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Abstract:
Motivation:
The Wegscheider conditions follow from the principle of detailed balance and the second law of thermodynamics. They constrain possible values of kinetic parameters in reaction networks. A mathematical model that violates these conditions describes a thermodynamically impossible system. Large reaction networks, e.g. in cellular signal transduction or metabolism, contain usually a large number of Wegscheider conditions. This makes thermodynamically consistent modeling difficult [1].
Thermodynamic-Kinetic Modeling (TKM):
TKM is a formalism for formulation of kinetic rate equation that is based on thermodynamic flux-force relationships [1]. Chemical potentials and thermodynamic forces (negative Gibbs reaction energies) do not scale linearly with concentrations and fluxes, respectively. Thus they are not suited for kinetic modeling of far-from-equilibrium systems. For this reason TKM uses an alternative system of thermokinetic potentials and forces, that are proportional to concentrations and mass-action fluxes, respectively. By using flux-force relationships we structurally avoid violation of Wegscheider conditions.
Features of Thermodynamic-Kinetic Modeling:
Since TKM structurally avoids thermodynamically infeasible models, it is suited for modeling large networks with many Wegscheider conditions. Widely used kinetic laws, as mass-action or Michaelis-Menten-kinetics, have a simple expression in TKM; e.g. the thermokinetic resistance of a mass-action reaction is constant. The TKM formalism provides a natural framework for model reduction. In particular, rapid-equilibrium assumptions that correspond to a zero thermokinetic resistance can be applied systematically and easily. This is a further important prerequisite for modeling large network.
References:
[1] Ederer, M. and Gilles, E.D. Thermodynamically feasible kinetic models of reaction networks. Biophys J, 2007, 92, 1846-1857
