COMPUTER SIMULATION OF ACTION POTENTIALS IN SQUID AXON

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Please use this proforma to record your data. You should aim to complete the experimental part and answer all the questions before you leave.

Please show your completed pro-forma to one of the demonstrators before leaving so that they can check with you that you can answer all the questions.

This will form also be available as electronically on studynet. You can use the electronic form to produce a final version of your report for submission online.

Introduction

In 1952, Hodgkin and Huxley published a series of four papers in the Journal of Physiology (London) reporting their experiments to investigate the underlying events of the action potential. In their final paper, they derived a series of equations that describe the relationship between sodium conductance (gNa+), potassium conductance (gK+) and the membrane potential in a squid axon following electrical stimulation. Hodgkin and Huxley were awarded the Nobel Prize for this work.

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In this practical, you will use a computer program based on the Hodgkin and Huxley equations to show what is happening to the membrane potential, gNa+ and gK+ during and after electrical stimulation. An example of the output from the program is illustrated in figure 1. It can be seen that the electrical stimulation depolarises the membrane. Once a depolarisation of 30mV has occurred, the conductance to sodium ions increases rapidly and the membrane potential rises to +20mV. The rise in gK+ is slower in onset and lasts for longer than the increase in gNa+. The fall in gNa+ and the associated rise in gK+ returns the membrane potential towards the resting value.

Figure 1: Simulation of changes in membrane potential, Na+ and K+ conductances following the application of a single electrical stimulus of 50 mA/cm2 for 1 ms. The peak height, amplitude, latency and threshold of the action potential are shown.

Methods and Results

Run the Squid Giant Axon simulation from the Start menu, HHX.

Experiments using a single electrical stimulus

In the first series of experiments, you will use a single electrical stimulus to initiate an action potential. Run a simulation with the following parameters:

Stimulus 1 Amplitude (mA/cm2)

Stimulus 1 Duration (ms)

Delay (ms)

Stimulus 2 Amplitude (mA/cm2)

Stimulus 2 Duration (ms)

50

1

0

0

0

A trace similar to figure 1 will be obtained. From this trace, you can measure the peak height, amplitude, latency and threshold of the action potential:

Peak Height

(mV)

Amplitude

(mV)

Latency

(ms)

Threshold Voltage (mV)

+19

109

0.46

-66

Q1 and 2. Investigate the effects of varying stimulus amplitude and duration by running all the simulations shown in the matrix below in Table 1: Enter a 'X' in the Table 1 matrix for experiments that produce an action potential, and record the peak height, amplitude, latency and threshold of any action potentials in Table 2 overleaf. For experiments that fail to elicit an action potential, enter a 'O' in the matrix below, and record a value of ¥ (infinity) for the latency and - for the other parameters in the table overleaf.

Table 1. Success/failure matrix

Stimulus Strength (mA/cm2)

Stimulus Duration (ms)

0.1

0.5

1

2

5

50

O

X

X

X

X

20

O

X

X

X

X

10

O

O

X

X

X

7

O

O

X

X

X

5

O

O

O

X

X

2

O

O

O

O

O

Table 2: Action potential characteristics

Stimulus

Response

Strength

(mA/cm2)

Duration

(ms)

Peak Height

(mV)

Amplitude

(mV)

Latency

(ms)

Threshold Voltage (mV)

2

0.1

-

-

¥

-

0.5

-

-

¥

-

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1

-

-

¥

-

2

-

-

¥

-

5

-

-

¥

-

5

0.1

-

-

¥

-

0.5

-

-

¥

-

1

-

-

¥

-

2

14

104

2.74

-70

5

15

105

2.59

-69

7

0.1

-

-

¥

-

0.5

-

-

¥

-

1

12

102

4.25

-76

2

15

115

1.84

-74

5

16

116

1.84

-74

10

0.1

-

-

¥

-

0.5

-

-

¥

-

1

15

105

1.75

-73

2

16

106

1.45

-72

5

16

106

1.43

-73

20

0.1

-

-

¥

-

0.5

15

105

1.41

-72

1

16

106

0.91

-69

2

17

107

0.91

-69

5

17

107

0.89

-70

50

0.1

-

-

¥

-

0.5

17

107

0.46

-67

1

19

109

0.48

-65

2

19

109

0.50

5

19

109

0.50

Q3. Plot two graphs to show the relationship between: (i) Stimulus strength and latency and (ii) Stimulus duration and latency.

How these graphs should be plotted is not immediately obvious, and information on how to complete this task will not be explicitly given! The optimal solution to the problem is for you to find, but the following points are provided for guidance:

It is not legitimate to plot infinity on graphs

It is not appropriate to extrapolate beyond data points

It is not legitimate to plot average latencies. The graphs must be plotted so that every value of latency (except ¥) is represented.

Use the blank sheet on the proforma, there is no need to use graph paper.

Graph 1: Stimulus strength and latency

Graph 2: Stimulus Duration and Latency

Experiments with dual stimuli

Q4. Run a simulation with the following parameters to demonstrate the absolute refractory period:

Simulation

Stimulus 1 Amplitude (mA/cm2)

Stimulus 1 Duration (ms)

Delay (ms)

Stimulus 2 Amplitude (mA/cm2)

Stimulus 2 Duration (ms)

A

50

0.5

4

50

0.5

B

50

0.5

4

100

0.5

Stimulation A shows a normal single, action potential, with the second action potential not being produced as the stimulation doesn't depolarise the membrane fully, it only caused a minor depolarisation of -92mV. The reason there isn't a second action potential is due to the fact that there is a lack of repolarisation, this is called the absolute refractory period. During this period, a second action potential cannot be initiated, no matter how large the stimulus is being applied.

Stimulation B still only produces one action potential, which peaks at 17mV. Again a second is not produced because the stimulus is not large enough to create an action potential, however the second depolarisation is slightly larger than the one from stimulation A, as its peak is -81mV. This shows that this time, the neurone is again in absolute refractory period.

Q5. Repeat the simulations, but with a longer delay between stimuli:

Simulation

Stimulus 1 Amplitude (mA/cm2)

Stimulus 1 Duration (ms)

Delay (ms)

Stimulus 2 Amplitude (mA/cm2)

Stimulus 2 Duration (ms)

C

50

0.5

7

50

0.5

D

50

0.5

7

100

0.5

Stimulation C again produces a single action potential; however the second peak of depolarisation is larger than both those found in stimulation A and B. The peak of the action potential is 17mV. The second depolarisation reaches -81mV, which is higher than stimulation A or B.

Stimulation D produces two action potentials. The first action potential is larger than the second. Stimulation D shows a period of relative refractory period as when stimulus 2 is increased to 100 mV and the duration is increased to 7ms.

Discussion

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Q6. Briefly justify why a latency of ¥ was recorded if an action potential was not produced.

As there is no action potential, so this means it will never occur, so the latency will never be reached. This is the same for infinity, we can never reach it, so this is an appropriate number.

Q7. What evidence from your results suggests that action potentials are threshold phenomena?

As we can see, action potential depends on the threshold voltage being reached. The threshold voltages are all around the same value, about -70mV. From this we can see that once this threshold is reached then the action potential will occur.

Q8. Comment briefly on the amplitude of the action potentials generated in these experiments.

All the amplitudes from the action potential are around the same value. This is due to the all or nothing principle. Once an action potential is fired, it is always the same strength.

Q9. From Graph 1, describe the effect of increasing stimulus strength on the latency of the action potential.

Overall, the trend of the graph is that as you increase stimulus strength, the latency of the action potential reduces. On average, most of the stimulus durations follow the same pattern. Duration

0.5 ms doesn't have enough data to create a curve. The point 20µA/cm2, duration 0.5 ms, is an anomaly, as it doesn't match in with the rest of the graph. It is nearly 0.5 ms too high. Also, the graph has an unusual peak at 10 µA/cm2, duration 1 ms. This is about 2 ms above the rest of the graph.

Q10. From Graph 2, describe the effect of increasing stimulus duration on the latency of the action potential.

Overall, the trend of the graph is that as you increase stimulus duration, the latency remains constant. After 2 ms, all of the latencies remain steady, except from stimulus strength 7µA/cm2. This has a slight reduced latency, making a parabola shaped graph. However, all the latencies before 1 ms, are all increased compared to the points at 2 ms.

Q11. Draw a simple flow diagram to illustrate the positive feedback cycle that results in the rapid depolarizing phase of the action potential.

Q12. What event at the ion channel level terminates the above cycle?

The potassium ions move out of the cell and the sodium ion channels shut.

Q13. What physiological mechanism is responsible for the absolute refractory period?

Absolute refractory period is caused by sodium ion channels being open even after an action potential has occurred. This means you cannot generate another action potential, until the membrane hyperpolarises. Once the channels close, they activate again, so an action potential can be generated again.

Q14. Explain your observations to simulations C and D in the Methods and Results section.

Stimulation C only has one action potential; this is due to the fact that the second amplitude is during the relative refractory period. This is shown as the second stimulation produces a slight depolarisation of the membrane; however it isn't large enough to produce an action potential. However, the depolarisation is larger than that in stimulations A or B, and this is due to the delay of 7 ms.

Stimulation D has two action potentials. This is due to the fact that the second stimulation is large enough to create a large depolarisation during the relative refractory period. This large depolarisation then causes the second action potential. Also, the delay of 7 ms allows the second action potential.

Q15. Briefly summarise two effects that refractory periods impose on the behaviour of neurones (N.B. restatement of the definitions of refractory periods is not what is asked here)

The refractory periods have two main effects on the behaviour of neurones. These are frequency coding and unidirectional propagation of action potentials. Frequency coding is the stimulus intensity of the action potential; this determines the number of action potentials that occur per specific time period. A stimulus with a longer duration will produce more than one action potential, as the time period for a second action potential to occur is longer. This means that it can overcome the relative refractory period. Unidirectional propagation of action potential makes sure that action potentials only travel in one direction. This makes sure that the second action potential doesn't occur in the wrong direction.

Questions to answer after the practical.

Q 16 . Most Local anaesthetics are Sodium channel blockers. Describe how these compounds work, the side-effects and what their main clinical uses are. ( max 300 words).

Local anaesthetics work by inhibiting the voltage dependant sodium channels located in the neurones. By inhibiting these channels, depolarisation doesn't occur. This will lead onto action potentials not being produced in the neurone. If this occurs in the sensory neurones, this will prevent action potentials being fired towards the central nervous system. This means communication has broken down, so no pain will be felt during clinical procedures.

The side effects of local anaesthetics are that the effect is total. All neurones will not be able to fire any action potentials, so all feelings and movement in the area is lost. Other side effects include confusion, respiratory depression and convulsions, hypotension and bradycardia, which could lead onto a cardiac arrest. Also, hypersensitivity has also been reported.

The main clinical use for local anaesthetics is during dental procedures and during minor surgery on a small part of the body, often performed by a GP or a surgeon.