Photosynthesis models¶
The photosynthesis tool fits net CO₂ assimilation A as a function of
intercellular CO₂ Ci, absorbed light Q and leaf temperature T. Three
models are available:
| Model | --model |
Use it for |
|---|---|---|
| Farquhar–von Caemmerer–Berry C3 | fvcb (default) |
C3 leaves: A–Ci, light and temperature responses |
| von Caemmerer C4 | fvcbC4 |
C4 leaves |
| Empirical | empiricalA |
A smooth response surface without a biochemical interpretation |
All three take Q as absorbed light (PPFD × leaf absorptance) and T in
Kelvin. When you fit a file, PhytKit prefers a Qabs column over Q, and
converts temperatures below 200 from °C to Kelvin.
FvCB C3¶
Assimilation is the least of three carboxylation rates, less photorespiration and day respiration:
| Rate | Limited by | Expression |
|---|---|---|
| \(w_c\) | Rubisco | \(\dfrac{V_{cmax}\,C_c}{C_c + K_c(1 + O/K_o)}\) |
| \(w_j\) | RuBP regeneration (electron transport) | \(\dfrac{J\,C_c}{4C_c + 8\Gamma^*}\) |
| \(w_p\) | Triose-phosphate utilization (TPU) | \(\dfrac{3\,TPU\,C_c}{C_c - (1 + 3\alpha_G)\Gamma^*}\) |
The minimum is slightly smoothed, so the fitter's derivatives stay continuous where the limitation changes. The smoothing is a fixed internal constant, not a parameter.
Light. Electron transport \(J\) follows a non-rectangular hyperbola in
absorbed light, with quantum yield alpha and curvature theta.
Temperature. Vcmax, Jmax and TPU follow a peaked Arrhenius response.
Each has a value at 25 °C (Vcmax25), an activation energy (_dHa), a
deactivation energy (_dHd) and an optimum temperature (_Topt, in Kelvin;
values below 200 are read as °C). Γ*, Kc, Ko and Rd follow a plain Arrhenius
response.
The formulation matches PhoTorch. Rubisco kinetic constants (GammaS25,
Kc25, Ko25 and their activation energies) and O are fixed by default.
Mesophyll conductance¶
Rubisco sees the chloroplast CO₂ \(C_c\), not \(C_i\). During fitting PhytKit uses the measured A to set
gm is a fitted parameter by default (bounds 0.01–0.5 mol m⁻² s⁻¹ bar⁻¹).
Mesophyll conductance is hard to estimate from gas exchange alone, so many
analyses fit an apparent model with \(C_c = C_i\) instead. To do that, fix
gm at a very large value:
Soft constraints¶
FvCB adds penalties that steer the fit toward biologically sensible limitation patterns (from PhoTorch). They matter most when a curve doesn't clearly show every limitation.
| Key | Encourages |
|---|---|
ap_nonneg |
A non-negative TPU-limited rate at every point |
aj_le_ac_mid |
Light limitation at or below Rubisco limitation at Ci 500–700 |
rubisco_region |
A Rubisco-limited stretch at low Ci |
ap_above_cross |
No TPU limitation where Rubisco and light limitation cross |
ap_limits_high |
TPU limitation at the highest Ci |
vcmax_window |
Vcmax25 between 20 and 130 |
alphag_zero |
alphaG near zero |
vj_ratio |
Jmax25/Vcmax25 between 1.6 and 2.0 |
The four marked per curve in Models and parameters
are applied to each curve separately when the file has a CurveID column, and
to all rows together otherwise. Turn one off with --no-constraint <key>,
all of them with --constraints none, or change a weight with
--weight <key>=<w>.
von Caemmerer C4¶
The C4 model follows von Caemmerer (2021), as implemented in PhoTorch and Helios. Defaults are for Setaria viridis.
- Mesophyll CO₂: \(C_m = C_i - A/g_m\).
- PEP carboxylation: \(V_p = \min\big(C_m V_{pmax}/(C_m + K_p),\ V_{pr}\big)\).
- Enzyme-limited rate \(A_c\) and electron-transport-limited rate \(A_j\): each the lower root of a quadratic.
- Assimilation: \(A = \min(A_c, A_j)\). C4 photosynthesis has no TPU limitation.
Empirical model¶
A light-saturation term times a CO₂-saturation term, with temperature responses on each coefficient. It has many parameters for what A–Ci data alone can determine, so fits often reach equally good results with different parameter values. See How fitting works.