Chapter 3: Calvin Cycle & Carbon Fixation

Part I — Energy & Transport

3.1 RuBisCO: Structure & Kinetics

Ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) is the primary CO₂-fixing enzyme, constituting ~25–50% of leaf nitrogen. In C3 plants, it exists as an L₈S₈ hexadecameric complex (8 large catalytic + 8 small regulatory subunits). Its slow catalysis (~3 s⁻¹) and poor CO₂/O₂ discrimination are key limitations on photosynthetic efficiency.

Competitive Inhibition by O₂:

\[v_c = \frac{V_c[CO_2]}{K_c\!\left(1+\dfrac{[O_2]}{K_o}\right)+[CO_2]}\]

Typical kinetic constants (spinach RuBisCO):

V_c,max = 120 µmol CO₂ m⁻² s⁻¹
K_c = 260 µM (CO₂ in solution)
K_o = 179,000 µM (O₂ in solution)
k_cat(carboxylation) ≈ 2–5 s⁻¹

Specificity factor S_c/o:

\[S_{c/o} = \frac{V_c K_o}{V_o K_c} \approx 80\text{–}100\]

Higher values favor carboxylation. Some red algae RuBisCOs have S_c/o ~ 200, but slower k_cat.

3.2 The Three Phases of the Calvin Cycle

Phase 1: Carbon Fixation

RuBisCO adds CO₂ to ribulose-1,5-bisphosphate (RuBP, 5C) → unstable 6C intermediate → 2× 3-phosphoglycerate (3-PGA, 3C each)

\[\text{CO}_2 + \text{RuBP} \xrightarrow{\text{RuBisCO}} 2\,\text{3-PGA}\]

Phase 2: Reduction

3-PGA is phosphorylated by ATP (→ 1,3-bPGA), then reduced by NADPH (→ glyceraldehyde-3-phosphate, G3P). One G3P is exported per 3 CO₂ fixed.

\[\text{3-PGA} \xrightarrow{ATP,\,NADPH} \text{G3P}\]

Phase 3: Regeneration

5 G3P molecules are rearranged via transketolase/aldolase reactions (consuming 3 ATP) to regenerate 3 RuBP — closing the cycle.

\[5\,\text{G3P} \xrightarrow{3\,ATP} 3\,\text{RuBP}\]

Overall Stoichiometry (per G3P):

\[3\,CO_2 + 9\,ATP + 6\,NADPH \rightarrow G3P + 9\,ADP + 6\,NADP^+ + 8\,P_i\]

3.3 Light-Dependent Regulation via Thioredoxin

Calvin cycle enzymes are activated in the light and inactivated in the dark through the ferredoxin–thioredoxin system. Reduced ferredoxin (from PSI) reduces thioredoxins (Trx-m, Trx-f) via ferredoxin:thioredoxin reductase (FTR). Reduced Trx reduces disulfide bonds on target enzymes:

Light-activated enzymes:

FBPase (fructose-1,6-bisphosphatase) — regeneration
SBPase (sedoheptulose-1,7-bisphosphatase)
PRK (phosphoribulokinase) — RuBP regeneration
GAPDH (NADPH-dependent, chloroplastic)
RuBisCO activase — removes inhibitory sugar phosphates

Additional Regulatory Mechanisms:

pH: Stroma pH rises from ~7 to ~8 in light → activates enzymes
Mg²⁺: Released from thylakoid lumen in light → activates RuBisCO
CO₂ carbamylation: CO₂ binds Lys201 → activates RuBisCO
RCA (RuBisCO activase): ATP-dependent, removes tight-binding inhibitors

Calvin Cycle Diagram

Simulation: RuBisCO Kinetics & Calvin Cycle Stoichiometry

RuBisCO carboxylation vs oxygenation rates, the specificity factor diagram, and Calvin cycle ATP/NADPH stoichiometry.

Python

script.py85 lines

import numpy as np
import matplotlib.pyplot as plt
# Simulation: RuBisCO kinetics

fig, axes = plt.subplots(1, 3, figsize=(15, 6), facecolor='#0a0f0a')
fig.subplots_adjust(wspace=0.38)

# Panel 1: RuBisCO carboxylation and oxygenation rates vs CO2
ax1 = axes[0]
ax1.set_facecolor('#0d1a0d')
CO2 = np.linspace(0, 1000, 300)  # uM
O2 = 210000  # uM (atmospheric)
Vc_max = 120.0  # umol m-2 s-1
Kc     = 260.0  # uM
Ko     = 179000.0  # uM
Vo_max = 60.0

# Competitive inhibition: Vc = Vcmax*[CO2]/(Kc*(1+[O2]/Ko)+[CO2])
Vc = Vc_max * CO2 / (Kc * (1 + O2/Ko) + CO2)
Vo = Vo_max * O2  / (Ko * (1 + CO2/Kc) + O2)
net_CO2_fix = Vc - 0.5 * Vo

ax1.plot(CO2, Vc, color='#4ade80', lw=2.5, label='Carboxylation (Vc)')
ax1.plot(CO2, Vo * np.ones_like(CO2) if False else Vo, color='#f87171', lw=2, ls='--', label='Oxygenation (Vo)')
ax1.plot(CO2, net_CO2_fix, color='#d9f99d', lw=2, ls=':', label='Net CO2 fixation')
ax1.axvline(280, color='#fbbf24', lw=1.5, ls=':', alpha=0.7, label='Pre-industrial CO2')
ax1.axvline(420, color='#fb923c', lw=1.5, ls=':', alpha=0.7, label='Current CO2')
ax1.set_xlabel('[CO2] (uM in solution)', color='#a3e635', fontsize=9)
ax1.set_ylabel('Rate (umol m-2 s-1)', color='#a3e635', fontsize=9)
ax1.set_title('RuBisCO Kinetics', color='#d9f99d', fontsize=10)
ax1.legend(fontsize=7.5, labelcolor='#d9f99d', facecolor='#0d1a0d', edgecolor='#4ade80')
ax1.tick_params(colors='#a3e635', labelsize=8)
ax1.grid(True, alpha=0.2, color='#4ade80')
for sp in ax1.spines.values(): sp.set_edgecolor('#4ade80')

# Panel 2: Specificity factor and carboxylation/oxygenation ratio vs CO2/O2
ax2 = axes[1]
ax2.set_facecolor('#0d1a0d')
CO2_O2_ratio = np.linspace(0.001, 0.008, 200)
Sc_So = (Vc_max / Vo_max) * (Ko / Kc)  # ~85 for C3 plants
Vc_Vo_ratio = Sc_So * CO2_O2_ratio
ax2.plot(CO2_O2_ratio * 1000, Vc_Vo_ratio, color='#4ade80', lw=2.5)
ax2.axhline(1, color='#f87171', lw=1.5, ls='--', label='Vc = Vo breakeven')
ax2.axvline(0.00067 * 1000, color='#fbbf24', lw=1.5, ls=':', label='Current atmosphere')
ax2.fill_between(CO2_O2_ratio * 1000, Vc_Vo_ratio, 1,
    where=(Vc_Vo_ratio > 1), alpha=0.15, color='#4ade80', label='Net carboxylation')
ax2.fill_between(CO2_O2_ratio * 1000, Vc_Vo_ratio, 1,
    where=(Vc_Vo_ratio < 1), alpha=0.15, color='#f87171', label='Net oxygenation')
ax2.set_xlabel('CO2/O2 ratio (x 10-3)', color='#a3e635', fontsize=9)
ax2.set_ylabel('Vc/Vo ratio', color='#a3e635', fontsize=9)
ax2.set_title('Specificity Factor (Sc/So)', color='#d9f99d', fontsize=10)
ax2.legend(fontsize=7.5, labelcolor='#d9f99d', facecolor='#0d1a0d', edgecolor='#4ade80')
ax2.tick_params(colors='#a3e635', labelsize=8)
ax2.grid(True, alpha=0.2, color='#4ade80')
ax2.text(0.1, 0.95, f'Sc/So = {Sc_So:.1f}', transform=ax2.transAxes, color='#d9f99d', fontsize=9)
for sp in ax2.spines.values(): sp.set_edgecolor('#4ade80')

# Panel 3: Calvin cycle ATP/NADPH consumption
ax3 = axes[2]
ax3.set_facecolor('#0d1a0d')
n_CO2 = np.arange(1, 7)
atp_needed = 3 * n_CO2
nadph_needed = 2 * n_CO2
g3p_produced = n_CO2 / 3.0

x = np.arange(len(n_CO2))
width = 0.28
ax3.bar(x - width, atp_needed, width, label='ATP consumed', color='#4ade80', edgecolor='#0d1a0d')
ax3.bar(x, nadph_needed, width, label='NADPH consumed', color='#86efac', edgecolor='#0d1a0d')
ax3.bar(x + width, g3p_produced, width, label='G3P produced', color='#fbbf24', edgecolor='#0d1a0d', alpha=0.9)
ax3.set_xticks(x)
ax3.set_xticklabels([f'{n} CO2' for n in n_CO2], color='#a3e635', fontsize=8)
ax3.set_ylabel('Molecules / cycle', color='#a3e635', fontsize=9)
ax3.set_title('Calvin Cycle Stoichiometry', color='#d9f99d', fontsize=10)
ax3.legend(fontsize=8, labelcolor='#d9f99d', facecolor='#0d1a0d', edgecolor='#4ade80')
ax3.tick_params(colors='#a3e635', labelsize=8)
ax3.grid(True, alpha=0.2, color='#4ade80', axis='y')
for sp in ax3.spines.values(): sp.set_edgecolor('#4ade80')

fig.suptitle('Calvin Cycle & RuBisCO Carbon Fixation', color='#d9f99d', fontsize=13, fontweight='bold')

plt.savefig('output.png', bbox_inches='tight', facecolor=fig.get_facecolor(), dpi=110)
plt.close()
print('RuBisCO kinetics and Calvin cycle simulation complete.')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

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