Synchronization of Protein Motors Modeled by Asynchronous Cellular Automata

Spermatozoa propel themselves in fluids through a rhythmically beating flagellum. Though it is known that the motor protein “dynein” is at the base of such movements, it is unclear how the behaviors of individual elements add up to the coordinated movement of the flagellum. Being single-cell entities, spermatozoa lack nerve systems, so an explanation for their movements ought to be found in a mechanism on molecular scales. This paper aims to clarify part of a possible mechanism in terms of asynchronous cellular automata. The question answered is: “Given a 1-dimensional cellular automaton with von Neumann neighborhood of which each cell—being updated at random times—cycles through three states; how can waves, i.e., patterns of cells in certain states, be formed that on average move in one direction?”

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