Just over a year ago I attended the International Congress for Industrial and Applied Mathematics in Zurich. Among the huge number of talks given there were quite a few on biological topics. In one of these (unfortunately I do not remember the speaker or the exact topic) a video was shown of bacteria shooting around at high speed in an infected eukaryotic cell. As they move they leave trails which have been called ‘comet tails’. The effect which drives this motion is the polymerization of actin filaments. This is related to, but different from, the mechanism driving the motion of dendritic cells I mentioned in a previous post on chemotaxis. It has a thermodynamic component. Gaps between the end of the fibres and the cell which arise randomly by something like Brownian motion are used by actin monomers to squeeze in and increase the length of the chain.
There are videos of excellent lectures on this subject by Julie Theriot available on the internet. The web page which hosts these videos is a wonderful source of information on various biological and medical topics, presented in lectures by leading researchers. The details of the propulsion mechanism are not so clear and Theriot discusses various alternatives in her lectures. There has been both analytical (mathematical) modelling and numerical work. Unfortunately (from my biased point of view) it seems that it is only the numerical work which has been able to reproduce the experimental data. The biological example she discusses is that of Listeria monocytogenes but similar motion can be achieved with polystyrene beads. While a lot is said about how the bacteria move nothing is said about why they do so and I do not know the answer to the latter question.
In her last lecture Theriot introduces some very interesting ideas on the question of what is the basic difference between eukaryotes and the rest of the living world (bacteria and archaea). First the idea is introduced and discarded that the key point is the existence of a cytoskeleton in eukaryotes. In fact the main elements of the cytoskeleton (actin filaments, microtubules and intermediate filaments) have recently been found to have molecular analogues in bacteria. Next she suggests that all structures in bacteria are based on helices and that this determines the limited range of forms they produce. After emphasizing that every rule in biology has an exception she presents examples of bacteria which are (flat) squares or six-pointed stars. Explaining these forms sounds like a great challenge for geometers.