CHAPTER 3: NMR Spectroscopic Assays
3.2 Quantitative NMR Spectroscopy
The NMR experiment as it is normally conducted is not a quantitative one. In principle, the integrals of peaks from the 1
H-NMR experiment should reflect the number of nuclei which gave rise to them. That is, a -CH3, -CH2 and CH group should give rise to relative integrals of 3, 2, and 1, respectively, regardless of the species in the sample tube which gave rise to them. The integrals from a single pulsed Fourier Transform 1H NMR (FT-NMR) experiment are not normally quantitative, however, and can often have an error of 20-30%.
3.2.2 T1 Relaxation
In order for quantitative measurements to be gathered from the NMR experiment, several considerations must be taken into account. First, if the nuclei are not allowed to relax fully to their ground state then the second 90º RF pulse will flip them past 90º. Consequently, their signals will decrease from each subsequent iteration of the pulse sequence. To avoid this, a delay is inserted between each iteration, enabling M to fully return to the ground state magnetization. In practical terms, a value of 5 T1 is used and is easily adopted in 1
Measuring T1 values is performed by a pulse sequence known as ‘inversion recovery ’. Essentially, the sample is subjected to a 180º pulse, allowed to recover and then a further 90º pulse is followed by data acquisition [Figure 3.3]. The recovery delay is varied over a range of values, and as the sample relaxes, the bulk magnetisation vector returns along the z’ axis to zero, and then back to the ground state. The rate at which this occurs is a direct measure of T1 (there is no net x-y magnetisation, so there is little influence from T2). The second 90º pulse
will take the bulk vector and place it along the y’ axis, which then allows a signal which can be acquired and Fourier transformed to give a spectrium.
A plot of the final peak versus relaxation time will show an ‘inverted’ signal that passes through zero (when the bulk magnetization vector passes through the origin – no resulting signal along the y’ axis) and finally into a positive signal. If the delay is sufficiently long enough, the 180º pulse will relax away so that it has no effect on the size of the spectrum. An example is shown in Figure 3.4.
Figure 3.3 A typical ‘inversion recovery’ experiment used for measuring T1. The ‘p1’ pulse is a hard 180º pulse which ‘inverts’ all the resonances along the z axis. The ‘d2’ delay is arrayed over a rage of times (in s) to allow the signals to partially recover before ‘pw’, a 90º pulse, and data acquisition. ‘D1’ is set high (20 s) to allow total relaxation before the next iteration of the experiment.
The time required to give a zero point spectrum (τnull) can be used to gauge the value of T1. This follows from the exponential nature of T1 relaxation:
Mt = M0(1-2e-τ/T1
) Equation 3.4
Where Mτis proportional to the magnitude of the signal observed after delay τ. M0 is
the initial magneton, seen at τ = 0, and T1 is the exponential decay constant for longitudinal relaxation. It follows that:
T1 = τnull
ln2 = 1.443 τnull Equation 3.5
Figure 3.4 An example of the result from an ‘inversion recovery’ experiment, as outlined in the text. The delay required to give a ‘zero point’ spectrum, where no resultant NMR signal is seen, is used to gauge the value of T1.
3.2.3 T2 Relaxation
There is a second mechanism by which nuclei can release the energy imparted by the pulse, known as transverse relaxation, or T2. Where T1 was the loss of magnetisation along the z’ axis, ultimately giving a null signal, transverse relaxation or T2 relaxation results in a ‘blurring’ or fanning of the individual magnetisation vectors in the x’-y’ plane [Figure 3.5].
Figure 3.5 T2 relaxation. The bulk magnetisation vector along the y’ axis is lost as individual groups of magnetisation vectors, often isochromats, with different Lamor frequencies.
In terms of observable effects on the acquired spectrum, having a rapid relaxation from T2 effects (a ‘short’ T2) will lead to line broadening in the post-Fourier transform spectrum.
The field inhomogenities that give rise to T2 relaxation can arise from two distinct but inseparable sources. The first is static field inhomogeneity, i.e., the magnetic field is not the same over the sample volume; some nuclei experience a larger field than others, and so the Lamor frequency is different for these nuclei. Correctly calibrating or ‘shimming’ the NMR magnet prior to spectrum acquisition minimises effects resulting from an irregular magnetic field.
The second major contributing factor giving rise to transverse relaxation is small local differences in magnetic field resulting from molecular components in solution – i.e., arising from solution components.
3.2.4 Internal Standards for Quantification
Another consideration for quantitative NMR spectroscopy is that there is no equivalent to the molar extinction coefficient (ξ) from UV spectroscopy. That is, the peak integrals cannot easily be converted to absolute concentrations from the standard FT-NMR experiment. In order
to quantify the concentration of substances present, an internal standard of known concentration must be present to give a measure of the relative intensity to the sample.
Internal standards must be carefully chosen. It must be non-reactive (in order to not interfere with the chemicals present in the sample) and ideally give rise to a singlet which is easily discernable from the rest of the spectrum. For kinetic analysis, there is the extra requirement for the reference compound to be kinetically neutral to the enzyme. It was found that tert-butanol did not affect BHMT activity, so was used for kinetic measurements of BHMT [Chapters 4, 5, 6]. Acetonitrile is not a normal component of mammalian urine, so was used for quantitative measurements in urine [Chapter 7].
3.2.5 Aqueous Measurements Water presents a problem for 1
H-NMR spectroscopic measurements. Since the water molecule contains two protons, and is present at 55 M concentrations, it gives rise to a dominating peak (110 M 1
H equivalent) at about 4.7 ppm. Furthermore, the protons on the water peak are in rapid exchange with any amine or hydroxyl peaks in the sample.
There are several methods for removal of water signals from 1H-NMR spectra. The simplest is the presaturation technique, which uses a selective irradiation on the water signal for several s prior to the 90° pulse, which effectively scrambles the magnetisation of water protons, giving them no signal, therefore removing them from the spectrum. The consequences of this technique include the substitution of the excited protons from the solvent to exchangeable protons, like that on the hydroxy, or amine moiety. However, there is little disturbance to the baseline when this technique is used. A second technique used during the course of the work of this thesis was the double pulsed field gradient spin echo (DPFGSE) technique. This technique uses field gradients to selectively excite the solvent molecules, scrambling their magnetisation and therefore rendering them invisible to the proton spectrum.
The consequences of this technique include the distortion of the baseline in ways which can be obstructive to the quantification of the peaks in the spectrum, particularly if the underlying molecules differ significantly in concentration.17 The DPFGSE, however, achieves much better suppression of the solvent peaks than the presaturation technique. There are other techniques which were not employed in the course of this thesis, including WATR (Water Attenuation by Transverse Relaxation).18-20