Resting Membrane Potential Simulation
– Section 5 –
Equations and Calculators
Links to Other Sections
Nernst Equation
What It Calculates
The Nernst equation calculates the equilibrium potential of a particular ion at a given concentration.
The equilibrium potential is the opposing force or voltage generated by an electrical gradient that prevents an ion’s net movement across the cell membrane along its concentration gradient.
At equilibrium, ions still move across the membrane but in equal numbers, preventing either side of the membrane from gaining or losing charge.
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.
Factors Considered
The Nernst 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.
Full Nernst Equation
E(ion) = membrane equilibrium potential for a particular ion.
E(ion) = RT/zF * ln ( [ion outside the cell] / [ion inside of the cell] ).
R = gas constant = 8.314472 J · K-1 (joules per kelvin per mole).
T = temperature (Kelvin) = 310 (body temperature).
F = Faraday constant = 9.65 x 104 C mol-1 (Coulombs per mole).
Z = ion charge (1 for a monovalent ion such as K+).
Below are Nernst calculators for K+, Na+, and Cl+ ions. Each displays the Nernst equation, ion concentrations, and ion gradient indicators. Buttons allow users to increase or decrease the ion concentrations. The calculated equilibrium potential appears to the left of the Nernst equation and is expressed in mV.
E(K) Calculator
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E(Na) Calculator
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E(Cl) Calculator
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Analysis Questions
1. What does the Nernst equation calculate?
It calculates the equilibrium potential of a particular ion.
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.
3. How does the magnitude of an ion’s concentration gradient affect the magnitude of its opposing electrical?
The electrical gradient of an ion changes in proportion to its concentration gradient. The larger the concentration gradient, the stronger the opposing electrical gradient.
4. Do ions stop moving across the membrane at equilibrium?
No, ions continue moving in equal numbers across the membrane in both directions.
5. Why is the direction of the electrical gradient reversed for ENa and ECl compared to EK?
The Na+ and Cl– electrical gradients are reversed because their concentration gradients are reversed compared to EK.
Goldman-Hodgkin-Katz Equation
The Goldman-Hodgkin-Katz (GHK) equation is a widely used formula that helps to determine the resting membrane potential in excitable cells. It can be considered a combination of multiple Nernst equations, each representing a different ion species. Typically, the GHK equation includes K+, Na+, and Cl– ions, but it can also include other ion species that are able to cross the cell membrane, such as calcium (Ca2+).
| Ion | Extracellular Fluid (mmol/L) | Intracellular Fluid (mmol/L) | Permeability |
|---|---|---|---|
| K+ | Kout = 3.5 – 5.5 | Kin = 130 – 150 | 1 |
| Na+ | Naout = 135 – 145 | Nain = 5 – 15 | 0.01 – 0.05 |
| Cl– | Clout = 96 – 106 | Clin = 4 – 12 | 0.4 – 0.5 |
The value produced by the GHK is a weighted compromise (or tug-of-war) between the equilibrium potentials of the ions in the equation. The greater the membrane’s permeability to a given ion, the more that ion’s equilibrium potential dominates the tug-of-war and pulls the measured membrane potential towards it.
The GHK equation reveals that under normal physiological conditions, K+ ions impact the resting membrane potential most because the cell membrane is highly 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 -95 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. This positive 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. The small leakage of Na+ ions into the cell causes a modest depolarization. This depolarization moves the resting membrane potential from -95 mV, caused by K+ ions, closer to -70 mV.
Under normal physiological conditions, chloride (Cl–) ions do not significantly impact an excitable cell’s resting membrane potential. This is due to two factors. Firstly, the cell membrane is less permeable to Cl– ions than to K+ ions. Secondly, Cl– ions have an equal potential close to the resting membrane potential produced by the combination of sodium (Na+) and potassium (K+) ions.
Analysis Questions
1. Why is the Goldman-Hodgkin-Katz equation used to calculate the resting membrane potential rather than the Nernst equation?
The GHK is used instead of the Nernst equation because it considers multiple ion species and the cell membrane’s permeability to each ion. The Nernst equation only considers one ion species at a time.
GHK Calculator
The following GHK calculator shows the inner and outer ion concentrations of K+, Na+, and Cl+ ions. It also displays the permeability of each ion species. Buttons allow users to increase or decrease the displayed values. The calculated membrane potential is shown on a grid displaying voltage vs time.
Analysis Questions
1. 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+.
The resting membrane potential would be approximately -95 mV, the equilibrium potential for K+.
2. What does this value indicate about the movement of K+ ions?
Because the membrane potential is positive, it indicates K+ ions would move out of the cell along their concentration gradient.
3. What would be the resting membrane potential value (EM) if the cell membrane only contained open channels for sodium (Na+)?
The resting membrane potential would be approximately +65 mV, the equilibrium potential for Na+.
4. What does this value indicate about the movement of Na+ ions?
Because the membrane potential is negative, it indicates Na+ ions would move into the cell along their concentration gradient.
5. What would be the resting membrane potential (EM) value if the cell membrane only contained open channels for sodium (Cl–)?
The resting membrane potential would be approximately -65 mV, the equilibrium potential for Cl–.
6. What does this value indicate about the movement of Cl– ions?
Because the membrane potential is negative, it indicates Cl– ions would move into the cell along their concentration gradient.
7. Why is the membrane potential less negative than the equilibrium potential for K+?
The cell membrane is relatively impermeable to Na+ ions. However, the small leakage of Na+ ions into the cell causes a modest depolarization. This depolarization moves the resting membrane potential from -95 mV, caused by K+ ions, closer to -70 mV.
GHK Calculator
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References
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