Generalized-Mass-Action

In Reaction 10.11 the change Az in surface charge is —zq because the uncom-plexed sites Ap carry no charge. With this in mind, we can write a generalized mass action equation cast in the form of Equation 10.8,... 

Despite its limitations, the reversible Random Bi-Bi Mechanism Eq. (46) will serve as a proxy for more complex rate equations in the following. In particular, we assume that most rate functions of complex enzyme-kinetic mechanisms can be expressed by a generalized mass-action rate law of the form... 

To simulate the overall network behavior, the power-law formalism is applied in two different ways. Within a generalized mass-action model (GMA), each biochemical interconversion is modeled with a power-law term, resulting in a differential equation analogous to Eq. (5)... 

In contrast to generalized mass-action models, an S-system model is obtained by lumping (or aggregating) all synthesizing and consuming reactions of each metabolite into a single power-law term, respectively. The mathematical structure of a S-System is independent of the complexity of the network. For any metabolite. S, -, we obtain... 

Similar to generalized mass-action models, lin-log kinetics provide a concise description of biochemical networks and are amenable to an analytic solution, albeit without sacrificing the interpretability of parameters. Note that lin-log kinetics are already written in term of a reference state v° and S°. To obtain an approximate kinetic model, it is thus sometimes suggested to choose the reference elasticities according to simple heuristic principles [85, 89]. For example, Visser et al. [85] report acceptable result also for the power-law formalism when setting the elasticities (kinetic orders) equal to the stoichiometric coefficients and fitting the values for allosteric effectors to experimental data. 

F. J. M. Horn and R. Jackson, General mass action kinetics. Arch. Rational Mech. Anal. 47(2), 81 116(1972). 

To construct the general mass action law system we need the list of components, — A, A and the list of reactions (the reaction mechanism) ... 

There are a number of representations that are considered fundamental descriptions of the basic entities in various fields. The Mass-Action representation and the Michaelis-Menten representation provide two common examples. It has been demonstrated (Savageau, 1995) that these are, in fact, restricted special cases of the Generalized-Mass-Action (GMA) representation. 

Schuster, S., Schuster, R. A Necessary and Sufficient Condition for Open Reacting Systems Endowed with Generalized Mass Action Kinetics to be Detailed Balanced. Z. Phys. Chemie Leipzig 271(2), 337-345 (1990)... 

Write complex reactions using the General Mass Action (GMA) representation Calculate equilibrium constants from kinetic data Understand the concept of steady state ... 

The General Mass Action (GMA) representation for complex reactions... 

Horn, F., Jackson, R. (1972). General mass action kinetics. Archive for Rational Mechanics and Analysis, Vol.47, No.2, pp. 81-116, ISSN 0009-2509... 

Horn and Jackson 2004. General mass Action Kinetics. Archive for rational Mechanics and Analysis 47 81-116. 

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