The mechanistic bases of electrical signaling in neurons can be understood by considering a simple spherical

cell (Figure 7.2(a)) with a membrane that is semi-permeable (i.e., a membrane that passes ions, but only slowly,

so that the internal and external concentrations of the ions can be assumed constant). Two factors influence

the movement of ion X through the membrane. First, any concentration gradient of X across the membrane

will drive a diffusive flux, according to Fick’s first law. Second, because the ion has charge, its movement will be

influenced by any electrical field across the membrane. The Nernst equation describes the equilibrium

condition for ion X, in which these two sources of ionic flux cancel each other out, resulting in zero net flux:

In Equation (7.1), E

is the equilibrium or Nernst potential, the value of membrane potential (inside minus

outside, by convention) at which this single-ion system is at equilibrium. R is the molar gas constant,

8.31 J/(mol K). T is absolute temperature in degrees Kelvin. z

is the valence of X (þ1 for Na

and K

). F is

Faraday’s constant, 96,500 C/mol. ½X

and ½X

are the external and internal concentrations of X, typically

expressed in mM. It is often more convenient to convert the Nernst equation to log

, and to assume a value of

temperature. At 37

C, the Nernst equation reduces to

where E

has units of mV.