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

7. Photorespiration: The C3 Achilles Heel

Photorespiration is the wasteful oxygenation reaction catalyzed by RuBisCO — the same enzyme responsible for carbon fixation. This “design flaw” evolved when atmospheric O\(_2\) was negligible, but now costs C3 plants approximately 25% of their fixed carbon at 25\(°\)C, rising to 40% or more in hot conditions.

The Oxygenation Reaction

\[ \text{RuBP} + \text{O}_2 \xrightarrow{\text{RuBisCO}} \text{3-PGA} + \text{2-phosphoglycolate} \]

2-phosphoglycolate must be salvaged through the C2 photorespiratory pathway, consuming ATP and releasing CO\(_2\)

The photorespiratory pathway spans three organelles: chloroplast \(\rightarrow\) peroxisome\(\rightarrow\) mitochondrion \(\rightarrow\) peroxisome \(\rightarrow\) chloroplast. For every 2 molecules of 2-phosphoglycolate processed, one CO\(_2\) is released and one NH\(_3\) is produced (requiring re-fixation at additional ATP cost).

Deriving the Oxygenation/Carboxylation Ratio

RuBisCO catalyzes two competing reactions at the same active site. The ratio of oxygenation to carboxylation rates:

\[ \frac{v_o}{v_c} = \frac{V_o / K_o \cdot [\text{O}_2]}{V_c / K_c \cdot [\text{CO}_2]} = \Phi \cdot \frac{[\text{O}_2]}{[\text{CO}_2]} \]

where \(\Phi = \frac{V_o K_c}{V_c K_o}\) is the inverse of the specificity factor\(S_{\text{C/O}}\). For C3 plants, \(S_{\text{C/O}} = 1/\Phi \approx 80\text{-}100\).

At current atmospheric conditions (\([\text{O}_2] = 21\%\), \([\text{CO}_2] = 420\) ppm), and accounting for the Henry's law solubility ratio:

\[ \frac{v_o}{v_c} \approx \frac{1}{85} \times \frac{210{,}000}{420} \approx 0.33 \quad \text{at 25°C} \]

This means approximately one oxygenation for every three carboxylations, wasting ~25% of the carbon fixation effort.

Temperature Dependence: Why C3 Fails in the Tropics

The \(v_o/v_c\) ratio increases with temperature for two reasons:

Solubility effect: CO\(_2\) solubility decreases faster than O\(_2\) solubility with increasing temperature (Henry's law constants have different temperature coefficients)
Kinetic effect: The \(V_o/V_c\) ratio increases with temperature because the oxygenation reaction has a higher activation energy than carboxylation

Combined, the specificity factor \(S_{\text{C/O}}\) decreases approximately 2-fold from 15\(°\)C to 35\(°\)C:

\[ S_{\text{C/O}}(T) \approx S_{\text{C/O}}(25) \cdot \exp\!\left(-\frac{E_{\text{spec}}}{R}\left(\frac{1}{298} - \frac{1}{T}\right)\right) \]

with \(E_{\text{spec}} \approx -24{,}000\) J/mol (negative — specificity decreases with temperature).

The CO\(_2\) Compensation Point \(\Gamma^*\)

\(\Gamma^*\) is the CO\(_2\) concentration at which photosynthesis exactly equals photorespiration (net carbon fixation = 0):

\[ \Gamma^* = \frac{0.5 \cdot [\text{O}_2]}{S_{\text{C/O}}} \]

The factor 0.5 arises because only half the carbon in glycolate is released as CO\(_2\)during photorespiratory recycling. Temperature dependence:

\[ \Gamma^*(T) = 42.75 \cdot \exp\!\left(\frac{37{,}830}{R}\left(\frac{1}{298.15} - \frac{1}{T + 273.15}\right)\right) \quad \mu\text{mol/mol} \]

Temperature	\(\Gamma^*\) (ppm)	Carbon lost to photorespiration
15\(°\)C	~29	~18%
25\(°\)C	~43	~25%
35\(°\)C	~72	~40%
45\(°\)C	~120	~55%

8. Drought Biochemistry: ABA & Osmotic Adjustment

When soil water potential drops below a critical threshold, plants activate a rapid biochemical defense centered on the phytohormone abscisic acid (ABA). This triggers a signaling cascade that closes stomata within minutes, reducing water loss but simultaneously restricting CO\(_2\) entry for photosynthesis.

ABA Signaling Cascade

The ABA signal transduction pathway is one of the best-characterized hormone signaling networks in plants:

Drought perception: Soil drying reduces root water potential (\(\Psi_{\text{soil}} < -1.5\) MPa triggers stress response)
ABA biosynthesis: 9-cis-epoxycarotenoid dioxygenase (NCED) catalyzes the rate-limiting step: cleavage of violaxanthin/neoxanthin to xanthoxin in root plastids. ABA concentration rises 10-50 fold within hours.
PYR/PYL/RCAR receptors: ABA binds to these soluble receptors, creating a complex that inhibits PP2C phosphatases(ABI1, ABI2, HAB1)
SnRK2 activation: With PP2C inhibited, SnRK2 protein kinases are released from repression and auto-phosphorylate
SLAC1 activation: SnRK2 phosphorylates the SLAC1 anion channel in guard cells, opening it. Cl\(^-\) and malate\(^{2-}\) efflux depolarizes the membrane
K\(^+\) efflux & stomatal closure: Depolarization activates outward-rectifying K\(^+\) channels (GORK). K\(^+\) loss reduces guard cell turgor, closing the stomatal pore within 5-15 minutes

Stomatal Conductance Model

The Ball-Berry-Leuning model describes stomatal conductance as a function of environmental variables:

\[ g_s = g_{\max} \cdot f(\text{ABA}) \cdot f(\text{VPD}) \cdot f(\Psi_{\text{leaf}}) \]

where each modifier follows a physiological response function:

\[ f(\text{ABA}) = \frac{1}{1 + [\text{ABA}]/K_{\text{ABA}}} \quad (K_{\text{ABA}} \approx 0.5\text{-}2 \text{ μM}) \]

\[ f(\text{VPD}) = \frac{1}{1 + \text{VPD}/D_0} \quad (D_0 \approx 1\text{-}3 \text{ kPa}) \]

\[ f(\Psi_{\text{leaf}}) = \frac{1}{1 + (\Psi_{\text{leaf}}/\Psi_{50})^n} \quad (\Psi_{50} \approx -1.5 \text{ to } -3 \text{ MPa}) \]

The Ball-Berry formulation couples stomatal conductance to photosynthesis:\(g_s = g_0 + g_1 \cdot A \cdot h_s / c_s\), where \(A\) is assimilation rate,\(h_s\) is relative humidity at the leaf surface, and \(c_s\) is CO\(_2\)concentration at the leaf surface.

Osmolyte Accumulation & Osmotic Adjustment

Plants synthesize compatible solutes (osmolytes) that lower cellular water potential without disrupting protein function, maintaining turgor under drought:

Proline

Accumulates 10-100 fold under drought. Synthesized from glutamate via \(\Delta^1\)-pyrroline-5-carboxylate (P5C). Also acts as a ROS scavenger and protein stabilizer. Concentration can reach 50-100 mM.

Glycine Betaine

A quaternary ammonium compound (N,N,N-trimethylglycine). Synthesized from choline via betaine aldehyde dehydrogenase. Accumulates to 40-400 mM in halophytes and drought-tolerant grasses. Stabilizes PSII under combined heat + drought stress.

Trehalose

A non-reducing disaccharide (\(\alpha\)-D-glucopyranosyl-\(\alpha\)-D-glucopyranoside). Stabilizes membranes and proteins by hydrogen bonding to replace water. “Resurrection plants” (e.g., Selaginella) accumulate trehalose to survive nearly complete desiccation.

Deriving Osmotic Adjustment from the van't Hoff Equation

The osmotic potential (\(\Psi_s\)) generated by solute accumulation follows the van't Hoff equation:

\[ \Psi_s = -iCRT \]

where \(i\) = van't Hoff factor (1 for non-electrolytes like proline),\(C\) = molar concentration, \(R = 8.314\) J/(mol\(\cdot\)K),\(T\) = temperature (K).

Example: proline at 100 mM (0.1 M) at 25\(°\)C:

\[ \Psi_s = -(1)(0.1)(8.314)(298.15) \times 10^{-3} = -0.248 \text{ MPa} \]

Total osmotic adjustment is the sum over all osmolytes:

\[ \Delta\Psi_s = -RT \sum_j i_j C_j \]

Typical osmotic adjustment in crop plants: 0.3-1.0 MPa, achieved by accumulating a cocktail of organic osmolytes plus inorganic ions (K\(^+\), Cl\(^-\)). Turgor is maintained as long as \(\Psi_{\text{turgor}} = \Psi_{\text{total}} - \Psi_s > 0\).

9. Fire Ecology & Biochemistry

Fire has shaped terrestrial ecosystems for at least 420 million years, since the first land plants created sufficient fuel and atmospheric O\(_2\) exceeded ~13%. The biochemistry of fire involves both destructive pyrolysis chemistry and remarkable fire-adaptive traits in plants.

Pyrolysis Chemistry

Plant biomass undergoes thermal decomposition in a predictable sequence of temperatures:

Temperature	Process	Products
100-200\(°\)C	Dehydration	Water vapor, volatilization of terpenes (flammable!)
200-300\(°\)C	Hemicellulose pyrolysis	Furans, acetic acid, CO, CO\(_2\)
~300\(°\)C	Cellulose pyrolysis	Levoglucosan (anhydrosugar marker), tar, CO
~400\(°\)C	Lignin pyrolysis	Aromatic char (biochar), phenols, guaiacol
>500\(°\)C	Complete combustion	CO\(_2\), H\(_2\)O, ash (mineral residue)

Biochar (pyrogenic carbon) is the aromatic, highly condensed carbon residue from incomplete lignin combustion. Its resistance to further decomposition (mean residence time: 100-10,000 years) makes fire-derived char a significant long-term carbon sink — storing ~0.05-0.3 Gt C/yr globally. Terra preta soils in the Amazon demonstrate that biochar improves soil fertility for centuries.

Fire-Adapted Traits

Serotinous Cones

Many pine species (e.g., Pinus banksiana, P. contorta) produce resin-sealed cones that remain closed for years. The resin melts at approximately 50-60\(°\)C, releasing seeds precisely when fire has cleared competitors and created mineral-rich ash beds. This is a bet-hedging strategy — an aerial seed bank triggered by the very disturbance that creates the optimal regeneration niche.

Smoke-Responsive Germination

Over 1,200 plant species require smoke compounds for germination. The active molecule is karrikinolide (KAR\(_1\)) — a butenolide (3-methyl-2H-furo[2,3-c]pyran-2-one) produced from cellulose combustion. KAR\(_1\) is perceived by the KAI2 receptor (a karrikin-insensitive homolog), which triggers germination at concentrations as low as \(10^{-9}\) M. The signaling pathway involves MAX2 and SMAX1 — shared with strigolactone signaling.

Bark as Thermal Insulation

Thick bark is the primary defense mechanism of fire-resistant trees. The thermal insulation provided by bark follows Fourier's law of heat conduction:

\[ \Delta T = \frac{Q \cdot L}{k \cdot A} \]

Temperature difference across bark = heat flux \(\times\) bark thickness / (thermal conductivity \(\times\) area)

Bark thermal conductivity: \(k \approx 0.1\text{-}0.15\) W/(m\(\cdot\)K) — approximately 3\(\times\) lower than wood (\(k \approx 0.3\text{-}0.4\)).

For a surface fire at ~400\(°\)C lasting ~60 seconds, the critical bark thickness to keep the cambium below the lethal temperature of ~60\(°\)C can be estimated from the transient heat equation:

\[ L_{\text{crit}} = 2\sqrt{\alpha \cdot t_{\text{fire}}} \quad \text{where } \alpha = \frac{k}{\rho c_p} \]

With \(\alpha \approx 1.5 \times 10^{-7}\) m\(^2\)/s and \(t_{\text{fire}} = 60\) s:

\[ L_{\text{crit}} = 2\sqrt{1.5 \times 10^{-7} \times 60} \approx 6 \text{ mm} \]

Fire-adapted species like ponderosa pine (Pinus ponderosa) develop bark up to 10-15 cm thick, providing massive safety margins. Tropical thin-barked species (<5 mm) are catastrophically vulnerable to fire introduction — a major concern as fire enters tropical forests through deforestation.

10. Advanced Simulations: Photorespiration, Stomatal Conductance & Fire

The following simulations model: (1) the photorespiration ratio \(v_o/v_c\) as a function of temperature and CO\(_2\) concentration; (2) the Ball-Berry stomatal conductance model showing ABA, VPD, and water potential effects; (3) bark thermal insulation during fire exposure at different thicknesses.

Python

script.py205 lines

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

R = 8.314  # J/(mol·K)

# ══════════════════════════════════════════════════════════════════════
# Panel 1: Photorespiration Ratio vo/vc vs Temperature and CO₂
# ══════════════════════════════════════════════════════════════════════
T_range = np.linspace(10, 45, 200)  # °C

def gamma_star(T_C):
    """CO2 compensation point (umol/mol) as function of temperature"""
    return 42.75 * np.exp(37830 / R * (1/298.15 - 1/(T_C + 273.15)))

def vo_vc_ratio(T_C, CO2_ppm):
    """Ratio of oxygenation to carboxylation"""
    gs = gamma_star(T_C)
    Ci = CO2_ppm * 0.7  # intercellular CO2
    return 2 * gs / Ci

CO2_levels = [280, 420, 560, 800, 1200]
colors_co2 = ['#60a5fa', '#2dd4bf', '#fbbf24', '#f87171', '#a78bfa']

# Also compute carbon lost to photorespiration
def carbon_loss_frac(T_C, CO2_ppm):
    r = vo_vc_ratio(T_C, CO2_ppm)
    return r / (2 + r) * 100  # approximate % carbon lost

# ══════════════════════════════════════════════════════════════════════
# Panel 2: Ball-Berry Stomatal Conductance Model
# ══════════════════════════════════════════════════════════════════════
# gs = g_max * f(ABA) * f(VPD) * f(Psi_leaf)
ABA = np.linspace(0, 10, 200)  # μM
VPD = np.linspace(0, 5, 200)   # kPa
Psi = np.linspace(0, -4, 200)  # MPa

g_max = 0.4  # mol/m²/s
K_ABA = 1.5  # μM
D0 = 1.5     # kPa
Psi50 = -2.0 # MPa
n_psi = 3    # steepness

f_ABA = 1.0 / (1.0 + ABA / K_ABA)
f_VPD = 1.0 / (1.0 + VPD / D0)
f_Psi = 1.0 / (1.0 + (Psi / Psi50) ** n_psi)

# Combined drought scenario: ABA rises, Psi drops
drought_progression = np.linspace(0, 1, 200)  # 0 = well-watered, 1 = severe drought
aba_drought = 0.5 + 9.5 * drought_progression ** 2
psi_drought = -0.5 - 3.0 * drought_progression
vpd_drought = 1.0 + 3.0 * drought_progression

gs_combined = g_max * (1.0 / (1.0 + aba_drought / K_ABA)) * \
              (1.0 / (1.0 + vpd_drought / D0)) * \
              (1.0 / (1.0 + (psi_drought / Psi50) ** n_psi))

# ══════════════════════════════════════════════════════════════════════
# Panel 3: Bark Thermal Insulation During Fire
# ══════════════════════════════════════════════════════════════════════
# Transient heat conduction through bark
# Using simplified solution: T(x,t) = T_surface * erfc(x / (2*sqrt(alpha*t)))
from scipy.special import erfc

bark_thicknesses = [2, 5, 10, 20, 50]  # mm
alpha = 1.5e-7  # thermal diffusivity (m²/s)
T_fire = 400    # °C fire temperature
T_ambient = 25  # °C
T_lethal = 60   # °C cambium death

t_fire = np.linspace(1, 300, 200)  # fire exposure time (seconds)

def cambium_temp(L_mm, t_sec, T_surf=400, T_init=25, alpha=1.5e-7):
    L_m = L_mm / 1000.0
    return T_init + (T_surf - T_init) * erfc(L_m / (2 * np.sqrt(alpha * t_sec)))

# ══════════════════════════════════════════════════════════════════════
# Panel 4: Osmotic Adjustment — van't Hoff equation
# ══════════════════════════════════════════════════════════════════════
conc = np.linspace(0, 0.5, 200)  # mol/L
T_K = 298.15  # 25°C

osmolytes = {
    'Proline (i=1)': {'i': 1, 'color': '#2dd4bf', 'typical': 0.1},
    'Glycine betaine (i=1)': {'i': 1, 'color': '#60a5fa', 'typical': 0.2},
    'Trehalose (i=1)': {'i': 1, 'color': '#fbbf24', 'typical': 0.15},
    'KCl (i=2)': {'i': 2, 'color': '#f87171', 'typical': 0.15},
    'Sucrose (i=1)': {'i': 1, 'color': '#a78bfa', 'typical': 0.3},
}

# Plot 1: Photorespiration ratio
ax1 = axes[0, 0]
for co2, color in zip(CO2_levels, colors_co2):
    ratio = vo_vc_ratio(T_range, co2) * 100
    ax1.plot(T_range, ratio, color=color, linewidth=2.5, label=f'{co2} ppm CO₂')

ax1.axhline(33.3, color='gray', linewidth=0.8, linestyle=':', alpha=0.5)
ax1.text(12, 35, '1 oxygenation per 3 carboxylations', color='gray', fontsize=9)
ax1.set_xlabel('Leaf Temperature (°C)', color='white', fontsize=11)
ax1.set_ylabel('vo/vc × 100 (%)', color='white', fontsize=11)
ax1.set_title('Photorespiration Ratio vs Temperature & CO₂\nΦ·[O₂]/[CO₂] increases with warming', color='white', fontsize=12, fontweight='bold')
ax1.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#2dd4bf', labelcolor='white')
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')
ax1.set_ylim(0, 80)

# Plot 2: Stomatal conductance components
ax2 = axes[0, 1]
ax2.plot(drought_progression * 100, gs_combined / g_max * 100, color='#2dd4bf', linewidth=3, label='Combined gs')
ax2.plot(drought_progression * 100, 1.0/(1.0 + aba_drought/K_ABA) * 100, color='#f87171', linewidth=2, linestyle='--', label='f(ABA)')
ax2.plot(drought_progression * 100, 1.0/(1.0 + vpd_drought/D0) * 100, color='#fbbf24', linewidth=2, linestyle='--', label='f(VPD)')
psi_factor = 1.0/(1.0 + (psi_drought/Psi50)**n_psi)
ax2.plot(drought_progression * 100, psi_factor * 100, color='#60a5fa', linewidth=2, linestyle='--', label='f(Ψ_leaf)')

ax2.set_xlabel('Drought Severity (%)', color='white', fontsize=11)
ax2.set_ylabel('Relative Stomatal Conductance (%)', color='white', fontsize=11)
ax2.set_title('Stomatal Closure During Drought\ngs = g_max · f(ABA) · f(VPD) · f(Ψ)', color='white', fontsize=12, fontweight='bold')
ax2.legend(fontsize=9, 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')

# Plot 3: Bark thermal insulation
ax3 = axes[1, 0]
bark_colors = ['#f87171', '#fbbf24', '#2dd4bf', '#60a5fa', '#a78bfa']
for L, color in zip(bark_thicknesses, bark_colors):
    T_cambium = cambium_temp(L, t_fire)
    ax3.plot(t_fire, T_cambium, color=color, linewidth=2.5, label=f'{L} mm bark')

ax3.axhline(60, color='#f87171', linewidth=2, linestyle='--', alpha=0.7)
ax3.text(200, 65, 'Cambium lethal (60°C)', color='#f87171', fontsize=10)
ax3.set_xlabel('Fire Exposure Time (seconds)', color='white', fontsize=11)
ax3.set_ylabel('Cambium Temperature (°C)', color='white', fontsize=11)
ax3.set_title('Bark Thermal Insulation During Fire\nT_fire = 400°C, α = 1.5×10⁻⁷ m²/s', color='white', fontsize=12, fontweight='bold')
ax3.legend(fontsize=9, 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')
ax3.set_ylim(20, 420)

# Plot 4: Osmotic adjustment
ax4 = axes[1, 1]
for name, props in osmolytes.items():
    psi_s = -props['i'] * conc * R * T_K * 1e-3  # convert to MPa
    ax4.plot(conc * 1000, psi_s, color=props['color'], linewidth=2.5, label=name)
    # Mark typical biological concentration
    psi_bio = -props['i'] * props['typical'] * R * T_K * 1e-3
    ax4.plot(props['typical'] * 1000, psi_bio, 'o', color=props['color'], markersize=10,
             markeredgecolor='white', markeredgewidth=1.5, zorder=5)

ax4.axhline(-1.5, color='gray', linewidth=0.8, linestyle=':', alpha=0.5)
ax4.text(350, -1.4, 'Typical wilting point', color='gray', fontsize=9)
ax4.set_xlabel('Osmolyte Concentration (mM)', color='white', fontsize=11)
ax4.set_ylabel('Osmotic Potential Ψs (MPa)', color='white', fontsize=11)
ax4.set_title('Osmotic Adjustment: van\'t Hoff Equation\nΨs = -iCRT (dots = typical biological conc.)', color='white', fontsize=12, fontweight='bold')
ax4.legend(fontsize=8, 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("=== Advanced Climate-Dependent Biochemistry Simulations ===\n")

print("--- Photorespiration Analysis ---")
for co2 in [280, 420, 800]:
    r25 = vo_vc_ratio(25, co2)
    r35 = vo_vc_ratio(35, co2)
    loss25 = carbon_loss_frac(25, co2)
    loss35 = carbon_loss_frac(35, co2)
    print(f"CO₂ = {co2} ppm: vo/vc at 25°C = {r25:.3f} ({loss25:.1f}% lost), at 35°C = {r35:.3f} ({loss35:.1f}% lost)")
print(f"Γ* at 25°C = {gamma_star(25):.1f} ppm, at 35°C = {gamma_star(35):.1f} ppm\n")

print("--- Stomatal Conductance Model ---")
print(f"Well-watered: gs = {g_max:.2f} mol/m²/s (100%)")
idx_50 = np.argmin(np.abs(gs_combined/g_max - 0.5))
print(f"50% closure at drought severity = {drought_progression[idx_50]*100:.0f}%")
print(f"  ABA = {aba_drought[idx_50]:.1f} μM, Ψ_leaf = {psi_drought[idx_50]:.2f} MPa, VPD = {vpd_drought[idx_50]:.1f} kPa")
print(f"Severe drought: gs = {gs_combined[-1]/g_max*100:.1f}% of maximum\n")

print("--- Bark Thermal Insulation ---")
for L in bark_thicknesses:
    T60 = cambium_temp(L, 60)
    T120 = cambium_temp(L, 120)
    print(f"Bark {L} mm: cambium T at 60s = {T60:.1f}°C, at 120s = {T120:.1f}°C {'(LETHAL)' if T60 > 60 else '(safe)'}")

print("\n--- Osmotic Adjustment ---")
for name, props in osmolytes.items():
    psi_bio = -props['i'] * props['typical'] * R * T_K * 1e-3
    print(f"{name}: {props['typical']*1000:.0f} mM → Ψs = {psi_bio:.3f} MPa")

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.
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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.
Farquhar, G.D. et al. (1980). A biochemical model of photosynthetic CO\(_2\) assimilation in leaves of C3 species. Planta, 149(1), 78-90.
Cutler, S.R. et al. (2010). Abscisic acid: emergence of a core signaling network. Annual Review of Plant Biology, 61, 651-679.
Pausas, J.G. & Keeley, J.E. (2019). Wildfires as an ecosystem service. Frontiers in Ecology and the Environment, 17(5), 289-295.
Flematti, G.R. et al. (2004). A compound from smoke that promotes seed germination. Science, 305(5686), 977.

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