Surfing the Hyperbola Equations of the Steady-State Farquhar–von Caemmerer–Berry C3 Leaf Photosynthesis Model: What Can a Theoretical Analysis of Their Oblique Asymptotes and Transition Points Tell Us?

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.