Thermodynamic-Kinetic Modeling of Complex Formation in Signal Transduction

Objective: The Wegscheider conditions follow from the principle of detailed balance and the second law of thermodynamics. They constrain possible values of the kinetic parameters in reaction networks. A mathematical model that violates these conditions describes a thermodynamically impossible system. Large reaction networks contain usually a large number of Wegscheider conditions. This makes the thermodynamically consistent, kinetic modeling of such networks difficult. For this reason we developed the Thermodynamic-Kinetic Modeling (TKM) formalism, that provides a structurally consistent parameterization of kinetic models (Ederer & Gilles, Biophys J, 92(6), 2007). The parameters of the TKM approach are capacities of species and resistances of reactions. Networks that model the formation of multi-protein complexes contain a particularly high number of Wegscheider conditions. Since the formation of protein complexes is a central motif of cellular signal transduction, we will show how the TKM formalism can be applied to such networks. Results: The thermokinetic capacities of protein complexes can be written by a product of a base capacity with interaction factors. The interaction factors depend on the binding energies of the proteins. Higher order interaction factors are possible, if more than two proteins interact. In a similar way, thermokinetic resistances can be decomposed into a base resistance and interaction factors that describe the influence of the binding state of the participating proteins. This decomposition of capacities and resistances allows us to formulate a thermokinetic model in a rule-based manner. Conclusions: Kinetic models that describe the formation of protein complexes are prone to a violation of the Wegscheider conditions. The Thermodynamic-Kinetic Modeling (TKM) formalism provides a thermodynamically consistent and intuitive parameterization of such networks by capacitive and resistive interaction factors. It allows for a rule-based formulation of thermokinetic models. This is important since due to the combinatorial complexity of protein complexation, the number of occurring species and reactions increases exponentially with the number of proteins. © 2008 University of Göteborg [accessed December 22, 2008