Membrane Potentials / RMP / E_{rev}
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 E_{rev}, the chemical and electrical forces are in balance. E_{rev} 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 ^{o}K)
 z = ion charge
 F = Faraday's constant
 for a mammalian neuron at 37^{o}C, 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
 using this equation, and the extracellular and intracellular concentrations listed in the electrochemical gradient discussion, the equilibrium potential for
 consider a neuron that has:
 a resting membrane potential of 12 mV (as established by Na^{+}/K^{+} ATPase)
 no voltage or ligandgated channels
 initially, no leak channels
K^{+} Reversal Potential (as an example)

V_{m}Electrical
GradientConcentration
GradientNet Ion Flow+100
out
(strong)out
out+60
out
(weaker)outout0noneoutout12in
(weak)outout88in
(stronger)outnone100in
(strong)outin  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 E_{rev}
 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)