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.
Wiley Interdiscip Rev Syst Biol Med. 2009 Nov-Dec;1(3):348-358. doi: 10.1002/wsbm.50.
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.
韦歇塞尔循环条件是复杂反应网络中速率系数之间的关系，这些关系确保了动力学方程与热力学平衡条件的兼容性。在平衡时的详细平衡，即每个基本反应的正向和反向速率的平衡，导致了动力学和热力学平衡条件的兼容性。因此，韦歇塞尔循环条件可以通过从详细平衡条件中消除平衡浓度来推导出来。我们开发了矩阵代数工具，用于进行这种消除，重新检查了韦歇塞尔循环条件一般形式的旧推导，并开发了新的推导方法，得到了更紧凑和更易于使用的公式。我们推导出了复杂反应网络的非平衡速率的标度律，其中包括韦歇塞尔条件作为一个特例。速率的标度律用于澄清韦歇塞尔循环条件的动力学和热力学意义。最后，我们讨论了在系统生物学中使用韦歇塞尔循环条件进行动力学计算的不同方法。
