Electrochemical Gradients and Membrane Potential

1. The Concentration Gradient (Chemical Push): Particles naturally want to move from areas of high concentration to areas of low concentration through a process called diffusion.
2. The Electrical Gradient (Voltage Push): Because opposite charges attract and like charges repel, ions will drift toward areas of opposite charge.

These two forces can work together or against each other. For example, if a cell is negatively charged inside, it will pull positive $\text{K}^+$ ions inward (electrical push), even if those ions are already highly concentrated inside (concentration push working against it). When these two forces reach a perfect balance where there is no net flow of ions, the system has reached equilibrium.

Membrane Potential and the Resting State

The membrane potential is the specific voltage across a cell's membrane. In a typical neuron, we observe a resting potential, where the inside of the cell is more negative than the outside. For most neurons, this resting potential is approximately $-70\text{ mV}$.

This "charged" state is not a passive accident; it is actively maintained by two biological components:

• The Pump (Active Transport): The Sodium-Potassium Pump is an energy-intensive mechanism that uses ATP to move $3\text{ Na}^+$ ions out of the cell and $2\text{ K}^+$ ions into the cell. This creates the high concentration of $\text{Na}^+$ outside and $\text{K}^+$ inside that we see at rest.
• Ion Channels (Passive Transport): These are specialized pores in the membrane that allow specific ions to flow "downhill" through diffusion without using ATP.

Calculating Equilibrium: The Nernst Equation

How do we know exactly what voltage is required to balance the chemical and electrical pushes for a single specific ion? We use the Nernst Equation. This equation calculates the equilibrium potential ($E$) for an ion based on its concentration ratio across the membrane:

$$\begin{aligned} E = \frac{RT}{zF} \ln \frac{[\text{ion}]_{\text{outside}}}{[\text{ion}]_{\text{inside}}} \end{aligned}$$

Where:

• $R$ is the gas constant
• $T$ is the absolute temperature (in Kelvin)
• $z$ is the charge of the ion (e.g., $+1$ for $\text{Na}^+$, $+2$ for $\text{Ca}^{2+}$)
• $F$ is the Faraday constant
• $\ln$ is the natural logarithm

Each ion has its own unique "balance point". For instance, $\text{K}^+$ is highly concentrated inside the cell, and its equilibrium potential is determined by the electrical pull of negative proteins that are too large to leave the cell.

From Rest to Action: Depolarization

The resting potential is a state of readiness. Because the electrochemical gradient for $\text{Na}^+$ is so strong (high concentration outside and a negative charge inside), the cell is essentially a loaded spring.

If a stimulus causes $\text{Na}^+$ channels to open, the electrochemical gradient drives $\text{Na}^+$ into the cell. This influx of positive charge makes the internal environment less negative, a process called depolarization. If this depolarization reaches a certain threshold, it triggers an action potential—a rapid wave of voltage change that travels down the neuron to transmit information.

Check your understanding: If a poison were to stop all of a neuron's $\text{Na}^+/\text{K}^+$ pumps, the neuron would initially keep firing action potentials, but it would eventually fail as the concentration gradients "run down" and the resting potential disappears.