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Goldbeter (2006), Human Weight Cycling

August 2007, model of the month by Melanie I. Stefan
Original model: BIOMD0000000079

Ever wondered why it is so difficult to maintain a low body weight after a diet? The phenomenon of weight regain following weight loss is referred to as weight cycling or Yo-yo dieting [1]. Goldbeter presents a simple mathematical model for human weight cycling [2], which can explain some of the mechanisms and suggests possible solutions to the problem.

The PQR model contains three variables, body weight (P), dietary intake (Q), and cognitive restraint (R). If body weight increases above a certain threshold value, it triggers the commitment to lose weight. This increases the level of cognitive restraint, resulting in a voluntary reduction of dietary intake. Dietary intake decreases dramatically once cognitive restraint exceeds a threshold value. Therefore, the model contains two threshold responses. It also accounts for time delays and factors in several additional parameters, such as energy expenditure, or the rate at which the resolution to lose weight wanes.

Figure 1 shows an instance of weight oscillations generated according to the model. An important consequence of the model is, however, that it does not necessarily lead to oscillations. With the appropriate parameters, the system reaches a stable steady state. This is good news for those trying to lose weight because it indicates that weight cycling is not a necessary consequence of diets and because it offers starting points for therapeutic intervention.

It is also good news for modellers. The model shows that the concepts and methods of biological modelling are applicable to a wide range of problems and phenomena. Goldbeter himself had studied oscillating systems before, including calcium oscillations ([3] - BIOMD0000000098), mitosis ([4] - BIOMD0000000003 and BIOMD0000000004) and the circadian clock ([5] - BIOMD0000000016). The power of this modelling approach lies in its wide-spread applicability for biological systems.

Example for oscillations generated from the Goldbeter model

Figure 1: Oscillations of body weight (P), dietary intake (Q), and cognitive restraint (R) over time. Note that all variables are normalised to one and that time units are arbitrary. From [2]

Bibliographic References

  1. K. D. Brownell, M. R. Greenwood, E. Stellar, and E. E. Shrager. The effects of repeated cycles of weight loss and regain in rats. Physiol Behav, 38(4):4590-464, Oct 1986. [SRS@EBI]
  2. Albert Goldbeter. A model for the dynamics of human weight cycling. J Biosci, 31(1):129-136, Mar 2006.[SRS@EBI]
  3. A. Goldbeter, G. Dupont, and M. J. Berridge. Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation. Proc Natl Acad Sci U S A, 87(4):1461-1465, Feb 1990. [SRS@EBI]
  4. A. Goldbeter. A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc Natl Acad Sci U S A, 88(20):9107-9111, Oct 1991. [SRS@EBI]
  5. A. Goldbeter. A model for circadian oscillations in the Drosophila period protein (PER). Proc Biol Sci, 261(1362):319-324, Sep 1995. [SRS@EBI]