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Item Open Access Thermokinetic modeling and model reduction of reaction networks(2010) Ederer, Michael; Gilles, Ernst Dieter (Prof. Dr.-Ing. Dr. h.c. mult.)This work introduces the thermokinetic modeling formalism (TKM). TKM is a framework for thermodynamically consistent, kinetic modeling and model reduction of biochemical reaction networks. Kinetic models describe the dynamics of the concentrations and fluxes in a biochemical reaction network by means of the network stoichiometry and the kinetic rate equations. The laws of thermodynamics constrain the possible dynamics of reaction networks and thus constrain physically feasible kinetic models. Especially for large networks, as they are considered in computational systems biology, finding thermodynamically consistent parameters can be difficult. TKM is a convenient and user-friendly formalism to build thermodynamically consistent kinetic models. The TKM formalism is based on thermokinetic potentials of compounds and thermokinetic forces of reactions. These quantities are derived from chemical potentials and Gibbs reaction energies. In the case of ideal dilute solutions, thermokinetic potentials are proportional to the corresponding concentrations. The constant proportionality factors are the thermokinetic capacities of the compounds. In the case of mass-action kinetics, the thermokinetic forces and the reaction fluxes are proportional: The constant proportionality factors are the thermokinetic resistances of the reactions. Non-ideal solutions or complex kinetics lead to non-constant, state-dependent capacities and resistances. Each model described by capacities and resistances is thermodynamically consistent and structurally fulfills the Wegscheider conditions. In addition, each thermodynamically consistent, kinetic model can be expressed by capacities and resistances. Thus, the use of these quantities provides a simple and comprehensive way for thermodynamically consistent modeling. If a thermokinetic model fulfills certain conditions, the model size can be reduced by suited transformation and reduction steps. In particular, the model size can be reduced if the model contains conservation relations or stoichiometric cycles. Further, a reduction is possible if resistances or capacities have a value of zero. Capacities of zero correspond to quasi-stationary compounds and resistances of zero correspond to reactions in rapid equilibrium. Due to the formal structure of thermokinetic models, model reduction based on the rapid equilibrium assumption is particularly simple. It can be easily applied to reaction rules as they are used to describe protein-protein interaction networks with inherent combinatorial complexity. Thermokinetic models can be depicted in a diagram as a connection of basic network elements representing the compounds and reactions. Several model reduction methods can be formulated as graphical rules, which allow for a simple and intuitive reduction of the model size. The TKM formalism is used to model the oxygen response of the bacterium Escherichia coli, which is strongly determined by thermodynamic constraints. In order to restrict the model to the relevant parameters and dynamics, model reduction techniques are applied. The model is able to explain the measured metabolic fluxes and concentrations in the wild type and a regulatory mutant in dependence of the oxygen availability. This example also shows that TKM is useful for modeling large networks. TKM unifies thermodynamic and kinetic approaches for the modeling of biochemical reaction networks in a natural and formally appealing way. In particular, it introduces thermodynamic flow-force relationships into kinetic modeling. In this way, TKM guarantees the thermodynamic consistency of the model equations. In the conventional kinetic modeling approach, the kinetic parameters are formally attributed to reactions but not compounds. However, the equilibrium constants that, in the conventional modeling approach, are ratios of kinetic parameters are solely determined by the thermodynamic properties of the compounds. This finally may lead to kinetic models violating thermodynamic constraints unless the Wegscheider conditions are explicitly considered. TKM clearly distinguishes between the thermodynamic parameters, the capacities, and the kinetic parameters, the resistances. Thus, TKM provides a thermodynamically consistent parameterization of kinetic models. TKM also provides thermodynamically consistent and conveniently usable model reduction methods. Altogether, TKM strongly simplifies the mathematical modeling of complex biochemical networks.