Complexity in subnetworks of a peroxidase–oxidase reaction model

Abstract

The peroxidase–oxidase (PO) reaction is a paradigmatic (bio)chemical system well suited to study the organization and stability of self-sustained oscillatory phases typically present in nonlinear systems. The PO reaction can be simulated by the state-of-the-art Bronnikova–Fedkina–Schaffer–Olsen model involving ten coupled ordinary differential equations. The complex and dynamically rich distribution of self-sustained oscillatory stability phases of this model was recently investigated in detail. However, would it be possible to understand aspects of such a complex model using much simpler models? Here, we investigate stability phases predicted by three simple four-variable subnetworks derived from the complete model. While stability diagrams for such subnetworks are found to be distorted compared to those of the complete model, we find them to surprisingly preserve significant features of the original model as well as from the experimental system, e.g., period-doubling and period-adding scenarios. In addition, return maps obtained from the subnetworks look very similar to maps obtained in the experimental system under different conditions. Finally, two of the three subnetwork models are found to exhibit quint points, i.e., recently reported singular points where five distinct stability phases coalesce. We also provide experimental evidence that such quint points are present in the PO reaction.

Complex dynamics in an unexplored simple model of the peroxidase–oxidase reaction

“…These maps are very similar to those obtained for a four-dimensional subnetwork model of the Bronnikova-Fedkina-Schaffer-Olsen (BFSO) model. 24,25,49 The maps are also similar to those obtained in the experimental PO reaction under certain experimental conditions, 12,18 but they This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.…”

“…47,49 In fact, the Olsen model studied here has bifurcation structures more similar to the original BFSO model compared to equivalent four-variable subnetwork models of this model. 25 However, it is interesting to note that one of these subnetwork models exhibits return maps that are almost identical to those displayed in Fig. S6 in the Supplementary Material.…”

“…Here, the most relevant parameters to vary are those that relate to experimental parameters, e.g k 8 , which is the equivalent of the flow rate of NADH into the experimental system and k 1 and k 3 , which are associated with positive feedbacks (autocatalytic reactions), which again relate to the amount of enzyme or the amount of phenolic modifier. 25 In addition we have studied the change of other parameters such as k 2 and k 5 , which cannot be tested so easily in the laboratory.…”

“…S6 in the Supplementary Material. 25 While the Olsen model with n = 2 is a hypothetical model containing the essential features of the chemistry of the PO reaction, it is probably also the most realistic among the simple models of the reaction. The net reaction of reaction steps (1)-( 5) is:…”

“…However, in one case it has been possible to decompose a detailed model to a set of three simple four-variable subnetwork models, whose dynamics could be analyzed in detail. 24,25 One of a few simple hypothetical models of the PO reaction is the so-called Olsen model. This model is in fact two closely related models, 17,18 but only one of them 18 has been This is the author's peer reviewed, accepted manuscript.…”