The Diffusion Ordered Spectroscopy technique (DOSY) can also be applied to monitor molecular interactions. DOSY is a versatile NMR technique that provides a semiquantitative estimation of the translational diffusion coefficient (D) of a given molecule or mixture of molecules. In fact, the typical representation of DOSY corresponds to a simple 2D spectrum in which one the dimension corresponds to chemical shifts and the second one to log D. This diffusion coefficient is directly related to the hydrodynamic radius of the molecular entity and therefore, to the molecular weight (MW) of the species in solution. This behaviour is regulated through the Stokes–Einstein equation (Johnson C.S. Jr. (1999) Diffusion ordered NMR spectroscopy, principles and applications, Prog. NMR, 34, 203–255.). In principle, for a given mixture of molecules, it should be possible to extract the diffusion coefficient of all of them through the analysis of the individual NMR resonances of the 24 reports the diffusion coefficients associated with each of the resonances of the molecules. Moreover, if a complex is formed, the extracted diffusion coefficient for the supramolecular complex will be different to that of the individual interacting entities, since the MW of the complex will larger, as well as the corresponding hydrodynamic radius. However, the proper interpretation of DOSY data requires the establishment of a proper experimental protocol. In fact, different factors and parameters need to be considered, from the chemical nature of the entity to be studied to the acquisition and processing parameters. The extraction of log D is achieved through the fitting of the observed intensities I at a given point to the following equation
where Io is the signal in the absence of gradient, G is the employed gradient, δ is the duration of the gradient and Δ is the defocusing delay. According to this equation, either G, Δ or δ could be varied to cause the change in the observed intensity. However, usually the experiments are recorded for different G values, keeping or as constant values, as will be described below. In fact, the Stokes–Einstein equation only holds for spherical molecules. Therefore, a proper calibration curve needs to be built for the type of molecules under consideration. For instance, calibration curves for oligosaccharides (Groves P, Rasmussen MO, Molero MD, Samain E, Cañada FJ, Driguez H, Jiménez-Barbero J. Glycobiology. 2004;14:451-6) and proteins have been derived (Groves P, Palczewska M, Molero MD, Batta G, Cañada FJ, Jiménez-Barbero J. Anal. Biochem. 2004;331:395-7).
From the experimental perspective, several considerations are required before the acquisition starts: A regular NMR spectrometer equipped with z-gradients is required. For molecular recognition purposes and depending on the nature of the ligand, 500 or 600 MHz spectrometers should be excellent choices. The gradient synthesizer should induce a variation of the magnetic field of around 50 G/cm. Regular 3 or 5 mm NMR tubes may be employed. For comparison purposes, it is essential to control the viscosity of the medium and the temperature. These parameters obviously strongly affect the log D value.
The required concentration of the components corresponds to that required to get a good 1H NMR spectrum within a few minutes. A regular digital resolution in the acquisition dimension should be used for the corresponding spectral width. In fact, not many data points should be employed, since otherwise the corresponding data matrix would be rather large.
Typically 4k or 8k data points are employed. A typical 20 ppm window is required for applying a proper base line correction. As mentioned above, different experiments are performed for different gradient G values. The variation of the delay big-delta () is not advisable, since NMR relaxation mechanisms are active during all time periods in which magnetization is not in equilibrium and will provide variations in the intensities for different values. This diffusion delay big-delta () typically oscillate between 100-500 ms. On the other hand, since the duration of the gradient length small-delta () is fairly short, the variation of G is generally advisable. Typical values for and are 400 and 4 ms for proteins, and significantly smaller values, around 200 and 2 ms for small molecules. The selection of these values is due to the translational diffusion properties of small (fast) and large (slow) molecules. Since the experiment is based on the motion of the molecules during the delays, there is a compromise in the achieved translational motion and the recovered intensity. Therefore, for small fast moving molecules, smaller D and d values are selected. For resolution purposes in the diffusion coefficient dimension, a typical number of gradient increments is 16, which is fairly adequate for the analysis of small molecular weight molecules and complexes up to 2 kD. For larger molecules and molecular complexes, the number of different gradient values should be increased to either 32 or 64. The increase in the gradient value should be better regulated by using exponential spacing. When low MW complexes are monitored a sufficient number of datapoints should be acquired in the expected diffusion value. In this case, the large molecules whose intensities decay over the whole gradient range are not strongly affected and also yield accurate log D values. The processing protocol is also important to get the proper log D values. Since resolution in the acquisition dimension is not a key point, exponential line broadening multiplications may be applied to enhance signal-to-noise ratios. Especially when large complexes are the object of investigation, linebroadening factors beyond 10 Hz can be applied, even reaching 20 or 30 Hz. A proper baseline correction protocol should be also used to facilitate the proper processing. After F2-processing, processing in the gradient-evolution dimension should be performed, fist choosing the range in log D scale. It is essential that the log D of the complex upon investigation resides in between the estimated range. Depending on the size, typical log D values range between -8.0 to -12.0 range. Moreover, it is also advisable to zero-fill the numer of performed experiments in F1. A 1K value is recommended for F1 processing is recommended. The analysis of the diffusion coefficient from the 2D DOSY spectrum should be performed in a very careful manner using the proper computer programs provided by the spectrometer manufactures or by commercial sources. For instance, the addition of the different columns in the 2D spectra is advised, since it improves the signal-to-noise ratio and permits to extract log D and the associated uncertainty from the corresponding 1D traces. Indeed, the presence of line broadening in this dimension is probably associated to the presence of heterogeneous components.