When we first encounter electrical circuits in lecture, it is easy to get lost in an abstract sea of squiggles with no immediate applications. But these squiggles are an incredibly powerful tool that can allow us to understand the biological mechanisms that permit you to read this text. Indeed, the nerve impulse that is generated when a photon from the computer screen hits your retina and interacts with light-sensitive cells travels along the optic nerve as an electrical signal. All other sorts of stimuli in your body – movement of muscles, feeling of heat, taste, hearing, etc. – travel along your nerves and cells in the form of electrical signals that follow the same transmission process: given a physical stimulus within the cell, a change in the cell membrane potential arises, leading to an electrical signal that is transferred between neurons and muscle cells.

In this experiment, you will model the transport of electrical signals that arise due to changes in the cell membrane potential – otherwise known as the action potential – as a reaction to external stimuli. This sort of signal transport due to changes in action potentials in the cell membrane is known as passive transport. In this type of transport, there is no energy input from the cell but solely depends on changes in the electrical potential and ionic concentration within and without the cell membrane, which differentiates it from active transport.

By completing this experiment, you will:

1. Apply Ohm's law and Kirchhoff's rules to develop a circuit model of the resting potential of a cell membrane;
2. Model the main phases of the generation of an action potential of a cell by manipulating the resting potential circuit;
3. Determine how a potential difference across nerve cells, more specifically, across the axon, spreads along the cell using concepts of resistivity and capacitance.

Before thinking about action potentials, let us first consider the electrochemical properties of cells and the resting potential that arises across a cell membrane due to these properties. The cell membrane consists primarily of a phospholipid bilayer that separates the inner fluid of the cell from the outer fluid in its environment. Both of the fluids inside and outside the cell consist of a solution full of ions and, while the bilayer impedes free flow of the fluids between the membrane, there are proteins on the surface of the cell that selectively permit ions to flow. This creates a gradient in the concentration of ions and thus the charge density inside and outside the cell, which in turn leads to a potential difference between the inner and outer surfaces of the cell. In the absence of metabolic processes and transport mechanisms, the potential difference between the inner and outer surfaces is around $-70 \text{ mV}$ for most animal cells and arises largely from the presence of $\text{Na}^+$, $\text{K}^+$ and $\text{Cl}^-$ ions. See Figure 1 for a pictorial model of the cell membrane and resting potentials.

Given the presence of concentration and charge we could in theory apply