The asymptotes and transition points of the net CO2 assimilation (A/Ci) rate curves of the steady-state Farquhar–von Caemmerer–Berry (FvCB) model for leaf photosynthesis of C3 plants are examined in a theoretical study, which begins from the exploration of the standard equations of hyperbolae after rotating the coordinate system. The analysis of the A/Ci quadratic equations of the three limitation states of the FvCB model—abbreviated as Ac, Aj and Ap—allows us to conclude that their oblique asymptotes have a common slope that depends only on the mesophyll conductance to CO2 diffusion (gm). The limiting values for the transition points between any two states of the three limitation states c, j and p do not depend on gm, and the results are therefore valid for rectangular and non-rectangular hyperbola equations of the FvCB model. The analysis of the variation of the slopes of the asymptotes with gm casts doubts about the fulfilment of the steady-state conditions, particularly, when the net CO2 assimilation rate is inhibited at high CO2 concentrations. The application of the theoretical analysis to extended steady-state FvCB models, where the hyperbola equations of Ac, Aj and Ap are modified to accommodate nitrogen assimilation and amino acids export via the photorespiratory pathway, is also discussed. Electronic supplementary material The online version of this article (10.1007/s11538-019-00676-z) contains supplementary material, which is available to authorized users.

中文翻译：

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探索稳态 Farquhar-von Caemmerer-Berry C3 叶片光合作用模型的双曲线方程：对其斜渐近线和过渡点的理论分析可以告诉我们什么？


对C3植物叶片光合作用稳态Farquhar-von Caemmerer-Berry (FvCB)模型的净CO2同化(A/Ci)速率曲线的渐近线和转变点进行了理论研究，该研究从探索开始旋转坐标系后的双曲线标准方程。通过对 FvCB 模型的三个极限状态（缩写为 Ac、Aj 和 Ap）的 A/Ci 二次方程的分析，我们可以得出结论，它们的斜渐近线具有共同的斜率，该斜率仅取决于叶肉对 CO2 扩散的电导（通用汽车）。三个极限状态c、j和p中任意两个状态之间的转变点的极限值不依赖于gm，因此结果对于FvCB模型的矩形和非矩形双曲线方程均有效。对渐近线斜率随 gm 变化的分析对稳态条件的满足提出了质疑，特别是当净 CO2 同化率在高 CO2 浓度下受到抑制时。还讨论了理论分析在扩展稳态 FvCB 模型中的应用，其中 Ac、Aj 和 Ap 的双曲线方程被修改以适应氮同化和通过光呼吸途径的氨基酸输出。电子补充材料 本文的在线版本 (10.1007/s11538-019-00676-z) 包含补充材料，可供授权用户使用。