A Diffusion Model for Phyllotaxis

The mechanism of phyllotaxis is examined by computer simulation based on an inhibitor diffusion model in which the inhibitor is secreted from each new leaf formed at a shoot apex. It is assumed that leaf initiation can only take place in competent tissue which is in an initiation ring. Initiation occurs where the inhibitor concentration drops under the threshold value as older leaves increase their distance from the ring. Inhibition from a leaf is viewed as a spheroid or ellipsoid. It is the values in the plane of the initiation ring which are significant. In earlier models, the concentration distribution curve of the inhibitor has been represented by the simple exponential function C = exp (-x). In this paper, two modifications are added. (i) The nature of the descending "tail" of the inhibitor concentration curve is varied. The way that the concentration falls to an effective zero level is important. That is, the inhibitor concentration profile beyond the threshold level (i.e. out to where the concentration is effectively zero) can take different forms. Variation in this parameter brings on major effects on the phyllotaxis as it influences the pattern of summation of inhibitions within the initiation ring. (ii) The inhibition sphere is converted to an ellipsoid by assuming polar transport. This facilitates opposite phyllotaxis. With these two modifications an inhibition scheme can simulate a wide variety of known patterns.