Peroxidase-oxidase reaction model

C.G.Steimnetz and R.Larter, The Quasiperiodic Route to Chaos in a Model of the Peroxidase-Oxidase Reaction, Journal of Chemical Physics, 94, 1388-1396(1991). 

Besides the ordinary HoO -consuming oxidation, peroxidase also catalyzes Oo-consuming oxidation (the peroxidase-oxidase reaction). In recent years considerable attention has been directed to elucidating the peroxidase-oxidase mechanism. Controversy was centered about the participation of ferrous enzyme in O2 activation. Is peroxidase reduced to the ferrous state during the reaction 3,13,19, 21, 23) Does peroxidase compound III, which appears in the reaction, correspond to oxygenated ferroperoxidase (3, 5, 15) If so, is O2 in Compound III activated (15) As discussed here, these problems seem to be almost solved, and it is very likely that the peroxidase-oxidase reaction is a good model for analyzing the mechanism of other oxidases. 

Let us illustrate this technique with the results of simulated measurements of the peroxidase-oxidase reaction based on a skeleton model proposed by Degn et al. [51] (the DOP model). There are four species involved in the model Si = O2, S2 = NADH, S3 and S4 are intermediates associated according to Olsen et al. [52] with free radical... 

Table 11.3 Sign-symbolic phase shift matrix obtained from the DOP model of the peroxidase-oxidase reaction...

Rgnre 29 A circle map derived from simulations with the DOP model of die peroxidase-oxidase reaction. (From Ref. 73 used with permission.)... 

A studyof a fairly simple model of an enzyme reaaion that exhibits chaotic behavior, the peroxidase-oxidase reaction, provides a good illustration of the role of circle map dynamics and mixed-mode oscillations in the transition to chaos. In the peroxidase-oxidase reaction, the peroxidase enzyme from horseradish (which, as its name implies, normally utilizes hydrogen peroxide as the electron acceptor) catalyzes an aerobic oxidation... 

Figure 33 Evolution of a torus attractor found in simulations with the DOP model of the peroxidase-oxidase reaction, equations [115]. Parameter values used are k2 = 1250, fea = 0.046875, = 1. 104, = 0.001,...

This example shows that mixed-mode oscillations, while arising from a torus attractor that bifurcates to a fractal torus, give rise to chaos via the familiar period-doubling cascade in which the period becomes infinite and the chaotic orbit consists of an infinite number of unstable periodic orbits. Mixedmode oscillations have been found experimentally in the Belousov-Zhabotin-skii (BZ) reaction 2.84 and other chemical oscillators and in electrochemical systems, as well. Studies of a three-variable autocatalator model have also provided insights into the relationship between period-doubling and mixedmode sequences. Whereas experiments on the peroxidase-oxidase reaction have not been carried out to determine whether the route to chaos exemplified by the DOP model occurs experimentally, the DOP simulations exhibit a route to chaos that is probably widespread in the realm of nonlinear systems and is, therefore, quite possible in the peroxidase reaction, as well. 

An example of a calculation of the Lyapunov exponents and dimension, for a simple four-variable model of the peroxidase-oxidase reaction will help to clarify these general definitions. The following material is adapted from the presentation in Ref. 94. As described earlier, the Lyapunov dimension and the correlation dimension, D, serve as upper and lower bounds, respectively, to the fractal dimension of the strange attractor. The simple four-variable model is similar to the Degn—Olsen-Ferram (DOP) model discussed in a previous section but was suggested by L. F. Olsen a few years after the DOP model was introduced. It remains the simplest model the peroxidase-oxidase reaction which is consistent with the most experimental observations about this reaction. The rate equations for this model are ... 

The biochemical model contains the pathways of the enzymatic reactions in the synthetic routes. Model can be constructed for each alkaloid. Eigure 75 presents biochemistry model of Catharantus alkaloids. The most important enzymes on this model are TDC (tryptophan decarbocylase), GlOH (geraniol 10-hydroxylase) and SS (strictoside synthase). NADPH+, PO (Peroxidase), O (oxidase) and NADH+ are all active in different Catharantus alkaloid formations. The biochemical models are subject to both qualitative and quantitative alkaloid... 

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