Animals in nature have an uncanny ability to operate as a single unit with collective movement when they group together. Flocks of birds have been found to fit statistical models, people walking together naturally match each others step, bacteria can form groups that then move as one, with each individual responding to the same chemical stimuli.
Now most biological fluids such as blood or polysaccharides are described as viscoelastic meaning that they are slightly viscous and slightly elastic. Now although biology classes attempt to portray sperm cells as in it for themselves, trying to out race the competition, the truth is the viscoelastic properties actually cause the sperm to strongly interact with each other. This causes a noticeable pattern with sperm cells swimming in unison with the exact dynamic possibly being controlled by the medium.
In order to study these effects bovine sperm was used as the swimmers for various similarities to human sperm despite the slightly different shape (as seen on the right) with the more flat and larger head. A long chain polyacrylamide (LC-PAM) solution in order to mimic the fluids that the sperm would likely be swimming through. In order to investigate the viscosity polyvinylpyrrolidone (PVP) was added to the solution up to about 3% to make it thicker. On a nice flat surface the sperm were observed swimming in a simple Newtonian fluid; a Newtonian fluid with some added PVP to increase viscosity; and the non-Newtonian polymer solution. This all occurred in a micro fluid chamber as otherwise there could have been rampant unwanted fluid motion which the small area cuts down on.
In the Newtonian it was unsurprising to see the sperm swim randomly in any direction as, of course, how would they know what way they were supposed to head. When the viscosity was increased 36 times by the addition of the glue, the same result was found. There were occasional pairing up of sperm cells but this connection was fleeting and soon they off on their way again. However when it came to the 1% LC-PAM solution suddenly sperm decided they would be better off working together. Clusters formed with between 2 to 16 sperm swimming in the same direction at roughly the same speed. They weren’t physically connected but instead dynamically associated with sperm leaving and new sperm joining the cluster as it went. It was concluded that this must be due to the elastic component although the exact mechanism is still unknown. This offers a secondary way, after bird flocking, to study collective movement in nature which hopefully is a demonstration of the crossover between statistical maths and biology.