The Bellasio 2019 model is a generalized C3 leaf-photosynthesis model, that includes simplified representations of the light and dark reactions and a stomatal behavior submodule. A lot of its implementation is based on past work by the same author and is mainly inspired by the common Farquhar-von Caemmerer-Berry model. The light reactions are modified from Yin et al. (2004) and include the potential rates of ATP and NADPH production based on light intensity. This model has been created with the simple user in mind, and the author has made an effort to show its simplicity, by giving access to a Microsoft Excel Workbook containing the entire model. To showcase the model's capabilities, the author creates common steady-state carbon assimilation curves, against intercellular CO₂ concentration and light intensity, and compares them to experimental data from the literature. As many models of photosynthesis rely on purely stead-state assumptions, this model is also validated in dynamic conditions, showing for example the response of the model to a fluctuation of ambient oxygen concentration.
This model was created to stay as simple as possible, while still being able to accurately represent the main features of C₃ photosynthesis. As such, it can be used as a base for more complex models, or as a starting block in larger models of plant physiology. While giving access to the entire model in an Excel Workbook format is transparent and great, the execution of said practice has been inefficient in this instance. The entire mathematical description of the model is also given in the Appendix of the publication, however there are missing or different equations between the publication and the Excel Workbook, which can lead to confusion. On top of that, the simulation protocols used for each figure are only given in small details, which leads to further confusion when trying to reproduce the results and see which equations are correct or not.
Scheme
Model definition
Variables
| Symbol | ID | Initial value | Unit |
|---|---|---|---|
| CO2 | |||
| HCO3 | 0.1327 | ||
| RUBP | 2 | ||
| PGA | 4 | ||
| DHAP | 4 | ||
| ATP_st | 0.68 | ||
| NADPH_st | 0.21 | ||
| RU5P | 0.34 | ||
| Ract | 1 | ||
| J_NADPH | 0.1 | ||
| J_ATP | 0.16 | ||
| Ci | |||
| gs | 0.334934046786077 |
Parameters
| Symbol | ID | Value | Unit |
|---|---|---|---|
| AP_tot | 1.5 | ||
| Pi_tot | 15 | ||
| p_o2 | 210000 | ||
| Kh_o2 | 833300 | ||
| V_m | 0.03 | ||
| PPFD | 1500 | ||
| RLight | 0.001 | ||
| s | 0.43 | ||
| PhiPSII_LL | 0.72 | ||
| PhiPSI_LL | 1 | ||
| alpha_ppfd_PhiPSII | 0.00125 | ||
| V0_ppfd_PhiPSII | -0.8 | ||
| theta_ppfd_PhiPSII | 0.7 | ||
| f_pseudocycNR | 0.01 | ||
| fq | 1 | ||
| f_ndh | 0 | ||
| h | 4 | ||
| Ca | 350 | ||
| alpha_ppfd_rub | 0.0018 | ||
| V0_ppfd_rub | 0.16 | ||
| theta_ppfd_rub | 0.95 | ||
| alpha_co2 | 400 | ||
| V0_co2 | -0.2 | ||
| theta_co2 | 0.98 | ||
| tau_i | 360 | ||
| tau_d | 1200 | ||
| km_v_RuBisCO_c_CO2 | 0.014 | ||
| km_v_RuBisCO_c_RUBP | 0.02 | ||
| km_v_RuBisCO_c_O2 | 0.222 | ||
| ki_v_RuBisCO_c_PGA | 2.52 | ||
| ki_v_RuBisCO_c_NADP_st | 0.21 | ||
| ki_v_RuBisCO_c_ADP_st | 0.2 | ||
| ki_v_RuBisCO_c_Pi_st | 3.6 | ||
| vmax_v_RuBisCO_c | 0.2 | ||
| kcat_v_RuBisCO_c | 4.7 | ||
| S_co_gas | 2200 | ||
| vmax_v_PRKase | 1.17 | ||
| keq_v_PRKase | 6846 | ||
| km_v_PRKase_ATP_st | 0.625 | ||
| ki_v_PRKase_ADP_st | 0.1 | ||
| km_v_PRKase_RU5P | 0.034 | ||
| ki_v_PRKase_PGA | 2 | ||
| ki_v_PRKase_RUBP | 0.7 | ||
| ki_v_PRKase_Pi_st | 4 | ||
| vmax_v_pgareduction | 0.4 | ||
| km_v_pgareduction_ATP_st | 0.3 | ||
| km_v_pgareduction_PGA | 10 | ||
| km_v_pgareduction_NADPH_st | 0.05 | ||
| ki_v_pgareduction_ADP_st | 0.89 | ||
| vmax_v_carbohydrate_synthesis | 0.2235 | ||
| keq_v_carbohydrate_synthesis | 0.8 | ||
| km_v_carbohydrate_synthesis_DHAP | 22 | ||
| ki_v_carbohydrate_synthesis_ADP_st | 1 | ||
| vmax_v_rpp | 0.0585 | ||
| keq_v_rpp | 0.06 | ||
| km_v_rpp_DHAP | 0.5 | ||
| H | 0.00005012 | ||
| vmax_v_co2_hydration | 200 | ||
| keq_v_co2_hydration | 0.00056 | ||
| km_v_co2_hydration_CO2 | 2.8 | ||
| km_v_co2_hydration_HCO3 | 34 | ||
| keq_v_FNR | 502 | ||
| km_v_FNR_NADP_st | 0.0072 | ||
| km_v_FNR_NADPH_st | 0.036 | ||
| Kj_NADPH | 200 | ||
| keq_v_ATPsynth | 5734 | ||
| km_v_ATPsynth_ADP_st | 0.014 | ||
| km_v_ATPsynth_Pi_st | 0.3 | ||
| km_v_ATPsynth_ATP_st | 0.3 | ||
| Kj_ATP | 200 | ||
| gm | 0.5 | ||
| Kh_co2 | 30303.0303030303 | ||
| Kd | 150 | ||
| Ki | 900 | ||
| tau0 | -0.1 | ||
| chi_beta | 0.5 | ||
| phi | 0 | ||
| pi_e | 1.2 | ||
| Kh | 12 | ||
| Ds | 10 | ||
| gs0 | 0.01 | ||
| NADP_tot | 0.5 |
Derived quantities
| Symbol | ID | Equation | Unit |
|---|---|---|---|
| ADP_st | |||
| NADP_st | |||
| Pi_st | |||
| Et | |||
| km_v_RuBisCO_c_RUBP_extra | |||
| f_rubp | |||
| O2 | |||
| Ract_eq | |||
| I2_0 | |||
| I1_0 | |||
| chi | |||
| I1 | |||
| f_cyc | |||
| I2 | |||
| PhiPSII | |||
| J2 | |||
| J1 | |||
| f_pseudocyc | |||
| J_NADPH_steady | |||
| J_ATP_steady | |||
| gs_steady | |||
| A |
Reactions
| Symbol | ID | Rate | Stoichiometry | Unit |
|---|---|---|---|---|
| Ract_rate | ||||
| v_J_NADPH | ||||
| v_J_ATP | ||||
| v_gs | ||||
| v_RuBisCO_c | ||||
| rubisco_oxygenase | ||||
| glycine_decarboxylase | ||||
| v_PRKase | ||||
| v_pgareduction | ||||
| v_carbohydrate_synthesis | ||||
| v_rpp | ||||
| v_co2_hydration | ||||
| v_RLight | ||||
| v_FNR | ||||
| v_ATPsynth | ||||
| CO2_dissolution | ||||
| CO2_stomatal_diffusion |
Curation
- July 2026: Maintenance by Marvin van Aalst
- June 2026: Initial implementation by Elouen Corvest
This model was validated by reproducing the following figures of the original publication. Due to copyright restrictions, a side-by-side comparison of the original figures is not shown here.
The model shows discrepancies between the paper's description and the provided Excel Worksheet. However, the latter is deemed to be the absolute truth. Still, some figures in the publication are inconsistently reproduced. After deeper analysis, it is assumed the errors mostly come from the implementation of and , as the mathematical expressions cannot be truly replicated inside a continuous integration solver. Additionally, the simulation used for each figure is not given in full detail, so thoughtful assumptions had to be made to fulfill the replications. Even if some figures are not fully reproduced, others are. Therefore, caution is advised when using this version of the model, and any support towards a better implementation is encouraged.
Figures
Fig3
Fig4
Fig5
Fig6
Fig7
