Part 8 · Chapter 8.1

Osmotic Principles

Cell volume is tightly regulated: variation of >10% compromises membrane integrity, cytoskeletal function, and enzyme activity. Understanding volume regulation starts with osmotic equilibrium: tonicity, osmolarity, and reflection coefficient. This chapter lays the quantitative framework for volume regulation (M8.2-8.5).

1. Osmolarity & Osmotic Pressure

Van’t Hoff’s equation gives osmotic pressure as the pressure needed to prevent water flow across a perfectly selective membrane:

\[ \Pi \;=\; i\,c\,R\,T \]

Plasma osmolarity ~300 mOsm L^-1 corresponds to Π ≈ 760 kPa (~7.5 atm) at body temperature. Tightly regulated by the hypothalamus–vasopressin axis within ±1% around 280–295 mOsm. Plasma osmolality can be estimated clinically as:

\[ \text{Osm} \approx 2[\text{Na}^+] + [\text{glucose}]/18 + [\text{BUN}]/2.8 \]

2. Osmolarity vs Tonicity

Osmolarity: total solute concentration (thermodynamic). Tonicity: the effective osmolarity — only solutes that do not penetrate the membrane contribute. Urea is osmotically active but membrane-permeant, so it contributes to osmolarity but not tonicity. A 300 mOsm urea solution is isosmotic but hypotonic — cells placed in it swell and lyse as urea equilibrates and pulls water in.

Simulation: Boyle-van’t Hoff Plot

Python

script.py39 lines

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

# RBC in solutions of different tonicity (Boyle-van't Hoff)
# V/V0 = (pi0/pi) for osmotically active volume; non-osmotic fraction (b) ~0.4
pi = np.linspace(100, 600, 200)  # mOsm
pi0 = 300
b = 0.4
V_Vo = (1 - b) * (pi0/pi) + b

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5), facecolor='#0a0f1e')
for ax in (ax1, ax2):
    ax.set_facecolor('#111e2f'); ax.tick_params(colors='#bae6fd')
    for s in ax.spines.values(): s.set_color('#334155')
    ax.grid(True, color='#334155', alpha=0.3)

ax1.plot(1/pi, V_Vo, color='#60a5fa', lw=2.6)
ax1.axvline(1/pi0, color='#fbbf24', ls='--', label='Isotonic 300 mOsm')
ax1.set_xlabel('1/pi (1/mOsm)', color='#bae6fd')
ax1.set_ylabel('V / V0', color='#bae6fd')
ax1.set_title("Boyle-van't Hoff: RBC volume vs tonicity",
              color='#67e8f9', fontweight='bold')
ax1.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')

# Tonicity categories
labels = ['Hypertonic\n450 mOsm', 'Isotonic\n300', 'Hypotonic\n200', 'Water\n0']
Vs = [0.75, 1.0, 1.33, 4.0]  # stylised
cols = ['#f87171', '#34d399', '#60a5fa', '#a78bfa']
ax2.bar(labels, Vs, color=cols, edgecolor='#bae6fd')
ax2.axhline(1.0, color='#34d399', ls='--')
ax2.set_ylabel('Equilibrium V / V0', color='#bae6fd')
ax2.set_title('Cell volume in clinical tonicities',
              color='#67e8f9', fontweight='bold')

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0f1e')
print('van\'t Hoff: pi = i c RT; plasma ~300 mOsm = 760 kPa')
print('RBC lyses below ~150 mOsm; crenates above ~600 mOsm')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

3. Reflection Coefficient

Staverman’s σ describes how well a membrane reflects a given solute (0 = free passage, 1 = perfect exclusion). Effective driving force for water across a membrane is σ·ΔΠ. In capillary endothelium, σ_albumin ≈ 0.9 while σ_Na ≈ 0.05: albumin generates “colloid osmotic pressure” across capillary walls (~25 mm Hg oncotic) even though it is a tiny fraction of total osmolarity.

4. Osmotic Disorders

Clinically relevant disturbances: hyponatremia (Na < 135 mM, water excess → cell swelling, cerebral oedema, seizures); hypernatremia (Na > 145 mM, cell shrinkage, brain bleeding); hyperosmolar coma (diabetes, glucose-driven plasma osmolarity rise); cerebral salt wasting vs SIADH (diagnostic challenge). Rapid correction of chronic dysnatremia can cause osmotic demyelination; correction rates are standardised in clinical guidelines.

Key References

• Lang, F. et al. (1998). “Functional significance of cell volume regulatory mechanisms.” Physiol. Rev., 78, 247–306.

• Adrogue, H. J. & Madias, N. E. (2000). “Hyponatremia.” N. Engl. J. Med., 342, 1581–1589.

• Kleyman, T. R. & Eaton, D. C. (2020). “Regulating ENaC’s gate.” Am. J. Physiol. Cell Physiol., 318, C150–C162.

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