [140]. As such, an HSQC spectrum will show clean peaks for each unique proton directly connected to the heteronuclear nuclear atom of interest [140,141]. In 1H,13C/15N HSQC experiments, the magnetization is transferred from the more sensitive nucleus (I:1H) to the less sensitive nucleus (S:13C/15N) [142,143,144] (Figure 3). This is especially useful when applying NMR spectroscopy to drug design, as most drugs are organic (i.e., contain carbon atoms), and the relative abundance of 13C (1.1%) is quite low [143]. By transferring sensitivity from 1H to 13C, one can circumvent the long experimental time required for 1D 13C experiments [143].
For example, De Castro et al. [145] studied Ptac2S and its related cytotoxicity to the cisplatin-resistant epithelial ovarian carcinoma (EOC), Skov-3 cells. In the study, they used NMR spectroscopy and multi-variate statistical analysis to observe how Skov-3 cells reacted to treatment with Ptac2S. In particular, they used 1H,13C-HSQC along with 1H-COSY and Heteronuclear Multiple Bond Correlation (HMBC), and the Human Metabolome Database to assign the chemical shifts of the lipid metabolites present in the studied samples. Interestingly, Skov-3 cells treated with Ptac2S produced more pyruvate than Skov-3 cells treated with cisplatin. The authors also noticed an unexpected difference in lipid metabolite expression levels between the cells treated with Ptac2S and those treated with cisplatin. These results provide a possible explanation for how Ptac2S is able to overcome cisplatin resistance in Skov-3 cells [145].

2.2.4. 2D 1H, 13C-HMBC
Heteronuclear 2D experiments are useful for transferring magnetization from sensitive nuclei (i.e., 1H) to less sensitive nuclei (i.e., 13C) [146] thereby reducing the time needed for the acquisition of spectra [147]. Heteronuclear Single Quantum Coherence (HSQC) will only show one cross peak for each coupled pair [92,128] of nuclei. This makes HSQCs useful for assigning the backbone of proteins [148] and in metabolites of complex biofluids [149], whose 1D 1H-NMR spectra can suffer from severe spectral overlap.
The HMBC technique, while similar to HSQC, is an example of a heteronuclear 2D experiment that reveals correlations between nuclei separated by two or more chemical bonds while also suppressing one-bond correlations at the same time. This experiment combined with HSQC is often used to assign NMR spectra for studied molecules in drug design experiments [65,66,137,145].
As an example, HMBC was used in a recent study by Xu et al. [66] to investigate the changes in the metabolic profiles of rats treated with different dosages of the “RenqingMangjue” pill, a traditional Tibetan medicine. In this study, the rats were divided into four groups based on the amount of “RenqingMangjue” administered: low dose group (LD)-83.33 mg/kg/day, middle dose group (MD)-333.33 mg/kg/day, high dose group (HD)-1333.33 mg/kg/day and a control group (NC). After 15 days of consecutive administration, half of the rat population was used to collect samples such as serum, kidney, and liver tissue, while the other half underwent an additional 15 days of recovery before the same samples were acquired. The samples were measured using 1H-NMR CPMG (an experiment used to suppress signals from larger molecules, see below) [150,151,152] along with 1H,1H-COSY, 1H,13C-HSQC, and 1H,13C-HMBC used for molecules assignment. The obtained spectra showed that the “RenqingMangjue” pill alters many metabolites, which are related to a variety of metabolic pathways including energy metabolism, amino acid metabolism, and lipid metabolism indicating potentially harmful effects on kidneys and liver.

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.