Overview
This lecture explains the Nernst equation, how it predicts ionic equilibrium potential, and its relevance to ion movement across cell membranes in physiology.
Equilibrium Potential and Ionic Gradients
- The Nernst equation calculates the voltage needed to offset an ion’s movement down its concentration gradient.
- Ions move from high to low concentration (down their concentration gradient) and are influenced by electrical gradients.
- The law of electrical neutrality states that each compartment must have equal total positive and negative charges.
- The magnitude of ionic movement depends on the strength of the concentration or electrical gradient.
- When concentrations equalize across a membrane, net ion movement ceases (equilibrium).
Electrical Gradients and Ion Movement
- Ions also move according to electrical gradients: they are attracted to oppositely charged areas.
- The direction and strength of movement due to the electric field can be visualized as a vector.
- Stronger electrical fields cause stronger tendencies for ions to move down the gradient.
Combining Concentration and Electrical Gradients
- In cells, both concentration and electrical gradients usually act together, sometimes in opposition.
- The Nernst equation determines which gradient "wins" by calculating the equilibrium potential.
The Nernst Equation and Its Forms
- The Nernst equation: ( E_{ion} = \frac{RT}{Fz} \ln \left(\frac{[\text{ion}]{out}}{[\text{ion}]{in}}\right) ), yielding the equilibrium potential in volts.
- R = gas constant; T = temperature (Kelvin); F = Faraday constant; Z = ion valence (charge).
- Alternate forms exist, including negative signs or switching numerator/denominator in the log, but these are mathematically equivalent.
Physiologically Simplified Nernst Equation
- At 37°C (310 K) and in millivolts: ( E_{ion} = \frac{61.5}{z} \log_{10} \left(\frac{[\text{ion}]{out}}{[\text{ion}]{in}}\right) ) mV.
- At room temperature (25°C), the constant may be 50.
Example Calculation
- For a monovalent cation: [in] = 100 mM, [out] = 5 mM, Z = +1.
- ( E = 61.5 \times \log_{10}(0.05) = 61.5 \times -1.3 = -80 ) mV.
- If the actual membrane potential is less negative than -80 mV, ions move down the concentration gradient; more negative, they move up.
Importance of Nernst Potential
- The Nernst (equilibrium) potential predicts the electrical influence of a specific ion on the membrane potential.
- Typical equilibrium potentials vary by ion, species, and location.
Key Terms & Definitions
- Nernst Equation — Formula calculating the equilibrium potential for an ion across a membrane.
- Equilibrium Potential — The membrane voltage that exactly opposes the ion's concentration gradient.
- Concentration Gradient — Difference in ion concentration across a membrane.
- Electrical Gradient — Difference in charge across a membrane influencing ion movement.
- Ion Valence (Z) — The charge of the ion (e.g., +1 for K⁺ or Na⁺).
- Faraday Constant (F) — Relates electric charge to moles of ions.
Action Items / Next Steps
- Review how equilibrium potentials influence overall membrane potentials in cells.
- Look for additional resources or lectures on the relationship between equilibrium and membrane potentials.