Introduction

 Paramecium caudatum, a kind of ciliates, exhibits very strong galvanotaxis, a behavioral response to an electrical stimulus; when a DC electric field is applied, cells can be made to swim toward the cathode. Pioneers in this field of microbiology found that it is caused by a change in direction of the ciliary beating (Ludloff 1895), which is called the Ludloff phenomenon. However, there has been almost no quantitative discussion of the physical relationship between the microscopic ciliary beating pattern and the macro-scopic behavior of a cell. Although several properties of Paramecium cells 

 have been modeled (Jahn 1961; Cooper and Schliwa 1985), conventional models have mainly been physiological and biochemical ones, ignoring the physical properties. Moreover, the few physical models that have been pre-sented have tended to disregard galvanotaxis. One rare physical model of galvanotaxis is that constructed by Roberts (Roberts 1970); however, its validity is uncertain because his assumptions were rough, and the accu-racy of his model was not fully verified by comparing it with experimental data. Here in this article, we present a first attempt to construct a physical model of Paramecium galvanotaxis based on mechanics using a bottom-up approach, accompanied by experimental validation.

 Dynamics Model of Paramecium Galvanotaxis 

 Paramecium and Its Galvanotaxis

 In this article, we consider Paramecium caudatum because it has been ex-tensively studied and its behavior is well known. P. caudatum is a unicel-lular protozoan with an ellipsoidal shape. It swims by waving cilia on its body; thousands of cilia beat the water backward to yield a forward reac-tion force (Naitoh and Sugino 1984). When an external electrical stimulus is applied, it modifies the membrane potential and alters the ciliary move-ments, thus affecting the cell motion. Viewed macroscopically, the cell is made to swim toward the cathode. This phenomenon is called negative galvanotaxis. A Paramecium cell in an electric field shows a characteristic ciliary move-ment pattern. Assume an imaginary plane perpendicular to the electric field and located near the center of the cell, slightly closer to the cathodal end, dividing the cell into two parts, as illustrated in Fig. 1. The electric field causes cilia on the anodal end to beat more frequently (ciliary augmenta-tion) (Kamada 1929), and the cilia on the cathodal end also beat more fre-quently but in the opposite direction (ciliary reversal) (Ludloff 1895). This is called the Ludloff phenomenon, and it provides a simple and qualita-tive explanation for galvanotaxis: the asymmetry in direction of the ciliary beatings generates a rotational force and orients the cell toward the cath-ode. Several previous works have reported existence of substantial bound-ary (Ludloff 1895; Statkewitsch 1903; Jennings 1923; Kamada 1931), and we also confirmed it in our wet experiments. The deviation of the boundary to the cathode is considered to be due to interaction between the medium and the negative resting potential of the cell (Gortz 1988)