Equilibrium Potential
- Electrical potential across a membrane that exactly prevents diffusion of a specific ion due to its concentration gradient.
- Measured in millivolts (mV), calculated for one ion at a time using the Nernst equation:
- z= absolute ionic charge (K⁺, Na⁺, Cl⁻ = 1; Ca²⁺ = 2).
- Example Nernst Calculations
- ENa=(−60/+1)log10140≈+68.8 mVE_{Na} = (-60/+1) \log \frac{10}{140} \approx +68.8\ \text{mV}ENa=(−60/+1)log14010≈+68.8 mV
- EK=(60/+1)log14010≈−87 mVE_{K} = (60/+1) \log \frac{140}{10} \approx -87\ \text{mV}EK=(60/+1)log10140≈−87 mV
- For K⁺, EK=−80 mV:
- At -80 mV → no net K⁺ movement.
- At -81 mV → K⁺ moves into cell.
- At -79 mV → K⁺ moves out.
- Determines direction, not rate, of diffusion.
ㅤ | Plasma | Intracellular | Equilibrium Potential |
Na ⁺ | 140 mM (140 mEq/l) | 10 mmol/l (10 mEq/l) | +68 mV |
K ⁺ | 4.5 mM (4.5 mEq/l) | 160 mmol/l (160 mEq/l) | –93 mV |
Cl- | 110 mM (110 mEq/l) | 9 mmol/l (9 mEq/l) | –86 mV |
Ca² ⁺ | 2 mM (4 mEq/l) | 0.0001 mmol/l (mEq) | +129 mV |
HCO₃ | 22-26 mmol/l | 10 mmol/l (mEq) | ㅤ |
Resting Membrane Potential (Eₘₑₘ)
- Most cells ≈ -90 mV.
- Calculated as:
- Greater closeness to an ion's E means higher conductance for that ion.
- For example:
- Emem=−77 mV, EK=−95 mV, EK=−95 mV → K⁺ flows until Emem=EK.
- Inside cells:
- High K⁺ (EK=−95 mV, high G) → small changes in [K⁺]ₑₓₜ strongly affect Eₘₑₘ (hyper/hypokalemia dangerous).
- Low Na⁺ inside (ENa=+45 mV, low G) → extracellular changes in Na⁺ have little effect on Eₘₑₘ.
- Cl⁻ generally at equilibrium with ECl≈−90 mV → no net flow.
- Hypocalcemia tetany: Is when there is less Ca2+ in the interstitial fluid, the Na+ opens sooner (at about −80 mV), so the membrane is more excitable.
Concept Link
- Equilibrium potential extends from diffusion potential: concentration gradients create a voltage difference that halts ion movement when electrical and chemical driving forces are equal and opposite.
Goldmann Equation
- Used to calculate actual resting potential considering multiple ions.
- In neurons, ~80% conductance is from K⁺, so resting Vm (~ -70 mV) is close to EKE_KEK.
Length Constant (λ)
- Distance over which voltage decays to 37% (1/e) of original value.
- Longer λ → further passive current spread; shorter in leakier axons.
- Dependent on:
- Rₘ (membrane resistance)
- Rᵢ (axoplasmic resistance)
- R₀ (extracellular resistance)
- To improve current flow:
- ↑ Rₘ (e.g., myelination)
- ↓ Rᵢ
- ↓ R₀
Time Constant (τ)
- Time for membrane potential to reach 63% of its final value after a current change.
- Due to membrane capacitance delaying voltage change.
- Dependent on:
- Rₘ (membrane resistance)
- Cₘ (membrane capacitance)
- Larger cells:
- Lower R,
- higher C → shorter τ
Action potential
- General
- The velocity of an action potential is affected
- Inversely by internal resistance
- Inversely by membrane capacitance
- Proportionately by transmembrane resistance
- Myelin increases transmembrane resistance and decreases membrane capacitance.
- Conduction velocity
- Small unmyelinated nerves 0.5M/S
- Large myelinated nerves 120M/S
- Resting membrane potential: membrane is more permeable to K⁺ than Na⁺ at rest. Voltage-gated Na⁺ and K⁺ channels are closed.
- Membrane depolarization: Na⁺ activation gate opens → Na⁺ flows inward.
- Membrane repolarization: Na⁺ inactivation gate closes at peak potential, thus stopping Na⁺ inflow. K⁺ activation gate opens → K⁺ flows outward.
- Membrane hyperpolarization: K⁺ activation gates are slow to close → excess K⁺ efflux and brief period of hyperpolarization. Voltage-gated Na⁺ channels switch back to resting state. Na⁺/K⁺ pump restores ions concentration.
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