Random sample through an axoneme. Credit: Wikipedia
Alan Turing is best known for cracking Germany’s “Enigma” communications code during the Second World War. He also developed a theory where patterns can form simply through chemical substances spreading out (diffusing) and reacting with one another. This became known as reaction-diffusion theory for pattern development.
Ph.D. student James Cass and I recently published a study in Nature Communications that revealed the tail of a sperm, called a flagellum, produces patterns as it moves– which these patterns can be explained by Turing’s theory.
Patterns formed by chemical interactions create a large range of shapes and colors such as spirals, stripes and spots. They are all over in nature and are thought to be behind animal markings such as those on zebras and leopards, the whorl of seeds in a sunflower head and patterns formed by beach sand.
Turing’s theory can be applied to different fields in science, from biology and robotics to astrophysics
We wanted to explore whether there was a mathematical connection between these chemical patterns and how sperm tails move. If there was, it may suggest that nature uses similar templates to develop patterns of movement at small scales.
The mathematics of how the sperm flagellum relocations is very complicated. The flagellum uses molecular scale “motors” to effectively shape-shift. They use energy in one form and convert it into mechanical work, producing movement. These motors power small fibers that exist in a bundle called an axoneme. These are beautiful, geometric and slender structures that can be as much as 0.05 millimeters long in human sperm– about half the width of a human hair.
The axoneme is highly flexible, meaning micrometer-scale waves can travel along it. It is the active core of the flagellum and is responsible for moving sperm cells along. They can even sense the environment around them.
The fluid environment in which sperm travel creates drag that resists movement by the flagellum. In order for sperm to travel, several, partially antagonistic, elements need to reach a balance where undulations by the flagellum move sperm along.
We were partly inspired by scientific findings that suggest the surrounding fluid has little impact on sperm flagellum motions. To examine this, we developed a digital “twin” of the sperm flagellum in a computer.
This twin is a representation in the computer that must act in a very similar way to the real thing. This complex task was carried out by James F. * Read More*
