10 - Walking the Tightrope: The Dilemma of Hierarchical Instabilities in Turing's Morphogenesis

Summary

Dedicated to Bashir Ahmad and a bright future for physics in his Afghanistan.

Ever since we understood that living organisms are made of fundamentally the same stuff as the rest of the universe, we have been puzzling about what makes life different, and how that difference arose. Alan Turing made a major contribution in putting forth a model for morphogenesis that attempts to bridge the gap between the molecules we are made of and how we look. This is a huge gap to span in trying to solve the problem of how an embryo builds itself. People are about 1.5m = 1.5×10⁹nm (nanometers) tall and the typical protein molecule is about 30 nm wide, a ratio of 50 000 000 = 5 × 10⁷ to 1. That protein might contain 1000 amino acids and, if we take into account the relative volumes, not just length, say 70 liters for an adult human and 0.15nm³ for an amino acid (Sühnel and Hühne, 2005), this raises the ratio to 5×10²⁶ to 1.

When we build a bridge, unless it's over a small ditch, we use many parts and assemble them in sections called spans (Figure 10.1). In biology this has come to be known as ‘modularity’, and the grand search has been on to discover just what the modules of life are (von Dassow and Munro, 1999; Gilbert and Bolker, 2001; Redies and Puelles, 2001; Newman and Bhat, 2009; Peter and Davidson, 2009; Christensen et al., 2010). At first it was thought that cells represented modules. The ‘cell theory’ was resisted by a minority of 19th century biologists, who thought that the basic module was the whole organism, not the cell. Certain observations support this ‘organismal’ theory. First, single cell organisms, such as Parameciumand diatoms (Figure 10.2), can have quite complex morphologies; see Gordon (2010); Tiffany et al. (2010); Gordon and Tiffany (2011). Second, some green algae have many nuclei that move in cytoplasmic streaming, unhindered by cell boundaries, yet “… exhibit morphological differentiation into structures that resemble the roots, stems, and leaves of land plants and even have similar functions” (Chisholm et al., 1996); see Cocquyt et al., 2010.