Within error

“Within error” is one of the more useful phrases in science and one of the easier ones to hide behind.  It means: yes, those two numbers are different, but not by more than the wobble in my hands and my instrument, so I’m not going to make anything of it.  Most of the time that is exactly the right call.

A paper from January has been sitting in my head, and not because of anything in its conclusions.  Because of a number in its methods.

The study was about how diatoms handle light and temperature that change quickly, which is the ordinary condition of most water and almost never the condition of a laboratory experiment.  Reasonable question.  But somewhere in the setup they took a single culture - one clone, one genotype, all of it descended from one original cell - split it into 384 small subpopulations, and measured a standard indicator of photosynthetic health on each.

The indicator is a quick fluorescence reading.  Shine light at the cells, some of it comes back, and the proportion that comes back tells you how much of the photosynthetic machinery is working properly.  It takes seconds and doesn’t destroy the sample, which is why it’s everywhere.

The 384 subpopulations did not agree.

Sit with how odd that should be.  Same genome, because it’s a clone.  Same medium, same shelf, same lamp, same afternoon.  Every variable anyone would normally reach for to explain a difference has been held still, and the readings still spread out further than the instrument can account for.

There are at least three explanations, and they aren’t small.

The first is the cell cycle.  A growing population isn’t one thing doing one thing.  At any moment some cells are copying their DNA, some are dividing, some have just finished and are rebuilding.  Those states are not physiologically equivalent.  Two subpopulations of a few hundred cells can easily be caught at different points in that mixture, and the average will move accordingly.

The second is epigenetic.  Chemical marks on the DNA and on the proteins it’s wound around change how loudly a gene gets read, and those marks are copied through cell division without any change to the underlying sequence.  Two cells can hold the same instructions and read them at different volumes, and pass that difference to their descendants.

The third is that gene expression is simply not steady.  Genes don’t get transcribed at a constant trickle.  They tend to fire in bursts - a run of activity, then quiet, more like a dripping tap than a flow.  In a small population, whether a burst happened recently is a real, physical difference between one well and the next.

The paper doesn’t distinguish between them.  The variability appears as a caution about how much confidence to place in culture-based measurements.

Which is a fair caution, and I want to be careful not to complain that someone didn’t write the paper I’d have written.  Their question was about fluctuating conditions and they went and answered it.  But it is still the case that if you have genetically identical cells in identical conditions producing non-identical outputs, and three plausible causes, and nothing separating them, you’ve found something rather than merely tripped over a nuisance.

There’s a second thing in the design that I keep turning over.  The study covers nine species.  Nine is a lot of work, and it also means each species gets less individual attention than one species would have - they function almost as replicates of the category “diatom”.  Which is precisely the assumption that gets undermined every time anyone looks closely.  So the study that found unexpected variation inside a single clone is also, structurally, averaging across species.  I don’t think that’s hypocrisy.  I think it’s what happens when you have limited hands and a broad question, and it’s worth naming because everyone does it, including me.

The general version of the problem is about averages.

A mean is the answer to a question nobody asks out loud, which is roughly: if all of these were the same thing, what would that thing be?  That’s a perfectly good question when they nearly are the same.  It becomes a strange question when they aren’t, because the mean will still come back with a confident number and it won’t tell you whether everyone moved a little or a few moved a lot.  Those are different worlds.  In one, a population is shifting.  In the other, a subgroup is doing something and the rest aren’t, and if you only have the mean you can’t see the subgroup at all.

I’ve reported means like that.  Treatment, mean, standard deviation, next paragraph.  The spread was sitting right there in the table.  I just wasn’t reading it as information about the organism - I was reading it as information about how carefully I’d pipetted.

“Within error” means within the error I was expecting.  Which is a statement about me.