Phys Rev E Stat Nonlin Soft Matter Phys 2005 Oct 01;724 Pt 1:041925. doi: 10.1103/PhysRevE.72.041925.

Simplified dynamic model for the motility of irregular echinoids.

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Inspired by the locomotion mechanism of sea urchins, we study the locomotion of an irregular echinoid by means of a simplified dynamical model. We prove that if two conjectures are assumed, the geometrical arrangement of the five ambulacral petals of irregular echinoids should form a eutactic star in order to optimize motility. We firstly propose an adequate "measure" of eutacticity that allows us to to verify the statistical tendency to such a property for a representative collection of fossil specimens. Next, regarding dynamics, the biological advantage of eutactic stars is addressed as a minimal path problem. Finally, we study the stability of some eutactic stars under small perturbations.

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Genes referenced: LOC100887844