E1 Resting membrane potential (Nernst/Goldman-Hodgkin-Katz)

Topic

The neuronal membrane separates an intracellular medium from an extracellular medium in which ions—primarily potassium, sodium, and chloride—are unevenly distributed. This unequal distribution of ions across the neuronal membrane is maintained by three factors: the concentration gradients of each ion, the selective permeabilities of the neuronal membrane to each ion type, and the active transport performed by the sodium-potassium pump, which moves ions against their concentration gradients by consuming energy.

For a single ion type, there exists a specific membrane potential at which the electrical force driving the ion exactly balances the diffusive force driving it in the opposite direction; this electrochemical equilibrium point for an individual ion is known as its Nernst potential, and it depends on the ion's valence, the temperature, and the ratio of the ion's concentrations on either side of the neuronal membrane. The greater the concentration ratio of an ion across the neuronal membrane, the further that ion's Nernst potential deviates from zero.

However, a real neuronal membrane is not permeable to only one type of ion; rather, it is simultaneously permeable to several ions, each with its own relative permeability. Consequently, the observed membrane potential does not match the Nernst potential of any single ion. Instead, the observed membrane potential results from a weighted average—based on each ion's relative permeability—of the Nernst potentials of all ionic species to which the membrane is permeable: the higher an ion's relative permeability compared to the others, the closer the observed membrane potential comes to that specific ion's Nernst potential. This method of averaging Nernst potentials weighted by permeability is the relationship described by Goldman, Hodgkin, and Katz, and it ultimately determines the membrane potential observed in a real neuronal membrane. Each individual ionic current crossing the neuronal membrane can be described as the product of two factors: the conductance of the channel through which the ion passes and the electrochemical driving force acting on that ion—that is, the difference between the observed membrane potential and the Nernst potential for that specific ion. The greater the difference between the observed membrane potential and an ion's Nernst potential, the greater the electrochemical driving force for that ion and, consequently, the greater the individual ionic current flowing across the neuronal membrane for that ion.

At steady state, the sum of all individual ionic currents crossing the neuronal membrane is zero: currents entering the membrane are exactly balanced by currents leaving it, and it is precisely this condition of a net sum of zero that defines the equilibrium point known as the neuronal membrane's resting potential.

The neuronal membrane's capacitance, together with its total conductance, also determines the time constant with which the membrane potential responds to a perturbation: the higher the membrane capacitance, the slower the response of the membrane potential to the perturbation; conversely, the higher the total membrane conductance, the faster the response of the membrane potential to that same perturbation.

This model of the resting neuronal membrane forms the foundation upon which subsequent models are built—models describing the generation and propagation of action potentials, as well as the membrane abnormalities associated with other pathologies included in this catalog. Ultimately, it is this neuronal membrane—with its unequal ion distribution, individual Nernst potentials, observed membrane potential, and characteristic time constant—that lays the groundwork for all subsequent models of the nervous system.

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