202. Membrane Potential

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Membrane Potential

This simulation models the resting membrane potential of a cell, demonstrating how ion channels, concentration gradients, and the Na⁺/K⁺-ATPase pump work together to establish and maintain the electrical potential across the cell membrane.

The Goldman-Hodgkin-Katz Equation

The membrane potential (Vm) is calculated using the GHK equation, which accounts for the permeability and concentration of multiple ions:

Vm = (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)]

Key Concepts

• Potassium Dominance: At rest, the membrane is most permeable to K⁺ (P_K = 1), so Vm is closest to E_K (~-90 mV)
• Sodium Leak: Small Na⁺ permeability (P_Na ≈ 0.05) slightly depolarizes the membrane toward E_Na
• Chloride: Passively distributes near equilibrium; E_Cl ≈ Vm

Na⁺/K⁺-ATPase Pump

This essential enzyme maintains concentration gradients by actively transporting:

• 3 Na⁺ ions OUT of the cell
• 2 K⁺ ions INTO the cell
• Uses 1 ATP per cycle (20-40% of brain's energy consumption)

Electrogenic Nature

The pump is electrogenic (3 out : 2 in), contributing approximately -5 to -10 mV to the resting potential. Without the pump, ionic gradients would eventually dissipate and the membrane potential would collapse.

Driving Force

The driving force on each ion = (Vm - E_ion). At rest:

• K⁺: +20 mV driving force (outward)
• Na⁺: -137 mV driving force (inward)

Despite the larger driving force on Na⁺, K⁺ carries more current due to its ~20× higher permeability at rest.