1. Copyright © 2007 Dan Nettleton
Using lowess curves for dealing with technical variation in cDNA microarrays
Adapted from
Dan Nettleton
Iowa State University
Copyright © 2007 Dan Nettleton

2. We can now actually measure the amount of mRNA (a surrogate for protein) being produced at a particular point in time at thousands of genes for a single organism using…. MICROARRAYS
Usually, we compare the gene expression across groups:
Cancer vs. Healthy
Wild type vs. Mutant
High yield vs. low yield
We’re looking for genes that show a big difference.

3. Usually, we expect most of the thousands of genes to be similar between the two groups (standard functioning of organism), but that a few will be very different.
We collect a 1 sample from group 1 and dye it green.
We collect a 1 sample from group 2 and dye it red.
The samples are mixed and placed on the same array.
Yellow suggests similar expression…

4. We don’t want any of our found differences to be due to technology (we want found differences to be due to biology).
Therefore, we usually have to make some adjustments to our data.
Here is a side-by-side boxplot of the red and green expression values from a slide:

5. Here is the log(red) expression plotted against the log(green) expression level… notice the deviation from the diagonal.
Log Green
Log Red
Slide 1 Log Signal Means
Since we expect most of the red vs. green genes to be equal, the bulk of the points should fall near the 45o line or diagonal (shown in blue).
The technology is introducing some bias, a deviation from the diagonal.

6. M vs. A Plot for Slide 1 Log Signal Means
We can rotate the previous plot to show the expected `mean curve’ (blue line) as a horizontal line:
A = (Log Green + Log Red) / 2
M = Log Red - Log Green
M vs. A Plot for Slide 1 Log Signal Means
Now, we will use a lowess curve to straighten out the plot as the biology suggests it should be…

7. M vs. A Plot for Slide 1 Log Signal Means
The lowess fitted curve:
A = (Log Green + Log Red) / 2
M = Log Red - Log Green
M vs. A Plot for Slide 1 Log Signal Means
with lowess fit (f=0.40)

8. Each point will be adjusted with respect to the lowess curve (the fitted mean curve)…
A = (Log Green + Log Red) / 2
M = Log Red - Log Green
Adjust M Values

9. M vs. A Plot after Adjustment
Giving the final adjusted expression values to be used in the analysis.
M vs. A Plot after Adjustment
M = Adjusted Log Red – Adjusted Log Green
A = (Adjusted Log Green + Adjusted Log Red) / 2