Abstract
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.
Highlights
The steady-state Farquhar–von Caemmerer–Berry (FvCB) leaf photosynthesis model is broadly recognised by plant biologists and physiologists as one of the most useful models to assess in vivo the net C O2 assimilation rate (A) of plant leaves as a function of C O2 concentration (C) under different environmental cues
In the basic FvCB model, the analysis of the net C O2 assimilation rate did not consider the mesophyll conductance to CO2 diffusion—hereafter defined as the conductance for CO2 diffusion from the intercellular space to the site of Rubisco carboxylation assuming that photorespiratory and respiratory C O2 release occurs in the same compartment as Rubisco carboxylation—and its value was assumed to be infinite
FvCB model we present here, the rotation of the coordinate system has been a key strategy to reach the conclusion that the quadratic equations of the FvCB model cannot explain the inhibition of the net CO2 assimilation rate at very high Ci
Summary
The steady-state Farquhar–von Caemmerer–Berry (FvCB) leaf photosynthesis model is broadly recognised by plant biologists and physiologists as one of the most useful models to assess in vivo the net C O2 assimilation rate (A) of plant leaves as a function of C O2 concentration (C) under different environmental cues. When the A/Ci rate curves of the FvCB model are analysed under steady-state conditions and the photorespiratory and respiratory C O2 release is assumed to take place at the site of the Rubisco carboxylation, the quadratic equations for Ac, Aj and Ap (see “Appendix 1”, Eqs. A8–A10) can be fitted following different approaches, where gm is taken as a constant parameter (Duursma 2015; Gu et al 2010; Sharkey 2016; Su et al 2009).
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