# 2014 Ion Channel Physiology

## Equilibrium (or reversal) potentials

 For each ion, the equilibrium (or reversal) potential is the membrane potential where the net flow through any open channels is 0. In other words, at Erev, the chemical and electrical forces are in balance. Erev can be calculated using the Nernst equation. In mammalian neurons, the equilibrium potential for Na+ is ~+60 mV and for K+ is ~-88 mV.
• ions can move in either direction through a channel (i.e., either into or out of the cell)

• the direction of ion movement (i.e., whether there is an inward or outward current) changes depending upon the membrane voltage, because the concentration gradients are essentially unchanging (they are maintained by the transporters)

• for a given ion, the reversal potential can be calculated by the Nernst equation where:
• R = gas constant
• T = temperature (in oK)
• z = ion charge

• for a mammalian neuron at 37oC, the Nernst equation can be simplified to:
• using this equation, and the extracellular and intracellular concentrations listed in the electrochemical gradient discussion, the equilibrium potential for
• K+ is -88 mV
• Na+ is +60 mV
• Cl- is -61 mV

• consider a neuron that has:
• a resting membrane potential of -12 mV (as established by Na+/K+ ATPase)
• no voltage- or ligand-gated channels
• initially, no leak channels

### K+ Reversal Potential (as an example)

•  Vm Electrical Gradient Concentration Gradient Net Ion Flow +100 out (strong) out out +60 out (weaker) out out 0 none out out -12 in (weak) out out -88 in (stronger) out none -100 in (strong) out in
What will be the effect on the membrane potential of adding leak K+ channels to this fictitous cell?

• Start by determining the electrical and chemical gradients
• The electrical gradient will move K+ ions into the cell at negative voltages and out of the cell at positive voltages
• The concentration gradient is always out because [K+]in >>> [K+]out

• When the electrical and concentration gradients are in agreement, the direction of flow is obvious:
• at +100 and +60 mV, K+ will flow OUT of the cell through any open K+ channels

• as the membrane potential hyperpolarizes, the electical driving force weakens, until --- at 0 mV --- it reverses polarity and grows in strength as membrane potentials become more hyperpolarized
• although there is no electrical gradient at 0 mV, there is a concentration gradient, so the net K+ flow will still be OUT of the cell

• at the equilibrium potential for K+ = -88 mV, there is no net flow
• the reason that the equilibrium potential is also called the reversal potential is because the direction of ion flow will be in opposite directions for potentials on either side of Erev
• therefore, at -12 mV, the net flow of K+ will still be OUT
• at -100 mV, the net flow of K+ will be IN
• this occurs because the inward electrical force is now larger than the outward concentration gradient

### LEARNING EXERCISE:

• Construct the same table for Na+ and Cl- (you will want to pick different voltages)
Email: Dr. Janet Fitzakerley | ©2014 University of Minnesota Medical School Duluth | Last modified: 20-sep-14 10:16 AM