Chloroplast 3D Lab

Farquhar-von Caemmerer-Berry model

Net CO₂ assimilation is the smaller of three potential rates minus day respiration: A = min(Ac, Aj, Ap) − Rd. Rubisco-limited Ac = Vcmax (Ci − Γ*) / (Ci + Kc(1 + O/Ko)); light (RuBP-regeneration) limited Aj = J (Ci − Γ*) / (4Ci + 8Γ*); triose-phosphate-limited Ap = 3·TPU. The electron-transport rate J follows a non-rectangular hyperbola of absorbed light, θJ² − (αI + Jmax)J + αI Jmax = 0 with α = 0.3 e⁻ per photon and θ = 0.7. Temperature dependence uses Arrhenius factors (with a high-temperature deactivation term for V_cmax and J_max).

Stomata and water

The Ball-Berry rule sets stomatal conductance from the CO₂ actually being fixed: gs = g0 + g1β A hs / Ca (h_s = relative humidity, β = soil-water factor). Gas supply is A = (gs/1.6)(Ca − Ci) (1.6 = ratio of water-vapour to CO₂ diffusivity), so C_i is found where supply equals demand (bisection). Transpiration is E = gs·VPD / P, with VPD from the Tetens saturation curve. Water-use efficiency is A/E. Real guard cells respond over minutes (here τ_open 4 min, τ_close 2 min).

Light reactions and the Calvin cycle

Water is split at photosystem II; electrons pass PSII → plastoquinone → cytochrome b₆f → plastocyanin → PSI → ferredoxin → NADP⁺ reductase, while protons pumped into the lumen drive ATP synthase. Each CO₂ fixed in the Calvin cycle needs 3 ATP and 2 NADPH; each Rubisco oxygenation (photorespiration) needs about 3.5 ATP and 2 NADPH. With Vo/Vc = 2Γ*/Ci the net rate is A + Rd = Vc(1 − Γ*/Ci). Gross O₂ release equals J/4.

Independent checks (shown in the page)

(1) The CO₂ compensation point from the closed form Γ = Γ* + Rd(Km + Γ*)/(Vcmax − Rd) equals a numerical root of A(C_i). (2) With fixed g_s and Rubisco limitation the problem is a quadratic in C_i; its closed-form root equals the bisection solver. (3) The quantum yield at low light, dA/dI = α(Ci − Γ*)/(4Ci + 8Γ*), equals a finite difference of the code. (4) In the light-limited regime the electrons consumed, 4(V_c + V_o), equal the supplied J.

Honest simplifications

Parameters (V_cmax25 = 60, K_c = 404.9 ppm, K_o = 278.4 ppm, Γ* = 42.75 ppm, activation energies, g₁ = 9) are typical literature values for C3 leaves, not a fit to one species and not checked against your plant. Leaf temperature equals air temperature; boundary-layer and mesophyll resistances, photoinhibition, non-photochemical quenching, Rubisco activation lag and canopy shading are ignored. The day cycle is a simple sine for light and temperature. C4 and CAM plants work differently. The drawings are schematic (not to scale; one chloroplast stands for a whole leaf).

What the 3D scene shows

Everything is driven by the same model as the 2D page. Stomatal opening follows g_s; the number of falling photons follows the light; CO₂ streams in through the stoma at the rate A, O₂ and water vapour stream out at J/4 and E. In the chloroplast the glow of the thylakoid discs follows the electron-transport rate, electrons hop PSII → cyt b₆f → PSI, protons are drawn above the membrane for clarity (in reality they fill the lumen inside the disc), and ATP and NADPH travel to the Calvin ring where green tokens circulate at the carboxylation rate V_c. Sizes are not to scale: a real chloroplast is about 5 µm long and a leaf is about 0.2 mm thick.