Journal Article

Modular rate laws for enzymatic reactions: thermodynamics, elasticities and implementation

Wolfram Liebermeister, Jannis Uhlendorf and Edda Klipp

in Bioinformatics

Volume 26, issue 12, pages 1528-1534
Published in print June 2010 | ISSN: 1367-4803
Published online April 2010 | e-ISSN: 1460-2059 | DOI:
Modular rate laws for enzymatic reactions: thermodynamics, elasticities and implementation

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Motivation: Standard rate laws are a key requisite for systematically turning metabolic networks into kinetic models. They should provide simple, general and biochemically plausible formulae for reaction velocities and reaction elasticities. At the same time, they need to respect thermodynamic relations between the kinetic constants and the metabolic fluxes and concentrations.

Results: We present a family of reversible rate laws for reactions with arbitrary stoichiometries and various types of regulation, including mass–action, Michaelis–Menten and uni–uni reversible Hill kinetics as special cases. With a thermodynamically safe parameterization of these rate laws, parameter sets obtained by model fitting, sampling or optimization are guaranteed to lead to consistent chemical equilibrium states. A reformulation using saturation values yields simple formulae for rates and elasticities, which can be easily adjusted to the given stationary flux distributions. Furthermore, this formulation highlights the role of chemical potential differences as thermodynamic driving forces. We compare the modular rate laws to the thermodynamic–kinetic modelling formalism and discuss a simplified rate law in which the reaction rate directly depends on the reaction affinity. For automatic handling of modular rate laws, we propose a standard syntax and semantic annotations for the Systems Biology Markup Language.

Availability: An online tool for inserting the rate laws into SBML models is freely available at


Supplementary Information: Supplementary data are available at Bioinformatics online.

Journal Article.  4705 words.  Illustrated.

Subjects: Bioinformatics and Computational Biology

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