Nernst Equation: Meaning in Medicine and Physiology

What is the Nernst Equation?

The Nernst equation is a fundamental formula in electrochemistry that describes the electrical equilibrium potential of a specific ion across a semipermeable membrane. It was developed by the German physical chemist Walther Hermann Nernst (1864–1941), who was awarded the Nobel Prize in Chemistry in 1920 for his work in thermodynamics. In medicine and physiology, the Nernst equation is of central importance because it explains how electrical potentials arise across biological membranes, such as those found in nerve cells, muscle cells, and cardiac cells.

Basic Principle and Formula

The Nernst equation calculates the so-called equilibrium potential (also referred to as the Nernst potential or reversal potential) for a specific ion. This is the membrane voltage at which the electrical driving force and the diffusion force (caused by the concentration gradient) for that ion are exactly balanced, resulting in no net movement of the ion across the membrane.

The general form of the Nernst equation is:

E = (RT / zF) × ln([Ion]o / [Ion]i)

• E: equilibrium potential of the ion (in volts)
• R: universal gas constant (8.314 J · mol¹ · K¹)
• T: absolute temperature in Kelvin (310 K at body temperature)
• z: valence of the ion (e.g., +1 for sodium or potassium, +2 for calcium, –1 for chloride)
• F: Faraday constant (96,485 C · mol¹)
• [Ion]o: extracellular ion concentration
• [Ion]i: intracellular ion concentration

At body temperature (37 °C), the prefactor RT/F simplifies to approximately 26.7 mV, yielding the practical approximation for monovalent ions:

E ≈ (61.5 mV / z) × log⊂10;([Ion]o / [Ion]i)

Importance in Medicine and Physiology

In human physiology, the Nernst equation is used to calculate the equilibrium potentials of the key physiological ions, which serve as reference values for understanding resting membrane potential and action potentials:

• Potassium (K+): equilibrium potential approximately –90 mV (high intracellular concentration)
• Sodium (Na+): equilibrium potential approximately +60 mV (high extracellular concentration)
• Calcium (Ca2+): equilibrium potential approximately +130 mV (high extracellular concentration)
• Chloride (Cl–): equilibrium potential approximately –70 mV (higher extracellular concentration)

Resting Membrane Potential and the Goldman Equation

The actual resting membrane potential of a cell is not determined by the Nernst potential of a single ion alone, but by the weighted contributions of multiple ions. This is described by the extended Goldman-Hodgkin-Katz (GHK) equation, which takes into account the membrane permeabilities for different ions. The Nernst equation forms the basis for each individual ionic component within the GHK equation.

Clinical Relevance

Understanding the Nernst equation has practical implications across several medical disciplines:

Cardiology

In cardiology, the Nernst equation explains how changes in extracellular potassium concentration (hypokalemia or hyperkalemia) alter the cardiac action potential and can cause life-threatening cardiac arrhythmias. Hyperkalemia shifts the potassium equilibrium potential toward less negative values, altering the excitability of cardiac muscle cells.

Neurology

In neurology, the Nernst equation provides the theoretical basis for understanding nerve conduction. Disturbances in ion balance, such as hyponatremia (low blood sodium levels), can lead to seizures, confusion, and other neurological symptoms.

Nephrology and Intensive Care

In nephrology and intensive care medicine, knowledge of ionic equilibria is used to guide the treatment of electrolyte disorders. Calculating equilibrium potentials helps predict the clinical consequences of changes in electrolyte concentrations and supports therapeutic decisions, such as potassium supplementation.

Pharmacology

Many medications act specifically on ion channel function. Antiarrhythmics, local anesthetics, and antiepileptics all work by modulating ion channels. The Nernst equation provides the theoretical framework for understanding the mechanisms of action of these agents.

Historical Background

Walther Nernst formulated the equation bearing his name in the late 19th century within the context of physical chemistry, originally to describe electrochemical potentials in galvanic cells and electrolytic processes. It was only later that physiologists such as Julius Bernstein, and subsequently Alan Hodgkin and Andrew Huxley, recognized that the same principles apply to biological membranes. Hodgkin and Huxley received the Nobel Prize in Physiology or Medicine in 1963 for their work on the action potential, which is built on the foundation of the Nernst equation.

References

1. Hodgkin AL, Katz B. - The effect of sodium ions on the electrical activity of the giant axon of the squid. Journal of Physiology, 1949; 108(1): 37–77.
2. Kandel ER, Schwartz JH, Jessell TM et al. - Principles of Neural Science, 5th edition. McGraw-Hill, 2012.
3. Hille B. - Ion Channels of Excitable Membranes, 3rd edition. Sinauer Associates, 2001.