among plate correction - Springer Static Content Server

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Supplement 1
ENZYME MEASUREMENTS
Each fry-sample homogenate was loaded and prepared for enzyme assays on a 96-well plate. From
this plate, each sample was automatically replicated four times to a 384-well microplate using a
Personal Pipettor PP150-4S (Apricot Designs, Covina, CA, USA), which was also used for pipetting
assay reagents to the sample replicates.
GR AND GST KINETIC ACTIVITY MEASUREMENTS
Enzyme activity of GR and GST was determined kinetically as change in absorbance with increasing
time (i.e., as slope) at 412 nm (GR) or 340 nm (GST) with a maximum of 16 measurements for GR
and 24 for GST per sample. Absorbance for each well was automatically recorded every 0.20 min for
GR and every 0.17 min for GST using a temperature-controlled EnSpire Multilabel Plate Reader
(PerkinElmer, Waltham, MA, USA). As valid enzyme-activity measurements can only be obtained
when the absorbance changes as a linear function of time, we assessed on a plate basis if the slopes
were estimated from such a linear reaction-progress curve. Non-linear reaction-progress curves can
result from both decreasing enzyme activity and substrate depletion. On each plate we also included
water blanks at the reading start and the end of the plate.
The raw absorbance data was pruned of technical outliers. For this purpose, we used mixed-model
methodology and removed random effects that deviated from normality at a false-discovery rate
(FDR; Benjamini and Hochberg 1995) of < 5%. Deviation was assessed based on studentised slope
effects for residuals (plate-by-well-by-time effects), wells (well-by-time effects), and samples
(sample-by-well-by-time effects) that we obtained using the “alternative outlier model” function
implemented in the “asreml-R” R package (Butler et al. 2009). Any observation that was statistically
significant outside of the t-distribution of slope effects, which was inferred using all data, was
considered a technical artefact and therefore removed.
After removing raw outliers, we identified the linear portion of each sample across the four well
replicates. This was conducted under the assumption that we had successfully eliminated faulty well
measurements and that variation among remaining replicates for a sample merely reflect technical
variation. We identified the linear portion for each sample across wells by assessing the significance
of the first, second, and third order polynomial fits for the time covariate (mean-centred) fitted to each
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sample datum across wells (with well and well by time, well by time2, and well by time3 as random
effects). We did this for increasing data points across time, starting with four measurement time data.
Significances for the three slope terms (P ≤ 0.05) were assessed using sequential Wald-type F-tests,
fitting first the linear, then the squared and finally the cubic terms. For each plate, we based slopes on
those measurement points across time that resulted in choosing the plate-averaged squared and cubic
coefficients closest to zero while also obtaining the highest P-values for these terms given the number
of included measurement time points (i.e., we maximised for each plate the first order polynomial fit
that represents the linear parts of the curves).
For GST, we subtracted the plate-specific slope obtained for water samples (included at both reading
start and end of each plate) from each plate-specific well slope. For GR, we subtracted the amongplate-averaged slope for water samples. This was conducted as water blanks for GST slope
measurements did differ from zero (Wald’s test F1, 11 = 10510, P < 0.001) and among plates (Wald’s
test F10, 11 = 31.1, P < 0.001), and for GR water slopes differed from zero (Wald’s test F1, 8.8 = 16.2, P
= 0.003) but not among plates (Wald’s test F10, 11.3 = 0.4, P = 0.947).
From each water-corrected slope, raw GST activity per well was calculated using the equation:
A340nm *Vsample * dil
 mM *Venzyme
(1)
for which A340nm is the change in absorbance per minute at 340 nm (i.e., linear slopes), Vsample the
reaction volume of the original sample in mL, dil the dilution factor of the original sample, εmM the
extinction coefficient per cm (9.6), and Venzyme the volume of the sample tested in mL.
Similarly, from each water-corrected slope, raw GR activity per well was calculated using the
equation:
A412nm  *Vsample * dil
 mM *Venzyme
(2)
for which A412nm is the change in absorbance per minute at 412 nm (i.e., linear slopes), Vsample, dil ,
and Venzyme the same as for (1), and εmM the extinction coefficient per cm (0.007075).
Raw GR and GST activities were corrected for protein content of each sample by dividing the enzyme
activity by the sample-specific protein concentration in g*mL-1. Protein concentration of each
sample was determined based on quadruplicates and using the BCA protein assay kit (Thermo
Scientific Pierce; Rockford, IL, USA). Absorbance at 562nm was measured in 348-well plates using
the same plate reader as above. Absolute protein amount was determined based on the average slope
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from a dilution series of bovine serum albumin standards (1, 2, 3, 4, 5, 6, 7, 8 g*L-1) that was
included on all plates.
Within- and among-plate measurement precisions for GR and GST were determined based on slopes
of either raw (within) or blank-corrected, if applicable, absorbance data. Within-plate variation for
slopes was determined based on experimental samples as the intraclass correlation (ICC) among
samples, conditional for the experimental plates. We fitted a mixed model with fixed effects for plates
and random effects for samples within plates and wells within samples, as well as slopes for all
effects. The ICC was obtained as the ratio of the among-sample slope variance to the sum of the
among-sample slope and the among-well slope variance (that equals within-sample slope variance).
For ICs, we obtained standard errors according to the delta method using the R “nadiv” package
(Wolak 2012).
Among-plate variation for slopes was obtained as coefficient of variation (the absence of several
samples, replicated across plates, prohibited the calculation of the ICC) based on the fry standard that
was included on all plates twice in quadruplicates (Hõrak and Cohen 2010). We fitted a mixed model
with a common intercept and slope, and random effects for plates, for samples within plates (here,
“samples” refers to the two replicates of a standard sample replicated at two positions with four wells
each at the reading start or end of each plate), and for wells within samples within plates, and slopes
for all these effects. The coefficient of variation was obtained as the ratio of the square root of the
among-plate slope variance to the mean slope of the sample standard calculated across plates.
SOD ACTIVITY MEASUREMENTS
SOD activity was indirectly determined spectrophotometrically based on its ability to inhibit the
formation of a formazan dye from reduction of a highly water-soluble tetrazolium salt (WST-1) by
superoxide. SOD depletes superoxide and therefore inhibits the dye formation proportional to its
activity (Ukeda et al. 1999). We followed the methodology as outlined by the manufacturer of the kit
we used (SOD Assay Kit-WST; Sigma-Aldrich, St. Louis, MO, USA) using the same temperaturecontrolled automatic plate reader as for the other two enzymes. Blanks for SOD measurements did not
differ from zero (Wald’s test F1, 12 = 2.1, P = 0.172) or among plates (Wald’s test F11, 12 = 1.8, P =
0.173) and, therefore, we did not correct sample measurements for blank measurements. As for GR
and GST, the raw absorbance data was pruned of technical outliers with similar mixed model
methodology.
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AMONG PLATE CORRECTION
As outlined in the main manuscript, we also corrected measurement slopes for systematic amongplate variation to assess if fixed effects differed to results obtained when plate effects were included
as random effects in the model. For this purpose, we included a standard sample, prepared from 10
pooled individuals, in quadruplicate at both plate reading start and end of all plates. All plate-specific
slopes were then corrected for the deviation of the plate-specific averaged standard sample slope from
the average slope of the standard sample across all plates, i.e., we assumed an additive model for the
slope standardisation among plates.
REFERENCES
Benjamini Y, Hochberg Y. 1995. Controlling the false discovery rate - a practical and powerful
approach to multiple testing. Journal of the Royal Statistical Society: Series B (Statistical
Methodology) 57(1):289-300.
Butler DG, Cullis BR, Gilmour AR, Gogel BJ. 2009. Mixed models for S language environments
ASReml-R reference manual. Brisbane, Australia: Queensland Department of Primary
Industries and Fisheries, NSW Department of Primary Industries. 144 p.
Hõrak P, Cohen A. 2010. How to measure oxidative stress in an ecological context: methodological
and statistical issues. Functional Ecology 24(5):960-970.
Ukeda H, Kawana D, Maeda S, Sawamura M. 1999. Spectrophotometric assay for superoxide
dismutase based on the reduction of highly water-soluble tetrazolium salts by xanthinexanthine oxidase. Bioscience, Biotechnology and Biochemistry 63(3):485-488.
Wolak ME. 2012. nadiv: an R package to create relatedness matrices for estimating non-additive
genetic variances in animal models. Methods in Ecology and Evolution 3(5):792-796.
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