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Mathematical Sperm Tail Movements

Did you know that the way a sperm tail moves can be explained by mathematics worked out by Alan Turing?


Alan Turing is known for decoding the German Enigma machine during WWII. But did you know that he also proposed a theory that patterns can form through chemical compounds spreading out and reacting with one another? This theory became known as the Reaction-Diffusion Theory.

Patterns formed by chemical interactions generate a variety of shapes and colours everywhere in nature.

Two British professionals were interested in whether we could apply this theory to the movement of human sperm cells. They revealed in their article, published in Nature Communications, that the patterns the flagellum (tail of the sperm cell) generates with its movements can be described by this theory.

According to Hermes Bloomfield-Gadêlha flagellum uses a molecular scale ''motors'' to effictively shape-shift. Tiny fibres that stand behind this are axonemes.

The motions of the sperm are a result of complex interactions between axonemes, the molecular ''motors'' and the surrounding fluid.

Findings that the surrounding fluid has little effect on sperm flagellum movements inspired the researchers. They created a computer-based digital ''twin'' of the sperm flagellum.

The results are intriguing. The undulations in sperm tails arise spontaneously, without the influence of their watery surroundings. The flagellum has a mechanism to enable swimming in low-viscosity fluids.

Mathematically, those movements are equivalent to the route patterns that arise under Turing's Reaction-diffusion system.

This discovery can be practical in many fields - new robotic applications, and artificial muscles. To help us better understand diseases such as ciliopathies.

In contradiction, we ought to be more prudent, since we can't use only mathematic formulas to examine nature's work.



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