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. 2012 Oct 7;9(75):2723-34.
doi: 10.1098/rsif.2012.0244. Epub 2012 Apr 25.

Optimal homeostasis necessitates bistable control

Guanyu Wang  1
Affiliations

Optimal homeostasis necessitates bistable control

Guanyu Wang. J R Soc Interface. .

Abstract

Bistability is a fundamental phenomenon in nature. In biology, a number of fine properties of bistability have been identified. However, these properties are only consequences of bistability at the physiological level, which do not explain why it had to emerge during evolution. Using optimal homeostasis as the first principle, I find that bistability emerges as an indispensable control mechanism. It is the only solution to a dilemma in glucose homeostasis: high insulin efficiency is required to confer rapidness in plasma glucose clearance, whereas an insulin sparing state is required to guarantee the brain's safety during fasting. The optimality consideration renders a clear correspondence between the molecular and physiological levels. This new perspective can illuminate studies on the twin epidemics of obesity and diabetes and the corresponding intervening strategies. For example, overnutrition and sedentary lifestyle may represent sudden environmental changes that cause the lose of optimality, which may contribute to the marked rise of obesity and diabetes in our generation. Because this bistability result is independent of the parameters of the mathematical model (for which the result is quite general), some other biological systems may also use bistability to control homeostasis.

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Figures

Figure 1.
Figure 1.
The set of locally optimal controls whose utilization rates are within the range η ± Δη, where Δη = 5 × 10−5. (a) The distribution of control counts over the T-values. (b) Three u(t) are illustrated: the worst control (grey, T = 373), an average control (blue, T = 290) and the globally optimal control (red, T = 203.8). (c) The three controls in the form of u(I). They are obtained by following the conversion procedure in figure 2. The dashed lines are for illustration purpose only; they are not part of the controls.
Figure 2.
Figure 2.
A computer simulation of the glucose–insulin system. (a) The control u(t) is taken from the red control in figure 1b. The ‘on’ phase of the control is re-coloured in green. (b) The controlled (red and green) and uncontrolled (grey) insulin dynamics. (c) The controlled and uncontrolled glucose dynamics. (d) The control in the form of u(I). (e) Twenty-four hour profile of plasma insulin concentration averaged from 14 normal (red circles with solid lines) and 15 obese (yellow circles with dashed lines) subjects. There are three spikes, caused by the three meals at 09.00, 13.00 and 18.00. (f) Twenty-four hour profile of plasma glucose concentration. Normal person denotes red circles with solid lines and obese person denotes yellow circles with dashed lines.
Figure 3.
Figure 3.
(a) The globally optimal control u(I) for six η-values. The dashed lines are for illustration purpose only. (b) The actual controls A(I) with fixed β- and six α-values, under the limit condition K = 0. The α-values are specially chosen to render an exact match with (a). The solid and dashed lines indicate stable and unstable branches, respectively. (c) The same controls but with K = 10−4. (d) The same controls but with K = 10−2. (e) Under the condition K = 0, the solutions to electronic supplementary material, equation (S40) reduce to three straight lines, which constitute a bistable switch with Ion = cβ−1 and ΔI = cα. (f) Under the condition K = 0, the actual controls A(I) with fixed α- and four β-values.
Figure 4.
Figure 4.
A computer simulation of equations (4.3) and (4.4). (a) The control u(t) with umax = 1, ton = 2 and toff = 5. (b) The controlled (black) and uncontrolled (grey) insulin dynamics. (c) The controlled and uncontrolled glucose dynamics. (d) The control in the form of u(I). (e) The function m(t) is a triangular function centring on t = 2 and with height 10.
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