DOP model

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...

Now we can apply the concentration shift regulation method to the DOP model introduced as an example in the previous section and complete the analysis. Chevalier et al. [7] show that under conditions when S2 = NADH is nonessential. Si = O2 is inversely regulated, while the intermediates S3 and S4 show normal regulation. Therefore Si is of type Z, and S3, S4 are of type X (they are of the same type because they are mutually in phase) and the category is 2C. 

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

A model was proposed in 1979 by Degn, Olsen, and Perram to explain both the simple oscillations and the chaotic behavior that had been discovered a few years earlier. It is a four-variable model (now known as the DOP model) and is given by the following system of rate equations ... 

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 ... 

Figure 3 Putative model for the mechanism by which biogenic amines stimulate CE secretion across the rabbit corneal epithelium. Epn = epinephrine Nep = norepinephrine Tim = Timolol Ser = serotonin Msg = methysergide Dop = dopamine Hal = haloperi-dol (E = (E-adrenoceptor AC = adenylate cyclase. The scheme is consistent with the observation that epithelial responsiveness to serotonin and dopamine can be blocked by their receptor antagonists haloperidol and methysergide, respectively, and by both timolol treatment and sympathectomy. The probable source of serotonin or dopamine is the sympathetic fibers that innervate the cornea. (From Ref. 284.)...

DMP and DBP with the short alkyl-side chain phthalates can be degraded, whereas the DOP degradation under the same experimental conditions appeared to be relatively slow. It is noteworthy that both the ester groups and the phthalate ring were mineralized at a significant rate. The kinetics study demonstrated that biodegradation of the three phthalates conformed to a first-order model with respect to their concentrations. 

Sanborn JR, Metcalf RL, Yu CC, et al. 1975. Plasticizers in the environment The fate of di-n-octyl phthalate (DOP) in two model ecosystems and uptake and metabolism of DOP by aquatic organisms. Arch Environ Contam Toxicol 3 244-255. 

Environ. Contain. Toxicol. (1975) 3, Plasticizers in the Environment The Fate of Di-N-Octyl Phthalate (DOP) in Two Model Ecosystems and Uptake and Metabolism of DOP by Aquatic Organisms, 244-255. 

A peeling method, in conjunction with a radioactive tracer technique, was used to obtain actual profiles of DOP concentration developed through the matrix of a PVC disc dipped into a limited volume of olive oil. The plasticiser concentration distributions were reproduced to a good approximation using a known model, adjusted by neglecting the (small) amounts of oil which diffused into the polymer. 17 refs. 

Williamson DL (1992) Review of numerical approaches for modelling of global transport. In van Dop H, Kallos G (eds) Proceedings of the 19th NATO/CCMS ITM on air pollution modelling and its application. Sept 29-Oct 4, pp 377-398... 

Like other dissolved organic nutrients, the chemical composition of organic P is relatively unknown. Marine dissolved organic phosphorus (DOP) composition has been mostly identified as particular compound classes such as monophosphate esters, phosphonucleotides, nucleic acids, phospholipids, phosphonates and polyphosphates (Benitez-Nelson, 2000). Kolowith et al. (2001) found that monophosphate esters and phosphonates are major components in the Pacific Ocean, the Atlantic Ocean and the North Sea. ATP (adenosine triphosphate), ubiquitous in aU living cells, has been used as a model DOP compound in radiotracer experiments to obtain information on P sources and fluxes in natural environments (Bjorkman et al., 2000 Karl and Bossard, 1985) and cyanobacterial cultures (Fu et al., 2006). 

By this model, oxic settings (where iron scavenging is precluded) and sites of rapid euxinic siliciclastic accumulation show low to intermediate DOP values in association with FcR/Fex... 

While the details are almost certainly more complex than the model presented here and elsewhere (e.g., Raiswell et aL, 2001 Lyons et aL, 2003), nearshore-offshore gradients in DOP (and overall iron patterns of enrichment as... 

From Eq. (19), Egp should be linearly proportional to the solvent term (l/Dop 1/Ils)- This relationship has been demonstrated for weakly coupled mixed valence complexes (see Section (II.C.2.c) and this gives qualitative support to the Hush model. 

Kalinin S, Polak PE, Lin SX, Sakharkar AJ, Pandey SC, Feinstein DL (2011) The noradrenaline precursor L-DOPS reduces pathology in a mouse model of Alzheimer s disease. Neurobiol Aging 33 1651-1663... 

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