Qualitative explanation for galvanotaxis. Reproduced from Ogawa et al. ) with permission. Fig. 2006 with permission

 Based on electrochemical and electrophysiological knowledge (Jahn 1961; Cooper and Schliwa 1985), the mechanism of the Ludloflf phenomenon can be understood to be a combination of electrochemical, physiological, and physical factors. This article concentrates on physical factors, while regard-ing electrochemical and physiological factors as "black boxes

  Assumptions

 By making several assumptions focusing only on those properties that are essential and dominant in galvanotaxis (Ogawa et al. 2006), we can describe the cell motion in a two-dimensional plane including the cell axis and the electric field vector. Hereafter, we consider cell motion only in this plane. We define a global coordinate system {X, Y) and a local coordinate sys-tem (x,7) on the plane, as shown in Fig. 2. The global coordinate system is fixed with respect to the external world, with the X-axis parallel to the electric field E. Let (j) be the angle of the cell axis in the global coordi-nate system (0 < 0 in Fig. 2(a), for the sake of convenience in deriving the model). The local coordinate system is fixed with respect to the cell. Let the cell shape be an ellipsoid ^ with a major axis of length 21 and a minor axis of length 27?. We assume that cilia are distributed uniformly around the edge of the ellipsoid with linear density n. In the presence of an electric field, imagine a plane perpendicular to the field (hereinafter referred to as "a boundary plane"). The shortest distance between the plane and the center of the cell is defined as /. The propulsion force yielded by one cilium is assumed to be /o in the absence of an electric field. In the presence of an electric field E, the force increases to / = (1 + /3£')/o, where JS is a positive parameter