A model for morphogenetic map and clock

Abstract

The superposition of waves which are invariant in period but differ in length produces a stationary pattern of amplitude (zero group velocity) which is proposed as a source of topographical information for the development of a specific morphological character. The changing phase of the oscillations within the map would serve as a clock for temporal co-ordination of the development. Such waves invariant in period and obeying the superposition principle were observed in tree cambium. They control the orientation of cell division and other cambial events. Considering the problem of how genes can provide the organism with a map and a clock for morphogenesis it is proposed that genes responsible for a specific morphological character produce oscillators characterized by the same period, and control the phase difference between neighbouring oscillators so that waves invariant in period are produced. It is postulated too that the superposition of waves with nearly the same periods but with different lengths produces a secondary moving wave with reduced frequency.