The Resting Membrane Potential of Typical Neurons Is Heavily Influenced, but Not Completely Determined, by the Potassium Concentration Gradient

The K⁺ concentration inside neurons is much higher than that outside (because of ion pumps described a little later), and their surface membranes contain numerous K⁺ channels that are usually in the open state. If these were the only ion channels in the membrane, the following scenario would develop. The concentration gradient would drive K⁺ ions outward through the channels, creating a deficit of positive charges inside the cell. Opposite charges attract each other, so after a very small number of K⁺ ions had left, the resulting intracellular negativity would pull K⁺ ions back into the cell. At some point the concentration gradient and the electrical gradient would exactly counterbalance each other, and K⁺ ions would enter and leave at equal rates (Fig. 7-1). The system would be in equilibrium, with no net movement of K⁺ in either direction and no energy requirement to stay that way. The transmembrane potential at which this occurs, the potassium equilibrium potential or V_K, is a logarithmic function of the concentration gradient and is specified by the Nernst equation (THB6 Appendix 7B, p. 176). At body temperature, a tenfold change in the K⁺ concentration on one side of the membrane causes a 62 mv change in V_K.

Figure 7-1 Production of a membrane potential by K⁺ channels and a K⁺ concentration gradient. Very few ions need to move in order to create this potential, so there is no significant change in K⁺ concentration on either side of the membrane.

In reality, however, the K⁺ channels are not 100% selective for K⁺, and not all the channels in a resting membrane are K⁺ channels. As a result, Na⁺ ions are also able to flow across the membrane. The Na⁺ concentration outside neurons is much higher than that inside, so Na⁺ moves into the cell because of both the concentration gradient and the intracellular negativity. The result is competing ion flows (Fig. 7-2)—inward Na⁺ flow trying to move the membrane potential to V_Na and outward K⁺ flow trying to move the membrane potential to V_K—and a steady state is reached at a potential somewhere between V_Na and V_K. Just where the steady state is reached is determined by which ion the membrane is more permeable to (THB6 Appendix 7B, p. 176). Hence, V_Na and V_K are boundary values for the membrane potential, and changes in membrane permeability to Na⁺ or K⁺ will cause the membrane potential to move closer to one or the other; this is the usual basis for electrical signaling by neurons. The membranes of most neurons most of the time are much more permeable to K⁺ than to Na⁺, so the resting membrane potential is close to V_K.

Figure 7-2 Development of a steady-state membrane potential.

Concentration Gradients Are Maintained by Membrane Proteins That Pump Ions

A major difference between the theoretical K⁺-selective membrane and the real-life membrane permeable to both K⁺ and Na⁺ is that energy is required to maintain the concentration gradients across real-life membranes. If K⁺ continually flowed out and Na⁺ continually flowed in, the ionic concentration gradients across the membrane would fade away and the membrane potential would decline toward zero. This is averted by another class of membrane-spanning proteins, ion pumps, that use the energy liberated by hydrolysis of ATP to pump ions in the opposite direction and so maintain concentration gradients. The best known example is the Na⁺/K⁺ exchange pump that pumps Na⁺ out and K⁺ in, compensating for the steady-state leakage through channels.

Membrane Capacitance and Resistance Determine the Speed and Extent of the Response to a Current Pulse

Biological membranes behave electrically like combinations of capacitors (the lipid bilayer) and resistors (the ion channels). The gory details are recounted in THB6 Appendix 7A (p. 173), but suffice it to say for these purposes that capacitor/resistor combinations change the time course of electrical signals, slowing them down and smearing them out in time. So abruptly opening and then closing an ion channel causes not a square-wave voltage change, but rather one that builds up exponentially when the channel opens and then decays exponentially when the channel closes. Although this seems initially like a terrible way to build a signaling system, it actually has computational advantages, because it allows neurons to sum up multiple signals that are not quite simultaneous (temporal summation; see THB6 Figure 7-7, p. 157). The rate at which voltage changes (the time constant) determines the degree of temporal summation.

Current entering a neuron at one point spreads in all available directions, and before long all of it leaks out, either by passing through other ion channels or by changing the charge on the membrane capacitance. How far it spreads (i.e., the length constant) depends on things like the diameter of the neuronal process in question. Current takes the path of least resistance in its travels and, all other factors being equal, it is easier for current to move longitudinally through a large-diameter process than to squeeze through ion channels. Hence large-diameter dendrites and axons have long length constants and small-diameter ones have short length constants. This passive spread allows spatial summation of graded neuronal input signals arising at slightly different sites (THB6 Figure 7-9, p. 159).

Opening and Closing of Voltage-Gated Sodium and Potassium Channels Underlies the Action Potential

Action potentials are produced by the coordinated activity of special voltage-gated Na⁺ channels and K⁺ channels (Fig. 7-3), and areas of membrane that have sufficient quantities of these channels are electrically excitable (i.e., are able to produce action potentials). Depolarization of such an area of membrane (e.g., by depolarizing current flow from a nearby synapse) causes the voltage-gated Na⁺ channels to begin opening, which depolarizes the membrane even more. If enough channels are opened by the initial depolarization (i.e., the depolarization reaches threshold), this Na⁺ channel opening builds on itself explosively until most of the channels are open, Na⁺ permeability is greater than K⁺ permeability, and the membrane potential moves close to V_Na. This depolarization is short-lived, however, because the Na⁺ channels spontaneously enter a closed, inactivated state and cannot reopen until they are “reset” (deinactivated) by having the membrane potential return to near the resting level.

Figure 7-3 Production of an action potential by the coordinated opening and closing of voltage-gated Na⁺ channels and K⁺ channels.

The voltage-gated K⁺ channels are slower than the Na⁺ channels, opening only as the action potential nears its peak. Their opening, together with the inactivation of the Na⁺ channels, moves the membrane potential back toward V_K. The K⁺ channels stay open for a while even after all the Na⁺ channels have closed, causing an afterhyperpolarization phase during which the membrane potential is even closer to V_K than usual.

Action Potentials Are Followed by Brief Refractory Periods

The inactivation of voltage-gated Na⁺ channels has important consequences for the production of subsequent action potentials. For a brief period after the peak of an action potential, so many channels are inactivated that another action potential cannot be generated. This is the absolute refractory period, which grades into a relatively refractory period during which less than the full complement of channels is available. As a result, threshold is elevated because a greater percentage of this reduced population must be activated in order to produce another action potential. Because an action potential and the absolute refractory period following it last a millisecond or two, the maximum firing rate of neurons is about 1 kHz. The relative refractory period ensures that even this upper limit is rarely reached.

Action Potentials Are Propagated without Decrement along Axons

Neurons typically have a trigger zone with a low threshold, near where the axon emerges from the cell body, where action potentials are initiated (Fig. 7-4). Inputs to the dendrites and cell body sum temporally and spatially, spread passively (electrotonically) to the trigger zone, and initiate one or more action potentials if threshold is reached. Once initiated, an action potential spreads passively both down the axon and back into the cell body (THB6 Figure 7-13, p. 162). Cell bodies usually lack sufficient numbers of voltage-gated Na⁺ channels to make action potentials, so that’s the end of the story in that direction. The axon, on the other hand, has lots of them, so spread of the action potential in that direction brings neighboring regions to threshold and the action potential propagates down the axon. Once the action potential reaches the end of the axon, it cannot turn around and propagate back toward the cell body because the regions just traversed are refractory.

Figure 7-4 Overview of electrical signaling by neurons.

Unmyelinated axons have voltage-gated Na⁺ channels distributed all along them, and the action potential spreads down these axons by having each successive area of membrane depolarize to threshold (Fig. 7-5). It takes time for the channels to open, so the conduction velocity of action potentials in unmyelinated axons is limited by how far down the axon a depolarizing current spreads (i.e., by the length constant of the axon). Hence, the larger the diameter of an unmyelinated axon, the faster the conduction velocity. Even so, our largest unmyelinated axons are pretty slow, conducting at only about 2.5 m/sec. Myelinated axons conduct much more rapidly because the insulating myelin internodes prevent current from leaking out. Instead, it flows very rapidly from one node of Ranvier to the next. The voltage-gated Na⁺ channels of myelinated axons are concentrated at the nodes, so each successive node is depolarized to threshold and its channels open (the time-consuming step). Hence, the action potential skips from one node to the next (saltatory conduction), and conduction can be as rapid as 100 m/sec. The longer length constant of large-diameter axons allows their nodes to be spaced farther apart, so here too larger axons conduct more rapidly.

Figure 7-5 Propagation of action potentials along unmyelinated and myelinated axons.