Multiple oscillations in changing cell shape by the plasmodium of Physarum polycephalum: general formula governing oscillatory phenomena by the Physarum plasmodium

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Abstract
The long-term dynamics of an amoeboid cell shape were studied using Physarum polycephalum plasmodia with various sizes. Cell shape varied oscillatorily in a multiple periodic manner. The organism periodically elongated with period of T 7 = 10 h, branched with T 6 = 4 h, became uneven with T 5 = 30 min and T 4 = 10 min, and blew up with T 3 = 1.5 min. Tiny plasmodia changed shape much faster with T 3 = 1.3 min, T 2 = 24 s and T 1 = 3.3 s simultaneously. The plasmodial cytoskeleton also showed periodic pattern formation with T 6, T 5 and T 3. Periods of all known oscillatory phenomena in this organism correspond to some of the periods for the above seven rhythms, and the following geometric progression holds among the periods: Ti  + 1/Ti = 7 and Ti  + 2/Ti  + 1 = 3, where i = 1, 3, 5. Thus, multiple oscillations in the plasmodium are organized globally.