Overview
The transcript explains how ion concentration gradients and membrane permeability create membrane potentials, focusing on potassium and the Nernst equation to compute equilibrium potentials.
Potassium Gradient and Membrane Potential
- Inside cell K+ ≈ 150 mM; outside ≈ 5 mM; strong outward concentration gradient.
- K+ exits cell, leaving behind impermeant anions that create negative intracellular charge.
- Negative charge attracts K+ back; balance point is the K+ equilibrium potential.
- For K+, equilibrium potential is about −92 mV under the stated concentrations.
Thought Experiment: Injecting Positive Charge
- Adding positive charge makes membrane potential less negative (e.g., −92 mV to −46 mV).
- Electrical attraction back into cell weakens; more K+ leaves down its gradient.
- Leaving K+ increases negative intracellular charge, driving Vm back toward −92 mV.
- As long as K+ gradient (150 in/5 out) and K+-only permeability hold, Vm returns to −92 mV.
Conditions Required to Generate a Membrane Potential
- Two requirements:
- Concentration gradient: ion “desire” to move.
- Permeability: ion “means” to move through the membrane.
- Without either gradient or permeability, no membrane potential develops.
- With both present for K+, Vm reaches the K+ equilibrium potential (≈ −92 mV).
Nernst Equation and Equilibrium Potentials
- Membrane potential for a single ion (equilibrium potential) given by: Vm = 61.5 × log10([ion]out/[ion]in).
- For divalent ions (e.g., Ca2+), constant halves: 30.75 × log10([ion]out/[ion]in).
- Sign and magnitude depend on charge and concentration ratio inside vs. outside.
Equilibrium Potentials and Ion Movements
| Ion | Charge | Direction of Net Movement (given typical gradients) | Equilibrium Potential (mV) | Notes on Calculation |
|---|
| K+ (Potassium) | +1 | Out of the cell | −92 | Uses 61.5 × log10([K+]out/[K+]in) |
| Na+ (Sodium) | +1 | Into the cell | +67 | Uses 61.5 × log10([Na+]out/[Na+]in) |
| Cl− (Chloride) | −1 | Into the cell | −86 | Uses 61.5 × log10([Cl−]out/[Cl−]in) |
| Ca2+ (Calcium) | +2 | Into the cell | +123 | Uses 30.75 × log10([Ca2+]out/[Ca2+]in) |
Key Terms & Definitions
- Membrane potential (Vm): Electrical potential difference across the cell membrane.
- Equilibrium potential (Nernst potential): Vm at which an ion’s electrical and chemical gradients balance.
- Concentration gradient: Difference in ion concentration across the membrane driving diffusion.
- Permeability: Membrane’s ability to allow an ion to pass through channels.
Action Items / Next Steps
- Practice computing equilibrium potentials using Vm = 61.5 × log10([out]/[in]) for monovalent ions.
- Adjust constant to 30.75 for divalent ions like Ca2+.
- Analyze scenarios by checking both gradient (desire) and permeability (means) to predict Vm behavior.