Koeslag, J. H., P. T. Saunders, and J. A. Wessels. “Glucose homeostasis with infinite gain: further lessons from the Daisyworld parable?.” Journal of endocrinology 154, no. 2 (1997): 187-192.
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A major unresolved physiological problem is how the rate of hepatic glucose production is increased to match the increased rate of glucose utilization during exercise without a change in arterial blood glucose level. A homeostat with such capabilities is said to have infinite gain.
Daisyworld is an imaginary planet orbiting a variable star. The only life is black and white daisies. Black daisies retain heat, slightly warming the planet; white daisies cool it. When the two types of daisies grow best at slightly different temperatures, variations in solar luminosity (over a wide range) cause the ratio of white:black daisies to vary in a manner that keeps the planetary temperature constant. This model therefore achieves infinite gain by having two opposing but interdependent controllers.
Here we suggest that the pancreatic islet α- and β-cells might act as black and white daisies. For the analogy to apply, glucagon and insulin must not only have opposing effects on the blood sugar concentration, but the secretion of the one has, at some quantum level, to be at the expense of the other. Electrical coupling between heterocellular groups of α- and β-cells within the pancreatic islets suggests that this might indeed be the case. α-Cell activity must, furthermore, promote secretory activity in other α-cells; similarly with β-cells. This is probably mediated via pancreastatin and γ-amino butyric acid (GABA) which are paracrinically co-secreted with glucagon and insulin, respectively. α-Cell activity spreads (at the expense of β-cell activity) when the blood glucose level is below set point, while β-cell activity progressively replaces α-cell activity above set point. At set point changes in the ratio of α:β-cell activity are inhibited.