Exploration of Self-Regulation in the Natural Swimming of the Paramecium's Cilium

摘要

This report explores the mechanics of the motion (and the aspects of bio-physical self-regulation of this motion) in the paramecium's cilium. The paramecium is a single-cell animal widely found in oxygenated aquatic environments. These animals propel themselves, albeit with limited maneuverability, by the synchronous motion of numerous tiny cilia populated around their flexible bodies. Three theoretical models are given: (1) a torsional pendulum model of beat frequency, (2) a nonlinear self-regulation model of cilium motion, and (3) a bio-physical mechanism of hardness control of the cilium. The first two models reproduce the experimental data quite accurately; a full modeling of the hydrolysis of adenosine-tri-phosphate (ATP), the 'currency' of chemical energy (which is beyond the scope of this report), is awaited to quantitatively evaluate the third mechanism fully Essentially, these theoretical results, together with an analysis of the motion of the biological cilium and a comparison of the results with various scaled biorobotic hardware models, are used to construct a biophysical description of a self-regulating mechanism of natural swimming in the paramecium's cilium. It is theorized that cross-bridge links between the microtubule pairs are the source of cilium hardness during the power stroke; there is a critical phase near the end of the power stroke where one cross-bridge detaches at the point of inflection due to the arrival of ATP, causing a precipitous reduction in hardness that signals the start of the return stroke; therefore, in each beat cycle, there must be a reattachment process of the cross-bridge links and re- hardening of the cilium during the early phase of the return stroke. Also discussed is the invariance of the elementary oscillatory architecture of integrating sensors, actuators, and controllers from low to high Reynolds numbers (paramecia to fish).