Calculating Resting Membrane Potential Using Permeabilities
A professional Goldman-Hodgkin-Katz (GHK) Equation tool for electrophysiology.
Potassium (K⁺)
Sodium (Na⁺)
Chloride (Cl⁻)
Calculated Membrane Potential (Vₘ)
-64.88 mV
Intermediate Calculations
RT/F Constant: 26.72
Numerator (Numerator Sum): 16.75
Denominator (Denominator Sum): 190.25
Formula: GHK Voltage Equation
Ion Permeability Contribution Comparison
Visualization of relative permeability settings for each ion.
| Ion | Internal (mM) | External (mM) | Permeability | Nernst Potential |
|---|
Table 1: Summary of ionic concentrations and calculated equilibrium potentials.
What is Calculating Resting Membrane Potential Using Permeabilities?
Calculating resting membrane potential using permeabilities is a fundamental process in neurophysiology used to determine the electrical charge across a cell’s plasma membrane when it is not actively sending signals. Unlike the Nernst equation, which looks at a single ion, the Goldman-Hodgkin-Katz (GHK) equation allows for calculating resting membrane potential using permeabilities of multiple ions simultaneously, providing a much more accurate physiological model.
Physiologists, medical students, and researchers rely on calculating resting membrane potential using permeabilities to understand how changes in ion concentration or channel activity affect cellular excitability. A common misconception is that only the pump (Na+/K+-ATPase) sets the potential; while the pump maintains gradients, the actual potential is a result of selective permeability through leak channels.
Calculating Resting Membrane Potential Using Permeabilities Formula
The core mathematical framework for calculating resting membrane potential using permeabilities is the GHK equation:
Vₘ = (RT / F) * ln( (Pₖ[K⁺]ₒ + Pₙₐ[Na⁺]ₒ + Pcₗ[Cl⁻]ᵢ) / (Pₖ[K⁺]ᵢ + Pₙₐ[Na⁺]ᵢ + Pcₗ[Cl⁻]ₒ) )
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Vₘ | Membrane Potential | mV | -60 to -90 mV |
| R | Ideal Gas Constant | J/(K·mol) | 8.314 |
| T | Absolute Temperature | Kelvin | 310.15 (37°C) |
| F | Faraday’s Constant | C/mol | 96485 |
| Pₓ | Permeability of ion X | Relative | 0 to 1.0 |
Practical Examples
Example 1: Typical Neuron
In a standard mammalian neuron, the permeability to Potassium is much higher than Sodium. With [K+]out = 5mM, [K+]in = 140mM, [Na+]out = 145mM, [Na+]in = 15mM, and relative permeabilities of 1.0 (K) and 0.05 (Na), calculating resting membrane potential using permeabilities yields approximately -70 mV. This reflects the dominance of potassium leak channels.
Example 2: Hyperkalemia Effect
If external Potassium rises to 10mM (hyperkalemia), calculating resting membrane potential using permeabilities shows the potential shifting to a less negative value (e.g., -60 mV). This “depolarization” makes the cell more excitable, which can lead to cardiac arrhythmias.
How to Use This Calculator
Follow these steps for calculating resting membrane potential using permeabilities effectively:
- Enter the current Temperature in Celsius. The tool automatically converts this to Kelvin for the calculation.
- Input the internal and external concentrations for Potassium, Sodium, and Chloride in millimolar (mM).
- Adjust the Relative Permeability values. Potassium is typically set as the reference (1.0).
- The result updates in real-time in the blue box above.
- Review the Nernst potentials in the table below to see the equilibrium point for each individual ion.
Key Factors That Affect Results
Several physiological and environmental factors influence calculating resting membrane potential using permeabilities:
- Temperature: Higher temperatures increase the thermal kinetic energy, slightly increasing the magnitude of the potential.
- Ion Concentration Gradients: Established primarily by the Na+/K+ pump; changes in diet or kidney function can alter these.
- Gating of Ion Channels: Opening or closing channels changes the relative permeability, which is how action potentials are generated.
- Extracellular pH: Can affect the shape and function of channel proteins, indirectly modifying permeability.
- Metabolic Activity: ATP availability ensures that the pump maintains the gradients required for calculating resting membrane potential using permeabilities.
- Cell Type: Glial cells, for instance, are almost exclusively permeable to potassium, resulting in a more negative RMP than neurons.
Frequently Asked Questions (FAQ)
Q: Why is Chloride flipped in the numerator?
A: Since Chloride is an anion (negative charge), its contribution to the electrical potential is inverted compared to cations like Sodium and Potassium. In calculating resting membrane potential using permeabilities, we place [Cl-]in in the numerator and [Cl-]out in the denominator.
Q: What is the most important ion?
A: For calculating resting membrane potential using permeabilities in most resting cells, Potassium is the most influential because its resting permeability is much higher than other ions.
Q: Can the potential ever be positive?
A: Yes, during the peak of an action potential when Sodium permeability exceeds Potassium permeability, but the “resting” potential is almost always negative.
Q: Is this the same as the Nernst Equation?
A: No. The Nernst equation handles one ion at equilibrium. The GHK equation is for calculating resting membrane potential using permeabilities of multiple ions in a steady-state condition.
Q: How does the Na/K pump affect this?
A: The pump is electrogenic (3 Na out, 2 K in), which adds about -3 to -5 mV directly to the potential beyond what you get from calculating resting membrane potential using permeabilities alone.
Q: Does cell size matter?
A: Theoretically no, as it’s a concentration-driven potential, but smaller cells have higher input resistance, meaning small current changes cause larger voltage swings.
Q: Why use relative instead of absolute permeability?
A: In calculating resting membrane potential using permeabilities, only the ratios matter for the final voltage calculation.
Q: Can Cl- be ignored?
A: In many models, Cl- is assumed to be passively distributed, meaning its Nernst potential equals the RMP. However, in neurons with active Cl- transporters, it must be included.
Related Tools and Internal Resources
- Ion Concentration Calculator – Determine gradient shifts across various cell types.
- Nernst Equation Tool – Calculate equilibrium potential for single ions.
- Action Potential Simulator – See how permeability changes over time.
- Osmolarity Calculator – Balance your solutions for physiological experiments.
- Lab Buffer Prep Tool – Ensure your extracellular fluids match physiological standards.
- Neuroscience Unit Converter – Convert between mM, mEq/L, and mg/dL easily.