Fig. 6 : Linearity effects across sample matrixes at the U.S. EPA (left) and UNM CSI (right). The linearity effect is shown relative to the median observed isotope composition of each working standard. Vertical red lines indicate nominal peak amplitudes that were targeted for tuning and sample peak heights. Note that units of peak amplitude vary between instruments.

Discussion

  1. Two-point isotope normalizations are insufficient for EAIRMS

In this study, we conducted a total of 6272 normalizations for N and C at two laboratories using 8 certified isotope reference materials. Past work has found that one-point normalizations have larger normalization errors than two-point, three-point, and four-point normalizations11,17,27, and our results further suggest that normalization accuracy generally improves with the number of standards. Regardless of whether we test bounded, matrix-matched normalizations or extrapolated, matrix-mixed normalizations, three-point and four-point normalizations exhibit better accuracy than one-point and two-point normalizations (Fig. 2). The lowest range of normalization errors was consistently found for three-point and four-point normalizations, when samples were bounded within the range of calibration standards, and when the sample matrix matched between samples and calibration standards (Fig 2A).
The dramatic reduction in two-point normalization accuracy when the normalization was extrapolated and matrix mixed (Fig. 2B) was surprising given that foundational literature suggests that two-point normalizations are sufficient for the normalization of stable isotope results17,21,37. Extrapolating beyond the normalization and mixing matrixes between the samples and standards are expected to increase normalization errors, regardless of how many standards are used. However, the median error of two-point normalizations conducted under these abnormal conditions were 64%-230% greater than corresponding three-point and four-point normalizations, with the error of some two-point normalizations exceeding 1‰.
The sensitivity of two-point normalizations to matrix effects and extrapolation are evident in its derivation process (Eq 3-5). In a two-point normalization, the sensitivity of m to inaccuracies inδraw(std) is a function of the isotope range of the two standards – as the isotope range of the standards decreases,m becomes more sensitive to isotope variability of the standards21, including those due to matrix effects. Indeed, we find that two-point normalizations have the highest mvariability (Fig. 7A), and that the variability of m is inversely related to the isotope range of the standards (Fig. 7B). The effect ofm on δtrue(sample) also varies as a function of the isotope range between the standards and the samples: as the difference between δraw(std) andδraw(sample) increases, errors due to an incorrect m are compounded. Changes inδraw(std) due to matrix effects will manifest as inaccuracy when the matrix of the standards and the samples are mixed, which would subsequently be amplified by the effects of extrapolation. Thus, two-point normalizations that are extrapolated and matrix-mixed have poor performance – particularly with a small isotope range between the two standards (Fig. 5D). Overall, this work questions whether two-point linear normalizations are sufficient for biological applications of EAIRMS – in our study, many two-point normalizations were inferior to one-point normalizations because the actual mwas close to 1, the assumed slope for 1-point normalization. Notably, three-point and four-point normalizations are much more resilient to the effects of extrapolation and matrix mixing (Fig. 2B), even when the isotope range was less than 15‰ (Fig. 5C). Thus, we recommend that all users of EAIRMS systems use at least 3 calibration standards to compose their normalization curve.