XX TrxR Thioredoxin reductase
I. Introduction
5. Results and Discussion: Analysis and Identification of Compounds
5.2. Separate but Still Together: Diffusion-Ordered Spectroscopy as a Chromatography Technique
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Figure 5.10. 2D NOE spectrum of 6, showing connections between the various components.
5.2. Separate but Still Together: Diffusion-Ordered Spectroscopy as a
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upon condensation with a benzaldehyde. This is also indicated by the solvent dependence observed for the chemical shift of the methylene protons of compound 6 (Figure 5.12).
Figure 5.11. Overlap of the methylene peaks of 112 (shown in red) and 125 (shown in blue) in DMSO-d6. The second peak in the spectrum of 112 is a decomposition product due to the reaction of 112 with the water present in the NMR solvent.
Figure 5.12. Overlays of the methylene peak region from the 1H NMR spectra of 6, showing the solvent- dependance of these peaks. The spectrum shown in blue was run in DMSO-d6, the spectrum shown in green in a mixture of D2O and DMSO-d6 (5:1), and the red spectrum in D2O.
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Based on this observation, a diffusion experiment was carried out on compounds 125 and 6. These Diffusion-Ordered Spectroscopy (DOSY) experiments separate the components of a mixture on the basis of their diffusion coefficients, and simultaneously allows for measurement of the diffusion coefficient. It also provides a measure of the approximate size of the hydrodynamic radius for freely tumbling molecules in a solution,745 which in turn can provide a measure of the ability of a ligand molecule to enter into the active site of a protein. A compound with a large hydrodynamic ratio, for example, is less likely to be able to fit into the spatially-constrained active site within a protein than a compound with a small hydrodynamic ratio. As the main channel of the COX active site is relatively long and narrow, with restricted access through a small entry site, an elongated molecule with a small solvation sphere, such as arachidonic acid, will be able to enter into the active site of the COX enzymes much more easily than a large, bulky molecule with a large solvation sphere.
DOSY experiments can, in broad terms, be classified as a unique chromatographic technique, as the separation of compounds is based on physical characteristics.746 Unlike standard separation methods, however, it does not require sample preparation or method optimization, and does not affect the sample or the chemical environment during the analysis. In a DOSY experiment, a series of spin echo spectra, each with different pulsed gradient strengths, are recorded, and the decay of the signals observed. The reduction of the signals is due to the dephasing-diffusion-rephasing sequences employed.747 A 90˚ pulse aligns the magnetic moments of the molecules, and once this is complete, a dephasing gradient pulse disperses the magnetization. After a period of time, an 180˚ pulse is applied which inverts the remaining magnetization, and a second pulse then rephases these signals (Figure 5.13).
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Figure 5.13. Spatial spin encoding and decoding in DOSY experiments.748
Only those signals corresponding to nuclei which have not moved significantly up or down the tube can be refocused, and as diffusion causes some of the molecules to move away, the intensities of the signals are reduced (Figure 5.14). The longer and more intense the gradient pulse, the more spatially discriminating it is, which corresponds to a weaker signal. Therefore, the duration and intensity of this magnetic pulse determines the distance a molecule can diffuse while still yielding a detectable signal.749 All signals arising from the same molecular species will decay at the same rate, with the signal loss following an exponential decay curve.
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Figure 5.14. NMR diffusion spectra of a three-component mixture of water, 2-ethoxyethanol and caffeine.750
The degree of attenuation or spectral intensity (Sx) occurs at a rate proportional to the diffusion coefficient (D) of the molecule (Equation 1), where S0 is the intensity at zero gradient (the “normal”
spectrum) and Zx encodes the different gradient amplitudes used.746
= (1)
There are various formulae used to determine the value of Z in terms of the gyromagnetic ratio (δ), the amplitude of the gradient applied (G), as well as one or more time parameters, such as Δ, which is the time between two pulse gradients and is related to the echo time, and δ, the width of the gradient pulse. The original Tanner-Stejskal method751 (Equation 2) which uses two rectangular gradient pulses, holds for simple experiments, and this equation can undergo minor modifications for more complex pulse sequences.
= (∆ − ) (2)
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Following data processing, the 1D NMR spectra are transformed into a 2D DOSY spectrum (Figure 5.15), which allows for the identification of the number of components present in the solution, as well as identifying which signals correspond to each component.
Figure 5.15. 2D DOSY spectrum of the caffeine, 2-ethoxyethanol and water mixture showing the separation of the three compounds present.750
Once this transformation is complete, the diffusion coefficient for each compound in a mixture can be determined from the y-axis of the 2D plot. This, combined with the viscosity of the solvent can be used to determine the effective molecular size in that solvent, based on the Stokes-Einstein equation (Equation 3), where r is the Van der Waals radius in meters, k is the Boltzmann constant, T the temperature in Kelvin, and η the viscosity in Pascal seconds.749,752 Comparison of this radius with the measured mean Van der Waals radius provides an understanding of the solvation sphere surrounding each molecule.
= (3)
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DOSY experiments were carried out on 126 in both DMSO-d6 and D2O, and on compound 6 in D2O. The diffusion coefficients were then calculated for each compound using the 2D DOSY spectra (Table 5.1). As expected, the diffusion coefficients determined for 126 were different based on the solvent used, with the diffusion in DMSO-d6 slower than that noted for D2O.
Table 5.1. DOSY-derived diffusion coefficients for compounds 126 and 6 at 30˚C.
Entry Compound Solvent Diffusion coefficient,
/x10-10 M2.s-1
1 125 DMSO-d6 3.3
2 125 D2O 6.4
3 6 D2O 1.5
Diffusion coefficients for the non-deuterated water present in D2O, the water present in DMSO-d6, and the DMSO-d5 species present in DMSO-d6 were also calculated (Table 5.2), and these values show good correlation with those found in the literature.753
Table 5.2. DOSY-derived self-diffusion coefficients of solvents.
Entry Compound Solvent
Diffusion coefficient /x10-9 M2.s-1
This worka Literature753
1 H2O D2O 2.5 2.6a
2 H2O DMSO-d6 1.1 -
3 DMSO-d5 DMSO-d6 0.76 0.73, 0.89b
aT = 30˚C, bExperiments carried out at 25˚C and 35˚C.
With the diffusion coefficients for compounds 126 and 6 in hand, the Stokes radius for each molecule was calculated using the Stokes-Einstein equation (Equation 3, above) and compared to the Van der Waals radii, as calculated using the volume_calc.py script available in the Schrödinger package172 (Table 5.3).
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Table 5.3. Stokes Radii for compounds 126 and 6.
Entry Compound Solvent Stokes Radius /Å VDW radius /Å
1 125 DMSO-d6 3.72 3.34
2 125 D2O 4.45 3.34
3 6 D2O 18.9 3.68
Based on these results, it is immediately apparent that the size of the solvation sphere which forms around the molecules is dependent on the solvent used, with a larger solvation sphere forming with the use of D2O (Table 5.3, entries 1 and 2). This increase is most likely due to the increased interactions between the anionic compound 125 and the more polar water molecules than the interactions possible in DMSO. Comparison of the Stokes radii to the calculated Van der Waals radii also shows an increase in the “effective” size of the molecule in solution due to the presence of the solvation sphere. This is not unexpected, as Van der Waals volumes and radii are calculated as isolated gas-phase molecules without the solvent interactions inherent in solutions. The number of solvent molecules present in the solvation shell could theoretically be determined from these radii, however these estimates depend on the sixth root of the gradient strength calibration, and slight theoretical and experimental errors lead to large changes in the number of solvent molecules present.749 As the solvation sphere is constantly fluctuating, the number of molecules calculated depends on the timescale of the method used to calculate it – the smaller the timescale, the larger the solvent shell. The diffusion timescale is several collisions in the order of 100 picoseconds, whereas NMR timescales are milliseconds to seconds-long, and as a result signals arising from bound solvent molecules do not arise.749
The large difference between the Stokes radius and the Van der Waals radius for compound 6 (Table 5.3, entry 3) appears to show a huge five-fold increase in the size of the molecule on solvation. However, as the Stokes-Einstein equation makes use of literature values for η, it does not take into account the changes in the viscosity of the solution, and as such an inflated value is obtained for the Stokes radius for this compound. A more accurate measurement of the Stokes radii for this and other compounds requires the determination of the viscosity of the solution used for these DOSY experiments and the subsequent use of that value for η, rather than making use of literature values. This is a complex undertaking, requiring extensive study into areas such as the concentration-dependence of the viscosity, and as such is beyond the scope of this project.
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