Goodwin model (biology)

The Goodwin model is a mathematical model of genetic regulation proposed in 1963 by the British theoretical biologist Brian C. Goodwin[1][2]. It describes how a simple negative feedback loop between a gene, its messenger RNA, the corresponding protein and a metabolite can generate sustained oscillations in concentration. It has been used to describe circadian rhythms or enzymatic regulation (such as lactose in bacteria).

Although the original two-variable Goodwin model can sustain oscillations, it possesses no limit cycle: the system is conservative, so its closed orbits form a continuous family and the amplitude of the oscillation depends on the initial conditions rather than converging to a single attracting cycle. In this respect the Goodwin model resembles the Lotka–Volterra equations. Limit cycles do arise in extended formulations of the model[3][4] .

References

  1. ↑ Goodwin, B. Oscillatory behavior in enzymatic control processes. Advances in Enzyme Regulation, 3, 1965, pages 425–428. doi:10.1016/0065-2571(65)90067-1
  2. ↑ Goodwin, Brian C. (1963). Temporal organization in cells; a dynamic theory of cellular control processes. London: Academic Press. doi:10.5962/bhl.title.6268.
  3. ↑ M. Mincheva., M.R. Roussel., Turing-Hopf instability in biochemical reaction networks arising from pairs of subnetworks, Mathematical Biosciences, 240 (2012), 1-11
  4. ↑ T. Saithong, K. Painter, A. Millar, The contributions of interlocking loops and extensive nonlinearity to the properties of the circadian clocks models, PLOS One 5 (2010) e13867.
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