Sunday April 5th: Theme and variations

Mostly variations. Since the beginning of Feb when I started these stem-growth experiments in earnest, my efforts can be described as searching for and eliminating variability. First there was human error, as I forgot to add solution or some other part of the protocol. Then, equipment error (sometimes referred to as systematic error) as I overcame hassles with the computer, cutting segments, and lens distortion. And finally, what remains is biological error, the most difficult of all.

All of this narrowing down has the underlying expectation of precise relations between cause and effect. That is, adding such and such a concentration of growth hormone to the mesocotyl segments is supposed to stimulate their rate of expansion by a specific amount. We imagine the hormone molecules interacting with protein molecules, that themselves then interact with other molecules, ultimately changing the character of the cell or cells. All of these interactions are based on physical law, and the set of them together is spoken of, and thought of, as a mechanism. Cell guts as machines, albeit complex ones, is standard world view of pretty much all biologists

This machine metaphor is incomplete and therefor partly misleading. Consider a clock, the little wristwatch I wear on my wrist tells the same time, month after month. To be more exact, I can sense an error if it is as large as a minute, and there are something like 40,000 minutes in a month. So let’s say the watch is as good as 1 in 100,000 (2.5 months worth), probably a conservative estimate. Now, how about an E. coli cell? These cells are often said to have a doubling time of 20 min, but this is an average figure, for a population of cells. Put your eye on Alex, that bacterium over there, and they might take 16 min or 24 min to divide. In quantitative terms, that 20 min average doubling time has a standard deviation reflecting how close each member of the population comes to hitting the average. For E. coli doubling time, the standard deviation is around 4 min [*]. That’s 1 in 5, quite a comedown compared to the wristwatch. Machines don’t behave like that, even hugely complex ones like a computer.

The variability in biology probably originates in Brownian motion. Imagine if inside the watch were a sea of cams, gears, jewels, and rivets, each moving as though fired from a rifle. This metal maelstrom would break the watch in moments. That is why biological machines have to continually synthesize new parts and why targets, such as a time to divide, are reached approximately, despite having inner workings fitting together more snugly than any clock. The machine metaphor might be the best we have but it is important to recognize its limitations. One could even argue that the randomness of Brownian motion underlies actual free will, but I’ll leave that argument for another time.

Thoughts about variation were clamorous, based on this past week’s results. Here they are:

All numbers are %/hr

…         elongation          swelling

….     auxin   acid        auxin   acid

one     6.0       3.0          0.4       0.2

two     4.3       2.2         -0.8     -0.1

three   4.4       4.0          0.7     -0.2

_______________________

avg.     4.9       3.1             0.1     0.0

sem     0.5     0.5             0.5     0.1

 

I set up this experiment with replicates. That is, I had three washer dishes with the same auxin (3 µM) and another three with the same acid (10 mM citrate, pH 4.1). Now, looking at the averages, it is clear that auxin caused more elongation than the acid did, and neither of them changed the radius. No fattening or thinning (the relevance of thinning was discussed last week). But, in comparing the three dishes, it is obvious that the reproducibility is low, or in other words, the variability is high.

Now, this time, because of success with standardizing segment cutting, and correcting the lens distortion, the initial lengths are uniform. So much so, that I could look at the growth rate of each segment by assuming it started out at the average initial length. Here are the elongation rates of each of the six segments in auxin-dish two:

%/hr

7.20, 0.95, 0.34, -0.60, 8.79, 7.58

 

Three of them grew at the kind of rate I had been hoping to get, around 8 %/hr but three others hardly grew at all. Likewise, in the other two auxin dishes, three segments were fast and three were slow. The average of the 9 fast segments was 7.4 %/hr (standard deviation = 1.3 %/hr) and of the slow ones was 2.2 %/hr (standard deviation = 2.2 %/hr, yes the same number!). That’s a huge difference, and statistically significant too. It means that the variability was not continuous but instead reflected the presence of two different populations.

Since I take three segments per plant, two plants per dish, and this population difference breaks down by threes, it seems plausible that there are fast plants and slow plants, present in the growth box about 50/50. A tidy explanation but suffering from the absence of any visible difference in the plants in the box; rather it would have to be that half of the plants give rise to auxin-responsive segments, and the other half don’t. Logical but biologically odd.

A further problem with the 50/50 plants explanation: why would I unfailingly choose one of each per dish? By chance, I ought to pick two of the same class for a dish (this rule of three seems to hold for the acid too but the lower overall effect makes it harder to say for sure).

I noticed while I was measuring that many segments had a notable constriction in the middle, as if wearing a belt cinched in a bit too tight. I suspect this is caused by my grabbing them too hard with the tweezers. Do these tweezer marks indicate mortal wounds? Or maybe the tweezer grab evokes a “stay put – don’t grow” signal? I have found a small strip of plastic that I can use as a spatula to transfer each segment from between the cutting blades to the solution. This could be a hidden source of experimental error, although it surprises me that I should be wounding precisely half of the segments.

Discouraged by these still disobedient segments, I ordered pea, cucumber, and sunflower seed. All of them have nice big fat hypocotyls, ideal for this kind of work. And one of the papers claiming acid causes shrinkage used pea. There is no requirement for me to using maize. Let’s see how other material behaves, perhaps more like a watch?

 

*OK, I don’t know what it is really, it might be smaller, it might be larger. That 4 min is perfectly plausible in this context is all that matters.]

 

By Maurice Sendak, because cats

By Maurice Sendak, because cats

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