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Resting Membrane Potential Simulation: Section 3

Nernst Equation, Goldman-Hodgkin-Katz Equation, and Calculators

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Nernst Equation

The Nernst equation calculates (or predicts) the equilibrium potential of a specific ion at a given concentration. The equilibrium potential is the point at which an ion’s electrical gradient balances its opposing concentration gradient, stopping the ion’s net movement across the cell membrane. The equilibrium potential of an ion changes in proportion to its initial concentration gradient. The larger the original concentration gradient, the greater the opposing electrical gradient and corresponding equilibrium potential. Ions still move across the membrane at equilibrium but in equal numbers, preventing either side of the membrane from gaining or losing charge.

The equation considers factors such as the ion’s concentrations on either side of the cell membrane, the ion’s valence, and the surrounding temperature. It is important to note that the Nernst equation assumes that the cell membrane is only permeable to the ion that is being evaluated.

It is important to note that the Nernst equation assumes that the cell membrane is only permeable to the ion that is being evaluated.

Nernst equation diagram

Full Nernst Equation and Contributing Factors

Nersnt Calculators

E(K) Calculator

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E(Na) Calculator

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E(Cl) Calculator

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Review Questions.

Question 1: What does the Nernst equation calculate?

Question 2: What does the calculated value represent?

It represents the point where the concentration gradient of an ion is equal to its opposing electrical gradient.

Question 3: How does the magnitude of an ion’s concentration gradient affect the magnitude of its opposing electrical?

Question 4: Do ions stop moving across the membrane at equilibrium?

Question 5: Why is the direction of the electrical gradient reversed for ENa and ECl compared to EK?

Goldman-Hodgkin-Katz Equation

The Goldman-Hodgkin-Katz (GHK) equation is a commonly used formula for determining the resting membrane potential in excitable cells.

One can think of the GHK equation as a combination of multiple Nernst equations, each representing a different ion species. The number of ions in the GHK is often limited to K+, Na+, and Cl. However, it could include other ion species capable of crossing the cell membrane, like calcium (Ca2+).

The value produced by the GHK is a weighted compromise (or tug-of-war) between the equilibrium potentials of the ions in the equation.

Each ion’s equilibrium potential in the GHK equation is weighted or influenced by the cell membrane’s permeability to the ion.

Because it considers multiple ion species, the GHK equation provides a better model of biological membranes than the Nernst equation, which only considers one ion species at a time.

IonExtracellular Fluid
(mmol/L)
Intracellular Fluid
(mmol/L)
Permeability
K+Kout = 3.5 – 5.5Kin = 130 – 1501
Na+Naout = 135 – 145Nain = 5 – 150.01 – 0.05
ClClout = 96 – 106Clin = 4 – 120.4 – 0.5

The GHK equation reveals that under normal physiological conditions, K+ ions have the most significant influence on the resting membrane potential because the cell membrane is most permeable to this ion. If K+ are the only ions considered, the resting membrane potential (Vm) will tend to equal the equilibrium potential for K+. The equilibrium potential for K+ ions (EK) is approximately -94 mV, indicating the net movement of these ions is out of the cell.

The actual resting membrane potential of excitable cells is approximately -70 mV. The shift in membrane potential is due primarily to the added influence of Na+ ions. The equilibrium potential for Na+ ions (ENa) is approximately +65 mV, meaning these ions tend to move into the cell. However, their movement is restricted because the membrane is much less permeable to Na+ ions.

As the Na+ ions enter the cell, it offsets the negative charge created by the efflux of K+ ions, causing the resting membrane potential to move from -94 mV to -70 mV.

Under normal physiological conditions, the contribution made by Cl ions to the value of the resting membrane potential is minimal.

Two factors diminish the impact made by Cl ions. First, the cell membrane has a relatively low permeability to Cl ions. Second, the equilibrium potential for Cl ions is approximately equal to the resting membrane potential established by K+ and Na+ ions.

How the potassium, sodium, and chloride equilibrium potentials influence the resting membrane potential, tug-of-war between potentials, animation

GHK Calculator

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Review Questions.

Question 1: Why is the Goldman-Hodgkin-Katz equation used to calculate the resting membrane potential rather than the Nernst equation?

Question 2: What would be the resting membrane potential (VM) value if the cell membrane only contained open channels for potassium (K+)? To determine the answer, adjust the membrane potentials of the two other ions to 0.0. Closing the membrane to these ions eliminates them from the equation, leaving the value for K+.

Question 3: What would be the resting membrane potential value (EM) if the cell membrane only contained open channels for sodium (Na+)?

Question 4: What would be the resting membrane potential (EM) value if the cell membrane only contained open channels for sodium (Cl)?

Question 5: How does removing Cl from the equation affect the value of the resting membrane potential? Why is this the case?

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