If you found calculus hard be prepared to be shamed, as is appropriate, by a small bacterium. Escherichia coli, aka E.coli, has the smarts to be able to compute a derivative and use it to optimize its behavior.

I have to admit that I'm not convinced that E. coli actually does symbolic manipulation, in fact I'm 100% sure it doesn't, but it does employ an algorithm which has been found to be optimal in using a gradient to optimize a quantity. The basic idea is that E. coli may be a dumb, brainless, in fact neuronless, bacterium, but its sensors and responses form an optimal filtering system. E. coli, and many other bacteria  can sense a chemical gradient that indicates the direction that food lies in and move towards it. This hunting behavior is not the sort of thing we associate with such single-celled creatures, but a research team at the University of Tokyo has demonstrated that it is an optimal algorithm in a noisy environment. Disgracefully the resulting research paper is behind a paywall making it difficult for us to benefit fully from its findings.

Credit: Institute of Industrial Science, the University of Tokyo

The researchers have taken the standard model of chemotaxis, the name for the behavior of following a chemical gradient, and demonstrated that it is equivalent to optimal dynamics in the given environment. The interesting part is that the gradient-following is stochastic. E. coli have a very simple method of moving. They can either move in a straight line or they can tumble randomly. By using the chemical gradient to increase or decrease the probability of tumbling, they can arrange things so as to move in the direction indicated by the gradient:

"These results suggest that the biochemical network of E. coli chemotaxis is designed to optimally extract the binary information along an exponential gradient in a noisy condition."

This means that evolution didn't end up with a "just good enough" solution but found an optimal answer. The suggestion is that this is also true of similar sensory systems in equally simple organisms. Perhaps also this is the starting point for the ability of multi-cellular systems to optimize things in simple ways and ultimately create a brain.

More Information

Connection between the bacterial chemotactic network and optimal filtering
Kento Nakamura and Tetsuya J. Kobayashi

LABORATORY FOR QUANTITATIVE BIOLOGY

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