On the road and in your genome with Poisson

This will probably seem simple and obvious to many Finch and Pea patrons, but one of the mind-blowing features of nature, the real world, Plato’s cave, or what have you, is that very different phenomena often give rise to the same pattern, because they share a fundamental quantitative relationship. The world really does run on math. Some of the best examples of this are probability distributions, like the Poisson distribution, which is basically the law of rare events. I like to think of the Poisson distribution as the result of an infinite number of flips of some giant cosmic coin which only rarely, very rarely, lands on the side I’m hoping for.

The classic illustration of a Poisson distribution is the randomly-passing car problem. Imagine that you like to look out your window at the road and count the number of cars that drive by on your street. Suppose that during morning rush hour, on average five cars pass by every minute. If you count cars for 10 minutes each morning during rush hour, on average you’ll count fifty cars. But the cars arrive randomly of course, so some mornings you’ll count fifty, others you’ll count thirty-three, and some mornings you’ll count seventy-six. What’s the probability that on a given morning, you’ll count N cars? Poisson tells you the answer.

But Poisson applies not just to cars, but to genes as well. Imagine a gene, which is bound most of the time by a protein that keeps the gene off. But occasionally, the protein randomly falls off, and the gene switches on, producing mRNA. (The word ‘falls’ here is of course inappropriate, suggesting the effect of gravity, but you get the point.) If the protein really off randomly, say on average once every hour, what’s the probability that your gene will come on twice in one hour? Poisson should tell you the answer, if what’s going inside the cell is random falling off of protein. And, when we check this, we do in fact see a Poisson distribution. A group of scientists in Sunney Xie’s lab at Harvard took a look at how often a gene came on in bacteria, and found that Poisson could explain what they saw:

Figure A, Probing Gene Expression in Live Cells, One Protein Molecule at a Time, Ji Yu, Jie Xiao, Xiaojia Ren, Kaiqin Lao and X. Sunney Xie, Science 17 March 2006:Vol. 311 no. 5767 pp. 1600-1603

What this says is that the math behind nature’s infinite, cosmic coin flips is the same on the road and in your genome. We should be glad that it is, because it really makes it a lot easier to figure out what’s going on in the world.

Author: Mike White

Genomes, Books, and Science Fiction

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