New research uncovers fascinating links between the mathematical foundations of pattern formation, Alan Turing, and the dynamic movement of sperm tails as they are swimming. This connection provides insights not only into biological processes but also has implications for advancements in robotic technology.
Alan Turing, predominantly recognized for decrypting the enigma code during WWII, contributed significantly to the comprehension of natural patterns. Turing’s reaction-diffusion theory proposed that patterns in nature could spontaneously form due to the interaction and diffusion of chemicals, even with just two components involved.
The universal patterns envisioned by Turing are now referred to as Turing patterns and are believed to be the underlying principle for various natural patterns including leopard spots and seed arrangements in sunflowers, although direct experimental validation is still pending.
The recent study spearheaded by mathematician Dr. Hermes Gadêlha and his PhD student James Cass from the University of Bristol reveals that the movement of flagella, found in structures like sperm tails and cilia, abide by the same mathematical principles Turing set for pattern formation. Flagella create spatial-temporal stripe patterns through undulations, generating waves along their structure to propel sperm and microbes.
The team, deriving inspiration from recent observations in low viscosity fluids, utilized mathematical modeling, simulations, and data fitting to demonstrate that the undulations in flagella can form spontaneously without being influenced by the surrounding environment.
In instances like sperm swimming, the chemical reactions of molecular motors energize the flagellum, dispersing bending movements along the tail in waves. These discoveries highlight the inherent capability of flagella to maintain motion in environments with low viscosity, essential for the survival of numerous aquatic microorganisms.
The synchronization between visual patterns and movement patterns is remarkable and opens up prospects for more extensive applications. The new insights may lead to enhanced understanding of fertility complications and other ciliopathies resulting from dysfunctional cilia in human bodies.
Moreover, the implications of this study extend to developing innovative robotic applications, artificial muscles, and animated materials by employing the discovered ‘mathematical recipe’ for creating movement patterns.
Dr. Gadêlha, a member of the SoftLab at Bristol Robotics Laboratory (BRL), applies pattern formation mathematics to pioneer the development of the next generation of soft robots.
“In 1952, Turing unveiled the reaction-diffusion basis of chemical patterns,” remarked Dr. Gadêlha. “We demonstrate that the cellular world’s ‘atom’ of motion, the flagellum, employs Turing’s template to shape patterns of movement, propelling sperm forwards.”
The synchronization of Turing’s reaction-diffusion system with flagellar movements is a stride towards decoding spontaneous animation in nature mathematically.
However, Dr. Gadêlha emphasizes that their model is yet too simple to capture the entire complexity of nature’s patterns. He believes there could be other models that align equally or even better with experiments, which are yet unknown, emphasizing the need for continued and extensive research in this domain.
This intriguing study was accomplished with the support of the Engineering and Physical Sciences Research Council (EPSRC) and a DTP studentship for James Cass’s PhD. It has successfully laid the foundation for future research by establishing an unanticipated connection between Turing’s mathematical principles of pattern formation and the intricate movements seen in flagella.
This research brings us a step closer to understanding the fascinating patterns of nature and applying them innovatively across various scientific fields.
The full study was published in Nature Communications.
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