Understanding Membrane Potential and Ion Gradients

Concentration Gradient

A concentration gradient, also referred to as a chemical gradient, is present when there is a difference in the concentration of a substance across a membrane.

An electrical gradient exists when there is a difference in charge across a membrane, involving the positive and negative charges carried by ions.
Example: There are more positive charges outside the cell relative to the inside.
- This results in a membrane potential that can be conceptualized as a positive terminal outside the cell and a negative terminal inside the cell, similar to a battery.

Definition: The membrane potential is the electrical potential across a cell membrane, calculated as the total charge inside the cell minus the total charge outside the cell.
Typical Value: The membrane potential is often negative (e.g., around -70 millivolts) because of the typical distribution where there are more positive charges outside than inside.

If the inside has a charge of +2 and the outside has +50, the calculation would be:
- Membrane potential = Inside charge - Outside charge = 2 - 50 = -48.
Often, the calculation gives a negative value due to the typical ionic distributions maintained by pumps like the sodium-potassium pump.

When an ion channel (e.g., sodium ion channel) is introduced, it connects the charges across the membrane, allowing ions to flow according to their gradients.
Sodium ions (Na+) are more concentrated outside the cell, thus creating both an electrical and chemical gradient that drives sodium into the cell when the channel opens.

Resistance is determined by the number of ion channels available; more channels equal less resistance, facilitating easier movement of ions across membranes.
Ion channels enabling diffusion also help maintain or change the electrical gradient across the membrane.

Potassium (K+) has both electrical and chemical gradients:
- Chemical gradient pushes K+ out of the cell (higher concentration outside).
- Electrical gradient pulls K+ into the cell (negatively charged inside).
The strength of these gradients must be weighed to determine the net direction of K+ movement, which can be predicted mathematically.

The Nernst equation calculates the equilibrium potential for ions: E = \frac{RT}{zF} \ln \left( \frac{[ion]{outside}}{[ion]{inside}} \right)
- $E$ = equilibrium potential
- $R$ = universal gas constant (8.31 J/(mol K))
- $T$ = temperature (in Kelvin)
- $z$ = valence (charge) of the ion
- $F$ = Faraday's constant (96,500 C/mol)
Simplified form when calculating for monovalent ions:
E \approx 61/z \log{10} \left( \frac{[ion]{outside}}{[ion]_{inside}} \right)

For K+, if the concentration outside is 5 mm and inside is 140 mm:
- E{K^+} = \frac{61}{1} \log{10} \left( \frac{5}{140} \right)
Resulting in an equilibrium potential of approximately -88.29 millivolts.

At the equilibrium potential for K+, despite having gradients maintained, there is no net flow of K+ across the membrane because the electrical and chemical gradients balance each other out.
Movement of ions across a membrane can change the membrane potential significantly until reaching equilibrium, where net movement ceases.

For sodium (Na+), a similar calculation reveals equilibrium potential around +71.74 millivolts, indicating the strongly positive pull driving Na+ into the cell.
Once equilibrium is reached for Na+, there is still a concentration gradient present, resulting in potential future movements until conditions change.

Membrane potentials and ion movements are critical for cellular function, including generating action potentials in neurons.
Understanding how electrical gradients, chemical gradients, and the Nernst equation interact is crucial for comprehending cellular ion behavior.

Further discussions on action potentials and the physiological relevance of these electrical principles in neuronal activity and cell signaling will continue in subsequent lectures.