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
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.