The Hahn 1987 model is a kinetic model of C₃ leaf carbon metabolism that couples the Calvin-Benson-Bassham (CBB) cycle to the glycolate and glycerate pathways of photorespiration, formulated as a system of non-linear ordinary differential equations. It extends Hahn's earlier Calvin-cycle models (1984, 1986) by adding the competitive inhibition of ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) by oxygen, which is the entry point of photorespiration: the same enzyme that fixes CO₂ also reacts with O₂, diverting carbon into the photorespiratory pathway. By representing both processes in one connected network, the model can describe the competition between carboxylation and oxygenation that governs net assimilation in C₃ plants.
The model reaches an effectively stable steady state and behaves realistically when the external CO₂ and O₂ concentrations are varied: photosynthesis is inhibited by higher oxygen levels, while photorespiration is inhibited by higher carbon dioxide levels, reproducing the well-known reciprocal sensitivity of the two pathways to gas composition. As one of the earlier mechanistic treatments of photorespiration, it is included in GreenSloth mainly as a historical and conceptual reference point — a compact example of how the carbon-fixing dark reactions and their photorespiratory by-pass can be modelled together, complementing the more abstract CBB-only treatment of the Zhu 2009 model.
Scheme
Model definition
Variables
| Symbol | ID | Initial value | Unit |
|---|---|---|---|
| RuBP | 1 | ||
| PGA | 1 | ||
| ADP | 1 | ||
| Pi | 10 | ||
| TP | 1 | ||
| HP | 1 | ||
| GG | 100 | ||
| Pio | 1 | ||
| TPo | 0.1 | ||
| HPo | 0.1 | ||
| UDP | 10 | ||
| GF | 77.3 | ||
| GFV | 77.3 | ||
| TPGA | 0.1 | ||
| E4P | 0.1 | ||
| S7P | 0.1 | ||
| Ru5P | 1 | ||
| PGl | 1 | ||
| Gl | 1 | ||
| Gx | 1 | ||
| Sn | 10 | ||
| Gn | 1 | ||
| GA | 1 | ||
| GmA | 1 | ||
| Glm | 1 | ||
| OxA | 1 | ||
| NH3 | 1 | ||
| CO2 | 0.33 | ||
| O2 | 0.245 | ||
| Ci | 0.4 | ||
| Oi | 101 | ||
| AP_tot | 11 | ||
| UP_tot | 20 |
Parameters
| Symbol | ID | Value | Unit |
|---|---|---|---|
| k1 | 0.344 | ||
| k2 | 0.046 | ||
| k3 | 0.0261 | ||
| k4 | 0.0455 | ||
| k5 | 0.0455 | ||
| k6 | 0.455 | ||
| k7 | 0.455 | ||
| k8 | 0.909 | ||
| k9 | 0.0136 | ||
| k10 | 0.004 | ||
| k11 | 0.00004 | ||
| k12 | 0.0341 | ||
| k13 | 1.7 | ||
| k14 | 0.000852 | ||
| k15 | 0.00852 | ||
| k16 | 0.0928 | ||
| k17 | 0.0227 | ||
| k18 | 0.0467 | ||
| k19 | 0.00114 | ||
| k20 | 0.0114 | ||
| k21 | 0.00114 | ||
| k22 | 0.00114 | ||
| k23 | 0.0114 | ||
| k24 | 0.0114 | ||
| kc1 | 1 | ||
| kc2 | 0.933 | ||
| rd | 0.000011 | ||
| ko1 | 0.01 | ||
| ko2 | 4.31 | ||
| phic | 1.84 | ||
| phio | 0.0453 | ||
| phis | 0.0001 | ||
| D | 0.0001 | ||
| E | 0.5 | ||
| Oa | 100 | ||
| Ca | 0.45 | ||
| PAg | 0.001 | ||
| PAr | 0.0002 | ||
| h | 0.0002 |
Derived quantities
| Symbol | ID | Equation | Unit |
|---|---|---|---|
| ATP | |||
| UTP |
Reactions
| Symbol | ID | Rate | Stoichiometry | Unit |
|---|---|---|---|---|
| v1 | ||||
| v2 | ||||
| v3 | ||||
| v4 | ||||
| v5 | ||||
| v6 | ||||
| v7 | ||||
| v8 | ||||
| v9 | ||||
| v10 | ||||
| v11 | ||||
| v12 | ||||
| v13 | ||||
| v14 | ||||
| v15 | ||||
| v16 | ||||
| v17 | ||||
| v18 | ||||
| v19 | ||||
| v20 | ||||
| v21 | ||||
| v22 | ||||
| v23 | ||||
| v24 | ||||
| vrd | ||||
| vphis | ||||
| vD | ||||
| vc1 | ||||
| vc2 | ||||
| vo1 | ||||
| vo2 | ||||
| vphic | ||||
| vphio |
Curation
- July 2026: Maintenance by Marvin van Aalst
- June 2026: Initial implementation by Tim Nies
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.
Figures
Fig2
Fig3
Fig4
