Sperm swimming is caused by the same patterns that are believed to dictate zebra stripes
Patterns of chemical interactions are thought to create patterns in nature such as stripes and spots. This new study shows that the mathematical basis of these patterns also governs how sperm tail moves.
The findings, published today in Nature Communications, reveal that flagella movement of, for example, sperm tails and cilia, follow the same template for pattern formation that was discovered by the famous mathematician Alan Turing.
Flagellar undulations make stripe patterns in space-time, generating waves that travel along the tail to drive the sperm and microbes forward.
Alan Turing is most well-known for helping to break the enigma code during WWII. However he also developed a theory of pattern formation that predicted that chemical patterns may appear spontaneously with only two ingredients: chemicals spreading out (diffusing) and reacting together. Turing first proposed the so-called reaction-diffusion theory for pattern formation.
Turing helped to pave the way for a whole new type of enquiry using reaction-diffusion mathematics to understand natural patterns. Today, these chemical patterns first envisioned by Turing are called Turing patterns. Although not yet proven by experimental evidence, these patterns are thought to govern many patterns across nature, such as leopard spots, the whorl of seeds in the head of a sunflower, and patterns of sand on the beach. Turing’s theory can be applied to various fields, from biology and robotics to astrophysics.
Mathematician Dr Hermes Gadêlha, head of the Polymaths Lab, and his PhD student James Cass conducted this research in the School of Engineering Mathematics and Technology at the University of Bristol. Gadêlha explained: “Live spontaneous motion of flagella and cilia is observed everywhere in nature, but little is known about how they are orchestrated.
“They are critical in health and disease, reproduction, evolution, and survivorship of almost every aquatic microorganism in earth.”
The team was inspired by recent observations in low viscosity fluids that the surrounding environment plays a minor role on the flagellum. They used mathematical modelling, simulations, and data fitting to show that flagellar undulations can arise spontaneously without the influence of their fluid environment. More
