How To Compare Expression Values In Microarray Experiments?

Question

[Tomas]

Hi everybody,

I know that this is probably an easy question, but to be honest I am getting so confused at the moment, that I am not ashamed to ask any more.

I have a table (expressionSet) of expression values from an array experiment of two conditions. I would like to compare the two conditions to identify differentially expressed genes. I have five arrays for each of the conditions (total of 10 arrays).

The way I thought about doing it was to calculate the mean for the two conditions and than divide the treatment by the control:

gene1 mean_treat 1000
gene1 mean_ctrl  100
gene1 fold-change 1000/100 = 10

I would think, that gene1 has a differential expression of 10xfold. But if the values are already log-values? How do I calculate the differences than? Do I do it the same way? or do I subtract the two values from each other? Is this is the correct way?

gene1 mean_treat 9.965784 (log(1000,2))
gene1 mean_ctrl  6.643856 (log(100,2))
==>gene1 fold-change 9.965784/6.643856= 1.5 
==>gene1 fold-change 9.965784-6.643856= 3.321928

So which one of the two fold-changes is correct?

Again I am so sorry for needing to ask this question, but I would appreciate your help and maybe someone can refer me to a paper/book to read

Thanks a lot Tomas

Answer 1

[seidel]

If you are unsure if the values are logged, you might look at the distribution of numbers - what is the range? For a typical microarray experiment you'd expect linear data values between 0 and 65000 (in most cases, due to a 16 bit detector in the scanner). However an expressionSet object of affy arrays in the R environment typically has the data in log2 format. So if you examine your range of values and they are all between 0 and 16, chances are they are logged.

If they are in log scale, then to divide one set of arrays by the other, you subtract the numbers. The answer (or the result) will also be in log scale. So to see the real ratio you have to use your answer as an exponent (as described by Simon).

There's a couple of good reviews by John Quackenbush:

Computational Approaches to Analysis of DNA Microarray Data (2006) http://www.ncbi.nlm.nih.gov/pubmed/17051302 (free download)

Microarray data normalization and transformation.(2002) Nature Genetics http://www.ncbi.nlm.nih.gov/pubmed/12454644

[jonsnow]

your hint that affy expressionSet is typically in log2 scale (and thus I need to subtract, not divide) solved my troubles reproducing an existing study and saved my day :-)

Answer 2

[Simon Cockell]

The change in expression is the same in both circumstances (ie a 10-fold change).

A difference of magnitude of 1 in log2 values is the same as a 2[?]1[?], or 2-fold change in the raw data, a difference in magnitude of 2 is equivalent to a 2[?]2[?], or 4-fold change in the raw data.

To calculate the fold-change in the log2 scenario, you calculate 2[?](treat-cntrl)[?]. Or, in this case 2[?]3.321928[?] (=10).

[Tomas]

so basically the second way of calculating the difference between the expression values is correct? Otherwise I won't get the 3.321...?