Membrane potential

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membrane potential physiology overview

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Here is a comprehensive overview of membrane potential, drawn from Guyton & Hall, Costanzo Physiology, and Medical Physiology.

Membrane Potential

Definition

Membrane potential (Vm) is the electric potential difference across a cell membrane, measured as the intracellular potential relative to the extracellular potential. By convention, the extracellular fluid is set at 0 mV. In resting excitable cells (nerve and muscle), the interior is negative relative to the exterior.

Resting Membrane Potential (RMP)

The RMP of most excitable cells falls between −70 and −90 mV:

Large nerve fibers: ~−70 mV
Skeletal muscle: ~−90 mV
Erythrocytes: as low as ~−10 mV

How It Is Measured

A microelectrode (glass micropipette filled with electrolyte, tip < 1 µm, resistance > 1 MΩ) is impaled through the membrane. A voltage is recorded between the intracellular tip and an indifferent electrode in the extracellular fluid.

Ion distribution and membrane potential across a nerve fiber — the interior registers −70 mV relative to the extracellular space

Figure: Charge distribution across a nerve fiber and the resulting electrical potential. Outside the fiber = 0 mV; inside = −70 mV. — Guyton & Hall

Ionic Basis: Why Is the Inside Negative?

Ion Concentration Gradients

The Na⁺-K⁺ ATPase pump actively establishes and maintains these gradients:

Ion	Outside	Inside	Nernst Potential
K⁺	4 mEq/L	140 mEq/L	−94 mV
Na⁺	142 mEq/L	14 mEq/L	+61 mV
Ca²⁺	1.0 mM	0.0001 mM	+123 mV
Cl⁻	116 mM	4.2 mM	−89 mV

Differential Permeability

At rest, the membrane is ~100× more permeable to K⁺ than to Na⁺ (via K⁺ "leak" channels). K⁺ therefore diffuses down its concentration gradient (out of the cell), carrying positive charge outward and leaving the inside negative.

Three Contributions to the RMP

Three conditions establishing resting membrane potential: K⁺ diffusion alone (−94 mV), K⁺ + Na⁺ diffusion (−86 mV), and with the Na⁺-K⁺ pump (−90 mV)

Figure 5.5: Establishment of RMP under three conditions. — Guyton & Hall

Component	Contribution
K⁺ diffusion potential	Major driver: K⁺ leaving the cell → ~−94 mV if K⁺ were the only ion
Na⁺ diffusion potential	Small inward leak of Na⁺ offsets K⁺ effect → combined Goldman potential ~−86 mV
Na⁺-K⁺ pump (electrogenic)	Pumps 3 Na⁺ out for every 2 K⁺ in → adds ~−4 mV (small direct effect)
Overall RMP	~−90 mV

Key Equations

Nernst Equation

Predicts the equilibrium potential for a single ion:

$$E_x = \frac{-61.5 \text{ mV}}{z} \log_{10} \frac{[X]_i}{[X]_o} \quad \text{(at 37°C)}$$

For K⁺ (z = +1): slope = −61.5 mV per 10-fold change in [K⁺]
For Na⁺ (z = +1): E_Na ≈ +61 mV
For Ca²⁺ (z = +2): slope = ~−30 mV per decade

Goldman (Goldman-Hodgkin-Katz) Equation

Accounts for multiple ions simultaneously, weighted by their relative permeabilities (P):

$$V_m = \frac{RT}{F} \ln \frac{P_{K}[K^+]o + P{Na}[Na^+]o + P{Cl}[Cl^-]i}{P{K}[K^+]i + P{Na}[Na^+]i + P{Cl}[Cl^-]_o}$$

Chord Conductance Equation

Weights each ion's equilibrium potential by its relative conductance (g):

$$E_m = \frac{g_{K^+}}{g_T}E_{K^+} + \frac{g_{Na^+}}{g_T}E_{Na^+} + \frac{g_{Cl^-}}{g_T}E_{Cl^-} + \frac{g_{Ca^{2+}}}{g_T}E_{Ca^{2+}}$$

Ions with the highest conductance at rest (K⁺, Cl⁻) drive the RMP toward their equilibrium potentials. Ions with low conductance (Na⁺, Ca²⁺) have little influence at rest.

Role of the Na⁺-K⁺ ATPase

The pump has two roles:

Indirect (dominant): Maintains the K⁺ and Na⁺ concentration gradients that power diffusion potentials. Blocking the pump with cardiac glycosides only shifts Vm by ~1.4 mV acutely — confirming that the pump's direct electrogenic contribution is minor.
Direct (electrogenic, minor): 3 Na⁺ out / 2 K⁺ in per ATP → net export of 1 positive charge → adds ~−4 mV to the RMP.

Key Concepts

Term	Meaning
Depolarization	Vm becomes less negative (moves toward 0 or positive)
Hyperpolarization	Vm becomes more negative
Repolarization	Vm returns toward RMP after depolarization
Equilibrium potential (Ex)	Vm at which there is no net flux of ion X (chemical and electrical forces balance)
Threshold	Vm at which an action potential is triggered (~−55 mV in neurons)

Clinical Relevance

Hyperkalemia raises extracellular [K⁺] → reduces K⁺ concentration gradient → RMP becomes less negative → cells partially depolarize → increased excitability initially, then inexcitability (e.g., cardiac arrhythmias, muscle weakness)
Hypokalemia → more negative RMP → hyperpolarization → reduced excitability
Local anesthetics (e.g., lidocaine) block Na⁺ channels, preventing depolarization
Cardiac glycosides (e.g., digoxin) inhibit Na⁺-K⁺ ATPase, indirectly raising intracellular [Ca²⁺] (via Na⁺/Ca²⁺ exchanger)

Sources: Guyton and Hall Textbook of Medical Physiology; Costanzo Physiology 7th Ed.; Medical Physiology (Boron & Boulpaep)

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