Figure 1.
Normalisations of Western blot replicates in the literature.
We divide the normalisations found in literature into three categories: (A) normalisation by fixed normalisation point or control; (B) normalisation by sum of the replicate; (C) normalisation by optimal alignment. For illustration purposes we do not use actual Western blot data. Each normalisation is presented using three cartoon Western blots, representing three replicates, and highlighting with red circles the data points used in the normalisation procedure. The graphs show the normalised data, where the points belonging to the same replicate are connected with lines.
Figure 2.
Signal linearity obtained by different Western blot detection systems.
Representative experiments of Western blots containing 2-fold serial dilution of BSA. Shown are the representative results from 3 independent experiments. BSA was detected by (A,C) ECL with X-ray film and (B,D) ECL with CCD imager. Blue squares indicate data points that are linear, while red triangles indicate data points outside the linear range of detection. To highlight linear and non-linear data we use linear trend lines, reporting the coefficient of determination . In (A,B) data are in log-log scale to improve visualisation.
Figure 3.
Effect of the normalisation on the CV of the normalised data.
(A) Distribution of the data in a simulated scenario. In our theoretical analysis of the effects of the normalisation on the variability of the normalised data we consider a distribution of the response to eight conditions. We use log-normal distributions with CV 0.2 and mean of the response to the conditions from 1 to 8 as 1, 2, 3, 4, 7, 10.5, 18, 27. (B) CVs are shown for the distribution of the simulated data before normalisation, after normalisation by first condition, after normalisation by sum of all data points in a replicate and after normalisation by least squared differences. The mean CV is computed as the average across the eight conditions. (C) Data from Figure S3 of [25] (Figure S5 in this publication) were normalised using different normalisation strategies and the mean CV of the resulting normalised data is shown. As the mean CV obtained by the normalisation by fixed point depends on the choice of normalisation point, we report the mean and standard deviation obtained. We also report the mean CV obtained using ppERK and pAkt data and we compare them with the theoretical results of Figure 3B. (D) Before normalisation, the response to Condition 2 has a CV of 0.2, as shown in Figure 3A. Condition 2 is then normalised by fixed point, with Condition 1 as normalisation point. Here we show how the CV of normalised Condition 2 changes for increasing CV of the normalisation point Condition 1.
Figure 4.
Correlation between the intensity of the normalisation points and the CV of the normalised data.
Using data from (A) phosphorylated Akt and (B) phosphorylated ERK from Figure S3 in [25] (Figure S5 in this publication) we tested every point on a blot as normalisation point. For each resulting normalisation we computed the average of the CV of the normalised data points, and plotted the value of each data point (scaled so that the maximum of each replicate is equal to 1) against the average CV obtained by normalising with the corresponding data point. The result shows how the intensities of each normalisation point chosen correlate with the variability of the normalised data.
Figure 5.
Effects of normalisation on false positives and false negatives when applying t-test for equality of the mean.
(A) We consider responses to eight conditions with log-normal distributions with CV of 0.2 and means of the conditions from 1 to 8 equal to: 1, 2, 2, 4, 7, 7, 18, 18. A number n = 5 of sampled replicates are obtained from these distributions and normalised using the normalisations above. Using these replicates before and after normalisation, conditions are tested using a two-tailed t-test with threshold p-value of 0.05. We repeat this procedure a large number of times and estimate the percentage of false positives. (B) In analogy with (A), we estimate the number of false negatives considering means of the conditions from 1 to 8 equal to: 1, 2, 3, 4, 7, 10.5, 18, 27. Notice that for a fair comparison, when testing two conditions, one has a mean that is always 2/3 the mean of the other, e.g. Condition 5 has mean 7 and Condition 6 has mean 10.5, with 7/10.5 = 2/3.