Metabolic Dissipative Structures - Systems Biology of Metabolic and Signaling Networks - page 188

Fig. 8.2 Dissipative functional structure involved in the integration of catalytic processes .(a-d)
Under dissipative conditions, a quasiperiodic route to chaos emerges in the glycolytic system when
increasing the normalized amplitude of the periodic source of glucose substrate from A ~ 0:001 to
A ~ 0:023. The figure shows the time evolution of the normalized concentration β , fructose
1,6-bisphospfate. (a) Periodic pattern. (b) Quasiperiodic oscillations. (c) Complex quasiperiodic
motion indicating the transition towards chaos. (d) Deterministic chaos. (e-h) Biomolecular
information flows measured in bits between the irreversible enzymes for the same conditions in
the left panel . The strength of effective connectivity is plotted with arrows width proportional to
the transfer entropy divided by its maximum value. The numerical integration of the system was
performed with the package ODE Workbench, which is part of the Physics Academic Software.
Internally this package uses a Dormand-Prince method of order 5 to integrate differential
equations. Adapted from Fig. 2 in (De la Fuente and Cortes 2012 )