Kinetic derivation of the Hessian geometric structure in chemical reaction networks
Kinetic derivation of the Hessian geometric structure in chemical reaction networks
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DOI：
10.1103/physrevresearch.4.033066
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发表时间：
2022-07
影响因子：
4.2
通讯作者：
Tetsuya J. Kobayashi;Dimitri Loutchko;A. Kamimura;Yuki Sughiyama
中科院分区：
文献类型：
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作者：
Tetsuya J. Kobayashi;Dimitri Loutchko;A. Kamimura;Yuki Sughiyama
化学动力学理论是描述化学反应网络动力学的基础。由于物理和热力学的限制，网络具有各种结构，可以利用这些结构来表征网络的重要性质。在这项工作中，我们揭示了海森几何的化学反应网络的基础，并展示了它是如何起源于化学计量和热力学约束的相互作用。我们的推导是基于动力学，我们假设的质量作用定律和详细的平衡条件的平衡状态的特征。所得到的几何结构，然后通过出现在一个纯热力学推导的海森几何热力学。我们证明，平衡和复杂的平衡状态形成复曲面品种的事实的基础上，如何海森几何框架可以扩展到非平衡复杂的平衡稳态。我们的结论是，海森几何提供了一个自然的框架来捕捉化学反应网络的热力学方面。
The theory of chemical kinetics forms the basis to describe the dynamics of chemical reaction networks. Owing to physical and thermodynamic constraints, the networks possess various structures, which can be utilized to characterize important properties of the networks. In this work, we reveal the Hessian geometry which underlies chemical reaction networks and demonstrate how it originates from the interplay of stoichiometric and thermodynamic constraints. Our derivation is based on kinetics, we assume the law of mass action and characterize the equilibrium states by the detailed balance condition. The obtained geometric structure is then related to thermodynamics via the Hessian geometry appearing in a pure thermodynamic derivation. We demonstrate, based on the fact that both equilibrium and complex balanced states form toric varieties, how the Hessian geometric framework can be extended to nonequilibrium complex balanced steady states. We conclude that Hessian geometry provides a natural framework to capture the thermodynamic aspects of chemical reaction networks.