Computer Simulation Of Action Potentials In Squid Axons Biology Essay

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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.

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 A/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 (A/cm2)

Stimulus 1 Duration (ms)

Delay (ms)

Stimulus 2 Amplitude (A/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 ï‚¥ (infinity) for the latency and '-' for the other parameters in the table overleaf.

Table 1. Success/failure matrix

Stimulus Strength (A/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

(A/cm2)

Duration

(ms)

Peak Height

(mV)

Amplitude

(mV)

Latency

(ms)

Threshold Voltage (mV)

2

0.1

-

-

ï‚¥

-

0.5

-

-

ï‚¥

-

1

-

-

ï‚¥

-

2

-

-

ï‚¥

-

5

-

-

ï‚¥

-

5

0.1

-

-

ï‚¥

-

0.5

-

-

ï‚¥

-

1

-

-

ï‚¥

-

2

14

104

2.93

-56

5

15

105

2.74

-59

7

0.1

-

-

ï‚¥

-

0.5

-

-

ï‚¥

-

1

12

102

4.38

-57

2

15

105

2.16

-58

5

16

106

2.16

-57

10

0.1

-

-

ï‚¥

-

0.5

-

-

ï‚¥

-

1

15

105

2.07

-53

2

16

106

1.69

-58

5

16

106

1.69

-58

20

0.1

-

-

ï‚¥

-

0.5

15

105

1.66

-55

1

16

106

1.10

-58

2

17

107

1.17

-42

5

17

107

1.17

-42

50

0.1

-

-

ï‚¥

-

0.5

17

107

0.59

-61

1

19

109

0.54

-60

2

19

109

0.70

-35

5

19

109

0.63

-49

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 ï‚¥) is represented.

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

Graph 1 : Stimulus strength and latency

Remember you need to distinguish different stim durations in this graph

Stimulus

Duration

(ms)

Graph 2: Stimulus Duration and Latency

Make sure you distinguish different strengths as well

Stimulus

Strength

(A/cm2)

These can be plotted accurately using excel for your submitted report.

Experiments with dual stimuli

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

Simulation

Stimulus 1 Amplitude (A/cm2)

Stimulus 1 Duration (ms)

Delay (ms)

Stimulus 2 Amplitude (A/cm2)

Stimulus 2 Duration (ms)

A

50

0.5

4

50

0.5

B

50

0.5

4

100

0.5

Briefly describe the responses obtained in simulations A and B in the space below:

For simulation A and B in stimulus 1 they had peak heights of +17mv therefore producing an action potential.

In stimulus 2, there is very little depolarisation in simulation A as peak height is -92mv. This is lower than the resting potential, therefore showing that the neuron did not fully recover from stimulus1.

However, in simulation B even with the amplitude as 100 there is some depolarization that gives a peak height of -85mv, which is not enough to cause an action potential.

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

Simulation

Stimulus 1 Amplitude (A/cm2)

Stimulus 1 Duration (ms)

Delay (ms)

Stimulus 2 Amplitude (A/cm2)

Stimulus 2 Duration (ms)

C

50

0.5

7

50

0.5

D

50

0.5

7

100

0.5

Compare and contrast the responses obtained in simulations C and D with those of A and B.

Simulation A, B, C, & D all have the same peak height of +17mv for stimulation 1.

However, there is a longer delay in simulations C and D of 7ms where as simulations A and B have a delay of 4ms causing the depolarisation of simulation C & D to take place later giving a longer time for the refectory period and therefore a longer time for the neurons to recover.

In simulation, C there is some depolarisation but not producing an action potential, which is the similar effect in simulations A and B

In simulation D and stimulus 2, there was an action potential, this is due to the neurons were able to hyperpolarise for stimulus 1 before stimulus 2 occurred.

Discussion

Answer the questions below in the spaces provided. This will provide the basis of your report discussion

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

Latency is the time taken for membrane potential to increase from the stimulus to the threshold voltage, which is the response.

The latency is ï‚¥ due to the time between the onset of a stimulus and the threshold cannot be calculated as no depolarisation has taken place as the stimulus is too weak.

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

The threshold phenomenon is similar to all-or-none principle, which is the generation of an action potential. This principle explains that if there is enough depolarisation to meet the threshold then an action potential will occur, if there is not enough depolarisation then an action potential will not generate. Table 1 shows this as it represents where an action potential was generated and where not.

The all-or-none principle is shown by the weaker stimulus strengths such as 2(A/cm2), this is due to there is little or no depolarisation occurs so a action potential was not generated. Furthermore, with shorter stimulus durations there is little or no depolarisation. Whereas stronger stimulus strengths and longer durations create an action potential, which gives us evidence that the action potentials are threshold phenomena as it is all-or-none principle. All-or-none principle is that either there is an action potential or not, there is no semi-action potentials.

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

The results from the experiment show that there is an increase in the amplitude as the stimulus duration increase and the stimulus strength increase. However, the increase is not a great amount. For example the increase of amplitude for stimulus strength 20(A/cm2), durations 0.5ms to 5ms is of 2mv from 105mv to 107mv. On the other hand when comparing stimulus strength 5(A/cm2) duration 5ms to stimulus strength 50(A/cm2) duration 5ms there is an increase of 4mv from 105mv to 109mv, which is not a great amount.

The maximum amount the amplitude can be from these experiments is 109mv as it does not change after stimulus strength 50(A/cm2) of duration 1ms.

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

As the stimulus strength increases, there is decrease latency. This trend is across all the durations from 0.1ms to 5ms.

The reason behind the latency decreasing as the stimulus strength increase is that the strong stimulus will cause the rate of sodium ion influx to increase causing the depolarisation to occur more rapidly, which in-turn decrease the time taken for stimulus to reach the threshold.

Stimulus strength 7(A/cm2), duration 1ms, this is an anomalous result as the latency is 4.38ms. The difference between the latency of the stimulation duration of 0.5ms, 2ms and 5ms is no more than 1ms, where as in duration 1ms there is a decrease of latency by 2.31ms from 10(A/cm2) with 1ms duration

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

As the duration increases the latency decreases for stimulus strengths 5, 7, 10 and 20(A/cm2). In stimulus, strength 50(A/cm2) the trend for durations does not occur in this case, as there is an increase in latency from 0.59ms to 0.63ms.

The reason behind the latency decreasing as the duration increase as the stimulus is over a longer period of time which allows more sodium ion channels to open then which causes a quicker depolarisation that causes the threshold value to be reached quicker

Stimulus strength 7(A/cm2), duration 1ms, this is an anomalous result as the latency is 4.38ms, which is extremely high. This is as there is a steep drop from the durations, where as in the other stimulus strengths the decrease in latency is not as steep.

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

Principles of human physiology

Germann & Stanfield

Benjamin Cummings, 2002

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

The sodium voltage gates slowly close and when the membrane voltage is equal to the sodium equilibrium voltage, which occurs at the peak of depolarisation. At this point, the raise in voltage in the membrane causes the potassium voltage gates to open, allowing the potassium to come down the gradient. As the potassium ions rush in it decreases the membrane voltage, which is repolarisation.

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

The inactivation of the sodium channels cause the absolute refractory period, which takes place during the depolarisation stage and most of the repolarisation stage. As the sodium channels are inactive, the second action potential is unable to occur, even if the stimulus strength is high. Towards the end of repolarisation, the most of the sodium channels are at their resting state. At this stage, the inactive sodium channels that have been closed are able to open in response to the stimulus.

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

For simulation C and D in stimulation 1 has a resting potential of -90mv and they both created an action potential with a peak height of +17mv.

In stimulus 2 there is no action potential in but there was some depolarisation as the peak height is -81mv in C. Even though the delay was much longer and there was some recovery for the neuron, the second stimulus was not strong enough, so an action potential did not arise.

In stimulus 2 for D, there was an action potential as the peak height was +3mv. This occurred, as there was a longer refractory period for D, which allowed the period of reducing the excitability in the membrane. Furthermore, the stimulus strength played a part in the production of the action potential, as it was much stronger.

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)

There are a number of effects that the refractory period imposes on the behaviour of neurones.

Firstly, the refractory period limits the number of action potentials that can occur. This is, as during absolute refractory period the second stimulus cannot be generated. In addition, a second stimulus can only be generated when majority of the sodium channels are at their resting state.

The second effect, the second stimulus needs to be stronger than normal to create another action potential in the neurone in the refractory period.

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 works by decreasing the rate of depolarization that decreases the rate of repolarisation of the membrane. This occurs as the local anaesthetic acts as an inhibitor, inhibiting the sodium ion influx thought the sodium voltage gates, in the cell membrane of axons. The local anaesthetic interrupts the sodium ions, which enter the cell membrane, so an action potential is unable arise. Therefore, the pain signals are unable to reach the brain. (Fozzard, Lee, Lipkind, 2005)

There is a number of side-effect involved with taking local anaesthetics. Firstly, the major risks are having temporary or permanent nerve damage that can cause paralysis. Furthermore, local anaesthetics can cause a patient's blood pressure to decrease as loss of muscle control of some blood vessels. Finally, there are some small side-effects such as headaches, blurred vision, dizziness, light-headedness, and tiredness.

Even though there are a number of side-effects, local anaesthetic is used widely by surgeons, dentist, and patients.

Dentists use local anaesthetic for removal and filling of teeth as this can cause some discomfort to the patient.

In addition, surgeons use it during major surgical procedures such as brain surgery as they need to patient to be conscious is some cases, for example is removing a tumour which is near area of the brain which controls speech, they may need the patient to talk to show there are no effects. Furthermore during surgery to remove the cataract from the eye. In addition to the eye surgery, it is use in some skin surgeries such as removing warts and moles. (Retired on November 28th 2010, NHS, http://www.nhs.uk/conditions/Anaesthetic-local/Pages/Introduction.aspx)

Q17. Will these compounds work if they don't block all the Na channels ? Why ?

(Use your experimental data to help answer this question)

The compound will work is the all the sodium channels are not blocks. This is as is majority of the sodium channels are blocked, the depolarisation will not be high enough to create an action potential.

From the experimental data, you can see that there are some stimulus which were sent and an action potential did not arise, this is due to the stimulus being too weak and did not cause enough sodium channels to open to cause depolarisation. This is related to the all-or-none principle.

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