Re: nernst equation:how it tells bout active/passive transport of an ion

A membrane potential arises when there is a difference in the electrical 
charge on the two sides of a plasma membrane.  For example, the Na-K 
ATPase (figure 1) helps to maintain the osmotic balance across a plasma 
membrane by actively pumping 3 Na+ ions out of the cell and pumping 2 K+ 
ions into the cell per cycle of the ATPase.  However, animal cells also 
have K+ leak channels in the plasma membrane.  As a result of these 
channels, K+ will come to an equilibrium where the electrical force 
exerted by the negative charge inside the cell (due to the loss of K+ 
ions) is balanced by the tendency of K+ to leak out of the cell down its 
concentration gradient (remember, [K+] is low outside the cell due to the 
Na-K ATPase actively pumping K+ into the cell).  

The cell will eventually come to a dynamic equilibrium in which there is 
no net flow of ions across the plasma membrane, also known as the resting 
membrane potential.  

The Nernst equation is used for calculating the equilibrium potential of a 
single ion, the membrane potential at which equilibrium is reached for 
that particular ion.  

The Nernst equation is:

V=RT * ln*Co
  zF      Ci

V=equilibrium potential in volts
Co=outside concentration of the ion
Ci=inside concentration of the ion
R=gas constant (2 cal mol-1 K-1)
T=absolute temperature (in Kelvin)
F=Faraday's constant (2.3x104 cal V-1 mol-1)
z=valence of the ion
ln=log base e

If we simplify the above equation and assume a temperature of 37* C, we 
get V=61.5*log10*(Co/Ci)

If we further assume that we are talking about a typical cell, the outside 
concentration of K+ would be about 5mM and the inside concentration of K+ 
would be about 140mM.  Therefore, VK= ~(-89mV).  At this membrane 
potential there is no net flow of K+ across the plasma membrane.

The Goldman equation is used more frequently in cellular physiology since 
it is used to calculate the potential across a plasma membrane taking into 
account all of the ions that are permeable through the membrane, not just 
taking into account a single ion like the Nernst equation.