Electrical Models of the Neuronal Cell Membrane

This is a first draft which has not been edited. If you have questions, or want to help in the writing or editing process, please contact the author: jacksonstringham@mail.weber.edu

Neurons communicate using a combination of electrical and chemical signals. This section will go in depth about the electrical part of neural communication. At its core, electricity involves the movement of charged particles. In electronic circuits, this means moving electrons through wires. In neurons, ions (such as sodium [Na⁺], potassium [K⁺], chloride [Cl⁻], and calcium [Ca²⁺]) carry electrical charge as they move across the cell membrane.

Three fundamental electrical properties that describe electrical activity:

1. Voltage (V) – Measures the difference in electrical potential energy between two points. In neurons, this refers to the membrane potential, which is the relative difference in charge and amount of ions between the inside and outside of the cell.
2. Current (I) – The flow of charged particles. In neurons, this refers to ions moving across the membrane.
3. Resistance (R) – When something disrupts the current’s flow. In neurons, ion channels act as resistors, controlling how ions can pass through the membrane. Resistance is also affected by the radius of the axon.

These relationships are described by Ohm’s Law:

V = IR

Using the common metaphor of water for electrical circuits, voltage is dictated by the potential energy of the water, current is the water pressure, and resistance is anything that impedes the water. An example would be a water tower providing water to a town. The Voltage is the water tower because the gravity is trying to pull the water down from the tower (high potential energy). The current is how fast the water flows out of the tower and the resistance would be the size of the pipes. Note that how fast the water flows and the size of the pipes are related variables.

Using a neuron as an example, if resistance is high then neuron has less open ion channels. This would contribute to less current or diffusion of ions. If resistance is low then the neuron has more open ion channels. This would contribute to more current or diffusion of ions.

In electrical models, there are often symbols signifying electrical properties or elements in a circuit. Here are key components and their meanings:

Symbol	Name	Circuit Component	Neuronal Equivalent
	Battery	Voltage source	Membrane potential between intracellular and extracellular
	Resistor	Resistance in wire or module	Total ion channels or amount of open ion channels
	Capacitor	Two metal plate	Cell membrane (the phospholipid bilayer)

Now we present a neuronal model first proposed by Hodgkin and Huxley (1952) that has since been confirmed by experimental research and is widely used in neuroscience. The following paragraphs discuss the model in detail.

The neuronal model contains a capacitor (C). In traditional electrical circuits, a capacitor consists of two metal plates that store charge by allowing electrons to accumulate on one plate while creating an opposite electrical field on the other. This enables the capacitor to store and release energy quickly. In neurons, the cell membrane functions as a capacitor by storing electrical charge and separating ions between the intracellular (inside) and extracellular (outside) environments. This capacitance is essential for maintaining the membrane potential, which regulates how neurons generate and transmit electrical signals.

Each ion channel in the membrane is represented as a conductance (g) in the circuit. These conductance, symbolized by zigzag lines, act like resistors that control the flow of specific ions across the membrane. For this textbook all you need to know is conductance is basically the inverse of resistance. The conductance of sodium (g_Na), potassium (g_K), chloride (g_Cl), and calcium (g_Ca) determines how easily these ions move in and out of the cell. The arrow through the symbol signifies that there is an ability to change the conductance. When an ion channel is open, its conductance is high (low resistance), allowing ions to flow more freely, whereas a closed channel has low conductance (high resistance) and restricts ion movement.

In addition to conductance, the model includes batteries (V) that represent the equilibrium potential of each ion. These potentials, denoted as V_Na, V_K, V_Cl, and V_Ca, correspond to the voltage at which there is no net movement of a particular ion across the membrane. Each ion’s equilibrium potential is determined by the Nernst equation, discussed later, which depends on its concentration inside and outside the cell. The voltage created by a neuron is due to the concentration gradient of these ions, supported by the processes like the sodium-potassium pump. These values influence the overall membrane potential energy of the neuron.

This summary model explains neuronal behavior through the following steps. At rest, the neuron maintains a resting membrane potential (about -70 mV) due to ion gradients and selective permeability of the membrane. When stimulated, ion channels open, changing the resistance and allowing specific ions to flow, altering the membrane potential. This leads to the generation of an action potential, discussed in detail later, where the neuron rapidly shifts from negative to positive charge and then returns to rest. Further sections cover the intricacies of this process.