Resting Membrane Potential

RMP Fundamentals - Cell's Quiet Charge

• Resting Membrane Potential (RMP): Electrical potential difference across a cell membrane at rest. Typical range: -70mV to -90mV.
• Major Ions: $K^+$, $Na^+$, $Cl^-$, large intracellular anions ($A^-$).
• Concentration Gradients:
  • High $[K^+]{in}$, Low $[K^+]{out}$
  • High $[Na^+]{out}$, Low $[Na^+]{in}$
  • High $[Cl^-]{out}$, Low $[Cl^-]{in}$
• Electrochemical Equilibrium & Nernst Potential:
  • Balance of chemical & electrical forces.
  • $K^+$ Nernst ($E_{K^+}$): ≈ -94mV
  • $Na^+$ Nernst ($E_{Na^+}$): ≈ +61mV
• Relative Permeability: At rest, membrane highly permeable to $K^+$ ($P_K >> P_{Na}$).

  ⭐ RMP is primarily determined by potassium ions due to their high membrane permeability, making RMP close to the potassium equilibrium potential.

Calculating RMP - Ion Equation Showdown

• Nernst Equation: Predicts equilibrium potential ($E_{ion}$) for one ion type.
  • General: $E_{ion} = (RT/zF) \ln([ion]{out}/[ion]{in})$.
  • Simplified (37°C): $E_{ion} = (61.5/z) \log([ion]{out}/[ion]{in})$.
  • $z$: ion valence; $[ion]_{out/in}$: outer/inner concentrations.
• Goldman-Hodgkin-Katz (GHK) Equation: Calculates membrane potential ($V_m$) using multiple ions & their permeabilities ($P$).
  • Formula: $V_m = (RT/F) \ln((P_K[K^+]{out} + P{Na}[Na^+]{out} + P{Cl}[Cl^-]{in}) / (P_K[K^+]{in} + P_{Na}[Na^+]{in} + P{Cl}[Cl^-]_{out}))$.

⭐ At rest, RMP (approx. -70mV to -90mV) is primarily dictated by K+ due to its highest permeability an_d proximity of $E_K$ to RMP_

RMP Maintenance - The Unsung Heroes

RMP stability relies on these key mechanisms:

• Na+/K+ ATPase Pump:
  • Actively expels 3 $Na^+$ ions for every 2 $K^+$ ions imported.
  • Electrogenic nature: directly adds ~-4mV to RMP.
  • Crucially maintains steep $Na^+$ and $K^+$ concentration gradients.
• Selective K+ Permeability:
  • At rest, membrane highly permeable to $K^+$ (vs $Na^+$) via $K^+$ leak channels.
  • Continuous $K^+$ efflux down its gradient is a major RMP determinant.
• Gibbs-Donnan Equilibrium:
  • Trapped intracellular non-diffusible anions (proteins, phosphates) enhance internal negativity.

⭐ The Na+/K+ pump's main role: maintaining ion gradients for diffusion potentials (bulk of RMP); direct electrogenic effect ~-4mV.

RMP Clinical Links - Potential Problems

Extracellular $K^+$ concentration ([$K^+$]o) is a critical determinant of RMP.

• Effect of [$K^+$]o on RMP & Excitability:

  Condition	[$K^+$]o	$K^+$ Efflux	RMP Change	Membrane Excitability
  Hyperkalemia	↑	↓	Less negative (depol.)	Initial ↑, then ↓ (due to $Na^+$ channel inactivation)
  Hypokalemia	↓	↑	More negative (hyperpol.)	↓

• Channelopathies: Genetic disorders affecting ion channels (e.g., periodic paralysis) can alter RMP and muscle excitability.

⭐ Severe hyperkalemia causes muscle weakness/paralysis despite RMP being closer to threshold, due to sustained depolarization inactivating voltage-gated $Na^+$ channels, preventing action potentials.

High‑Yield Points - ⚡ Biggest Takeaways

• RMP: Electrical potential difference across a resting cell membrane, typically -70mV to -90mV.
• Major factors: High K+ permeability (via K+ leak channels) and the Na+/K+ pump.
• Na+/K+ pump: 3 Na+ out / 2 K+ in; maintains gradients, electrogenic (contributes to negativity).
• Nernst equation for single ion potential; Goldman-Hodgkin-Katz (GHK) equation for overall RMP.
• RMP is primarily determined by K+ gradient and its high membrane permeability at rest.