Module 4: Climate-Dependent Biochemistry

Ecological Biochemistry & Biodiversity

1. C3/C4/CAM Photosynthesis Distribution

The three photosynthetic pathways represent evolutionary solutions to the fundamental problem of carbon fixation in different climatic regimes. Their global distribution is governed by temperature, water availability, and atmospheric CO\(_2\) concentration.

C3 Photosynthesis — The Ancestral Pathway

Approximately 85% of plant species use C3 photosynthesis, where CO\(_2\) is directly fixed by RuBisCO into a 3-carbon compound (3-phosphoglycerate). The fundamental limitation is RuBisCO's oxygenase activity — it cannot perfectly distinguish CO\(_2\) from O\(_2\):

Carboxylation (productive):

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

Oxygenation (wasteful — photorespiration):

\[ \text{RuBP} + \text{O}_2 \xrightarrow{\text{RuBisCO}} \text{3-PGA} + \text{2-PG} \quad (\text{costs ATP, releases CO}_2) \]

The ratio of carboxylation to oxygenation:

\[ \frac{v_c}{v_o} = S_{\text{C/O}} \cdot \frac{[\text{CO}_2]}{[\text{O}_2]} \]

where \(S_{\text{C/O}} \approx 80\text{-}100\) is the specificity factor

Deriving Photorespiration Rate vs Temperature

Photorespiration increases with temperature because: (1) the solubility of CO\(_2\) decreases faster than O\(_2\) with temperature, and (2) \(S_{\text{C/O}}\) decreases at higher temperatures.

The CO\(_2\) compensation point (where photosynthesis = photorespiration):

\[ \Gamma^* = \frac{[\text{O}_2]}{2 \cdot S_{\text{C/O}}} \]

Temperature dependence of \(\Gamma^*\):

\[ \Gamma^*(T) = \Gamma^*_{25} \cdot \exp\left(\frac{E_\Gamma}{R}\left(\frac{1}{298} - \frac{1}{T}\right)\right) \]

where \(\Gamma^*_{25} \approx 42.75\) \(\mu\)mol/mol and \(E_\Gamma \approx 37,830\) J/mol.

At 25\(°\)C, \(\Gamma^* \approx 43\) ppm. At 35\(°\)C, it rises to ~72 ppm. This means photorespiration consumes ~25% of fixed carbon at 25\(°\)C but ~40% at 35\(°\)C.

C4 Photosynthesis — The CO\(_2\) Pump

C4 plants (maize, sugarcane, tropical grasses — ~3% of species but ~25% of terrestrial photosynthesis) evolved a biochemical CO\(_2\)-concentrating mechanism:

Mesophyll cells: PEP carboxylase (\(K_m^{\text{CO}_2} \approx 5 \mu M\), no O\(_2\) affinity) fixes CO\(_2\) into oxaloacetate (4C)
Transport: C4 acid (malate or aspartate) moves to bundle sheath cells via plasmodesmata
Bundle sheath: CO\(_2\) released (decarboxylation), concentrating it to ~2000 ppm around RuBisCO
Result: Photorespiration virtually eliminated; 2 extra ATP per CO\(_2\) fixed

The C4 energy trade-off:

\[ \underbrace{3 \text{ ATP} + 2 \text{ NADPH}}_{\text{C3 per CO}_2} \quad \text{vs} \quad \underbrace{5 \text{ ATP} + 2 \text{ NADPH}}_{\text{C4 per CO}_2} \]

C4 costs 2 extra ATP but saves the ~30% carbon lost to photorespiration in hot conditions

CAM Photosynthesis — Temporal Separation

Crassulacean Acid Metabolism (succulents, cacti, pineapple — ~6% of species) temporally separates CO\(_2\) fixation from the Calvin cycle:

Night: Stomata open (cooler, less water loss). PEP carboxylase fixes CO\(_2\) into malate, stored in vacuoles (pH drops from ~5.5 to ~3.5)
Day: Stomata closed (conserving water). Malate decarboxylated, releasing CO\(_2\) for Calvin cycle behind closed stomata

Why C4 dominates hot, dry grasslands: At temperatures above ~30\(°\)C and current CO\(_2\) levels, C4 plants fix more carbon per unit water transpired (higher water-use efficiency) due to eliminated photorespiration and faster carbon gain allowing shorter stomatal opening periods. However, rising CO\(_2\) shifts the crossover temperature upward, potentially favoring C3 expansion.

2. Temperature-Enzyme Kinetics

The relationship between temperature and enzyme activity is captured by the ecological rule of thumb \(Q_{10} \approx 2\): for every 10\(°\)C increase in temperature, reaction rates approximately double. However, this simple relationship breaks down at high temperatures due to protein denaturation.

Arrhenius in Ecology

The basic Arrhenius equation:

\[ k(T) = A \cdot e^{-E_a / RT} \]

The Q\(_{10}\) relationship follows directly:

\[ Q_{10} = \frac{k(T+10)}{k(T)} = \exp\left(\frac{10 E_a}{R T(T+10)}\right) \]

For typical biological activation energies (\(E_a \approx 50\text{-}70\) kJ/mol) and temperatures near 20\(°\)C, \(Q_{10} \approx 2.0\text{-}2.5\).

Note: \(Q_{10}\) is not truly constant — it varies with temperature. At very low temperatures,\(Q_{10}\) is higher; at high temperatures, it's lower. This is because the Arrhenius equation predicts an exponential (not linear) temperature response.

Sharpe-Schoolfield Model: The Complete Thermal Performance Curve

The Sharpe-Schoolfield model extends the Arrhenius equation to include high-temperature enzyme deactivation (denaturation), producing the characteristic asymmetric bell-shaped thermal performance curve:

\[ k(T) = \frac{k_{\text{ref}} \cdot \exp\!\left(\frac{E_a}{R}\left(\frac{1}{T_{\text{ref}}} - \frac{1}{T}\right)\right)}{1 + \exp\!\left(\frac{E_d}{R}\left(\frac{1}{T_d} - \frac{1}{T}\right)\right)} \]

Parameter definitions:

\(k_{\text{ref}}\) — rate constant at reference temperature \(T_{\text{ref}}\)
\(E_a\) — activation energy (J/mol), determines the rising phase slope (~50-70 kJ/mol for most enzymes)
\(E_d\) — deactivation energy (J/mol), determines how sharply performance drops above \(T_{\text{opt}}\) (~200-300 kJ/mol, reflecting cooperative protein unfolding)
\(T_d\) — temperature of half-deactivation (K), where 50% of enzymes are denatured

Deriving \(T_{\text{opt}}\) — set \(dk/dT = 0\):

\[ T_{\text{opt}} = \frac{E_d \cdot T_d}{E_d + R \cdot T_d \cdot \ln\!\left(\frac{E_d}{E_a} - 1\right)} \]

Note that \(T_{\text{opt}} < T_d\) always — the optimum occurs before half the enzymes denature, because the denaturation effect begins to reduce the rate before the midpoint is reached.

Why Tropical Species Have Narrow Thermal Windows

The thermal safety margin (TSM = \(T_{\text{opt}} - T_{\text{habitat}}\)) is much smaller for tropical ectotherms (~2-5\(°\)C) than for temperate ones (~10-15\(°\)C). This is because:

Tropical organisms evolved under stable, warm temperatures and their enzymes are already optimized near the upper thermal limit
The ratio \(E_d/E_a\) tends to be lower in tropical species — their enzymes denature more sharply
The thermal performance curve becomes narrower (higher \(E_d\)) when \(T_{\text{opt}}\) is already high, because protein stability decreases non-linearly

This makes tropical species disproportionately vulnerable to warming: even a 2\(°\)C increase can push them past their thermal optimum, while temperate species have much more headroom.

3. Cryoprotectants & Antifreeze Proteins

Organisms in cold environments have evolved remarkable biochemical strategies to survive sub-zero temperatures. These strategies fall into two categories: freeze avoidance(preventing ice formation) and freeze tolerance (surviving controlled extracellular ice formation).

Case Studies in Cryoprotection

Wood Frog (Rana sylvatica)

Plasma glucose surges from ~5 mM to ~300 mM within hours of freezing onset. Glucose acts as an intracellular cryoprotectant, preventing cell shrinkage as extracellular water freezes. Up to 65% of body water can freeze — the frog's heart stops, but cells survive intact.

Antarctic Fish (AFGP)

Notothenioid fishes produce antifreeze glycoproteins (AFGPs) — repeating Ala-Ala-Thr units with disaccharide side chains. These bind to ice crystal surfaces via hydrogen bonding, preventing growth through the Kelvin effect (adsorption-inhibition mechanism). AFGPs lower the freezing point by ~1.5\(°\)C without significantly affecting melting point — creating a thermal hysteresis.

Insect Trehalose

Many overwintering insects accumulate trehalose (\(\alpha\)-D-glucopyranosyl-\(\alpha\)-D-glucopyranoside) to ~0.5 M. Trehalose is uniquely effective because it forms a glassy (vitrified) state rather than crystallizing, stabilizing membranes and proteins in a state of suspended animation.

Colligative Freezing Point Depression

The simplest cryoprotection mechanism is colligative freezing point depression — adding solutes lowers the freezing point regardless of solute identity:

\[ \Delta T_f = K_f \cdot m \cdot i \]

\(K_f = 1.86\) \(°\text{C}\cdot\text{kg/mol}\) for water,\(m\) = molality, \(i\) = van't Hoff factor

Derivation from chemical potential:

At equilibrium, the chemical potential of liquid water equals that of ice:

\[ \mu_{\text{liquid}}^* + RT \ln a_w = \mu_{\text{ice}}^* \]

For an ideal dilute solution (\(\ln a_w \approx -x_s \approx -\frac{n_s}{n_w}\)):

\[ \Delta T_f = \frac{R T_f^{*2} M_w}{\Delta H_{\text{fus}}} \cdot m = K_f \cdot m \]

where \(T_f^* = 273.15\) K, \(M_w = 0.018\) kg/mol, and\(\Delta H_{\text{fus}} = 6.01\) kJ/mol, giving\(K_f = \frac{(8.314)(273.15)^2(0.018)}{6010} = 1.86\) \(°\text{C}\cdot\text{kg/mol}\).

Ice Recrystallization Inhibition (IRI)

Antifreeze proteins work through a fundamentally different mechanism than colligative depression — they are kinetic, not thermodynamic, antifreezes:

Adsorption-inhibition mechanism:

AFP/AFGP binds irreversibly to specific ice crystal faces via hydrogen bonding and van der Waals interactions
Ice growth between adsorbed AFPs creates convex ice fronts (the Kelvin/Gibbs-Thomson effect)
Growth of convex surfaces requires greater supercooling:\[ \Delta T_{\text{Kelvin}} = \frac{2 \gamma_{sl} T_f}{\Delta H_{\text{fus}} \rho_s \cdot r} \]where \(r\) is the radius of curvature between adsorbed AFPs
This creates a thermal hysteresis gap: the freezing point is lowered while the melting point is unchanged

Typical thermal hysteresis values: fish AFGPs ~1.0-1.5\(°\)C, insect AFPs ~3-6\(°\)C (insect AFPs are “hyperactive”, binding to multiple ice planes simultaneously). The combination of colligative cryoprotectants (glycerol/glucose) and AFPs allows some organisms to survive temperatures below \(-40°\)C.

4. Heat Shock Proteins (HSPs)

Heat shock proteins are molecular chaperones that stabilize and refold denatured proteins under thermal stress. They represent the cell's primary defense against heat damage and are among the most conserved proteins across all domains of life.

HSP70 and HSP90 as Molecular Chaperones

HSP70 (70 kDa) binds exposed hydrophobic patches on partially unfolded proteins, preventing aggregation and assisting refolding through ATP-dependent cycles. HSP90 (90 kDa) specifically stabilizes signaling proteins (kinases, transcription factors) — it is constitutively expressed at 1-2% of total cellular protein and increases 2-3 fold under stress.

The HSP70 chaperone cycle (simplified):

Substrate (unfolded protein) binds HSP70 in the ATP-bound open conformation
ATP hydrolysis triggers lid closure, trapping the substrate
Nucleotide exchange (ADP \(\rightarrow\) ATP) opens the lid, releasing the substrate
If properly refolded, the protein is released. If not, another cycle begins
Irreparably damaged proteins are directed to proteasomal degradation

Protein Unfolding Equilibrium

The thermodynamic basis of thermal denaturation can be derived from protein folding energetics:

The two-state unfolding equilibrium:

\[ \text{N (native)} \rightleftharpoons \text{U (unfolded)} \]

\[ K_{\text{unfold}} = \frac{[\text{U}]}{[\text{N}]} = \exp\!\left(-\frac{\Delta G_{\text{unfold}}}{RT}\right) \]

The free energy of unfolding depends on temperature through the Gibbs-Helmholtz equation:

\[ \Delta G_{\text{unfold}}(T) = \Delta H_m\!\left(1 - \frac{T}{T_m}\right) - \Delta C_p\!\left[(T_m - T) + T \ln\!\left(\frac{T}{T_m}\right)\right] \]

where \(T_m\) is the melting temperature (where \(\Delta G = 0\) and\(K_{\text{unfold}} = 1\)), \(\Delta H_m\) is the enthalpy of unfolding at\(T_m\), and \(\Delta C_p\) is the heat capacity change upon unfolding.

Upper Thermal Limit: When Unfolding Exceeds Refolding

The organism's critical thermal maximum (\(CT_{\max}\)) corresponds to the temperature where the rate of protein unfolding exceeds the combined rate of spontaneous refolding and chaperone-assisted refolding:

\[ \text{At } CT_{\max}: \quad k_{\text{unfold}}(T) \cdot [\text{N}] > k_{\text{refold}}(T) \cdot [\text{U}] + k_{\text{HSP}} \cdot [\text{HSP}] \cdot [\text{U}] \]

This simplifies to the condition:

\[ K_{\text{unfold}} > 1 + \frac{k_{\text{HSP}} \cdot [\text{HSP}]}{k_{\text{refold}}} \]

Without HSPs (\([\text{HSP}] = 0\)), the thermal limit occurs at \(K_{\text{unfold}} > 1\), i.e., at the protein melting temperature \(T_m\). HSPs effectively raise the thermal limit by increasing the denominator, shifting \(CT_{\max}\) above \(T_m\). Organisms with higher HSP expression capacity can tolerate higher temperatures.

Typical protein thermal parameters:

Organism	\(T_m\) (key enzymes)	\(CT_{\max}\)	HSP contribution
Antarctic fish	~5-10\(°\)C	~4-6\(°\)C	Minimal (lost HSP response)
Temperate fish	~40\(°\)C	~30-36\(°\)C	+2-4\(°\)C
Desert lizard	~55\(°\)C	~45-50\(°\)C	+3-5\(°\)C

5. C3/C4/CAM Distribution & Thermal Performance

The following diagram shows the global distribution of photosynthetic types along temperature and precipitation axes, and the characteristic shape of thermal performance curves:

6. Computational Simulations

The following simulations model: (1) C3 vs C4 photosynthesis rates across temperature and CO\(_2\)levels; (2) Sharpe-Schoolfield thermal performance curves for organisms with different thermal niches; (3) freezing point depression from various cryoprotectants; and (4) the C3/C4 crossover temperature as atmospheric CO\(_2\) changes.

Python

script.py222 lines

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

R = 8.314  # J/(mol·K)

# ══════════════════════════════════════════════════════════════════════
# Panel 1: C3 vs C4 Photosynthesis — Net Assimilation vs Temperature
# ══════════════════════════════════════════════════════════════════════
T_leaf = np.linspace(5, 50, 200)  # leaf temperature (°C)

# C3 photosynthesis model (simplified Farquhar)
def c3_assimilation(T, CO2=400):
    """Net CO2 assimilation for C3 plants (umol/m2/s)"""
    Vc_max25 = 80   # max carboxylation at 25°C
    # Temperature dependence of Vc_max
    Vc_max = Vc_max25 * np.exp(0.088 * (T - 25)) / (1 + np.exp(0.29 * (T - 41)))
    # Photorespiration increases with temperature
    Gamma_star = 42.75 * np.exp(0.0609 * (T - 25))  # CO2 compensation point
    # Net assimilation
    Ci = CO2 * 0.7  # intercellular CO2
    A = Vc_max * (Ci - Gamma_star) / (Ci + 404 * (1 + 248/Gamma_star * 0.21))
    Rd = 0.015 * Vc_max  # dark respiration
    return np.maximum(A - Rd, -2)

# C4 photosynthesis model
def c4_assimilation(T, CO2=400):
    """Net CO2 assimilation for C4 plants (umol/m2/s)"""
    Vp_max25 = 120  # max PEP carboxylation at 25°C
    Vp_max = Vp_max25 * np.exp(0.073 * (T - 25)) / (1 + np.exp(0.35 * (T - 45)))
    # C4 plants suppress photorespiration via CO2 concentrating
    A = Vp_max * 0.75
    Rd = 0.02 * Vp_max
    return np.maximum(A - Rd, -2)

# CAM photosynthesis (simplified)
def cam_assimilation(T, CO2=400):
    """Net CO2 assimilation for CAM plants (umol/m2/s)"""
    # CAM is more conservative, peak at moderate T
    A_max = 15
    return A_max * np.exp(-((T - 30)/10)**2) * (1 - 0.3 * np.exp(-((T - 30)/15)**2))

A_c3_400 = c3_assimilation(T_leaf, 400)
A_c3_800 = c3_assimilation(T_leaf, 800)
A_c4_400 = c4_assimilation(T_leaf, 400)
A_c4_800 = c4_assimilation(T_leaf, 800)
A_cam = cam_assimilation(T_leaf)

# ══════════════════════════════════════════════════════════════════════
# Panel 2: Thermal Performance Curves (Sharpe-Schoolfield)
# ══════════════════════════════════════════════════════════════════════
def sharpe_schoolfield(T_C, k_ref, Ea, Ed, Td, T_ref=25):
    """
    Sharpe-Schoolfield thermal performance model
    T_C: temperature in Celsius
    k_ref: rate at reference temperature
    Ea: activation energy (J/mol)
    Ed: deactivation energy (J/mol)
    Td: temperature of half-deactivation (K)
    """
    T = T_C + 273.15
    T_r = T_ref + 273.15
    numerator = k_ref * np.exp(Ea / R * (1/T_r - 1/T))
    denominator = 1 + np.exp(Ed / R * (1/Td - 1/T))
    return numerator / denominator

T_range = np.linspace(0, 55, 300)

# Different organisms with different thermal niches
organisms = {
    'Arctic fish\n(Topt≈10°C)': {'k_ref': 1.0, 'Ea': 50000, 'Ed': 200000, 'Td': 288},
    'Temperate insect\n(Topt≈25°C)': {'k_ref': 1.0, 'Ea': 60000, 'Ed': 200000, 'Td': 303},
    'Tropical lizard\n(Topt≈35°C)': {'k_ref': 1.0, 'Ea': 65000, 'Ed': 250000, 'Td': 313},
    'Thermophile bacterium\n(Topt≈55°C)': {'k_ref': 0.8, 'Ea': 70000, 'Ed': 300000, 'Td': 338},
}

colors_org = ['#60a5fa', '#2dd4bf', '#fbbf24', '#f87171']

# ══════════════════════════════════════════════════════════════════════
# Panel 3: Freezing Point Depression — Cryoprotectants
# ══════════════════════════════════════════════════════════════════════
# ΔTf = Kf · m · i
Kf_water = 1.86  # °C·kg/mol (cryoscopic constant for water)

molality = np.linspace(0, 3, 200)  # mol/kg solvent

cryoprotectants = {
    'Glucose (i=1)': {'i': 1, 'color': '#2dd4bf', 'conc_bio': 0.3},  # wood frog: 300 mM
    'NaCl (i=2)': {'i': 2, 'color': '#60a5fa', 'conc_bio': 0.15},
    'Glycerol (i=1)': {'i': 1, 'color': '#fbbf24', 'conc_bio': 2.0},  # insects
    'Trehalose (i=1)': {'i': 1, 'color': '#a78bfa', 'conc_bio': 0.5},  # insects
    'CaCl₂ (i=3)': {'i': 3, 'color': '#f87171', 'conc_bio': 0.1},
}

# ══════════════════════════════════════════════════════════════════════
# Panel 4: C3/C4 Crossover Temperature at Different CO2 Levels
# ══════════════════════════════════════════════════════════════════════
CO2_levels = np.linspace(200, 1000, 50)
crossover_temps = []

for co2 in CO2_levels:
    A3 = c3_assimilation(T_leaf, co2)
    A4 = c4_assimilation(T_leaf, co2)
    diff = A4 - A3
    # Find where C4 advantage begins (crossover)
    sign_changes = np.where(np.diff(np.sign(diff)))[0]
    if len(sign_changes) > 0:
        crossover_temps.append(T_leaf[sign_changes[0]])
    else:
        crossover_temps.append(np.nan)

crossover_temps = np.array(crossover_temps)

# ══════════════════════════════════════════════════════════════════════
# Plotting
# ══════════════════════════════════════════════════════════════════════
fig, axes = plt.subplots(2, 2, figsize=(15, 12))
fig.patch.set_facecolor('#0a0a1a')

# Plot 1: C3 vs C4 vs CAM
ax1 = axes[0, 0]
ax1.plot(T_leaf, A_c3_400, color='#2dd4bf', linewidth=2.5, label='C3 (400 ppm)')
ax1.plot(T_leaf, A_c3_800, color='#2dd4bf', linewidth=2, linestyle='--', label='C3 (800 ppm)')
ax1.plot(T_leaf, A_c4_400, color='#f87171', linewidth=2.5, label='C4 (400 ppm)')
ax1.plot(T_leaf, A_c4_800, color='#f87171', linewidth=2, linestyle='--', label='C4 (800 ppm)')
ax1.plot(T_leaf, A_cam, color='#fbbf24', linewidth=2, label='CAM')
ax1.axhline(0, color='gray', linewidth=0.5, alpha=0.5)
ax1.fill_between(T_leaf, A_c3_400, A_c4_400,
                 where=A_c4_400 > A_c3_400, alpha=0.1, color='#f87171', label='C4 advantage zone')
ax1.set_xlabel('Leaf Temperature (°C)', color='white', fontsize=11)
ax1.set_ylabel('Net CO₂ Assimilation (μmol/m²/s)', color='white', fontsize=11)
ax1.set_title('C3 vs C4 vs CAM Photosynthesis\nvs Temperature & CO₂', color='white', fontsize=12, fontweight='bold')
ax1.legend(fontsize=8, facecolor='#1a1a2e', edgecolor='#2dd4bf', labelcolor='white', loc='upper left')
ax1.set_facecolor('#0a0a1a')
ax1.tick_params(colors='white')
ax1.grid(True, alpha=0.15, color='#2dd4bf')
for sp in ax1.spines.values(): sp.set_color('#2dd4bf')

# Plot 2: Thermal performance curves
ax2 = axes[0, 1]
for (name, params), color in zip(organisms.items(), colors_org):
    k = sharpe_schoolfield(T_range, **params)
    k_norm = k / np.nanmax(k)
    ax2.plot(T_range, k_norm, color=color, linewidth=2.5, label=name)
ax2.set_xlabel('Temperature (°C)', color='white', fontsize=11)
ax2.set_ylabel('Relative Performance (k/k_max)', color='white', fontsize=11)
ax2.set_title('Sharpe-Schoolfield Thermal Performance Curves\nActivation + Deactivation', color='white', fontsize=12, fontweight='bold')
ax2.legend(fontsize=8, facecolor='#1a1a2e', edgecolor='#2dd4bf', labelcolor='white')
ax2.set_facecolor('#0a0a1a')
ax2.tick_params(colors='white')
ax2.grid(True, alpha=0.15, color='#2dd4bf')
for sp in ax2.spines.values(): sp.set_color('#2dd4bf')
ax2.set_ylim(-0.05, 1.15)

# Plot 3: Freezing point depression
ax3 = axes[1, 0]
for name, props in cryoprotectants.items():
    delta_T = Kf_water * molality * props['i']
    ax3.plot(molality, -delta_T, color=props['color'], linewidth=2.5, label=name)
    # Mark biological concentration
    bio_dT = -Kf_water * props['conc_bio'] * props['i']
    ax3.plot(props['conc_bio'], bio_dT, 'o', color=props['color'], markersize=10,
             markeredgecolor='white', markeredgewidth=1.5, zorder=5)

ax3.axhline(0, color='gray', linewidth=0.5)
ax3.axhline(-1.86, color='gray', linewidth=0.5, linestyle=':', alpha=0.5)
ax3.text(2.5, -1.7, '1 mol/kg limit', color='gray', fontsize=9)
ax3.set_xlabel('Molality (mol solute / kg water)', color='white', fontsize=11)
ax3.set_ylabel('Freezing Point (°C)', color='white', fontsize=11)
ax3.set_title('Colligative Freezing Point Depression\n(dots = biological concentrations)', color='white', fontsize=12, fontweight='bold')
ax3.legend(fontsize=8, facecolor='#1a1a2e', edgecolor='#2dd4bf', labelcolor='white')
ax3.set_facecolor('#0a0a1a')
ax3.tick_params(colors='white')
ax3.grid(True, alpha=0.15, color='#2dd4bf')
for sp in ax3.spines.values(): sp.set_color('#2dd4bf')

# Plot 4: C3/C4 crossover temperature vs CO2
ax4 = axes[1, 1]
ax4.plot(CO2_levels, crossover_temps, color='#2dd4bf', linewidth=3)
ax4.fill_between(CO2_levels, crossover_temps, 55, alpha=0.15, color='#f87171', label='C4 advantage')
ax4.fill_between(CO2_levels, 0, crossover_temps, alpha=0.15, color='#2dd4bf', label='C3 advantage')
ax4.axvline(280, color='#fbbf24', linewidth=1.5, linestyle='--', alpha=0.8, label='Pre-industrial (280 ppm)')
ax4.axvline(420, color='#f87171', linewidth=1.5, linestyle='--', alpha=0.8, label='Current (420 ppm)')
ax4.set_xlabel('Atmospheric CO₂ (ppm)', color='white', fontsize=11)
ax4.set_ylabel('C3/C4 Crossover Temperature (°C)', color='white', fontsize=11)
ax4.set_title('C3 vs C4 Advantage Boundary\nvs Atmospheric CO₂', color='white', fontsize=12, fontweight='bold')
ax4.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#2dd4bf', labelcolor='white')
ax4.set_facecolor('#0a0a1a')
ax4.tick_params(colors='white')
ax4.grid(True, alpha=0.15, color='#2dd4bf')
for sp in ax4.spines.values(): sp.set_color('#2dd4bf')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0a1a')

# ── Numerical Output ──
print("=== Climate-Dependent Biochemistry Simulations ===\n")

print("--- C3 vs C4 Photosynthesis ---")
opt_c3 = T_leaf[np.argmax(A_c3_400)]
opt_c4 = T_leaf[np.argmax(A_c4_400)]
print(f"C3 optimal temperature (400 ppm): {opt_c3:.1f}°C, Amax = {np.max(A_c3_400):.1f} μmol/m²/s")
print(f"C4 optimal temperature (400 ppm): {opt_c4:.1f}°C, Amax = {np.max(A_c4_400):.1f} μmol/m²/s")
print(f"C3 advantage at doubled CO2: Amax increases from {np.max(A_c3_400):.1f} to {np.max(A_c3_800):.1f} μmol/m²/s")
print(f"C4 shows minimal CO2 response (already CO2-saturated)\n")

print("--- Sharpe-Schoolfield Model ---")
for name, params in organisms.items():
    k = sharpe_schoolfield(T_range, **params)
    Topt = T_range[np.argmax(k)]
    name_clean = name.replace('\n', ' ')
    print(f"{name_clean}: Topt = {Topt:.1f}°C")

print("\n--- Cryoprotectant Freezing Point Depression ---")
for name, props in cryoprotectants.items():
    dT = Kf_water * props['conc_bio'] * props['i']
    print(f"{name}: biological conc = {props['conc_bio']} m → ΔTf = {dT:.2f}°C")
print(f"\nWood frog glucose: 300 mM ≈ 0.3 m → ΔTf = {Kf_water * 0.3:.2f}°C (insufficient alone!)")
print("Actual wood frog freeze tolerance relies on controlled extracellular ice formation,")
print("not complete freezing point depression. Glucose acts as an intracellular cryoprotectant.")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

References

Sage, R.F. (2004). The evolution of C4 photosynthesis. New Phytologist, 161(2), 341-370.
Sharpe, P.J.H. & DeMichele, D.W. (1977). Reaction kinetics of poikilotherm development. Journal of Theoretical Biology, 64(4), 649-670.
Schoolfield, R.M. et al. (1981). Non-linear regression of biological temperature-dependent rate models. Journal of Theoretical Biology, 88(4), 719-731.
Deutsch, C.A. et al. (2008). Impacts of climate warming on terrestrial ectotherms across latitude. Proceedings of the National Academy of Sciences, 105(18), 6668-6672.
Storey, K.B. & Storey, J.M. (2017). Molecular physiology of freeze tolerance in vertebrates. Physiological Reviews, 97(2), 623-665.
Feder, M.E. & Hofmann, G.E. (1999). Heat-shock proteins, molecular chaperones, and the stress response. Annual Review of Physiology, 61(1), 243-282.
Ehleringer, J.R. et al. (1997). C4 photosynthesis, atmospheric CO2 and climate. Oecologia, 112(3), 285-299.
DeVries, A.L. & Wohlschlag, D.E. (1969). Freezing resistance in some Antarctic fishes. Science, 163(3871), 1073-1075.

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