Part VI — Chapter 18

Photorespiration & C4/CAM

The oxygenase activity of RuBisCO wastes up to 25% of fixed carbon in C3 plants. C4 and CAM plants evolved elegant biochemical strategies to concentrate CO₂ at the RuBisCO active site, suppressing this costly reaction.

C3 vs C4 vs CAM: Spatial and Temporal CO₂ Concentration

The Photorespiratory Pathway

When RuBisCO reacts with O₂ instead of CO₂, the 2-phosphoglycolate (2-PG) product must be recycled through the photorespiratory pathway, which spans three organelles — chloroplast, peroxisome, and mitochondrion — and releases CO₂ and NH₃:

Chloroplast

1. RuBisCO oxygenase: RuBP + O₂ → 3-PGA + 2-PG

2. PGP phosphatase: 2-PG → glycolate

3. Glycolate exported to peroxisome

\( \text{RuBP} + \text{O}_2 \xrightarrow{\text{RuBisCO}} \text{3-PGA} + \text{2-PG} \)

Peroxisome

4. Glycolate oxidase: glycolate + O₂ → glyoxylate + H₂O₂

5. Catalase: 2 H₂O₂ → 2 H₂O + O₂

6. Glu:glyoxylate aminotransferase (GGAT): glyoxylate + Glu → glycine + KG

\( \text{glycolate} + \text{O}_2 \xrightarrow{\text{GOX}} \text{glyoxylate} + \text{H}_2\text{O}_2 \)

Mitochondrion

7. Glycine decarboxylase (GDC) + SHMT: 2 glycine → serine + CO₂ + NH₃ + NADH

8. Serine exported back to peroxisome → SGAT → hydroxypyruvate → NADH-HPR → glycerate

9. Glycerate returns to chloroplast, phosphorylated to 3-PGA

\( 2\,\text{glycine} \xrightarrow{\text{GDC+SHMT}} \text{serine} + \text{CO}_2 + \text{NH}_3 + \text{NADH} \)

Net Energy Cost of Photorespiration

\( \text{Cost per 2-PG recycled: } 3.5\,\text{ATP} + 2\,\text{NADPH} + 1\,\text{Fd}_{\text{red}} \)

At 25°C and 400 ppm CO₂, roughly 1 in 4 RuBisCO reactions are oxygenations. The ratio of carboxylation to oxygenation is: \( v_c/v_o = \tau \cdot [\text{CO}_2]/[\text{O}_2] \), where τ ≈ 90 at 25°C but falls to ~65 at 35°C, meaning photorespiration increases substantially with temperature — a major reason C4 plants dominate in hot climates.

C4 Decarboxylation Subtypes

NADP-ME type

Maize, sugarcane, sorghum

Malate decarboxylated by NADP-malic enzyme in BS chloroplasts. Produces NADPH in BS. Grana-deficient BS chloroplasts (agranal = bundle sheath specific). Most studied.

NAD-ME type

Amaranth, quinoa, millet

Aspartate is main C4 acid transported. Decarboxylation by NAD-malic enzyme in BS mitochondria. BS has well-developed mitochondria and chloroplasts.

PCK type

Panicum, Urochloa

Oxaloacetate decarboxylated by PEP carboxykinase (ATP-dependent) in BS cytosol. Often uses both aspartate and malate. Multiple decarboxylation enzymes operating simultaneously.

Python: C3, C4 & CAM Net Photosynthesis vs Temperature

Simulate net photosynthesis rates using the Farquhar-von Caemmerer-Berry model for C3, a bundle-sheath CO₂-concentrating model for C4, and a malate-pool-limited model for CAM across a temperature gradient.

Python

script.py157 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Compare net photosynthesis rate of C3, C4, and CAM plants as function of temperature
# Based on Farquhar-von Caemmerer-Berry (FvCB) model and published data

# Temperature range
T = np.linspace(10, 45, 200)  # Celsius
T_K = T + 273.15

R = 8.314  # J/mol/K

# RuBisCO kinetics - temperature dependence
# Arrhenius function
def arrhenius(T_K, param_25, Ea):
    return param_25 * np.exp(Ea / R * (1/298.15 - 1/T_K))

# Peaked function for thermally labile parameters
def peaked(T_K, param_25, Ea, S, H):
    num = param_25 * np.exp(Ea / R * (1/298.15 - 1/T_K))
    denom = 1 + np.exp((S*T_K - H) / (R*T_K))
    return num / denom

# C3 model parameters (Arabidopsis/wheat)
Vcmax25_C3 = 80e-6    # mol/m2/s (at 25C)
Jmax25_C3  = 150e-6
Ea_Vcmax   = 65000    # J/mol
Ea_Jmax    = 43900
S_J = 710             # J/mol/K  (entropy for Jmax deactivation)
H_J = 220000          # J/mol

# CO2 specificity factor of RuBisCO
# tau = Kc/Ko (specificity factor, ~80-100 at 25C)
# Decreases with temperature (more oxygenase activity at high T)
tau_25 = 90
Ea_tau = -28990  # negative: tau decreases with T

tau = tau_25 * np.exp(Ea_tau / R * (1/298.15 - 1/T_K))

# Photorespiratory CO2 compensation point (Gamma_star)
# Gamma_star = 0.5 * [O2] / tau
O2_conc = 210e-3   # mol/mol  (21% O2)
CO2_atm = 400e-6   # mol/mol  (400 ppm)
Gamma_star = 0.5 * O2_conc / tau  # mol/mol

# C3 net photosynthesis (simplified, limitation by Rubisco)
Vcmax = peaked(T_K, Vcmax25_C3, Ea_Vcmax, S_J, H_J)
# Gross A = Vcmax * (Ci - Gamma_star) / (Ci + Km_eff) - Rd
Km_eff = 450e-6  # effective Km CO2 (includes O2 competition)
Ci_C3 = 0.7 * CO2_atm  # typical Ci/Ca = 0.7 for C3
Rd_25 = 1.2e-6  # dark respiration at 25C
Rd = arrhenius(T_K, Rd_25, 46390)

A_C3_gross = Vcmax * (Ci_C3 - Gamma_star) / (Ci_C3 + Km_eff * (1 + O2_conc/(Km_eff * 2)))
A_C3_net = A_C3_gross - Rd
A_C3_net = np.clip(A_C3_net * 1e6, -5, 50)  # umol/m2/s

# C4 photosynthesis: PEP carboxylase CO2 pump raises bundle sheath CO2 ~10x
# Effective [CO2] in bundle sheath: ~1500 ubar vs ~280 ubar mesophyll
CO2_bs = 1500e-6  # bundle sheath CO2 concentration
Ci_C4_bs = CO2_bs
# PEPC has low Km for HCO3- (3-10 uM) and no O2 competition
Vcmax25_C4 = 40e-6   # lower Vcmax in bundle sheath C4
Vcmax_C4 = peaked(T_K, Vcmax25_C4, Ea_Vcmax, S_J, H_J)
A_C4_gross = Vcmax_C4 * (Ci_C4_bs - Gamma_star) / (Ci_C4_bs + Km_eff * 0.3)
# C4 has additional ATP cost for CO2 pump: ~2 ATP per CO2 pumped
# At high T, C4 advantage increases (more photorespiration in C3)
Rd_C4 = arrhenius(T_K, Rd_25 * 0.7, 46390)
A_C4_net = (A_C4_gross - Rd_C4) * 1e6
A_C4_net = np.clip(A_C4_net, -5, 60)

# CAM: daytime carbon gain depends on stored malic acid from night fixation
# Maximum photosynthesis limited by malate pool; temperature optimum ~28-35C
# Simplified: thermal bell curve shifted high
CAM_opt_T = 30  # optimal temperature
CAM_width = 8
A_CAM = 15 * np.exp(-0.5 * ((T - CAM_opt_T) / CAM_width)**2)
A_CAM = np.clip(A_CAM, 0, 20)

# CO2 compensation point comparison
Gamma_C3 = Gamma_star * 1e6  # umol/mol
Gamma_C4 = 2 * np.ones_like(T)  # ~2 ppm for C4 (very low due to CO2 pump)

# Quantum yield vs temperature
phi_C3 = 0.093 - 0.0014 * T  # decreases with T due to photorespiration
phi_C4 = 0.065 * np.ones_like(T)  # relatively temperature insensitive
phi_C3 = np.clip(phi_C3, 0, 0.1)

fig, axes = plt.subplots(2, 2, figsize=(13, 9))
fig.patch.set_facecolor('#0f172a')
for ax in axes.flat:
    ax.set_facecolor('#1e293b')
    ax.tick_params(colors='#94a3b8')
    ax.spines['bottom'].set_color('#475569')
    ax.spines['left'].set_color('#475569')
    ax.spines['top'].set_visible(False)
    ax.spines['right'].set_visible(False)

# Plot 1: Net photosynthesis vs temperature
axes[0, 0].plot(T, A_C3_net, color='#22c55e', linewidth=2.5, label='C3 (wheat, rice)')
axes[0, 0].plot(T, A_C4_net, color='#f59e0b', linewidth=2.5, label='C4 (maize, sugarcane)')
axes[0, 0].plot(T, A_CAM, color='#a78bfa', linewidth=2.5, label='CAM (cactus, agave)')
axes[0, 0].axhline(y=0, color='#475569', linestyle='-', alpha=0.5, linewidth=1)
axes[0, 0].set_xlabel('Temperature (degC)', color='#94a3b8', fontsize=9)
axes[0, 0].set_ylabel('Net Photosynthesis (umol CO2/m2/s)', color='#94a3b8', fontsize=9)
axes[0, 0].set_title('Net Photosynthesis vs Temperature', color='#e2e8f0', fontsize=10)
axes[0, 0].legend(fontsize=8, facecolor='#1e293b', edgecolor='#475569', labelcolor='#e2e8f0')

# Plot 2: CO2 compensation point
axes[0, 1].plot(T, Gamma_C3, color='#22c55e', linewidth=2.5, label='C3 (rises steeply with T)')
axes[0, 1].plot(T, Gamma_C4, color='#f59e0b', linewidth=2.5, label='C4 (~2 ppm, insensitive)')
axes[0, 1].set_xlabel('Temperature (degC)', color='#94a3b8', fontsize=9)
axes[0, 1].set_ylabel('CO2 compensation point (ppm)', color='#94a3b8', fontsize=9)
axes[0, 1].set_title('CO2 Compensation Point vs Temperature', color='#e2e8f0', fontsize=10)
axes[0, 1].legend(fontsize=8, facecolor='#1e293b', edgecolor='#475569', labelcolor='#e2e8f0')
axes[0, 1].annotate('Photorespiration
increases rapidly
in C3', xy=(38, Gamma_C3[np.argmin(np.abs(T-38))]),
                     xytext=(30, 70), color='#22c55e', fontsize=7,
                     arrowprops=dict(arrowstyle='->', color='#22c55e', lw=0.8))

# Plot 3: Quantum yield vs temperature
axes[1, 0].plot(T, phi_C3 * 1000, color='#22c55e', linewidth=2.5, label='C3 (decreases with T)')
axes[1, 0].plot(T, phi_C4 * 1000, color='#f59e0b', linewidth=2.5, label='C4 (stable with T)')
axes[1, 0].set_xlabel('Temperature (degC)', color='#94a3b8', fontsize=9)
axes[1, 0].set_ylabel('Quantum yield (mmol CO2/mol photons)', color='#94a3b8', fontsize=9)
axes[1, 0].set_title('Quantum Yield vs Temperature', color='#e2e8f0', fontsize=10)
axes[1, 0].legend(fontsize=8, facecolor='#1e293b', edgecolor='#475569', labelcolor='#e2e8f0')
axes[1, 0].axvline(x=25, color='#475569', linestyle=':', alpha=0.7)
axes[1, 0].text(26, 88, 'C3 > C4
at 25C', color='#94a3b8', fontsize=7)

# Plot 4: C3 vs C4 crossover and advantage
diff = A_C4_net - A_C3_net
crossover_idx = np.argmin(np.abs(diff))
axes[1, 1].plot(T, diff, color='#a3e635', linewidth=2.5)
axes[1, 1].fill_between(T, diff, where=(diff >= 0), alpha=0.2, color='#f59e0b', label='C4 advantage')
axes[1, 1].fill_between(T, diff, where=(diff < 0), alpha=0.2, color='#22c55e', label='C3 advantage')
axes[1, 1].axhline(y=0, color='#475569', linestyle='-', alpha=0.7)
axes[1, 1].axvline(x=T[crossover_idx], color='#ec4899', linestyle=':', linewidth=1.5, label=f'Crossover ~{round(T[crossover_idx],1)}C')
axes[1, 1].set_xlabel('Temperature (degC)', color='#94a3b8', fontsize=9)
axes[1, 1].set_ylabel('C4 - C3 net photosynthesis (umol/m2/s)', color='#94a3b8', fontsize=9)
axes[1, 1].set_title('C4 vs C3 Advantage by Temperature', color='#e2e8f0', fontsize=10)
axes[1, 1].legend(fontsize=8, facecolor='#1e293b', edgecolor='#475569', labelcolor='#e2e8f0')

fig.suptitle('C3 vs C4 vs CAM: Photosynthesis, Compensation Points & Temperature Responses',
             color='#e2e8f0', fontsize=12, fontweight='bold')
plt.tight_layout()
plt.savefig('output.png', dpi=110, bbox_inches='tight',
            facecolor='#0f172a', edgecolor='none')
print("C3-C4 crossover temperature:", round(float(T[crossover_idx]), 1), "degC")
print("C4 advantage at 38C:", round(float(diff[np.argmin(np.abs(T-38))]), 1), "umol/m2/s")
print("C3 CO2 compensation at 25C:", round(float(Gamma_C3[np.argmin(np.abs(T-25))]), 1), "ppm")
print("C3 CO2 compensation at 40C:", round(float(Gamma_C3[np.argmin(np.abs(T-40))]), 1), "ppm")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

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