I have been imaging western blots on a LI-COR Odyssey Fc. After looking into what the densitometry really means, I'm confused as to how only dividing the target protein's density by the same lane's loading control density is the best way to normalize the data. This imaging system uses base 10 logs to describe density, so if, for example, one lane's loading control returns a 1, then the band is 10x as dense as the surrounding background. If the target protein's band returns a value of let's say 0.1, then the band is ~1.26x the background, leading to a target protein / loading control of 0.126. If the next lane returns values "twice" as strong (i.e. target 0.2 & loading control 2), the common normalization procedure would show the same target protein / loading control as the first lane instead of 10^0.2 / 10^2 = 0.0158 != 0.126. Do the lanes actually have different target protein concentrations or am I misinterpreting the connection between density and concentration? Thanks!
Your confusion starts where you write about "protein values". This leaves quite undetermined what is concretely meant with "values". The normalization strategy is built on protein concentrations. To follow this route you need to ensure that the values you work with actually mean (or ar proportional to) concentrations.
Obvioulsely, your data are log-concentrations, what clearly is a different thing. An intellectually less demanding way to normalize logarithmic values is to undo the logarithms to get values that are proportional to the concentration and then to continue with these values. Example: let logA and logB be the measurements of two samples a and b, and you want the concentration of a normalized to b. You would first calculate A = exp(logA) and B=exp(logB), and then the normalized quantity is A/B.
This is a bit of a detur. We know that the log of a ratio is the difference of the logs, so:
log(A/B) = logA - logB
Therefore, taking the difference of the logarithms is how these values are to be normalized. These differences are log-ratios. The advantage to stay on this log-scale (and do all calculations with thes logarithms) is, that for these logarithms (and log ratios) the errors have a symmetric distribution, what considerably simplifies the statistical treatment and interpretation.
Take-home message:
Don't do calculations/analyses blindly (like thinking: "normalization must be a division"). Know your data, and identify appropriate procedures.
PS: It is good that you asked this question. To my experience this shows that you are some steps ahead of many (most?) of your collegues, who (generally) do not care much about what kind of data they have to analyze, and who do not question the methods they use.
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