# What is the Difference Between Nernst Equation and Goldman Equation

Both Nernst equation and the Goldman equation are used to calculate the membrane potential of a cell. Membrane potential is the voltage difference across a cell’s membrane. This potential is involved in nerve impulses, muscle contractions, and overall cell function.

What is the difference between Nerst equation and Goldman equation? Nerst equation focuses on a single ion, whereas Goldman equation focuses on multiple ions.

### Key Areas Covered

1. What is Nernst Equation
– Definition, Features
2. What is Goldman Equation
– Definition, Features
3. Similarities Between Nernst Equation and Goldman Equation
– Outline of Common Features
4. Difference Between Nernst Equation and Goldman Equation
– Comparison of Key Differences
5. FAQ: Nernst Equation and Goldman Equation

### Key Terms

Nernst Equation, Goldman Equation

## What is the Nerst Equation?

The Nernst equation is a mathematical formula that relates the reduction potential of an electrochemical reaction (redox reaction) to the standard electrode potential, temperature, as well as the activities (or concentrations) of the chemical species involved. In simple words, it helps to calculate the voltage of an electrochemical cell under nonstandard conditions.

The Nernst equation is expressed as:

E = E° – (RT/nF) * ln Q

Where:

E is the cell potential under nonstandard conditions
E° is the standard cell potential
R is the gas constant
T is the absolute temperature
n is the number of electrons transferred in the redox reaction
Q is the reaction quotient

When the concentrations of reactants and products are given, the voltage of the cell can be calculated. Finding the conditions where E = 0 helps to calculate the equilibrium constant of a reaction. It also explains how factors like concentration and temperature affect cell behavior.

## What is Goldman Equation

The Goldman equation is also called Goldman-Hodgkin-Katz (GHK) equation. Goldman equation considers the contributions of multiple ions to the membrane potential.

The Goldman equation is expressed as:

Em = (RT/F) * ln((Pk[K+]o + PNa[Na+]o + PCl[Cl-]i)/(Pk[K+]i + PNa[Na+]i + PCl[Cl-]o))

Where:
Em is the membrane potential
R is the gas constant
T is the absolute temperature
Pk, PNa, and PCl are the permeabilities of potassium, sodium, and chloride ions, respectively
[K+]o, [Na+]o, and [Cl-]o are the extracellular concentrations of potassium, sodium, and chloride
[K+]i, [Na+]i, and [Cl-]i are the intracellular concentrations of potassium, sodium, and chloride

This equation can explain the generation and propagation of electrical signals of neutrons and other excitable cells.

## Similarities Between Nerst Equation and Goldman Equation

1. Both equations consider the concentration differences of ions across the cell membrane.
2. Moreover, both equations include temperature as a variable, reflecting the kinetic energy of the ions.
3. Furthermore, physical constants, gas constant (R), and Faraday’s constant (F) are shared between the two equations.
4. In addition, these equations are based on thermodynamic principles.

## Difference Between Nernst Equation and Goldman Equation

### Definition

• Nernst equation is a mathematical formula that relates the reduction potential of an electrochemical reaction to the standard electrode potential, temperature, and the activities of the chemical species involved. Goldman equation, on the other hand, is a mathematical formula for the resting membrane potential of a cell by considering the permeability and concentrations of multiple ions.

### Focus

• Nernst equation focuses on a single ion at a time, while Goldman equation focuses on multiple ions simultaneously.

### Nature

• Nernst equation assumes the membrane is perfectly permeable to the ion being considered, whereas Goldman equation incorporates the relative permeabilities of different ions to the membrane.

### Calculation

• Nernst equation calculates the equilibrium potential for a single ion. Goldman equation, on the other hand, calculates the overall membrane potential based on multiple ion concentrations and permeabilities.

### Complexity

• Nernst equation is a relatively simple equation while Goldman equation is a more complex equation due to multiple variables involved.

## Conclusion

Nernst equation focuses on a single ion’s equilibrium potential, while Goldman equation provides a more accurate representation of membrane potential by considering multiple ions and their permeabilities. Thus, this is the basic difference between Nernst and Goldman equation. Moreover, both are found involved in electrophysiology.

## FAQ: Nerst Equation and Goldman Equation

### 1. What is the Goldman equation used for?

The Goldman equation is used to calculate the resting potential across a cell membrane by considering the concentrations and permeabilities of multiple ions.

### 2. What is meant by Goldman’s equation and Nernst equation of resting potential?

Nernst equation calculates the equilibrium potential for a single ion across a membrane. Goldman equation, on the other hand, calculates the overall membrane potential considering multiple ions and their permeabilities.

### 3. What does the Goldman equation take into account that the Nernst equation does not?

The Goldman equation considers the permeabilities of multiple ions (like sodium, potassium, and chloride) across the membrane, while the Nernst equation only focuses on a single ion at a time.

### 4. Does the Nernst equation calculate resting membrane potential?

No, the Nernst equation calculates the equilibrium potential for a single ion, not the overall resting membrane potential. The Goldman equation, which considers multiple ions and their permeabilities, is more accurate for determining resting membrane potential.

### 5. Why do we need the Nernst equation?

The Nernst equation predicts the voltage of an electrochemical cell under nonstandard conditions. Therefore, it helps understand how factors like ion concentration and temperature affect cell potential.

##### Reference:

1. “Goldman Equation – An  Overview.” Science Direct.
2. “Nernst Equation.” Wikipedia. Wikipedia Foundation.

##### Image Courtesy:

1. “Membrane Potential” By smonsays – Own work (CC BY-SA 4.0) via Commons Wikimedia

### About the Author: Hasini A

Hasini is a graduate of Applied Science with a strong background in forestry, environmental science, chemistry, and management science. She is an amateur photographer with a keen interest in exploring the wonders of nature and science.