Calculating the change in membrane potential involves determining the membrane potential at two different points in time or under two different conditions and finding the difference between the initial and final values.
The membrane potential of a cell, which is typically negative and measured in millivolts (mV), is fundamentally the electrical potential difference across the cell membrane. According to the reference, this potential can be calculated by the Nernst equation.
The Nernst equation is a key tool in electrochemistry and cell biology for calculating the equilibrium potential for a specific ion across a membrane. It considers several critical factors:
- Temperature
- Concentration of the ion on both sides of the membrane
- Charge of the ion
It also incorporates two important constants:
- Faraday's constant
- Universal gas constant R
Calculating the Change
While the Nernst equation calculates the membrane potential at a given point in time or under specific conditions (often for a single ion at its equilibrium), calculating the change in membrane potential requires comparing two states.
Here's how you approach calculating the change:
- Calculate the Initial Membrane Potential (Vinitial): Determine the membrane potential at the beginning of the period or under the initial conditions using appropriate methods (like the Nernst equation for equilibrium potentials of specific ions, or the Goldman-Hodgkin-Katz equation for the overall membrane potential considering multiple ions).
- Calculate the Final Membrane Potential (Vfinal): Determine the membrane potential at the end of the period or under the final conditions, again using the same methods based on the new conditions (e.g., changed ion concentrations).
- Find the Difference: Subtract the initial potential from the final potential.
Change in Membrane Potential (ΔVm) = Vfinal - Vinitial
Factors Causing Change
A change in membrane potential occurs when the underlying factors that determine the potential shift. Based on the Nernst equation as described in the reference, these changes are often driven by alterations in:
- Ion Concentrations: Changes in the concentration gradients of key ions (like Na⁺, K⁺, Cl⁻, Ca²⁺) across the membrane are a primary driver of membrane potential changes. For instance, opening ion channels can rapidly change ion concentrations near the membrane.
- Membrane Permeability: Although not explicitly listed as a factor in the Nernst equation itself (which is for equilibrium potential of one ion), changes in the membrane's permeability to different ions significantly impact the overall membrane potential (as described by the related Goldman-Hodgkin-Katz equation, which builds upon Nernst). This is how nerve impulses propagate, through the opening and closing of ion channels.
- Temperature: As indicated by the Nernst equation, temperature is a factor. Changes in temperature can influence ion movement and channel kinetics, thereby affecting potential.
Therefore, to calculate a change in membrane potential, you quantify the membrane potential before and after an event that alters these critical factors.
