Chapter 1: Water & Mineral Transport

Part I — Energy & Transport

1.1 Water Potential

Water movement in plants is governed by water potential (\(\Psi\)), defined as the chemical potential of water relative to pure water at the same temperature and pressure. Net water movement is always from regions of higher (less negative) to lower (more negative) water potential.

\[\Psi = \Psi_s + \Psi_p + \Psi_g\]

Solute Potential (\(\Psi_s\))

Also called osmotic potential. Always negative or zero. Quantified by the van't Hoff equation:

\(\Psi_s = -iCRT\)

where i = van't Hoff factor, C = molar concentration, R = gas constant, T = temperature (K).

Pressure Potential (\(\Psi_p\))

Turgor pressure in living cells (positive), or tension in xylem (negative, up to −4 MPa in transpiring trees).

Turgor drives cell expansion growth; loss of turgor causes wilting and stomatal closure.

Gravitational Potential (\(\Psi_g\))

Significant only over large height differences:

\(\Psi_g = \rho g h\)

At 100 m height, \(\Psi_g \approx +0.1\) MPa — a minor but real component in tall trees.

A typical transpiring leaf has \(\Psi \approx -1.5\) MPa, while soil water may be \(\Psi \approx -0.03\) MPa, providing a driving gradient of ~1.5 MPa from soil through root, stem, and leaf to the atmosphere (\(\Psi \approx -100\) MPa).

1.2 Osmosis and Aquaporins

Osmosis is the movement of water across a semipermeable membrane from high to low water potential. In plant cells, the tonoplast and plasma membrane are selectively permeable. The osmotic adjustment allows plants to maintain turgor under moderate water stress.

Aquaporins (Water Channel Proteins)

Aquaporins are integral membrane proteins of the Major Intrinsic Protein (MIP) family that dramatically accelerate water transport across membranes. Plants have ~35 aquaporin genes divided into five subfamilies: PIPs (plasma membrane), TIPs (tonoplast), NIPs, SIPs, and XIPs.

Structure:

Six transmembrane helices + two half-helices
NPA motifs form selectivity filter
ar/R constriction excludes ions/protons
Tetrameric assembly in membrane

Regulation:

Phosphorylation (Ser119, Ser274) by CDPK
pH-gating: loop D protonation closes pore
Reactive oxygen species
Mercury (HgCl₂) blocks pore — classic inhibitor

1.3 Transpiration–Cohesion–Tension Theory

Long-distance water transport in xylem is explained by the cohesion–tension theory. Water evaporating from leaf mesophyll cells (transpiration) generates tension (negative pressure) in xylem conduits. The extraordinary cohesive strength of water (~25 MPa) allows this tensile column to be pulled upward.

Three Components:

Transpiration: Evaporation at leaf cell walls → water potential gradient
Cohesion: H-bonding between water molecules → tensile strength
Adhesion: Water–cell wall interactions → capillary rise

Poiseuille Flow in Xylem:

\[J_v = \frac{\pi r^4}{8\eta} \frac{\Delta P}{\Delta x}\]

where r = vessel radius, η = viscosity, ΔP/Δx = pressure gradient. Xylem vessel radius (20–500 μm) strongly controls flux (4th power dependence).

Root pressure (generated by active ion pumping into xylem, creating osmotic water flow) contributes to water rise at night when transpiration ceases — observed as guttation.

1.4 Mineral Ion Uptake: Nernst Equation

Mineral ion transport across membranes is driven by the electrochemical gradient. The Nernst equation predicts the equilibrium potential for an ion at which the electrical driving force exactly balances the concentration gradient:

\[E_N = \frac{RT}{zF}\ln\frac{[X]_o}{[X]_i}\]

where z = ion charge, F = Faraday constant (96,485 C mol⁻¹), [X]_o and [X]_i are outside/inside concentrations. At 25°C: \(E_N = \frac{59.2\text{ mV}}{z}\log\frac{[X]_o}{[X]_i}\)

Ion Transport Systems:

H⁺-ATPase: Primary pump, −120 to −180 mV Em
K⁺ channels (KAT1): Inward-rectifying, stomatal opening
AKT2: Weakly rectifying, phloem loading
NRT1/NPF: Nitrate transporters (symport with H⁺)
AMT1: Ammonium transporters
PHT1: Phosphate transporters

Apoplastic vs Symplastic:

Radial transport in roots occurs via two pathways:

Apoplastic: Through cell walls — blocked at Casparian strip
Symplastic: Through plasmodesmata connections
Casparian strip: Suberin-impregnated endodermis — forces apoplastic ions into symplast for selectivity

Root Cross-Section: Water & Ion Pathways

Simulation: Water Potential Components & Ion Transport

Interactive plots showing water potential gradients across the plant, transpiration vs stomatal conductance, Nernst potentials for major ions, and Boyle–van't Hoff cell volume relationships.

Python

script.py94 lines

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
# output saved as output.png

fig = plt.figure(figsize=(14, 10), facecolor='#0a0f0a')
gs = gridspec.GridSpec(2, 2, figure=fig, hspace=0.45, wspace=0.35)

# Panel 1: Water potential components across root-to-leaf
ax1 = fig.add_subplot(gs[0, 0])
ax1.set_facecolor('#0d1a0d')
positions = ['Soil', 'Root', 'Stem', 'Leaf', 'Air']
psi_total = [0.0, -0.3, -0.6, -1.0, -100.0]
psi_s    = [-0.1, -0.5, -0.8, -1.5, -100.0]
psi_p    = [0.1, 0.2, 0.2, 0.5, 0.0]
x = np.arange(len(positions))
ax1.plot(x, psi_total, 'o-', color='#a3e635', lw=2, label='Total Psi', ms=7)
ax1.plot(x, psi_s,    's--', color='#86efac', lw=1.5, label='Solute Psi_s', ms=6)
ax1.plot(x, psi_p,    '^:', color='#d9f99d', lw=1.5, label='Pressure Psi_p', ms=6)
ax1.set_xticks(x)
ax1.set_xticklabels(positions, color='#a3e635', fontsize=8)
ax1.set_ylabel('Water Potential (MPa)', color='#a3e635', fontsize=9)
ax1.set_title('Water Potential Gradient', color='#d9f99d', fontsize=10)
ax1.tick_params(colors='#a3e635', labelsize=8)
ax1.legend(fontsize=7, labelcolor='#d9f99d', facecolor='#0d1a0d', edgecolor='#4ade80')
ax1.grid(True, alpha=0.2, color='#4ade80')
for spine in ax1.spines.values(): spine.set_edgecolor('#4ade80')

# Panel 2: Transpiration vs stomatal conductance
ax2 = fig.add_subplot(gs[0, 1])
ax2.set_facecolor('#0d1a0d')
gs_val = np.linspace(0, 0.5, 100)
VPD = 2.0  # kPa
transpiration = gs_val * VPD
ax2.plot(gs_val, transpiration, color='#4ade80', lw=2.5)
ax2.fill_between(gs_val, transpiration, alpha=0.2, color='#4ade80')
ax2.set_xlabel('Stomatal Conductance (mol m-2 s-1)', color='#a3e635', fontsize=9)
ax2.set_ylabel('Transpiration (mmol m-2 s-1)', color='#a3e635', fontsize=9)
ax2.set_title('Transpiration vs Stomatal Conductance', color='#d9f99d', fontsize=10)
ax2.tick_params(colors='#a3e635', labelsize=8)
ax2.grid(True, alpha=0.2, color='#4ade80')
for spine in ax2.spines.values(): spine.set_edgecolor('#4ade80')
ax2.text(0.3, 0.3, 'VPD = 2.0 kPa', color='#d9f99d', fontsize=8, transform=ax2.transAxes)

# Panel 3: Nernst potential for common ions
ax3 = fig.add_subplot(gs[1, 0])
ax3.set_facecolor('#0d1a0d')
ions = ['K+', 'Na+', 'Ca2+', 'Cl-', 'NO3-']
z_vals = [1, 1, 2, -1, -1]
c_out  = [1.0, 1.0, 0.5, 2.0, 0.5]  # mM outside
c_in   = [100, 10, 0.001, 20, 5]     # mM inside
R, T, F = 8.314, 298, 96485
E_nernst = []
for z, co, ci in zip(z_vals, c_out, c_in):
    E = (R * T / (z * F)) * np.log(co / ci) * 1000  # mV
    E_nernst.append(E)
colors_bar = ['#4ade80', '#86efac', '#a3e635', '#d9f99d', '#bbf7d0']
bars = ax3.bar(ions, E_nernst, color=colors_bar, edgecolor='#0d1a0d', linewidth=1)
ax3.axhline(-120, color='#f87171', lw=1.5, ls='--', label='Typical Em = -120 mV')
ax3.set_ylabel('Nernst Potential (mV)', color='#a3e635', fontsize=9)
ax3.set_title('Nernst Potentials for Plant Ions', color='#d9f99d', fontsize=10)
ax3.tick_params(colors='#a3e635', labelsize=9)
ax3.legend(fontsize=8, labelcolor='#d9f99d', facecolor='#0d1a0d', edgecolor='#4ade80')
ax3.grid(True, alpha=0.2, color='#4ade80', axis='y')
for spine in ax3.spines.values(): spine.set_edgecolor('#4ade80')

# Panel 4: Osmotic adjustment - cell volume vs external osmolarity
ax4 = fig.add_subplot(gs[1, 1])
ax4.set_facecolor('#0d1a0d')
osm_ext = np.linspace(0.05, 1.0, 200)
# Boyle-van't Hoff: V = b + (pi_i * V_i) / osm_ext
pi_i = 0.5  # MPa internal osmotic pressure
V_i = 1.0   # relative initial volume
b = 0.1     # non-osmotic volume
V = b + (pi_i * V_i) / osm_ext
V = V / V[0]  # normalize
ax4.plot(osm_ext, V, color='#a3e635', lw=2.5)
ax4.fill_between(osm_ext, V, 0, alpha=0.15, color='#a3e635')
ax4.axvline(pi_i, color='#fbbf24', lw=1.5, ls='--', label='Incipient plasmolysis')
ax4.set_xlabel('External Osmolarity (MPa)', color='#a3e635', fontsize=9)
ax4.set_ylabel('Relative Cell Volume', color='#a3e635', fontsize=9)
ax4.set_title('Boyle-van't Hoff: Cell Volume', color='#d9f99d', fontsize=10)
ax4.tick_params(colors='#a3e635', labelsize=8)
ax4.legend(fontsize=8, labelcolor='#d9f99d', facecolor='#0d1a0d', edgecolor='#4ade80')
ax4.grid(True, alpha=0.2, color='#4ade80')
for spine in ax4.spines.values(): spine.set_edgecolor('#4ade80')

fig.suptitle('Water Relations & Ion Transport in Plants', color='#d9f99d', fontsize=13, fontweight='bold')

plt.savefig('output.png', bbox_inches='tight', facecolor=fig.get_facecolor(), dpi=120)
plt.close()
print('Simulation complete.')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

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