Systems Biology (Methods in Molecular Biology)

The B-Z reaction mechanism, a nonlinear chemical oscillator, serves

as an example for non-equilibrium thermodynamics.

The Brusselator is a simplified theory to model non-equilib-

rium, nonlinear chemical system, developed by Ilya Prigogine and

colleagues in Brussels that has been shown to reproduce the

dynamics of B-Z reactions. Although the Brusselator (named after

combining Brussels and Oscillator) considers six species in its four

chemical reactions, the solution is given only for two autocatalytic

species that can produce limit-cycle oscillations. The remaining

four species act as regulators for the self-organizing behavior.

To illustrate the six-species Brusselator:

A!

k 1

X 1

2 X 1 þX 2!

k 2

3 X 1

BþX 1!

k 3

X 2 þC

Fig. 6Belousov–Zhabotinsky (BZ) reaction dynamics. (a) The oscillations of BZ species after the induction
period, adapted from [24]. (b) BZ reaction in 2-D petri dish (left) and similar pattern found onDictyostelium
discoideum, adapted from [25]. Copyright (2006) National Academy of Sciences, U.S.A.

Complex Biological Responses Using Simple Models 183