Absolute Amounts of Analytes: When Gravimetric Methods are Insufficient

Introduction.

Tandem mass spectrometry (MS/MS), often combined with liquid chromatography (LC-MS/MS), has emerged as an extremely versatile platform for quantification of analytes in complex biological samples {Clarke:tg}. The method is rendered highly quantitative by use of a chemically-identical, but isotopically-differentiated internal standard. Such an internal standard corrects for losses of analyte signal in the assay due to sample handing or MS/MS signal loss due to suppression of analyte ionization in the electrospay source. At a minimum, it is required that the true concentration of the analyte in a stock solution be known as accurately as possible. Then one can inject an absolute number of moles of analyte into the instrument (the true moles) together with an aliquot of a solution of internal standard and determine the ratio of analyte to internal standard MS/MS response (response ratio). It is not required that the true moles of internal standard in the stock solution be accurately known. Even if a truly equi-mole mixture of analyte and internal standard are analyzed, the response ratio may not be 1 because of biases in the tuning of the quadrupole mass filters and/or an isotope effect on the fragmentation of the parent ion to give the product ions (no isotope effect is expected if a bond to the heavy isotope does not break in the fragmentation reaction). Thus, the measured response ratio will reflect the true difference in absolute moles of analyte and internal standard analyzed, tuning bias, and any isotope effects on fragmentation. For example, if one injected truly 1 nmole of analyte and nominally 1 nmole of internal standard in the MS/MS instrument and observed response ratio of 1.2, one can obtain the true moles of analyte in a new sample via the following equation:

$$\mathrm{moles}\mathrm{of}\mathrm{analyte}\mathrm{in}\mathrm{sample}=[(\mathrm{measured}\mathrm{analyte}-\mathrm{to}-\mathrm{internal}\mathrm{standard}\mathrm{MS}∕\mathrm{MS}\mathrm{response}\mathrm{ratio}\times (\mathrm{moles}\mathrm{of}\mathrm{internal}\mathrm{standard}\mathrm{in}\mathrm{the}\mathrm{sample})]\mathrm{divided}\mathrm{by}1.2$$

The above equation is valid even if the absolute moles of internal standard in the stock solution (and thus added to the sample) is not the true value as long as the same internal standard stock solution is consistently used for all samples, and the absolute moles of analyte in the stock solution used to determine the response ratio is the true value. If the true moles of internal standard in the stock solution is also known, one can measure the effect of tuning bias and fragmentation isotope effect on the response ratio, but this is not required. The challenge comes in knowing the true moles of analyte in the stock solution as discussed next.

Gravimetric analysis.

Many reference laboratories rely on gravimetric methods in which a microbalance (accurate to say 0.1-1 mg) is used to weight out a few milligrams of commercial standard compound that is reported to have a high purity (say > 99%). However, it is critically important to investigate how purity is measured. For example, purity of lipid standards is often based on thin layer chromatography in which lipids are visualized with a stain that binds to hydrophobic molecules (i.e. iodine staining). High pressure liquid chromatography may be used in cases of molecules that absorb UV light. However, these methods cannot establish that the standard compound is pure by weight. For example, chromatographic methods will not detect impurities such as water, silica gel (often left over from chromatographic purifications), salts, and metals, just to name a few. Without knowing the weight purity of the standard compound, one cannot know the true moles of standard compound in the stock solution.

Purity by weight and quantitative nuclear magnetic resonance.

Purity by weight may be assessed by combustion analysis in which the amounts of CO₂, H₂O and NO₂ are measured and compared to the amounts of carbon, oxygen, and nitrogen calculated based on the molecular formula of the standard. This method is rarely carried out on heavy isotope-substituted internal standards because of the relatively large amounts of material needed. Residue after burning is also used, but again requires large amounts, and has some pitfalls. Arguably, the most appropriate method to determine the true moles of standard in a container is quantitative proton nuclear magnetic resonance (qNMR). This technique is well known to most analytical chemists, and it relies on the ability of qNMR to provide a count of the number of hydrogen atoms in the sample tube. As an example, consider the sphingolipid psychosine (Figure 1), which is a useful biomarker for diagnosis of Krabbe disease (1-3). The qNMR is shown in Figure 1. A series of peaks is seen in this spectrum that reflect the different kinds of hydrogen atoms, and assignment of each peak to the various hydrogens in psychosine is easily done using reference tables of NMR data from countless molecules over the past half-century. For example, psychosine has one double bond, and each of the hydrogens attached to the doubly-bonded carbons can be found in the NMR at a specific chemical shift position along the X-axis (Figure 1). Also seen are peaks due to the hydrogens of the internal standard N,N-dimethylformamide (DMF). Internal standards used for qNMR are simple organic molecules that are reliably obtained from commercial sources in near 100% purity by weight. They are usually purified by distillation and thus free of non-volatile impurities such as salts and metals. The possible presence of impurities that could co-distill with DMF can be ruled out by the absence of spurious NMR signals (signals other than those from the hydrogens of DMF). Since DMF is taken as 100% pure by weight with high confidence, the moles of this standard in the NMR sample tube along with psychosine are known by adding an accurate weight or volume of DMF to the tube. The nice feature of qNMR is that the area under each signal peak is proportional to the number of hydrogen atoms in the molecule. For example, if the number of molecules of psychosine in the NMR tube is equal to the number of DMF molecules in the same tube, the area under the NMR peak due to the methyl group of psychosine (3 hydrogens) will be 3-times that under the NMR peak of DMF due to its single formyl proton (Figure 1). One may worry that there are impurities (non psychosine molecules) in the sample that contribute to peak area for say the psychosine methyl group (burried in the methyl peak), but the ratio of peak areas for the various NMR peaks of the psychosine hydrogens can be compared to each other and with those predicted from the chemical structure of this molecule (Figure 1) (the same is true for the internal standard).

Figure 1.

qNMR spectrum of psychosine in deuterated methanol (CD₃OD) containing DMF as an internal standard. The Y-axis is NMR signal intensity in arbitrary units, and the X-axis is the chemical shift (f1) in units of parts per million (ppm). The peak at 8.0 ppm is from the formyl hydrogen of DMF (H-CON(Me)₂), and the peaks at ~2.85 and ~3.00 ppm are due to the methyl groups of DMF. The number below each peak is the peak area; note that the methyl peaks of DMF are ~3-fold the area of the formyl peak (which was assigned to 1.00 for convenience). The peaks at ~5.55 and ~5.90 ppm are due to the hydrogens attached to the double bond of psychosine, the peak at ~0.90 ppm is due to the methyl group, and the peak at ~2.20 ppm is due to the CH₂ next to the double bond. Other peak assignments are known but not indicated in the Figure. Note that the area ratios are very close to those expected based on the structure of psychosine except that the peak at ~5.55 is of slightly higher area than the peak at ~5.90 ppm suggesting a small amount of impurity that contributes proton area to the ~5.55 ppm peak. By using these areas and those of the DMF internal standard and knowing the absolute moles of DMF in the tube (based on gravimetric analysis of DMF that is essentially pure by weight), one obtains the absolute moles of psychosine in the sample. This is valid even if the psychosine contains impurities that lower its purity by weight. If the moles of psychosine determined by qNMR agrees with the moles measured gravimetrically, only then can it be said that psychosine is pure by weight.

A good description of the qNMR experiment is available at: https://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Sigma-Aldrich/Brochure/1/qnmr-brochure-rjo.pdf. This document describes the instrument settings for a reliable qNMR experiment including the important need for a longer than normal recycle delay between radio-frequency pulses. The latter is sometimes overlooked by NMR operators.

Psychosine analysis as an example.

The issues discussed in this opinion piece are not trivial as they have led to differences in psychosine reference ranges seen in multiple laboratories involved in the diagnosis of Krabbe disease. Table 1 gives the results of a study in which adult blood was spiked with various amounts of qNMR-quantified psychosine for preparation of standard dried blood spots. These spots were distributed to 5 labs (author's labs) along with stock solutions of d₀- and d₅-psychosine, both quantified by qNMR. Each lab measured the MS/MS response ratio and psychosine concentrations in the spike samples using either qNMR- or gravimetric-quantified stock solutions, and results are given in Table 1.

Table 1.

Psychosine analysis in 5 laboratories.¹

Lab	Psychosine Concentration (nM)
	0 nM spike Gravimetric IS	0 nM spike qNMR IS	1.0 nM spike Gravimetric IS	1.0 nM spike qNMR IS	7.5 nM spike Gravimetric IS	7.5 nM spike qNMR IS	15 nM spike Gravimetric IS	15 nM spike qNMR IS
1	0.4	0.3	1.3	0.9	8.9	5.4	25	13
2	0.1	0.2	0.4	0.7	3.6	6.5	8.6	14.6
3	0.8	0.5	1.5	0.8	6.7	5.3	13.6	13.3
4	0.8	1.0	1.2	1.6	6.6	7.5	12.1	19.5
5	2.7	0.0	3.3	1.0	10.0	5.7	19.7	13.4

All 5 laboratories showed close agreement with the target psychosine concentrations in the standard DBS with 7.5 and 15 nM when the qNMR-quantified internal standard was used but not with internal standard quantified gravimetrically. More variability was seen for the 0 and 1 nM spiked DBS, but this is of little concern because patients with infantile Krabbe disease are expected to have higher psychosine elevations (> 10 nM) (1-3).

Closing remarks.

Similar concerns may arise for other LC-MS/MS studies where the standard solutions are made by gravimetric analysis. Great care is needed to interpret the purity specification sheets provided by manufacturers. Although each reference laboratory typically determines their own reference ranges for healthy versus affected samples, these ranges can only be usefully compared across multiple laboratories if steps are taken to ensure that the absolute amounts of analyte and internal standard in stock solutions are known accurately in each laboratory. While this may be common place for diagnostic tests done in thousands of laboratories worldwide, extra care is needed for tests for rare diseases where a rigorously quantified internal standard reference standard is usually not commercially available. If a reference laboratory does not have access to qNMR measurements they should request from the manufacturer that a qNMR-quantified reference standard be made available. This has recently be done for psychosine.

Abbreviations:

DMF

dimethylformamide

HPLC

high pressure liquid chromatography

LC-MS/MS

liquid chromatography-tandem mass spectrometry

qNMR

quantitative nuclear magnetic resonance