BIOPHYSICAL THEORY AND MODELING |
Thermodynamically Feasible Kinetic Models of Reaction Networks
Michael Ederer 1* and Ernst Dieter Gilles 1
1 Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
* To whom correspondence should be addressed. E-mail: ederer{at}mpi-magdeburg.mpg.de.
Submitted on July 28, 2006
Revised on August 28, 2006
Accepted on 27 November 2006
 |
Abstract |
|---|
The dynamics of biological reaction networks are strongly constrained by thermodynamics. A holistic understanding of their behavior and regulation requires mathematical models that observe these constraints. However, kinetic models may easily violate the constraints imposed by the principle of detailed balance, if no special care is taken. Detailed balance demands that in thermodynamic equilibrium all fluxes vanish. We introduce a Thermodynamic-Kinetic Modeling (TKM) formalism that adapts the concepts of potentials and forces from irreversible thermodynamics to kinetic modeling. In the proposed formalism the thermokinetic potential of a compound is proportional to its concentration. The proportionality factor is a compound-specific parameter called capacity. The thermokinetic force of a reaction is a function of the potentials. Every reaction has a resistance that is the ratio of thermokinetic force and reaction rate. For mass-action type kinetics the resistances are constant. Since it relies on the thermodynamic concept of potentials and forces the TKM formalism structurally observes detailed balance for all values of capacities and resistances. Thus it provides an easy way to formulate physically feasible, kinetic models of biological reaction networks. The TKM formalism is useful for modeling large biological networks that are subject
to many detailed balance relations.
Key Words:
Thermodynamic-Kinetic Modeling, detailed balance, irreversible thermodynamics, kinetic modeling, systems biology
