Resting Potential Calculators

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The resting membrane potential is the electrical potential difference across the plasma membrane of an unstimulated cell, typically around −70 mV in neurons (inside negative relative to outside). It arises from the unequal distribution of ions across the membrane and their selective permeability through ion channels and pumps. The Na⁺/K⁺-ATPase pump continuously maintains ion gradients, while the leak permeability of K⁺ channels predominantly determines the resting potential. The Goldman equation calculates the resting potential from the permeabilities and concentrations of all contributing ions.

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Ionic Basis of Resting Potential

At rest, K⁺ concentration is high inside (~140 mM) and low outside (~5 mM). Na⁺ is high outside (~145 mM) and low inside (~12 mM). Cl⁻ is predominantly extracellular. The membrane at rest is most permeable to K⁺ through inward-rectifying K⁺ leak channels. K⁺ diffuses outward down its concentration gradient, leaving behind negative charges and creating a negative interior — the resting potential.

The Na⁺/K⁺ Pump

The Na⁺/K⁺-ATPase pump actively transports 3 Na⁺ out and 2 K⁺ in per ATP hydrolyzed, maintaining the ion gradients that drive the resting potential. It also directly contributes −3 to −5 mV to the resting potential by being electrogenic (unequal ion transport). Without the pump, ion gradients would dissipate and cells would depolarize.

The Goldman-Hodgkin-Katz (GHK) Equation

The Goldman equation calculates Vm from the relative permeabilities and concentrations of K⁺, Na⁺, and Cl⁻:

Vm = (RT/F) × ln[(PK[K⁺]o + PNa[Na⁺]o + PCl[Cl⁻]i) / (PK[K⁺]i + PNa[Na⁺]i + PCl[Cl⁻]o)]

At rest, PK >> PNa, so the resting potential approaches the Nernst equilibrium potential for K⁺ (EK ≈ −90 mV), but is slightly depolarized from this value due to Na⁺ leak permeability.

Resting Potential and Excitability

The resting potential sets the 'electrical baseline' from which action potentials are generated. Hyperpolarization (more negative Vm) makes cells less excitable; depolarization (less negative Vm) moves Vm closer to the action potential threshold (~−55 mV for neurons). Many neurotransmitters and drugs act by modulating resting permeabilities to Na⁺, K⁺, or Cl⁻.

Glossary

Resting Membrane Potential
The electrical potential difference (~−70 mV in neurons) across the plasma membrane of an unstimulated cell, maintained by ion gradients and selective membrane permeability.
Goldman-Hodgkin-Katz Equation
An equation that calculates membrane potential from the relative permeabilities and concentrations of K⁺, Na⁺, and Cl⁻ across the membrane.
Na⁺/K⁺-ATPase
An electrogenic ion pump that transports 3 Na⁺ out and 2 K⁺ into the cell per ATP hydrolyzed, maintaining the ionic gradients essential for resting membrane potential.

Frequently Asked Questions

The resting membrane potential (~−70 mV in neurons) is the voltage difference across the cell membrane when the cell is not firing. It is caused by the unequal distribution of ions — particularly K⁺ (high inside), Na⁺ (high outside), and Cl⁻ (high outside) — and the selective permeability of the resting membrane, which is much more permeable to K⁺ than Na⁺. K⁺ diffuses outward down its concentration gradient, leaving the cell interior negatively charged.

The Na⁺/K⁺-ATPase pump uses ATP to transport 3 Na⁺ out of the cell and 2 K⁺ into the cell, actively maintaining the ion concentration gradients that drive the resting potential. Without this pump, Na⁺ would leak in and K⁺ would leak out until gradients dissipated. The pump also contributes directly ~3–5 mV to the resting potential because it is electrogenic (transports more positive charges out than in).

The Goldman-Hodgkin-Katz equation calculates the membrane potential from the concentrations and relative permeabilities of all permeant ions (typically K⁺, Na⁺, Cl⁻). It generalizes the Nernst equation for a single ion to multiple ions. At rest, K⁺ permeability dominates, pulling Vm toward EK (~−90 mV). Because some Na⁺ permeability also exists, the actual resting potential is around −70 mV, slightly depolarized from EK.

The resting potential determines how far the membrane voltage is from the action potential threshold (~−55 mV). A more negative resting potential (hyperpolarization) means a larger depolarization is needed to fire an action potential, making the cell less excitable. A less negative resting potential (depolarization) brings Vm closer to threshold, increasing excitability. Inhibitory neurotransmitters (GABA, glycine) hyperpolarize cells; excitatory neurotransmitters (glutamate) depolarize them.