Self-Organization in a Rhizoid Formation of Fucus Eggs

An early stage of development of a rhizoid in Fucus eggs is described theoretically by taking account of a stabilizing effect of Ca2+ on membranes of the rhizoid. Basic equations are coupled ones for a length of the rhizoid, a concentration of Ca2 + and a concentration of membrane-creating molecules accumulated in the rhizoid region. The present theory can explain the observed fact that an illumination of light becomes effective on the growth of rhizoid, only when the time after fertilization exceeds a certain threshold value. An effect of the number of neighboring eggs on the speed of rhizoid formation is discussed with the aid of the present equations, and the result agrees with the observed tendency.