All cells develop a difference in electrical potential on either side of their cell membrane. The inside of the cell ranging from 9mV lower than the outside in some crustaceans up to just under 100mV in some human nerve cells. Although each cell itself maintains a constant potential difference under resting conditions. Membrane potential is important to cells in processes of ion regulation and in the control of osmotic pressure and hence cell volume. In nerves, this membrane potential can be distorted due to changes in ion concentration and the effect of this action potential used to carve neural information.

The major energy store in relation to generating the membrane potential are the differences in ionic concentration across the membrane. These differences in ionic gradient are set up by the various carrier and channel proteins that are that are spread throughout the lipid bilayer of the cell membrane. Considering an individual cell, the extracellular fluid can be thought of as a mixture of nearly constant concentration. This being regulated by various mechanisms within the body tissues. For example, the kidney. The cell, maintains significantly different concentrations of the various ions and needs to able to regulate those. Some cells also need to regulate ion concentrations in response to external stimuli but these need not be covered here.

The major mechanisms for varying concentrations inside the cell are the proteins in the cell membrane. To be considered first are the carrier proteins. Many of these move ions against their electrochemical gradient. For this they require an energy source as moving an ion from a region a lower concentration to that of higher concentration (or towards a point of the same electrical charge) requires energy to be put in. Otherwise potential energy has been created which contravenes the laws of thermodynamics. This is known as active transport. Other carrier proteins exist that carry ions into the cell along their concentration/electrical gradient. This is called facilitated diffusion and is used to control the numbers of such molecules travelling into or out of the cell.

Probably the most important carrier protein is the sodium-potassium pump. This works by utilising the energy in the conversion of an ATP molecule down to an ADP molecule to bring two K+ ions into the cell and transport three Na+ ions out again. Thus the ion concentrations within the cell are maintained at constant levels. In skeletal muscle sodium is found outside the cell at approximately 150mMol/l and 15 mMol/l inside potassium at 150mMol/l and 15 mMol/l inside and outside respectively and chloride ions kept at 9mMol/l and 125mMol/l respectively. These concentrations varying in different types of cell. It is thought that on average about 33% of the ATP used in cell metabolism is used to drive the ATP pump in cells. Although in some neurons this can be up to 70%.

Initially it was thought that the sodium potassium pump was electroneutral in nature in that for every sodium pumped out one potassium ion was pumped in. Some evidence for the electrogenic nature of the sodium-potassium pump is in a series of experiments by Thomas in 1967 and 1972 on neurons in snails. The principle of the experiment was to inject sodium ions into the body of the neuron. This was done by using two microelectrodes (made of glass tube drawn to an ultra-fine point), filled with sodium acetate solution. These were placed through the cell membrane into the cell. Passing a current between the two electrodes caused sodium ions to be injected at the cathodal electrode. The change in membrane potential could then be measured using a third microelectrode.

Initially, when the sodium was injected there was a hyperpolarization of the cell membrane. The potential difference dropping by 15 mV this returned to its normal level in about ten minutes or so. Ouabain was added to the neurons and the hyperpolarity was reduced.. This suggested its connection to active sodium transport. pour qoui? ou quelle?

The neurons were then suspended in a potassium free solution and a second injection of sodium ions was made into the neurons. There was no hyperpolarization. Adding potassium to the solution again showed immediate hyperpolarization of the cell membrane and thus showed that potassium influx and sodium efflux were intimately linked. To prove that it wasn't simply the addition of a cation into the cell that caused the hyperpolarization Thomas also injected the cells with potassium and lithium ions in the same manner as before. Neither of these ions gave any hyperpolarization of the cell membrane.

The next question for Thomas was to find a quantitative link for this relationship. He used a voltage-clamp technique in which another microelectrode was use to hold the membrane potential at the same level and thus the current through the membrane could be measured. Integrating the current with respect to time allowed Thomas to calculate the charge that had flowed through the membrane. What he found was that the charge flowing out of the cell due to the sodium efflux was much less than the charge that had been added to the cell as sodium ions. Measurement of the fluid surrounding the neuron though showed that all the sodium added had actually left the cell. Therefore another ion must be flowing into the cell in order to replace the charge that left with the sodium ions. From the second experiment it was obvious that this was the potassium. Thomas was able to calculate that about 27% of the charge actually flowed out of the cell. This can be considered as very close to the 33% of charge if the pump worked as above. Further experiments with red blood cells have shown that the ratios of sodium ion transport work in this manner.

Another important carrier protein 'pumps' Ca2+ ions into and out of the cell. This also utilises the energy contained in the ATP molecule and maintains the concentration of calcium ions in the intracellular fluid at approximately 10,000 times lower level than that in the extracellular fluid.

With these gradients in place it is easy to make assumption on how membrane potential is developed. With the presence of potassium leak channels the high concentration of potassium within the cell causes K+ ions to diffuse out into the extracellular fluid. To be produce any cation it is also necessary for an anion to be formed at the same time. In the cell the anions balancing the potassium cations are formed by some of the amino acid side chains on proteins within the cell. These however are far too large to pass out of the cell membrane either by direct diffusion or through the carrier proteins. Hence the efflux of potassium ions will leave a residual negative charge inside the cell.

With a negative charge within the cell there will be some measure of attraction for the potassium ions and as such as more potassium ions diffuse out of the cell and the potential difference between the inside and outside of the cell membrane will cause the rate of diffusion to decrease. Eventually the potential across the membrane will be high enough that the net rate of diffusion out of the cell will drop to zero. At this point the cell has reached a dynamic equilibrium. One point to note is that the potential difference is caused by movement of a tiny number of ions and in any region of the cell except at either side of a membrane the number of positive and negative charge will be equal.

The Nernst equation,

gives us the ability to calculate the membrane potential based on the knowledge of the concentrations inside and outside the cell. Applying the equation to mammalian motor neurons we can calculate that the equilibrium potential of chloride ions is -70mV which exactly matches the resting membrane potential. And hence we could assume that simple rules of diffusion occur across the membrane. Calculating the resting membrane potential for potassium we get a value of about -90mV showing that there are actually more potassium ions in the cell than their should be if the ion were allowed to equilibrate across the membrane. There is also a big discrepancy with the sodium ions which because of a large concentration outside the cell can be calculated to have a membrane potential of +65mV.

The idea of a sodium-potassium pump is able to account for this in a tidy manner. The action of the pump means that sodium ions are unable to equilibrate at all and although a small number of Na+ ions diffuse across the membrane the overall effect is that no more sodium ions are allowed to cross the membrane. Hence the Nernst equation does not hold true.

A more important equation is the Goldman constant-field equation.