The Voltage Clamp Simulation
Hypothesis Testing With The Voltage Clamp Simulation
In the Action Potential simulation, you conducted tests of the Sodium and Potassium Hypotheses by varying [Na+] or [K+], and quantifying the impact of those changes on Vm recorded during various phases of an action potential. With the voltage clamp experiment, you’ll be conducting another test of each hypothesis, this time by monitoring the effect of Vm on INa+ and IK+. Once again, you’ll be working with the squid giant axon.
At this time, it may be helpful to you to view a short presentation of typical results of a voltage clamp experiment.
Important: you need the normal values for the squid axon’s resting Vm , eNa+, and eK+ to answer some of the questions provided with this simulation, and to test the Sodium and Potassium hypotheses. If you do not have those values available to you now, you will need to run the Action Potential simulation and record the default values for Vm , eNa+ , and eK+ before proceeding.
Tips and Hints
1. Unless otherwise instructed, don't use the value for dVm in your calculations or graph constructions. Instead, use the actual Vm value ( = resting Vm + dVm).
2. It’s sometimes helpful if you can see a simultaneous display of all three membrane currents (Total Im, INa+, and IK+). The following procedure provides an easy way to accomplish this:
a. Clear the display by clicking on the "Clear" button;
b. Use the sliders to set dVm, [Na+]ext and [K+]ext to the values you wish to use.
c. Select either depolarizing or hyperpolarizing dVm.
d. Instruct the simulation to display only Total Im by selecting the Total Im checkbox and deselecting the INa+ and IK+ checkboxes.
e. Click "Run". This will generate a plot of Total Im vs. time, using a black line.
f. Deselect the Im checkbox and select the INa+ checkbox. Click Go. This will display INa+ vs. time, using a red line.
g. Deselect INa+ and select IK+. Do one last run. This will display IK+ vs. time, using a blue line.
3. Recall Ohm’s Law:
E = I×R
where E is potential (in Volts), I is the current (in amperes) and R is the resistance (in ohms). Ohm’s Law is more useful for interpreting data from voltage clamp experiments if we rearrange it to yield:
I = E/R
and recall that conductance, g, is given by:
g = 1/R
Substituting this relationship into the rearranged expression for Ohm’s Law gives us:
I = E×g
This formulation is more useful because (i) it encourages us to think of current flux through a membrane (Im) as being the product of a driving force, E, acting ‘through’ a conductance, g, and (ii) it lends itself to calculating values for g, given I and E.
4. By convention, positive values in voltage clamp graphs represent efflux of positive charge, while negative currents represent influx of positive charge.
5. The numerical values for the delayed Itotal and IK+ are so nearly equal that if you choose to display numerical values of both, you will find that it is difficult to read their values at the right side of the display. There is no easy way around this, except to do a series of runs in which you display the value of one, then another series of replicate runs in which you display the value of the other.
6. When you change dVm from depolarizing to hyperpolarizing, you must click the Clear button to adjust the Im range of the upper set of axes so they will properly display the K+ current(s) you will observe when the membrane is clamped at Vm values greater than resting Vm. Likewise, when you select depolarizing dVm, you must again click the Clear button to display a y-axis with the correct range of Im values.
7. In general, only select for display the parameter(s) you need for the question you’re trying to answer. For example, if you’re investigating the Early Inward Current, you shouldn’t display the K+ current. Judicious choice of what you have displayed will help keep the display from becoming unnecessarily cluttered.
8. For most of the Exercises, you may choose to display numerical values for the various currents, or not. If you do activate the numerical value display option, be certain that you look carefully at the tracings produced by each simulation run. Otherwise, you may not understand your results as well as you could.
9. If you use a spreadsheet to fit regression models to your data, you may find that your spreadsheet’s regression function my refuse to fit certain models to data that contain negative values. You can often solve this problem by transforming your data prior to regression analysis.
Exercises
1. Load the simulation by clicking the “Run The Simulation” link. Select the Numerical Values checkbox. Click the Go button to do a trial run. Note the general appearance of the display. Now, increase dVm to 20 mV and click the Go button. Note the appearance of the dVm plot at the bottom of the display and the changes in the graph of Im.
2. Conduct a series of runs in which you vary dVm from 0 to +150 mV and record the maximum amplitude of the early inward current. Use 10 mV increments for dVm between runs. Note carefully how the appearance of the tracings differs at different dVm values.
3. Set the dVm slider to a value of 10 and, using an increment of 1 mV between runs, conduct a series of runs to determine the threshold of the axon.
4. Conduct a series of runs in which you vary dVm from –150 to +150 mV (use 20 mV intervals) and record the amplitude of the delayed outward current at t = 5 ms. You’ll probably want to turn off the displays of Itotal or INa+ for this exercise.
5. Click the Reset button, then clear the display. Select the INa+ and Numerical Values checkboxes, and deselect the Itotal and IK+ checkboxes. Set dVm to a value of 100 mV and [Na+]ext to its minimum value of 1. Do a run and record the value of INa+. Increase [Na+]ext to 10 and conduct a series of runs, incrementing [Na+]ext 10 units between each run until you reach [Na+]ext = 50, recording the value for INa+. Continue the series (recording data and clearing the display as necessary), now incrementing dVm by 100 units between runs, until [Na+]ext reaches its maximum value of 1000.
6. Click the Reset button, then clear the display. Select the IK+ and Numerical Values checkboxes, and deselect the Itotal and INa+ checkboxes. Set dVm to a value of 100 mV and [K+]ext to its minimum value of 1. Do a run and record the value of IK+. Increase [K+]ext to 10 and conduct a series of runs, incrementing [K+]ext 10 units between each run until you reach [K+]ext = 50, recording the value for IK+ after each run. Finish this experiment by setting [K+]ext to its maximum value of 100 and doing one last run.
Questions
Basic Questions
1. Are the maximum values for the Early Inward Current and the Na+ current equal to each other? Provide an explanation for your observation.
2. Are the values for the Delayed Outward Current and the K+ current (at t = 6 ms) identical? Provide an explanation for your observation.
3. What is the value of the threshold Vm for the squid giant axon used in this experiment?
4. Construct a graph of your results for Exercise #2. Determine the value for dVm at which the early inward current disappears ( = 0.0). Does this value match your prediction based on the Sodium Hypothesis? (Hint: to answer this question, you’ll need to use the values for resting Vm and eNa+ that you recorded from the Action Potential simulation) If so, defend your prediction. If the predicted and observed values do not coincide, can you suggest a reason why they do not?
5. According to the Hodgkin Cycle model, depolarizing the membrane increases gNa+, and the more we depolarize a membrane, the more gNa+ increases (up to a point, of course). Is this what you observed in the graph you constructed in the previous question? Propose an explanation for your observation.
6. Construct a graph of the delayed outward current's amplitude versus Vm (Exercise #4). Using the linear regression function of your spreadsheet (see “Working With Your Data”), fit a straight line to the linear portion of your data and determine the value for dVm at which the delayed outward disappears. How does that Vm value compare with the value for eK+ that you recorded during the Action Potential simulation? Is this result consistent with the Potassium Hypothesis? Why or why not?
7. Does varying [Na+]ext have the same effect on the early current at large dVm values (say > 120 mV) as a small dVm values ( < 40 mV)? Account for any difference(s).
8. What is the driving force for flux of Na+ and K+ through the membrane? Hint: from Tips and Hints # 3 above, when the driving force is exactly equal to 0, the flux should be zero as well.
Advanced Questions
9. Construct a graph of your results from Exercise #5. Use the curve-fitting function of your spreadsheet (see “Working With Your Data”) to fit a regression line to the data. Which regression model (linear, logarithmic, etc.) fits the data best? What does the ‘shape’ of the best fit regression line tell us about the mechanism(s) that produced your results?
10. With respect to the previous question, at what [Na+]ext does INa+ go to zero? Is this the same as [Na+]int for the squid axon? (you can run the Action Potential simulation to obtain the value for [Na+]int). If your answer to this question is “No”, explain why the two values differ.
11. Construct a graph of your results from Exercise #6. Use the curve-fitting function of your spreadsheet. What model (linear, logarithmic, etc.) fits the data best? What does the ‘shape’ of the best fit regression line tell us about the mechanism(s) that produced your results?
12. Use your data to calculate values for gNa+ and gK+ (see Tips and Hints #3, above) at different values for Vm. You’ll need to use the maximum value for the Na+ current and the K+ current at each dVm setting. Use these results to generate graphs of gNa+ and gK+ versus Vm. Discuss the significance of the appearance of the resulting plots.
13. Does a simple exponential or logarithmic regression line fit the data you obtained in Exercise #4? (you may have to transform your values for IK+ as discussed in the section on data transformation contained in the essay “Working With Your Data”). If your answer is no, provide an explanation. (Hint: see Tips and Hints #3, above)
Data Sheet For The Voltage Clamp Simulation
Run
#
[Na+]ext
[K+]ext
dVm
dVm < 0
or
dVm > 0
Maximum
Early Inward Current
Maximum
Delayed Outward
Current
Notes