C3 and C4 photosynthesis models: an overview from the perspective of crop modelling

Nearly three decades ago Farquhar, von Caemmerer and Berry published a biochemical model for C 3 photosynthetic rates (the FvCB model). The model predicts net photosynthesis ( A ) as the minimum of the Rubisco-limited rate of CO 2 assimilation ( A c ) and the electron transport-limited rate of CO 2 assimilation ( A j ). Given its simplicity and the growing availability of the required enzyme kinetic constants, the FvCB model has been used for a wide range of studies, from analysing underlying C 3 leaf biochemistry to predicting photosynthetic fluxes of ecosystems in response to global warming. However, surprisingly, this model has seen limited use in existing crop growth models. Here we highlight the elegance, simplicity, and robustness of this model. In the light of some uncertainties with photosynthetic electron transport pathways, a recently extended FvCB model to calculate A j is summarized. Applying the FvCB-type model in crop growth models for predicting leaf photosynthesis requires a stomatal conductance ( g s ) model to be incorporated, so that intercellular CO 2 concentration ( C i ) can be estimated. In recent years great emphasis has been put on the significant drawdown of Rubisco carboxylation-site CO 2 concentration ( C c ) relative to C i . To account for this drawdown, mesophyll conductance ( g m ) for CO 2 transfer can be added. We present an analytical algorithm that incorporates a g s model and uses g m as a temperature-dependent parameter for calculating A under various environmental scenarios. Finally we discuss a C 4 -equivalent version of the FvCB model. In addition to the algorithms already elaborated for C 3 photosynthesis, most important algorithms for C 4 photosynthesis are those that capture the CO 2 concentrating mechanism and the extra ATP requirement by the C 4 cycle. Although the current estimation of the C 4 enzyme kinetic constants is less certain, applying FvCB-type models to both C 3 and C 4 crops is recommended to accurately predict the response of crop photosynthesis to multiple, interactive environmental variables.