The Nernst Equation and Action Potentials in the Nervous System

Contents Abstract Introduction The Cell Membrane and Ion Pumps in a Neuron The Nernst Equation and Resting Potential Action Potentials Propagation of Action Potentials and Multiple Sclerosis Relation to Heart Disease Related Reading About the Author References Abstract This document discusses modeling of electric fields and ion concentration gradients in the nervous system.  In particular, equilibrium and action potentials in neurons will be modeled with the Nernst equation.  The relation to multiple sclerosis and heart health will also be discussed. Introduction A neuron is a nerve cell.  The axon is the tail of the neuron that carries electrical (nerve) impulses from many locations within the body to and from the central nervous system.  It is possible to model the differences in ion concentration and electrical gradients using basic chemistry.   The Nernst equation which relates electric potential to concentration can be used to model electric fields within the nervous system.  This web page will demonstrate calculations with the Nernst equation in an interactive way.  It will then demonstrate generation of sudden changes in electric potential, called action potentials, within axons.  An accompanying document, Getting Started Developing Interactive Web Interfaces for Scientific and Medical Applications, describes how to code the interactive parts of the user interface using dynamic HTML. The Cell Membrane, Ion Pumps, and Channels in a Neuron The structure of a neuron is shown below. Structure of a Neuron6

The table below lists typical concentrations of the most common ions on the inside and outside of the cell.

In the table mM is millimols / liter and μM is micromols / liter.  The concentrations are maintained by ion pumps embedded in the neuron cell membrane.  The ion pumps drive sodium ions out of and pump potassium ions into the cell.  The ion pumps are powered by adenosine triphosphate (ATP).  There are also channels that allow the free flow of ions in either direction when activated.

The Nernst Equation and Resting Potential

At resting potential the sodium - potassium pumps move approximately the same electrical charge inside as outside the cell.  However, potassium channels are also present allowing free flow of only potassium ions.  The higher concentration of potassium inside the cell drives potassium ions to the outside.  After a small number of potassium ions leave the cell the outside of the cell becomes positively charged compared to the inside, developing an electrical field.  This electrical field balances the force on the ions from the concentration gradient and is known as the resting potential.

The Nernst equation for the potassium equilibrium potential over the cell membrane is

where

EK	The electric potential across the membrane due to the potassium concentration gradient
R	Universal gas constant (8.314472 J · K-1)
T	Absolute temperature (Kelvin = 273.15 + ºC = 298.15) at 25ºC
[K+]out	potassium concentration outside membrane
[K+]in	potassium concentration inside membrane
zF	Number of electric charges carried by a mole of K+
z	Number of electrons (one for K+)
F	Faraday constant, equal to 9.6485309×104 C mol-1

Putting values in the equation gives this result.  Try changing the values in the text fields and clicking the update button to compute a new value for E_K (values in formula will be updated).

The 10³ term converts from Volts to milliVolts.  The computed number is a little higher than the quantity measured in experiments (-70 mV) but all the factors in this complex physical process have been accounted for.

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