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Prog Biophys Mol Biol. 2017 Aug;127:12-32. doi: 10.1016/j.pbiomolbio.2017.04.002. Epub 2017 Apr 6.

The non-equilibrium basis of Turing Instability and localised biological work.

Author information

1
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom. Electronic address: y.schiffmann@damtp.cam.ac.uk.

Abstract

Turing's theory for biological pattern formation is based on the instability of the homogeneous state, which occurs if certain key criteria are met. The problem of how chemical energy is converted to localised biological work requires one to understand not only the basis of localised power generation, but also the age-old puzzle of how organisms decrease their entropy; these problems can only be solved by the identification of the Turing Instability. At the heart of this is how natural selection, not chemistry, has fashioned the large non-equilibrium overall affinity (ΔG is a large negative quantity) for the oxidation of the fuel molecules. Natural selection has also resulted in the homeostasis at non-equilibrium values of the hydrolysis of molecules like ATP, GTP, which are the energy links between the overall oxidation of the fuel and biological work. The conditions for such homeostasis are central requirements for the Turing Instability and are the essence of being alive. The Turing-Child (TC) patterns are the spontaneous primary spatial cause not only of localised biological work in multicellular systems (especially those in patterning and development) but also of intracellular patterns including the mitotic spindle and the contractile ring. The Turing picture comprises the nonuniform distribution of the concentrations of the Turing morphogens, cAMP and ATP, and the Child picture is the resulting nonuniform distribution of the metabolic rate and of power. The TC pattern is shaped as the dominant eigenfunction in the combination of eigenfunctions which provides the spatial pattern of the Turing morphogens. The TC patterns and the bifurcation parameter manifest quantisation and symmetry as in music and in applications of quantum mechanics. The notion of correlation diagrams is also introduced.

KEYWORDS:

Apical constriction; Dissipative structure; Entropy; Morphogenesis; Self-organization; Turing-Child field

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