Early biological morphogenesis and nonlinear dynamics

Abstract

Biological pattern formation is a process that so far has gone largely unexplained. Mechanisms for cellular differentiation, and pattern forming processes, must both have emerged within the same short time interval. It now seems unlikely that the great diversity of observed patterns can be accounted for by the action of one or a few specific patterning genes, or, in its extreme form, the idea that there might be a single such proto pattern gene. Many seemingly related pattern forming processes, such as segment formation, depend on unrelated genetic mechanisms. Thus another common feature as a proto pattern gene is needed to understand the onset of pattern formation. Experimental biologists favour mechanisms in which morphogenetic gradients are the main source of positional information. Specific combinations of genes (cues) are activated differentially by thresholds along particular regions on the gradient. Among theoreticians the pattern forming processes are believed to some extent to be dependent upon true symmetry breaking processes, which can occur in most nonlinear control systems, of which the Turing mechanism is an example. It is argued here that the common fundamental feature of gene control systems is a high degree of cooperativity. Such highly nonlinear systems may originally have been capable of reading subtle differences in the concentration of a controller, but the evolutionary pressure to refine this kind of processes in single cells would eventually have led to gene clusters with steep off-on control, and this is seen experimentally in many such systems. Some nonlinear systems of this type have for some time been known among theoreticians to be prone to multistability (a necessary precondition for cell differentiation), chemical time oscillations and spontaneous spatial pattern formation by Turing’s mechanism. Increasing cooperativity in the defining rate laws greatly facilitates the tendency for such phenomena to arise, and we demonstrate this explicitly for Turing pattern formation. We argue that all these phenomena arose simultaneously with the capability of interpreting positional information along simple gradients.