Some physical, mathematical and evolutionary aspects of biological pattern formation

Abstract

An important mechanism in the generation of biological structures is the production of defined spatial patterns within initially near-uniform cells and tissues. This process can be modelled on the basis of conventional molecular kinetics if there is a shortrange activating effect in conjunction with depletion or inhibition extending over a wider range (‘lateral inhibition’). Such pattern-generating systems exhibit simple selfregulatory properties empirically observed in developmental biology such as polarity effects, proportion regulation and the inducibility of secondary centres. Autocatalysis and lateral inhibition have been shown to be mathematically necessary for the simplest two-factor case. Certain generalizations of these conditions to multicomponent systems are possible; they are suitable for modelling intercalary regeneration. The evolution of higher organisms seems to be determined to a considerable extent by many small changes of patterns and proportions. While evolution proceeds at varying rates in the course of time, the rate-limiting steps may be due to mutations of low selection pressure. A semi-quantitative argument suggests that there might be an upper limit of evolutionarily effective genetic complexity.