Thermodynamically based constraints for rate coefficients of large biochemical networks.
Wegscheider cyclicity conditions are relationships among the rate coefficients of a complex reaction network, which ensure the compatibility of kinetic equations with the conditions for thermodynamic equilibrium. The detailed balance at equilibrium, that is the equilibration of forward and backward rates for each elementary reaction, leads to compatibility between the conditions of kinetic and thermodynamic equilibrium. Therefore, Wegscheider cyclicity conditions can be derived by eliminating the equilibrium concentrations from the conditions of detailed balance. We develop matrix algebra tools needed to carry out this elimination, reexamine an old derivation of the general form of Wegscheider cyclicity condition, and develop new derivations which lead to more compact and easier-to-use formulas. We derive scaling laws for the nonequilibrium rates of a complex reaction network, which include Wegscheider conditions as a particular case. The scaling laws for the rates are used for clarifying the kinetic and thermodynamic meaning of Wegscheider cyclicity conditions. Finally, we discuss different ways of using Wegscheider cyclicity conditions for kinetic computations in systems biology.
Vlad
Marcel O
MO
Department of Chemistry, Stanford University, Stanford, CA 94305-5080, USA.|Institute of Mathematical Statistics and Applied Mathematics, Casa Academiei Romane, Calea 13 Septembrie 13, Bucharest, 050711 Romania.|Institute of Functional Genomics, University of Regensburg, Josef-Engert Strasse 9, 93053 Regensburg, Germany.
Ross
John
J
Department of Chemistry, Stanford University, Stanford, CA 94305-5080, USA.
D000465:Algorithms; D001669:Biochemical Phenomena; D007700:Kinetics; D008954:Models, Biological; D049490:Systems Biology; D013816:Thermodynamics