Origin of the resting membrane potential

The resting membrane potential of –70 mV is mainly due to the efflux of positively charged potassium ions (K⁺). These diffuse out of the cell via leak channels, leaving the inner face of the membrane slightly electronegative. The driving force for potassium efflux is passive diffusion, since the concentration of potassium inside the cell is 30 to 40 times higher than that of the extracellular fluid. Permeability to other ions is much less at rest, so the resting membrane potential is mainly determined by the potassium gradient. The sodium gradient is more important for changes that occur when the cell is stimulated (discussed below).

The sodium pump

The transmembrane gradients for sodium and potassium are maintained in the long term by the sodium-potassium exchange pump (‘sodium pump’) which works continuously in the background (Fig. 6.2). The sodium pump is a membrane-bound protein that hydrolyses adenosine triphosphate (ATP) and uses the energy released to move ions across the plasma membrane against their concentration gradients. In each cycle the sodium-potassium pump (or Na⁺/K⁺-ATPase) transfers three sodium ions out of the cell and moves two potassium ions into the cell, consuming a single molecule of ATP in the process. In this way, the intracellular potassium concentration is maintained at approximately 140 mM compared to the extracellular concentration of around 3–5.5 mM, representing a potassium gradient of around 35 : 1 (higher on the inside). In contrast, the sodium ion concentration is around 12 mM on the inside and 140 mM on the outside, which equates to a 12 : 1 gradient for sodium ions (higher on the outside).

The sodium pump accounts for two thirds of the basal energy expenditure in nerve cells. It also contributes to the excess of negative charge on the inner face of the plasma membrane since it expels three positively charged ions in each cycle but only imports two. It is therefore described as electrogenic and the resting membrane potential is 3–5 mV more negative than predicted from passive ion flow.

Key Points

 The neuronal membrane is polarized, with a resting membrane potential of –70 mV (negative on the inside) due to a slight excess of negative charge on the inner face of the membrane.

 An increase in the membrane potential (so that it becomes more negative) is called hyperpolarization. Movement of the membrane potential closer to zero is depolarization.

 The resting membrane potential is mainly due to efflux of potassium (K⁺) ions via leak channels. This depends on the steep concentration gradient for potassium (35× higher on the inside).

 Sodium is more concentrated in the extracellular fluid and the sodium gradient (12× higher on the outside) is more important for depolarizing the cell during a nerve impulse.

 The sodium and potassium gradients are maintained in the long term by the sodium-potassium pump, which is responsible for two thirds of the basal energy expenditure in the brain.

Ionic basis of the resting membrane potential

Consider the hypothetical membrane-bound cell depicted in Figure 6.3A. It contains a concentrated solution of potassium salt and is immersed in saline (a solution of sodium chloride). It is important to emphasize that although only potassium (K⁺) is illustrated in the figure, the intracellular and extracellular fluids contain many different positive and negative ions and are electrically neutral overall.

Now suppose that the cell membrane is exclusively permeable to potassium. Since the intracellular concentration is much higher, potassium will passively diffuse out of the cell down its steep concentration gradient (Fig. 6.3B). A slight excess of negative charge will therefore build up on the inner face of the membrane, since each potassium ion that leaves the cell carries a single positive charge. However, this generates a growing electrical field that acts in the opposite direction to the concentration gradient and tends to attract potassium back inside the cell. The net efflux of potassium ions is therefore gradually reduced as the opposing electrical field builds up.

Ultimately the rate of potassium efflux (down its concentration gradient) is exactly counterbalanced by potassium influx (down the electrical gradient) and there is no net movement of potassium ions into or out of the cell (Fig. 6.3C). At this equilibrium point the membrane potential is stable and will be slightly more negative on the inside. The potential difference across the membrane at this point is the equilibrium potential for potassium and is around –90 mV. It should be emphasized that this process is very rapid (the equilibrium point is reached almost instantaneously).

The absolute number of ions moving across the cell membrane to establish the equilibrium potential is a few tens of millions, which is a negligible fraction of the total number of potassium ions inside the cell. The intracellular potassium concentration is therefore unchanged.

Calculating the equilibrium potential

Under normal physiological conditions, such as constant body temperature, the equilibrium potential for a particular ion is mainly determined by the concentration difference between the inside and outside of the cell. Its value is given by the Nernst equation (Fig. 6.4). This takes into account the size of the transmembrane gradient together with a number of physical and chemical factors including the absolute temperature (measured in Kelvin) and the charge carried by the ion.

Effect of membrane permeability

The value of the membrane potential at a particular moment depends mainly on the relative permeability to sodium, potassium and chloride ions. This changes when ion channels open or close.

The resting membrane potential (–70 mV) is close to the equilibrium potential for potassium (–90 mV) because the neuronal membrane is normally 50–100 times more permeable to potassium than to other ions. If the sodium permeability were to increase suddenly – as it does when a nerve impulse is generated – then the membrane potential would move towards the equilibrium potential for sodium (+60 mV). Note that the value of the sodium equilibrium potential is positive. This is because positively charged sodium ions (Na⁺) are more concentrated in the extracellular fluid and therefore diffuse into the cell, making the inner face of the plasma membrane positive with respect to the extracellular fluid. If a membrane were equally permeable to sodium and potassium ions, then the membrane potential would be halfway between –90 mV and +60 mV (i.e. –15 mV).

The value of the resting membrane potential in a typical neuron (–70 mV) reflects the fact that the membrane is predominantly permeable to potassium and slightly permeable to sodium, therefore the membrane potential is close to, but a little less negative than, the potassium equilibrium potential.

The resting membrane potential can be calculated by considering the equilibrium potentials for sodium, potassium and chloride ions and factoring in the membrane permeability for each. This information is combined in the Goldman equation (Fig. 6.5) which gives a predicted membrane potential that closely matches recordings from intracellular electrodes.

The reversal potential

Increasing permeability to a particular ion causes the membrane potential to shift towards the equilibrium potential for that ion. Depending on the starting value of the membrane potential, this may therefore depolarize or hyperpolarize the cell. If the membrane potential is already the same as the equilibrium potential for that particular ion, then opening more ion channels will not alter its value. This concept is illustrated in Figure 6.6 with reference to the chloride channel, which has an equilibrium potential of –65 mV.

Figure 6.6A shows the effect of opening additional chloride channels in a membrane that is initially polarized to a value of –60 mV. In this case the membrane is hyperpolarized (from –60 mV to –65 mV). In Figure 6.6B the cell membrane is already at the equilibrium potential for chloride (–65 mV) when the additional chloride channels are opened, so there is no change in membrane voltage (no net ion flux). In Figure 6.6C, the cell membrane starts at a value of –70 mV, which is more negative than the chloride equilibrium potential. Therefore, as the chloride conductance is increased the membrane is depolarized (from –70 mV, towards –65 mV).

The point at which the direction of net current flow reverses is called the reversal potential and is the same as the equilibrium potential. The rate of net current flow for a particular ion is proportional to the difference between the membrane potential and the equilibrium potential for that ion. This is referred to as the driving force. If the membrane potential is the same as the reversal potential, then the driving force is zero.

Key Points

 The equilibrium potential for a particular ion is the stable membrane potential at which point the opposing electrical and concentration gradients are balanced and there is no net ion flux.

 It is mainly determined by the ionic concentration difference between the inside and outside of the cell and is calculated using the Nernst equation.

 The potassium equilibrium potential is –90 mV since the intracellular potassium concentration is higher and potassium tends to leak out of the cell, leaving the inside slightly negative.

 In the case of sodium, the equilibrium potential is +60 mV. The value is positive because sodium is more concentrated in the extracellular fluid and therefore diffuses into the cell.

 Increasing permeability to a particular ion (by opening ion channels) causes the membrane potential to shift towards the equilibrium potential for that particular ion.

 The value of the membrane potential at a particular moment therefore depends on the relative permeability of sodium, potassium and chloride ions, combined in the Goldman equation.

 The normal resting membrane potential (–70 mV) is close to the equilibrium potential for potassium since the membrane is predominantly permeable to this ion at rest.

Types of ion channel

The neuronal membrane is composed of a lipid bilayer. This is a natural barrier to charged species, but water molecules are able to cross freely by passing through channels called aquaporins. The plasma membrane also contains specific ion channels. These are large, transmembrane proteins, usually made up of multiple subunits surrounding an aqueous pore (Fig. 6.7).

Voltage-gated channel structure

Voltage-gated ion channels are integral membrane proteins. They have a similar molecular structure that includes a repeating motif with six membrane-spanning alpha helices (Fig. 6.8A). There is also a pore loop that contributes to the selectivity filter and a charged domain that acts as a voltage sensor. During depolarization the inner face of the cell membrane becomes more positive and the voltage sensor (which carries a positive charge) is thrust upwards through the membrane by electrostatic repulsion. This movement induces a conformational change in the channel complex which opens the pore. Conductance changes steeply, increasing 150-fold with a 10 mV shift in membrane potential.

Properties of the action potential

An action potential may be initiated in the neuronal cell body (where excitatory and inhibitory influences from other nerve cells have been integrated) or in sensory nerve endings in response to a sufficiently strong graded potential (triggered by mechanical, thermal or other forms of stimulation).

Nerve impulse generation

To trigger an action potential, a stimulus must be large enough to depolarize the neuronal membrane to a particular threshold value (typically –55 mV). Once this point has been reached a full action potential will occur. It is not possible for an action potential to vary in magnitude like a graded potential: a full action potential either occurs or does not occur. This is referred to as the ‘all or none’ law. Since each action potential depolarizes the adjacent membrane to threshold, the nerve impulse propagates along the full length of the axon like a row of falling dominoes (Fig. 6.10).

Refractory periods

Once a nerve impulse has been generated, a second action potential cannot occur until the membrane has recovered:

 The absolute refractory period is the interval in which it is not possible to trigger a second action potential, regardless of stimulus strength.

 The relative refractory period is the interval in which a second action potential can be generated, but only with a stronger stimulus than usual.

The absolute refractory period is due to inactivation of the voltage-gated sodium channels (Fig. 6.11). Another action potential is not possible until the sodium channel inactivation gate reopens (which does not happen until the membrane has repolarized). The relative refractory period is due to the after-hyperpolarization (undershoot) that follows the action potential, when the membrane is more negative than it was at rest; a larger than usual excitatory stimulus is therefore needed to overcome this and depolarize the membrane to threshold. Most local anaesthetic agents inhibit voltage-gated sodium channels and prolong the refractory period in sensory neurons (Clinical Box 6.1).

 Clinical Box 6.1:   Local anaesthesia

Local anaesthetics such as lignocaine (or lidocaine) are cocaine derivatives that work by blocking the voltage-gated sodium channel, preventing the generation of action potentials. The binding site for lignocaine is inside the channel pore so it can only act on open channels (preferentially blocking active nerve cells). These agents are used to provide regional analgesia for minor procedures such as dental surgery. The local anaesthetic agent can be injected into soft tissues such as the gums (infiltration anaesthesia) or a specific nerve can be targeted (nerve block). Injection of local anaesthetic into the extradural (epidural) space surrounding the spinal cord can be used to provide pain relief during childbirth (epidural anaesthesia).

Key Points

 An action potential is a stereotyped sequence of electrical changes in the neuronal membrane, with rapid depolarization followed by immediate repolarization.

 After repolarization the membrane potential is slightly more negative than it was at rest, which is referred to as the undershoot or after-hyperpolarization.

 The action potential is an ‘all or none’ phenomenon. This means that once the membrane has been depolarized to threshold (around –55 mV) a full action potential will occur.

 Since the amplitude of the action potential does not vary, stimulus strength is represented in the nervous system using frequency coding.

 Once a nerve impulse has been generated, a second action potential cannot occur until the membrane has recovered. This is the refractory period.

 The absolute refractory period coincides with inactivation of voltage-gated sodium channels which makes it impossible to generate another nerve impulse.

 The relative refractory period is due to the after-hyperpolarization that follows the action potential, which must be overcome in order to depolarize the neuron to threshold.

Ionic basis of the action potential

The action potential is mediated by voltage-gated sodium and potassium channels. Depolarization of the neuronal membrane causes both types of ion channel to open, but sodium channels open earlier.

Depolarization (Na⁺ influx)

Sodium channels open rapidly and are responsible for the depolarizing phase of the action potential in which there is brisk sodium influx. A threshold stimulus is one that is just strong enough to open the minimum number of channels necessary to set up a ‘positive feedback loop’ in the neuronal membrane, referred to as the Hodgkin cycle (Fig. 6.12). Once this critical threshold is reached, the membrane depolarization caused by inflowing sodium ions triggers more voltage-gated sodium ions to open, leading to a self-reinforcing cycle. Sodium influx drives the membrane potential towards zero, before overshooting to a positive value (+30 mV) which approaches the equilibrium potential for sodium (+60 mV). At this point the sodium channels close and inactivate.

Summary of ionic events

The ionic events responsible for the different phases of the action potential can be summarized as follows (Fig. 6.13):

 At rest: voltage-gated Na⁺ and K⁺ channels are closed but responsive.

 Depolarization (rising) phase: Na⁺ channels open; K⁺ channels remain closed.

 Maximum depolarization (overshoot): Na⁺ channels inactivate; K⁺ channels open.

 Repolarization (falling) phase: K⁺ channels remain open, Na⁺ channels remain inactivated.

 At rest: Na⁺ channels reset; both channels closed but responsive.

The after-hyperpolarization that follows an action potential (corresponding to the relative refractory period) occurs because some of the delayed rectifiers are still open and the membrane is therefore more permeable to potassium than it was at rest. This means that the membrane potential is closer to the equilibrium potential for potassium (closer to –90 mV). As the remainder of the voltage-gated potassium channels close the membrane returns to its resting value of –70 mV.

Key Points

 The action potential is mediated by voltage-gated sodium and potassium channels.

 Threshold depolarization causes the sodium channels to open first, followed by the potassium channels (after a millisecond delay).

 The depolarizing phase of the action potential is due to a rapid influx of sodium ions. At maximal depolarization the sodium channels close and inactivate. The potassium channels then open.

 The repolarizing phase of the action potential is due to a rapid efflux of potassium ions. Once the membrane has repolarized the sodium channel inactivation gate is reopened (‘reset’).

Passive current flow

Each action potential is associated with a brisk influx of positively charged sodium ions which enter the cell via voltage-gated channels. This creates an electrotonic wave of positive charge that enters the nerve fibre in the region of action potential generation and then spreads passively along the axon (in both directions). The electrotonic wave travels quickly, but rapidly dissipates as positive charge ‘leaks out’ across the plasma membrane, particularly in fibres that do not have a myelin sheath (Fig 6.14A).

Depolarization is therefore maximal in the part of the membrane where the action potential was initiated, falling rapidly on either side of this point as the distance increases. This can be plotted as an exponential decay curve and expressed mathematically as the length constant (lambda) of the axon (Fig. 6.14B). The length constant is defined as the distance along the axon at which the voltage change has decayed to 37% of its maximum value.

One advantage of myelination is to reduce current leakage across the axonal membrane: in other words to increase membrane resistance. This enables the fast-moving electrotonic wave to spread further before dissipating and to trigger the next action potential as far along the axon as possible, thereby increasing conduction speed.

Conduction in unmyelinated fibres

In fibres that lack a myelin sheath, the nerve impulse propagates gradually from one end of an axon to the other, like a slow-burning fuse (often travelling at speeds below 1.5 metres per second). As each action potential is generated, the electrotonic wave spreads passively along the axon for a short distance and generates a new action potential in the adjacent patch of membrane (Fig. 6.15). The impulse always continues in the forward direction since the more proximal or ‘upstream’ part of the axon (which has just generated an action potential) is refractory. By the time it has recovered, the nerve impulse has passed.

Axonal conduction velocity

A simple approach to increasing axonal conduction velocity is to use larger-diameter fibres. For instance, the giant axon of the squid (which is involved in an escape reflex) is up to 1 mm in diameter and is able to conduct impulses at more than 30 metres per second. This is because fibres with a greater cross-sectional area have lower internal resistance to current flow and this allows the electrotonic wave to reach and depolarize a more distant patch of membrane before dissipating (i.e. the length constant is increased).

In the vertebrate (including human) nervous system, rapid axonal conduction is achieved more efficiently by investing axons with multiple layers of lipid-enriched plasma membrane, creating a fatty myelin sheath (see Ch. 5). The insulating effect of myelin (reducing current leakage across the membrane and extending the reach of the electrotonic wave) has already been discussed. Myelin also increases conduction speed by reducing membrane capacitance (discussed below).

Conduction in myelinated fibres

In myelinated fibres, each action potential arises at a node of Ranvier. This is a small gap between adjacent myelinated segments where the axon is in direct contact with the extracellular fluid. The myelinated segments are called internodes (Latin: inter-, between) and are about 1 mm long. Figure 6.16A illustrates the sodium current flowing into the axon at a node of Ranvier and the electrotonic wave spreading away from the node in both directions, reaching the two adjacent nodes (both ‘upstream’ and ‘downstream’ of the active node). Note also that local circuit currents are generated in the extracellular fluid in response to the ion flow.

Figure 6.16B illustrates the process of nerve impulse propagation along a myelinated axon. This is referred to as saltatory conduction since the action potential ‘jumps’ from node to node (Latin: saltere, to leap). As discussed above, myelination (i) lowers membrane capacitance (decreasing the time constant) and (ii) reduces current leakage (increasing the length constant). In this way the electrotonic wave depolarizes the membrane very quickly and is easily able to reach the next node of Ranvier before dissipating, triggering a new action potential there.

As in continuous conduction, the more proximal node will always be refractory, therefore the nerve impulse can only ever move forward. Saltatory conduction can be compared to setting off a line of fire crackers that are spaced a little distance apart: the heat from each cracker being just sufficient to trigger an explosion in the next, always moving forward since at each point the previous one is spent. A margin of error or safety factor prevents signal failure part way along the axon. Saltatory conduction is not only rapid but also efficient, since voltage-gated sodium channels are only required at the nodes of Ranvier.