Estimating C₄ photosynthesis parameters by fitting intensive A/C_i curves

Measurements of photosynthetic assimilation rate as a function of intercellular CO₂ (A/C_i curves) are widely used to estimate photosynthetic parameters for C₃ species, yet few parameters have been reported for C₄ plants, because of a lack of estimation methods. Here, we extend the framework of widely used estimation methods for C₃ plants to build estimation tools by exclusively fitting intensive A/C_i curves (6-8 more sampling points) for C₄ using three versions of photosynthesis models with different assumptions about carbonic anhydrase processes and ATP distribution. We use simulation analysis, out of sample tests, existing in vitro measurements and chlorophyll-fluorescence measurements to validate the new estimation methods. Of the five/six photosynthetic parameters obtained, sensitivity analyses show that maximal-Rubisco-carboxylation-rate, electron-transport-rate, maximal-PEP-carboxylation-rate, and carbonic-anhydrase were robust to variation in the input parameters, while day respiration and mesophyll conductance varied. Our method provides a way to estimate carbonic anhydrase activity, a new parameter, from A/C_i curves, yet also shows that models that do not explicitly consider carbonic anhydrase yield approximate results. The two photosynthesis models, differing in whether ATP could freely transport between RuBP and PEP regeneration processes yielded consistent results under high light, but they may diverge under low light intensities. Modeling results show selection for Rubisco of low specificity and high catalytic rate, low leakage of bundle sheath, and high PEPC affinity, which may further increase C₄ efficiency.