The consequences of interactive noise for understanding the dynamics of complex biochemical systems

Abstract

The dynamical consequence of interactive noise in a model for complex biochemical systems is examined. Gaussian distributed noise is superimposed on the concentrations of metabolites in enzymatic reactions, and the effect of the noise amplitude on the dynamical behaviour is studied in a range of dynamical regimes. For a steady state far from a Hopf bifurcation, noise does not result in a qualitative change in the dynamical behaviour. For a steady state on one side of a Hopf bifurcation, and for the small amplitude oscillation which occurs just beyond the bifurcation point, noise may result in a qualitative change in dynamical behaviour: large amplitude bursting may be observed. Where two attractors coexist, noise may cause switching from one attractor to the other and renders the attractors indistinguishable. Complex oscillations which do not coexist with small amplitude oscillations are relatively insensitive to noise. The implications of these results for the understanding of complex biochemical systems are discussed