3.1.6. Diffusion Based Spectroscopy in Drug Design
Diffusion is the random, translational motion of molecules in solution as a consequence of their thermal energy [285]. This type of motion is often referred to as “Brownian motion”, a motion that describes molecular movement induced by random collisions between the molecules [286]. In the presence of a concentration gradient, molecules will naturally move from places of higher concentration to places of lower concentration [287] after a period of time, t, as shown in Figure 11. Fick’s Law can be used to model this type of movement [288]. The distribution of the diffusing molecules is accurately represented by a Gaussian curve, a normal distribution centered at a single point, which gradually “flattens” as t approaches infinity [213]. The extent to which a molecule diffuses is directly related to its shape, size, and mass [285]. In homogeneous isotropic solutions, the root mean square distance (zrms) traveled by a molecule is given by following equation [289,290]:zrms=(2Dt)12  where D is the diffusion coefficient of the molecule, and t is the diffusion time. Making the assumption that the molecules are solid rigid spheres, the value of D can be calculated according to the famous Einstein-Stokes equation (Equation (2)):(4) D=kbT6πηrs  where kb is the Boltzmann’s constant (1.3807 × 10−23 J/K), T is the absolute temperature, η is the solution viscosity, and rs is the hydrodynamic radius of the molecule [290]. Equation (1) and Equation (2), however, are not universally applicable; they only apply to molecules that are freely diffusing in isotropic, homogeneous solutions, and importantly that can be accurately described as hard, rigid spheres [285]. Different molecular geometries and additional modes of diffusion (i.e., restricted and anisotropic) require more advanced mathematics and theory [291,292], but the essential concepts of diffusion remain the same.
The earliest pulse sequence used to measure diffusion in NMR spectroscopy is the gradient spin echo sequence (SE), developed by Stejskal et al. [293]. The SE pulse sequence is shown in Figure 12. The SE pulse sequence uses a gradient (G) of the externally applied magnetic field, (pulsed field gradient), the first after the 90° pulse, and the other after the 180° refocusing pulse. The first gradient pulse (G1) labels or gradient-encodes the NMR-active nuclei based on their physical position in the sample tube. If the molecules diffuse during the time period they are not in the correct position to experience the second gradient which re-focuses the spins. This is detected via NMR as a signal intensity decrease. After a diffusion time (∆), the second gradient pulse is applied to decode the spatial labeling of NMR-active nuclei, obtaining a well-defined spectra of diffusing molecules in solution [294]. Additional NMR sequences are available for diffusion experiments [295], and are detailed in more comprehensive reviews dealing with the subject [296,297].
The signal intensity of the diffusing molecules depends on three factors, as described by Equation (3) [294]:(5) I=I0e−Dγ2g2δ2  where I is the observed intensity, I0 the reference intensity (unattenuated signal intensity), D is, of course, the diffusion coefficient referred to earlier, γ is the gyromagnetic ratio of the observed nucleus, g is the strength of the gradient, δ the length of the gradient, and ∆ the diffusion time [294]. From Equation (3), it is easy to see that the signal intensity decreases exponentially with time, so it is vital to optimize the values of g, δ, and ∆ for diffusion NMR measurements [294].
The drug design approach based on diffusion NMR is basically a screening technique used to differentiate the binding ligands (drug) from non-binding components [264]. Ligands able to bind should have significantly different diffusion coefficients (D) compared to non-binding ligands [297], i.e., the diffusion coefficients of binding ligands will be smaller than those of non-binding ligands [264]. Thus, diffusion-based NMR is a way of effectively “filtering” and identifying which ligands are binding [264].
Diffusion-based NMR spectroscopy has advantages in ligand based screening applied to drug discovery. For example, Diffusion Ordered Spectroscopy (DOSY) does not require prior separation/purification of the ligand/target solution [298]. Diffusion based NMR allows simultaneous determination of diffusion coefficients in multicomponent systems containing large molecules (i.e., proteins) and possible binding partners (i.e., small drug compounds) [285], and no special labeling or contrasting agents are required, though their use is not exclusively inhibited (for an example of the use of labeled compounds in diffusion NMR spectroscopy, see [299]). A problem occurs when there is significant chemical shift overlap between the binding molecule signals and the target. This situation makes it hard to distinguish the NMR signals [300], and the calculations typically assign an intermediate value to the diffusion rate (i.e., one gets a smear). Multidimensional diffusion NMR pulse sequences are available [301], which may help resolve spectral overlap in 1D experiments [300]. Another issue is that molecules in chemical databases may have generally low solubility [302,303]. Low solubility decreases the overall signal intensity and therefore makes accurately measuring diffusion experiments far more difficult [304].
There are many examples demonstrating the successful application of diffusion NMR in examining drugs of pharmaceutical interest [305], and ligand-target interactions [167]. Hajduk et al. [167] exploited the changes in diffusion rates to detect ligands that bind to the FK506 binding protein and the catalytic domain of stromelysin. Nishimura et al. [306] utilized DOSY, in combination with NOESY to determine the orientation of two guest molecules, p-ethoxyiodobenzene and 2-iodo-6-methoxynaphthalene, within a host composed of a tetrakis(4-hydroxyphenyl)-cavitand and a tetra(4-pyridyl)-cavitand.
Furthermore, Matthias et al. [307] used 1H molecular diffusion and 19F spin diffusion to probe the drug loading properties of the Rf-PEG hydrogel for 5-fluorouracil (FU) and 1,3-dimethyl-5-fluorouracil (DMFU), two anticancer drugs.
DOSY can be combined with Saturation Transfer Difference (STD, discussed earlier in this review) to yield new insights about ligand-target interactions. Kramer et al. [308] combined STD with DOSY to analyze a mixture composed of wheat germ agglutinin and two derivatives of N-acetyl glucosamine (ligands). Using this new technique they were able to obtain high quality spectra of the components in the mixture. Tanoli et al. [309] also combined STD and DOSY to explore the interactions of smaller molecules with bovine serum albumin.
These are just a few examples to show that diffusion NMR spectroscopy has played, and will continue to play, a prominent role in drug design.