How Will the Action Potential at R1 or R2 Change as You Continue to Increase the Stimulus Voltage

Chapter 1: Resting Potentials and Action Potentials

Video of lecture

Despite the enormous complexity of the brain, it is possible to obtain an understanding of its function by paying attention to two major details:

First, the ways in which individual neurons, the components of the nervous system, are wired together to generate behavior.
Second, the biophysical, biochemical, and electrophysiological properties of the individual neurons.

A good place to begin is with the components of the nervous system and how the electrical properties of the neurons endow nerve cells with the ability to process and transmit information.

1.1 Introduction to the Action Potential

Figure 1.1
Tap the colored circles (light stimulus) to activate.

Theories of the encoding and transmission of information in the nervous system go back to the Greek physician Galen (129-210 AD), who suggested a hydraulic mechanism by which muscles contract because fluid flowing into them from hollow nerves. The basic theory held for centuries and was further elaborated by René Descartes (1596 – 1650) who suggested that animal spirits flowed from the brain through nerves and then to muscles to produce movements (See this animation for modern interpretation of such a hydraulic theory for nerve function). A major paradigm shift occurred with the pioneering work of Luigi Galvani who found in 1794 that nerve and muscle could be activated by charged electrodes and suggested that the nervous system functions via electrical signaling (see this animation of Galvani's experiment). However, there was debate among scholars whether the electricity was within nerves and muscle or whether the nerves and muscles were simply responding to the harmful electric shock via some intrinsic nonelectric mechanism. The issue was not resolved until the 1930s with the development of modern electronic amplifiers and recording devices that allowed the electrical signals to be recorded. One example is the pioneering work of H.K. Hartline 80 years ago on electrical signaling in the horseshoe crab Limulus . Electrodes were placed on the surface of an optic nerve. (By placing electrodes on the surface of a nerve, it is possible to obtain an indication of the changes in membrane potential that are occurring between the outside and inside of the nerve cell.) Then 1-s duration flashes of light of varied intensities were presented to the eye; first dim light, then brighter lights. Very dim lights produced no changes in the activity, but brighter lights produced small repetitive spike-like events. These spike-like events are called action potentials, nerve impulses, or sometimes simply spikes. Action potentials are the basic events the nerve cells use to transmit information from one place to another.

1.2 Features of Action Potentials

The recordings in the figure above illustrate three very important features of nerve action potentials. First, the nerve action potential has a short duration (about 1 msec). Second, nerve action potentials are elicited in an all-or-nothing fashion. Third, nerve cells code the intensity of information by the frequency of action potentials. When the intensity of the stimulus is increased, the size of the action potential does not become larger. Rather, the frequency or the number of action potentials increases. In general, the greater the intensity of a stimulus, (whether it be a light stimulus to a photoreceptor, a mechanical stimulus to the skin, or a stretch to a muscle receptor) the greater the number of action potentials elicited. Similarly, for the motor system, the greater the number of action potentials in a motor neuron, the greater the intensity of the contraction of a muscle that is innervated by that motor neuron.

Action potentials are of great importance to the functioning of the brain since they propagate information in the nervous system to the central nervous system and propagate commands initiated in the central nervous system to the periphery. Consequently, it is necessary to understand thoroughly their properties. To answer the questions of how action potentials are initiated and propagated, we need to record the potential between the inside and outside of nerve cells using intracellular recording techniques.

1.3 Intracellular Recordings from Neurons

The potential difference across a nerve cell membrane can be measured with a microelectrode whose tip is so small (about a micron) that it can penetrate the cell without producing any damage. When the electrode is in the bath (the extracellular medium) there is no potential recorded because the bath is isopotential. If the microelectrode is carefully inserted into the cell, there is a sharp change in potential. The reading of the voltmeter instantaneously changes from 0 mV, to reading a potential difference of -60 mV inside the cell with respect to the outside. The potential that is recorded when a living cell is impaled with a microelectrode is called the resting potential, and varies from cell to cell. Here it is shown to be -60 mV, but can range between -80 mV and -40 mV, depending on the particular type of nerve cell. In the absence of any stimulation, the resting potential is generally constant.

It is also possible to record and study the action potential. Figure 1.3 illustrates an example in which a neuron has already been impaled with one microelectrode (the recording electrode), which is connected to a voltmeter. The electrode records a resting potential of -60 mV. The cell has also been impaled with a second electrode called the stimulating electrode. This electrode is connected to a battery and a device that can monitor the amount of current (I) that flows through the electrode. Changes in membrane potential are produced by closing the switch and by systematically changing both the size and polarity of the battery. If the negative pole of the battery is connected to the inside of the cell as in Figure 1.3A, an instantaneous change in the amount of current will flow through the stimulating electrode, and the membrane potential becomes transiently more negative. This result should not be surprising. The negative pole of the battery makes the inside of the cell more negative than it was before. A change in potential that increases the polarized state of a membrane is called a hyperpolarization. The cell is more polarized than it was normally. Use yet a larger battery and the potential becomes even larger. The resultant hyperpolarizations are graded functions of the magnitude of the stimuli used to produce them.

Now consider the case in which the positive pole of the battery is connected to the electrode (Figure 1.3B). When the positive pole of the battery is connected to the electrode, the potential of the cell becomes more positive when the switch is closed (Figure 1.3B). Such potentials are called depolarizations. The polarized state of the membrane is decreased. Larger batteries produce even larger depolarizations. Again, the magnitude of the responses are proportional to the magnitude of the stimuli. However, an unusual event occurs when the magnitude of the depolarization reaches a level of membrane potential called the threshold. A totally new type of signal is initiated; the action potential. Note that if the size of the battery is increased even more, the amplitude of the action potential is the same as the previous one (Figure 1.3B). The process of eliciting an action potential in a nerve cell is analogous to igniting a fuse with a heat source. A certain minimum temperature (threshold) is necessary. Temperatures less than the threshold fail to ignite the fuse. Temperatures greater than the threshold ignite the fuse just as well as the threshold temperature and the fuse does not burn any brighter or hotter.

If the suprathreshold current stimulus is long enough, however, a train of action potentials will be elicited. In general, the action potentials will continue to fire as long as the stimulus continues, with the frequency of firing being proportional to the magnitude of the stimulus (Figure 1.4).

Action potentials are not only initiated in an all-or-nothing fashion, but they are also propagated in an all-or-nothing fashion. An action potential initiated in the cell body of a motor neuron in the spinal cord will propagate in an undecremented fashion all the way to the synaptic terminals of that motor neuron. Again, the situation is analogous to a burning fuse. Once the fuse is ignited, the flame will spread to its end.

1.4 Components of the Action Potentials

The action potential consists of several components (Figure 1.3B). The threshold is the value of the membrane potential which, if reached, leads to the all-or-nothing initiation of an action potential. The initial or rising phase of the action potential is called the depolarizing phase or the upstroke. The region of the action potential between the 0 mV level and the peak amplitude is the overshoot. The return of the membrane potential to the resting potential is called the repolarization phase. There is also a phase of the action potential during which time the membrane potential can be more negative than the resting potential. This phase of the action potential is called the undershoot or the hyperpolarizing afterpotential. In Figure 1.4, the undershoots of the action potentials do not become more negative than the resting potential because they are "riding" on the constant depolarizing stimulus.

1.5 Ionic Mechanisms of Resting Potentials

Before examining the ionic mechanisms of action potentials, it is first necessary to understand the ionic mechanisms of the resting potential. The two phenomena are intimately related. The story of the resting potential goes back to the early 1900's when Julius Bernstein suggested that the resting potential (V_m) was equal to the potassium equilibrium potential (E_K). Where

The key to understanding the resting potential is the fact that ions are distributed unequally on the inside and outside of cells, and that cell membranes are selectively permeable to different ions. K⁺ is particularly important for the resting potential. The membrane is highly permeable to K⁺. In addition, the inside of the cell has a high concentration of K⁺ ([K⁺]_i) and the outside of the cell has a low concentration of K⁺ ([K⁺]_o). Thus, K⁺ will naturally move by diffusion from its region of high concentration to its region of low concentration. Consequently, the positive K⁺ ions leaving the inner surface of the membrane leave behind some negatively charged ions. That negative charge attracts the positive charge of the K⁺ ion that is leaving and tends to "pull it back". Thus, there will be an electrical force directed inward that will tend to counterbalance the diffusional force directed outward. Eventually, an equilibrium will be established; the concentration force moving K⁺ out will balance the electrical force holding it in. The potential at which that balance is achieved is called the Nernst Equilibrium Potential.

An experiment to test Bernstein's hypothesis that the membrane potential is equal to the Nernst Equilibrium Potential (i.e., V_m = E_K) is illustrated to the left.

The K⁺ concentration outside the cell was systematically varied while the membrane potential was measured. Also shown is the line that is predicted by the Nernst Equation. The experimentally measured points are very close to this line. Moreover, because of the logarithmic relationship in the Nernst equation, a change in concentration of K⁺ by a factor of 10 results in a 60 mV change in potential.

Note, however, that there are some deviations in the figure at left from what is predicted by the Nernst equation. Thus, one cannot conclude that V_m = E_K. Such deviations indicate that another ion is also involved in generating the resting potential. That ion is Na⁺. The high concentration of Na⁺ outside the cell and relatively low concentration inside the cell results in a chemical (diffusional) driving force for Na⁺ influx. There is also an electrical driving force because the inside of the cell is negative and this negativity attracts the positive sodium ions. Consequently, if the cell has a small permeability to sodium, Na⁺ will move across the membrane and the membrane potential would be more depolarized than would be expected from the K⁺ equilibrium potential.

1.6 Goldman-Hodgkin and Katz (GHK) Equation

When a membrane is permeable to two different ions, the Nernst equation can no longer be used to precisely determine the membrane potential. It is possible, however, to apply the GHK equation. This equation describes the potential across a membrane that is permeable to both Na⁺ and K⁺.

Note that α is the ratio of Na⁺ permeability (P_Na) to K⁺ permeability (P_K). Note also that if the permeability of the membrane to Na⁺ is 0, then alpha in the GHK is 0, and the Goldman-Hodgkin-Katz equation reduces to the Nernst equilibrium potential for K⁺. If the permeability of the membrane to Na⁺ is very high and the potassium permeability is very low, the [Na⁺] terms become very large, dominating the equation compared to the [K⁺] terms, and the GHK equation reduces to the Nernst equilibrium potential for Na⁺.

If the GHK equation is applied to the same data in Figure 1.5, there is a much better fit. The value of alpha needed to obtain this good fit was 0.01. This means that the potassium K⁺ permeability is 100 times the Na⁺ permeability. In summary, the resting potential is due not only to the fact that there is a high permeability to K⁺. There is also a slight permeability to Na⁺, which tends to make the membrane potential slightly more positive than it would have been if the membrane were permeable to K⁺ alone.

1.7 Membrane Potential Laboratory

Click here to go to the interactive Membrane Potential Laboratory to experiment with the effects of altering external or internal potassium ion concentration and membrane permeability to sodium and potassium ions. Predictions are made using the Nernst and the Goldman, Hodgkin, Katz equations.

Membrane Potential Laboratory

Test Your Knowledge

Question 1
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B
C
D
E

If a nerve membrane suddenly became equally permeable to both Na⁺ and K⁺, the membrane potential would:

A. Not change

B. Approach the new K⁺ equilibrium potential

C. Approach the new Na⁺ equilibrium potential

D. Approach a value of about 0 mV

E. Approach a constant value of about +55 mV

If a nerve membrane suddenly became equally permeable to both Na⁺ and K⁺, the membrane potential would:

A. Not change This answer is INCORRECT.

A change in permeability would depolarize the membrane potential since alpha in the GHK equation would equal one. Initially, alpha was 0.01. Try substituting different values of alpha into the GHK equation and calculate the resultant membrane potential.

B. Approach the new K⁺ equilibrium potential

C. Approach the new Na⁺ equilibrium potential

D. Approach a value of about 0 mV

E. Approach a constant value of about +55 mV

If a nerve membrane suddenly became equally permeable to both Na⁺ and K⁺, the membrane potential would:

A. Not change

B. Approach the new K⁺ equilibrium potential This answer is INCORRECT.

The membrane potential would approach the K+ equilibrium potential only if the Na⁺ permeability was decreased or the K⁺ permeability was increased. Also there would be no "new" equilibrium potential. Changing the permeability does not change the equilibrium potential.

C. Approach the new Na⁺ equilibrium potential

D. Approach a value of about 0 mV

E. Approach a constant value of about +55 mV

If a nerve membrane suddenly became equally permeable to both Na⁺ and K⁺, the membrane potential would:

A. Not change

B. Approach the new K⁺ equilibrium potential

C. Approach the new Na⁺ equilibrium potential This answer is INCORRECT.

The membrane potential would approach the Na⁺ equilibrium potential only if alpha in the GHK equation became very large (e.g., decrease PK or increase PNa). Also, there would be no "new" Na⁺ equilibrium potential. Changing the permeability does not change the equilibrium potential; it changes the membrane potential.

D. Approach a value of about 0 mV

E. Approach a constant value of about +55 mV

If a nerve membrane suddenly became equally permeable to both Na⁺ and K⁺, the membrane potential would:

A. Not change

B. Approach the new K⁺ equilibrium potential

C. Approach the new Na⁺ equilibrium potential

D. Approach a value of about 0 mV This answer is CORRECT!

Roughly speaking, the membrane potential would move to a value half way between E_K and E_Na. The GHK equation could be used to determine the precise value.

E. Approach a constant value of about +55 mV

If a nerve membrane suddenly became equally permeable to both Na⁺ and K⁺, the membrane potential would:

A. Not change

B. Approach the new K⁺ equilibrium potential

C. Approach the new Na⁺ equilibrium potential

D. Approach a value of about 0 mV

E. Approach a constant value of about +55 mV This answer is INCORRECT.

The membrane potential would not approach a value of about +55 mV (the approximate value of E_Na) unless there was a large increase in the sodium permeability without a corresponding change in the potassium permeability. Alpha in the Goldman equation would need to approach a very high value.

Question 2
A
B
C
D
E