# Membrane Potential: Definition, Equation & Calculation

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• 0:02 Plasma Membrane
• 1:29 Membrane Potential
• 3:20 Nernst Equation
• 5:52 Calculations
• 8:28 Lesson Summary

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Lesson Transcript
Instructor: Darla Reed

Darla has taught undergraduate Enzyme Kinetics and has a doctorate in Basic Medical Science

This lesson will define and explain membrane potential: what it is and what makes it. Discover how to calculate membrane potential using an equation, and find out what variables are most commonly used to do so.

## Plasma Membrane

Indoors we regulate temperature by using thermostats. To keep out bugs and unwanted animals, we use screens, doors and windows. Cells also want a regulated interior and to escape the outside environment. The wall that separates a cell from the outside is called the plasma membrane. It keeps unwanted molecules out and regulates what enters - but how?

Cell membranes are made up of a variety of components. Each component has a specific purpose and function. One component of a cell membrane is called the sodium (Na+)-potassium (K+) ATPase or Na+/K+ pump. It may sound a little complicated, but the function is similar to what you think a pump does. Pumps can be used to remove water or add air. The Na+/K+ pump kicks three sodium ions out of the cell, while at the same time importing two potassium ions.

Hold up! What are ions? An ion is a charged particle. The plus (+) or minus (-) attached to an element or molecule indicates it is charged. So Na+ and K+ are positively charged ions, or cations. Negatively charged ions are called anions. Ions play an important role in determining the potential of a membrane. What does that mean?

## Membrane Potential

Ions are present inside and outside a cell in varying amounts known as concentrations. Let's say you throw a party at your house. If it gets too crowded inside, many people may migrate outside for some fresh air, which we call efflux. If it gets too crowded outside, people will go back inside, which we call influx. Eventually, there will be an equal amount of people outside and inside: this situation is known as equilibrium. Ions behave similarly. A lower number of sodium ions (Na+) outside of the cell will make the ones inside want to go out, and vice versa, until equilibrium is achieved.

But this equilibrium comes with a cost because ions have something other molecules don't - a charge. The more positive ions that leave, the more negative a cell becomes. Since the number of cations and anions are not equal, the charge inside and outside cannot be equal. So, the cell must sacrifice either equal concentrations or equal charge.

So what does the cell do? A cell uses many of its membrane components, including the Na+/K+ ATPase pump, to regulate ion concentration inside and outside the cell. The balance between molecule number and charge is known as an electrochemical gradient. Cells actually prefer to be more negative inside. The difference between the concentration of molecules and charge inside and outside a cell is known as membrane potential.

The membrane potential of a cell is measured in voltage or volts (V), like electricity. Only the voltage is much smaller, so millivolts (mV) are used, where 1000 mV = 1V. How does one measure the membrane potential of a cell?

## Nernst Equation

Membrane potential (E) can be calculated using the Nernst equation. This equation gives us a cell's resting membrane potential, or baseline state. Delving into how membrane potential is measured can seem overwhelming, especially if you've seen the Nernst equation - it even sounds complicated. Before we get to the mathematics, let's look at the factors involved, including temperature, concentration, Faraday's constant, and the universal gas constant.

### Temperature (T)

You like to keep your house at a particular temperature to make it comfortable, and you change clothes accordingly if the air conditioning or heat isn't functioning properly. Temperature is a factor that controls membrane potential just like the temperature can control what you wear. Temperature in the equation, however, is not measured in Fahrenheit or Celsius but in units called Kelvin (K).

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