Fold change - a final explanation

Question

[Sebastian Hesse]

A colleague of mine and I have just been discussing the meaning of fold changes and though this question has been asked before non of the answers are actually as straight forward as needed so lets try here to solve this once and for all.

I list here what I understand so far and will update it from your answers.

What is the correct way to understand a fold change value of a gene or protein?

• A foldchange describes the difference of two values (eg. difference of expression in gene/protein A between healthy and diseased case)
• Biostatistical porgrams/packages calculate it via: "Log(FC)" = mean(log2(Group1)) - mean(log2(Group2))
• log2 fold changes are used/plotted in graphs as those are nicer to show because they center around 0, giving reductions a negative value and increments a positive value
• log2 fold change values (eg 1 or 2 or 3) can be converted to fold changes by taking 2^1 or 2^2 or 2^3 = 1 or 4 or 8
• To convert the fold change into change in % or anything that is actually tangible/understandable in "real life terms" ... need answers here! (= actual question I want to ask)

Lets get this solved once and for all, im looking forwards to your posts!

Here are great posts explaining more about fold changes:

graphical representations

conversion of log2 fold change to fold change

Answer 1

[i.sudbery]

There is what appears to be an error in your definition of fold change (could be an error, could be causal wording):

• A fold change describes the ratio of two values (not the difference). i.e. (expression condition 1)/(expression condition 2)
• The log2 fold changes are the log-of-the-fold-changes i.e. log2(condition1/condition2)
• Because log(A/B) = log (A) - log(B), many statistical programs will calculate the Log2FC = log2(condition1) - log2(condition2), but this is mathematically identical to Log2FC = log2(condition1/condition2)
• Biostats programs will often estimate log2(condition1) using mean(log2(condition1)). This is equivalent to taking the geometric mean of the original data. Thus, Log2FC = mean(log2(condition1)) - mean(log2(condition2)) is the same as Log2FC = log2(geo_mean(condition1)/geo_mean(condition2)).
• Log2 fold changes are used/plotted in graphs as those are nicer to show because they center around 0, giving reductions a negative value and increments a positive value
• log2 fold change values (eg 1 or 2 or 3) can be converted to fold changes by taking 2^1 or 2^2 or 2^3 = 1 or 4 or 8
• You can interpret fold changes as follows:
  • if there is a two fold increase (fold change=2, Log2FC=1) between A and B, then A is twice as big as B (or A is 200% of B).
  • If there is a two fold decrease (fold change = 0.5, Log2FC= -1) between A and B, then A is half as big as B (or B is twice as big as A, or A is 50% of B).

@kristoffer.vittingseerup has the formula for converting foldchange or LogFC into % change.

[h.mon]

Great answer, just a small addendum: as log2( 0 ) is undefined, most programs add a small constant to base expressions, so Log2FC becomes:

Log2FC = log2( (condition1 + constant ) / ( condition2 + constant ) )

Or

Log2FC = log2( condition1 + constant ) - log2( condition2 + constant )

[i.sudbery]

Well, that depends on the program. None of the standard rnaseq programs report regularized logs as default I don't think, other than DESeq, and even then it outputs the non-shrunk values as well.

[Sebastian Hesse]

Thanks a lot for your detailed and insightful corrections!

[biom.andressa]

Hi,

To find the fold decrease that you mentioned, I can calculate -1/FC, when FC <1. Right?

I do this with qPCR data, so I wasn't sure how to do in RNA Seq results.

thanks

[i.sudbery]

If you have a FC of 0.5, then that is a 2 fold decrease: i.e. the fold decrease is 1/FC, not -1/FC. Unless you want your 2 fold decrease to be written as -2.

1/FC is effectively changing the direction of the comparison - that is which of the two conditions is treatment and which control.

[biom.andressa]

Ok!! Thanks you! =]

Answer 2

[Kristoffer Vitting-Seerup]

Percent change = 2^(fold change) * 100, where the baseline then correspond to 100%

log2FC = 2 : 2^2 * 100 = 400, where the baseline then correspond to 100%

Log2FC = -2 : 2^-2 * 100 = 25, where the baseline then correspond to 100%

Hope this helps

Answer 3

[jomo018]

Fold change is ratio between values.

Typically, the ratio is final-to-inital or treated-to-control*.

Log2, or % are just representations of the ratio. Log2 in partcular, usually reduces the "dynamic range" of the ratios in a monotonic mapping. So rather than handling ratios between 1-1000, these map to about 0-10.

Ratios lower than 1 map to negative figures.