Membrane potential

Figure 2.1 represents a cylinder of a hypothetical cell with an excitable membrane, and shows the distribution of the main intracellular and extracellular ions. Potassium ions and large organic anions labelled A- (e.g. hexosephosphates, ATP, proteins) are more concentrated inside the cell, whereas sodium ions and chloride ions are more concentrated without. The uneven distribution of sodium and potassium ions is maintained by an active transport mechanism, the sodium-potasium pump, which utilizes the cell’s metabolic energy in the form of ATP, and involves the enzyme system, transport ATPase (Na+/K+-dependent ATPase). Each enzyme molecule extends across the membrane. At its outer surface it has binding sites for K+, Mg2+ and ouabain and at its inner surface it binds Na+ and vanadate ions. Na+ is transported outwards and K+ inwards. Mg2+ is necessary to activate the enzyme, and ouabain and vanadate inhibit enzyme activity. If it is assumed for the moment that Na+-K+ exchange occurs on a 1:1 basis, then one cation is merely exchanged for another so that the pump does not directly affect the membrane potential; that is, it is non-electrogenic. In fact, in many tissues, including nerve and muscle, part of the pump expels 3Na+ in exchange for 2K+ so that the pump directly contributes to the membrane potential to a small extent and is therefore electrogenic. Nevertheless, its main function is to maintain the concentration gradients on which the membrane potential depends, and for the purposes of the present discussion the pump itself is considered not to be directly electrogenic. There is no pump for chloride ions in peripheral nerve. The uneven distribution of Cl- (high outside, low inside) arises because the membrane is permeable to it and the anion is distributed largely in accordance with the potential difference across the membrane.

If, for simplicity, it is assumed that the membrane is permeable to K+, but not to Na+ and A-, then K+ will tend to move down its concentration gradient and there will be a small flux of K+ through the membrane from inside to outside; its anions will be left behind. Hence, the membrane will separate a few charges of opposite sign and will be polarized as illustrated in Figure 2.1, being positive on the outside with respect to the inside. The pores or channels through which K+ diffuses are known as leakage channels to distinguish them from the various other K+ channels present in the membrane.

The movement or flux of K+ through the membrane along its concentration gradient is opposed by the build-up of positive charge on the outside (like charges repel each other). At equilibrium the chemical force derived from the concentration gradient that tends to move K+ from inside to outside is balanced by the electrical force that repels further movement. Situations of this sort were studied and analysed by the German physical chemist Walter Nernst in 1888, who derived an equation based on basic thermodynamic principles for calculating the potential difference across the membranes (Em), in this case the K+ equilibrium potential (EK). Those who are not at ease with thermodynamics can nevertheless see that the Nernst equation includes factors relating to concentration gradient and to electrical forces. Those concerned to know how the equation is derived may consult any appropriate textbook.

According to the Nernst equation:

where R is the gas constant, F is Faraday’s constant, T is the temperature in degrees Kelvin and z is the valency of the ion concerned. For univalent ions and a body temperature of 37ºC (310K), and converting to logarithms to the base 10, the equation takes the simplified form shown below. Because it is conventional to refer to the potential of the inside of the cell relative to the outside, the concentration gradient in the equation is turned upside down to give a negative value; thus:

Substitution of the concentrations of potassium ions in Figure 2.1 gives a value of −88 mV and this would approximate reasonably closely to the true value detected by an intracellular microelectrode and measured on an oscilloscope as illustrated in Figure 2.1. In fact, the true membrane potential is usually a little less than that calculated from the Nernst equation, because in reality the resting membrane is not totally impermeable to sodium ions, nor completely permeable to potassium ions. The membrane of a frog muscle fibre, for example, is about one seventy-fifth as permeable to Na+ as to K+ (Katz, 1966). A modified equation known as the Goldman-Hodgkin-Katz equation takes the permeabilities to Na+ and K+ into account and gives values for frog muscle and cephalopod axons that agree more closely with the measured potentials.

According to the Goldman-Hodgkin-Katz equation:

where P, the permeability of a membrane to an ion, is defined as the net flux of that ion divided by the product of the concentration difference of the ion across the membrane times the area of membrane.

The lower the permeability to Na+ and the greater to K+, the closer Em approaches EK. This is the situation in glial cells, but in nerve and muscle cells the small permeability to Na+ opposes EK and subtracts a few mV from the resting membrane potential as suggested in Figure 2.1. (i.e. EK = 88 mV; measured Em = 85 mV).

Most of the experimental data on nerve are derived from giant axons from cephalopods, but it is believed that an essentially similar ionic basis underlies the membrane potentials in mammalian axons, including their fine terminal branches. Several mammalian muscles, including human muscles taken at biopsy, have been studied with intracellular microelectrodes. As stated above, there is evidence that a 1:1 ratio of Na+ to K+ ions shifted by a non-electrogenic pump in muscle fibres is an oversimplification. A proportion of the membrane potential is, in fact, produced by an electrogenic component of pump activity. This electrogenic component of pump activity appears to be under the trophic influence of the nerve; it disappears, and the membrane potential falls, after denervation (Bray et al., 1976).

The Na+/K+-dependent ATPase that catalyses the electrogenic component of pump activity appears to be more sensitive to inhibition by cardiac glycosides than the enzyme involved in non-electrogenic pumping. Small doses of cardiac glycosides, such as ouabain, therefore cause a depolarization which is similar in extent to that produced by...