1.2 Membrane Potential: Its components and maintenance

The plasma membrane surrounding every cell is selectively permeable. By itself, the lipid bilayer is not permeable to any ions. However, the introduction of channels and transporters allows for the exchange of some, but not all, ions. Channels are always selective for one to two ion types.

In a single ion system where the membrane is perfectly permeable to that ion, particles would exchange via channels until equilibrium is achieved. Given any concentration differential, an equilibrium potential that achieves equilibrium can be calculated. If the current charge differential across the membrane results in a membrane potential that deviates from the equilibrium potential, then ions would be exchanged in net until equilibrium is achieved.

In the brain, the concentration of ions surrounding a resting state neuron have already been characterized (Table 1). If a neuron was to be made perfectly permeable to only one ion, but perfectly impermeable to all other ions, then the Nernst equation could be used to calculate equilibrium potential. Ions would then be exchanged across the membrane to bring membrane potential closer to equilibrium. In this theoretical case, if one was to plug the numbers from Table 1 into the Nernst equation, they would calculate an equilibrium potential of +50mV for Na, -90mV for Potassium, +135mV for Calcium and -70mV for Chloride.

In reality, neurons exist as multi-ion systems, with varying membrane permeability for different ions. The plasma membrane surrounding a neuron is characterized as being selectively permeable. By itself, the lipid bilayer which forms the membrane is not permeable to any ions. However, the introduction of channels and transporters allows for the exchange of some, but not all, ions. Channels are always selective for one to two ion types. Therefore, if no channels exist to facilitate the transfer of one ion type, then the membrane is impermeable to it. If a cell has a low concentration of sodium channels but a high concentration of potassium channels, then it is permeable to both, but relatively much more permeable to potassium. There are two major types of passive transport channels; constitutive/leak channels and gated channels. The former are always open and facilitate the transfer of ions towards equilibrium constitutively. The latter are only opened after an event has occurred, lifting the proverbial gates that otherwise keep the channel closed and unable to facilitate ion transfer. Gated channels exist in two major subtypes: ligand-gated and voltage-gated. The former is only open when chemically bound by a ligand, while the latter only opens at certain voltage thresholds.

In reality, neurons exist as multi-ion systems, with varying membrane permeability for different ions. As a consequence, the Nernst equation cannot be used to calculate an equilibrium potential. In response to this, mathematicians, physicists and chemists were able to derive a similar equation to the Nernst system which applies to multi-ion systems; The Goldman equation:

[latex]V_{m} \approx -60 \, mV \; log_{10} \; \frac{P_{K}[K]_{in} + P_{Na}[Na]_{in} + P_{Cl}[Cl]_{out}} {P_{K}[K]_{out} + P_{Na}[Na]_{out} + P_{Cl}[Cl]_{in}}[/latex]

As can be seen above, the Goldman equation is very similar to the Nernst equation, the only difference being that it incorporates multiple ions, and introduces a new variable: . The value is a measure of the membrane’s permeability to that specific ion. It is basically a proxy for the number of open channels found on the membrane that are selective to that specific ions. Remember, leak channels are always open, but gated channels open in response to a stimulus. Gated channels can thus transiently change the permeability to an ion i.e only when a ligand is bound. For calculations of resting state neuronal potential, we assume that all gated channels are closed.

A neuron at resting state has an equilibrium potential of -70mV. There are three main components which contribute to this number; leak channels, Na/K pumps, and charged, non-permeable factors:

Leak channels:

In the resting state, neurons contain constitutively/continuously open channels, termed “leak” channels. The majority of these are potassium leak channels, allowing for regular exchange of potassium ions. To a much lesser extent, there are few chloride leak channels, and very few sodium leak channels. These exist in a ratio of 100:45:4 (K:Cl:Na).

With 100 potassium leak channels alone, the membrane potential would be -90mV (potassium’s equilibrium potential as calculated by the Nernst equation). However, the introduction of 45 chloride channels would raise that closer to -70mV, such that the membrane potential is somewhere between -90mV and -70mV. The third introduction of a very small number of sodium channels (i.e 4) is sufficient to then drag the average membrane potential up to around -70mV. This can be seen in the image below; while it initially starts with only potassium channels, the addition of chloride channels brings the membrane potential closer to -70, and the final introduction of sodium channels brings it all the way up to -70mV.

Na/K Pumps:

There is a third protein which actively aids in the maintenance of a resting membrane potential around -70mV: the Na+/K+ pump. This transport pump uses energy from ATP hydrolysis to move ions against their concentration gradient. Specifically, for every molecule of ATP that is hydrolyzed, 3 Na ions are pushed out into the extracellular space, and 2  K+ ions are brought into the intracellular space. This counteracts leak channels, which move these two ions in the opposite directions. It is the fact that this pump moves the ions in the direction opposing their chemical gradient that makes it necessitate the hydrolysis of ATP. This pump is very important for maintain membrane potential at resting levels of -70mV; it moves more positive charge out of the membrane, thus keeping the inside more negatively charged.

Non-permeable factors:

Neurons have additional charged molecules which contribute to the relatively negative intracellular charge differential. First of all, there is a high concentration of Calcium ions outside of the neuron. Since the resting state neuron is completely impermeable to Calcium, these positive charges are trapped outside, contributing to the fact that the intracellular side is more negative than outside. Similarly, intracellular proteins, which cannot pass through the membrane, are net negative in a neuron. This traps additional negative charge intracellularly.