Fischer Jakob, Kleidon Axel, Dittrich Peter
Bio Systems Analysis Group, Institute of Computer Science, Jena Centre for Bioinformatics and Friedrich Schiller University, Jena, Germany; Max-Planck-Institute for Biogeochemistry, Jena, Germany; International Max Planck Research School for Global Biogeochemical Cycles, Jena, Germany.
Max-Planck-Institute for Biogeochemistry, Jena, Germany.
PLoS One. 2015 Feb 27;10(2):e0117312. doi: 10.1371/journal.pone.0117312. eCollection 2015.
Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa -1.5 for linear and -1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.
反应网络对于分析化学、系统生物学或地球系统科学中发生的反应系统很有用。尽管热力学非平衡对其中许多系统很重要，但反应网络的一般热力学性质却知之甚少。为了规避热力学数据稀疏的问题，我们生成人工反应网络，并研究它们在各种边界通量下的非平衡稳态。我们使用四种不同的复杂网络模型（厄多斯 - 雷尼、巴拉巴西 - 阿尔伯特、瓦茨 - 斯托加茨、潘 - 辛哈）生成线性和非线性网络，并将它们的拓扑性质与真实反应网络进行比较。对于相似的边界条件下，通过线性网络的稳态流量比通过可比的非线性网络的流量高约一个数量级。在所有网络中，流量随着流入和流出边界物种之间的距离而减小，与其他三种网络类型相比，瓦茨 - 斯托加茨网络的斜率明显更小。网络内部各个反应的熵产生分布在中间区域遵循幂律，线性网络的指数约为 -1.5，非线性网络的指数约为 -1.66。在与弱连接物种相关的反应中发现了较高的熵产生率。这种效应在非线性网络中比在 线性网络中更强。增加通过非线性网络的流量也会增加循环的数量，并导致化学势的分布更窄。我们得出结论，耗散分布、网络拓扑和非平衡强度之间的关系是复杂的，可以通过人工反应网络进行系统研究。
