Oscillatory Behavior in Collective Phenomena

Collective phenomena on a biochemical level are assumed to involve the coupling of myriad enzymatic processes with the emergence of behavior observable at a macroscopic level. Models to explain dynamic processes such as evolution and morphogenesis have involved the use of oscillatory phenomena to achieve collective behavior. 

Computer modeling of hypercycles (Kiippers, 1975 Eigen and Schuster, 1977, 1978) demonstrates the development of oscillatory behavior around a steady state which, through feedback and coupling of the members of the hypercycle, minimizes the effect of mistakes in reproduction and thus allows for selection and optimization of the dynamic structures. So viewed, hypercycles represent the minimum structural organization for a system to accumulate, maintain, and process the information in the genome. 

The problem of differentiation and morphogenesis (i.e., the origin of spatial patterns in developing systems) constitutes one of the most enigmatic of all problems in biology. It involves the formation of dynamic patterns (i.e., patterns created and maintained by dissipation of energy), as opposed to patterns which may be termed static (e.g., immiscible liquids, a crystal, or a viral capsid), whose form is determined by specific affinities between each of the other components. 

Turing (1952) confronted this enigma and developed a mathematical model of morphogenesis which was dependent upon interaction between reactions and diffusions such that, as kinetic and transport coefficients traverse critical (bifurcation) values, the initial uniform state becomes unstable and a spatially nonuniform state emerges. 

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