First of all, WB is, at best, a semi-quantitative technique, so an elaborate statistical treatment may put gold on a lily.

If your antibody is specific (only one band in WB), quantification may work better with ELISA. Even better are dot-blots: The sample is spotted onto a PVDF membrane, using a 96-well vacuum manifold and then developed like a WB. Due to the manifold, all your samples have exactly the same size and shape, unlike WB, you do not have any loss from proteins not entering the well of the gel. The method is very quick, and unlike ELISA, you use nearly 100% of the protein, ensuring maximum sensitivity. If you can count the chemiluminescence directly (no detour via photography), you linear range will be 5-6 orders of magnitude.

In addition, if you normalise the raw data and then calculate averages, you do have a standard deviation. That your control value also has a standard deviation doesn't matter for normalisation, but would have to be taken into account if you do an error analysis (you get the maximal relative error of a quotient by adding the relative errors of enumerator and denominator, for the probable error divide that sum by sqrt(n)).

Engelbert Buxbaum

Well of course WB is not really a good quantitative method, yet still everybody uses it like a quantitative method in almost all publications.

Indeed I cannot use a Dot Blot method since I am quantifying only one isoform of a protein (LC3-II). There are people who quantify LC3-II in comparison to LC3-I, but many people doubt the validity of taking a ratio between LC3-I and LC3-II, because different antibodies from different companies might detect one isoform better than the other. Therefore the accepted quantification method is just normalization to a loading ctrl protein or total protein amount.

Regarding the statistic and normalization problem:

I don't think you quite understand what my problem is.

I quantify the volume of the signal for my POI by selecting an area for the signal and multiplying it by the average grey value of this area. I do a background substraction and get a completely arbitrary value for the signal for this particular band on this particular blot. The absolute number has no meaning at all and I can only compare the relative signal intensities between bands on the same blot.

But before I can even do that I need to account for protein loading. It doesn't even matter if I take the value of a ponceau for loading correction or the signal from a particular housekeeper. For my loading I get another completely arbitrary value. I then simply devide the arbitrary value from my POI by the arbitrary value of my loading ctrl. This fraction again is a completely arbitrary value that only has a meaning on this particular blot.

I have 4 independent experiments on 4 different blots. Therefore, the naked values (after loading correction) are factors appart (e.g. 1376 for my ctrl on blot 1 and 6164 for my ctrl on blot 4). The only thing that matters are the relative differences between the samples on the same blot. Therefore I normalize (not loading correction!) to the ctrl level, meaning I set the ctrl level to 1 and all other values are just in relative values of the ctrl. Then I have nice standard deviations for samples 2 to 4, but of course sample 1 does not have a standard deviation anymore.

The only thing I could now think of, but that doesn't seem right to me, would be if I normalize to another sample and check what the standard deviation for the ctrl sample would be and just take this as the standard deviation.

It wouldn't make sense to take the standard deviations of the raw values because as mentioned before, they are factors apart.

Normally, for "quantitative" WB you use a control in the same lane as your sample, to account for variations in loading. That, of course, requires that the chosen control protein is independent of the experimental treatment. Whether you quantify that protein by Ponceau- or immunostaining, is irrelevant (constant factor for all samples).

The value for "your" protein thus obtained should be reproducible from blot to blot, mathematically speaking, the values should be members of the same population, allowing mean and std to be calculated.

Engelbert Buxbaum

Thanks for your explanation, but I have to disagree on your last statement:

"The value for "your" protein thus obtained should be reproducible from blot to blot, mathematically speaking, the values should be members of the same population, allowing mean and std to be calculated."

The mathematical value of signal intensity depends on many things including

- the loading of protein on the gel (e.g. some samples are too diluted to load more than 12 µg, others are more concentrated and I can load up to 25 µg)

- the quality of the transfer (close to 100% most of the time but not always)

- the quality/age of the ECL solution

- the exposure time during imaging of the blot

That means taking an image for the POI or GAPDH loading ctrl on one blot could take 2 seconds to get the full range of luminosity, on another blot (with similar samples) this could be 5 seconds or 10 seconds or even 20 seconds. Therefore these numbers (luminosity) are completely arbitrary. That's why I argue that you can never compare samples that are on different blots unless you have a comparison sample (the same sample on different blots).

But my main point is rather that the absolute values are meaningless anyways. Unless you have a standard curve for your POI, you can't determine absolute protein amounts anyways (which most of the time is also unnecessary).

Only the relative differences on one blot between samples are of any meaning. Therefore my question points at exactly this fact.

How do you do statistics if you have only relative differences, meaning one value has no standard deviation?

That is why you normalise your raw data by those of the control protein. The ratio Measurement/Control is (should be) independent of the points you listed.