Purcell's Paper

A lecturer of mine (Timo Nieminen) put me onto a transcript of a talk originally given by E. Purcell in 1976, entitled "Life at low Reynolds number". This surprisingly conversational piece lays out quite a lot of the physics of cellular motion which we have already encountered in our biophysics `careers' thus far. Nonetheless, he draws some interesting analogies and provides some great examples of biophysical reasoning.

The content begins with a discussion of what it means to be at low Reynolds number and progresses to tackle nonreciprocal motion (the Scallop Theorem) and the advantages of swimming to bacteria. The very final section was most interesting, because it describes why there appears to be a minimum `run' distance in the bacterial `run and tumble' exploration of the world.

Recall that bacteria undergo chemotaxis i.e. they are able to respond to chemical gradients in their surroundings by undergoing a biased random walk up or down the concentration gradient. The bias is introduced by changing the path length distribution so that if the gradient is favourable the `run' phase lasts longer than usual, and if it is unfavourable it is shorter. Observations show that there is a lower limit to the length that is moved even if the gradient is unfavourable. Why?

Purcell goes on to show that if you can't outrun diffusion then there is no point to moving at all... which implies that there is some minimum distance that you must move in order to even sense that the chemical gradient exists! He shows that this is the minimum step size found experimentally.

There is also some neat discussion of the discovery of rotary motors in bacteria, which is such a well-accepted result nowadays that I hadn't even realised that there was controversy about it not long ago.

This is a well-written and interesting piece which I believe neatly sums up what biophysics is all about! For your interest, Purcell was also instrumental in the invention of NMR.