Model enzymatic network

In practice, a gray-box model is developed in steps. One early step is to decide which variables and interactions to include. This is often done by the sketching of an interaction-graph. It must then be decided if a variable should be a state or a dependent variable, and how the interactions should be formulated. In the case of metabolic reactions, the expression forms for the reactions have often been characterized in in-vitro experiments. If this has been done, there are also often in-vitro estimates of the kinetic parameters. For enzymatic networks, however, such in-vitro studies are much more rare, and it is hence typically less known which expression to choose for the reaction rates, and what a good estimate for the kinetic parameters is. In any case, the standard method of combining reaction rates, r,-, and an interaction graph into a set of differential equations is to use the stoichiometric coefficients, Sij... 

C. Campmajo, M. Poch, J. Robuste, F. Valero, and J. Lafuente, Analusis, 20, 127 (1992). Evaluation of Artificial Neural Networks for Modeling Enzymatic Glucose Determination by Flow Injection Analysis. 

A. Ciliberto, F. Capuani, and J. J. Tyson2, Modeling networks of coupled enzymatic reactions using the total quasi steady state approximation. PLoS Comput. Biol. 3(3), e45 (2007). 

Although the irreversible approximation successfully simulates the enzymatic flux in the range in which the reverse flux is small compared to the forward flux, the impact of approximating nearly irreversible reactions as entirely irreversible in simulations of reaction systems can be significant. It has been shown that feedback of product concentration in nearly irreversible reactions, either through reverse flux or product inhibition, is necessary for models of certain reaction networks to reach realistic steady states [36]. 

Electronic Properties Effects of the Surrounding. The proton affinity of the zinc-bound water molecule is a key property for the enzymatic mechanism. The acidity of the zinc bound water is the result of a subtle fine tuning via hydrogen-bonded networks and electrostatic environment effects. This quantity can thus serve as a sensitive indicator of differences in the electronic structure that will have a critical influence on the enzymatic reaction. As a first attempt to quantify the effect of the electrostatic environment and the varying size of the cluster model we have therefore calculated the proton affinities for the different models. 

Fig. 23.7. Dynamics of an enzymatic reaction in lipid nanotube networks with variable topology numeric calculations (bottom)/fluorescence intensity of the reaction product (top) vs. time for three differently chosen network geometries, (a) Reference experiment a static four-vesicle network. The product concentration displays a cascade-like behavior in time and space, (b) Linear-to-circular topology change in the four-vesicle network (c) A model study of the effect of product inhibition as the linear four-vesicle network (top panel) undergoes the same change in structure (bottom panel) as the network in the reference experiment ([28], reprinted with permission)...

In this chapter we present an experimental test case of the deduction of a reaction pathway and mechanism by means of correlation metric construction from time-series measurements of the concentrations of chemical species [1], We choose as the system an enzymatic reaction network, the initial steps of glycolysis (fig. 8.1). Glycolysis is central in intermediary metabolism and has a high degree of regulation [2]. The reaction pathway has been well studied and thus it is a good test for the theory. Further, the reaction mechanism of this part of glycolysis has been modeled extensively [3]. 

The measure S may be adjusted to include the effect of an energy cost imposed on the operation of the network. Such a cost is incurred when, for instance, ATP is hydrolyzed in an enzymatic reaction. In this study, as an illustration, a cost is imposed on the operation of enzyme a. The cost is assumed to be expended at the same rate as that of the reaction catalyzed by a, namely, v . This models a reaction that is driven by the hydrolysis of one stoichiometric equivalent of ATP. The reverse reaction requires no direct metabolic input. The cost in this model is taken to be independent of the concentration of species T, even though T serves as a rough analog of an energy carrier. The overall cost expended over a period of time r is thus the overall flux through a ... 

Microbial activities like growth and product formations can be regarded as a sequence of enzymatic reactions. On this basis Ferret (1960) constructed a kinetic model for a growing bacterial cell population. The main pathways for major nutrients are considered together with pathways for minor nutrients and trace elements linked to each other. This metabolic network can be simplified with the aid of the concept of the rate-determining step (rds), resulting in a master reaction or bottleneck that limits the total flux and the rate of the process. 

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