Ionic Basis Of Membrane Potentials. I.

Effects of Ion Concentrations and Conductances on Membrane Potential (V_m)

This simulation uses the Goldman Equation to calculate values for the membrane potential (V_m) of a cell. Only the monovalent ions Na⁺, K⁺, and Cl^-, are employed in the calculations Temperature is constant at 18^o C.

Tips and Hints

1. Each time you click the "Go" button to calculate a V_m value, any changes you may have made in ion concentrations and conductances are not sent to the simulation until after a delay of 1 ms. Instead, the simulation first calculates and displays the (resting) V_m based on the default values for the ion concentrations and conductances. This feature was put into place so that you would always have the default value of V_m available for visual comparison with the effects of any changes you make in the parameters’ values. The result of this feature is that the ‘resting’ V_m is displayed for 1 ms after you click the Go button. Once t = 1 ms, the new parameter values take effect and V_m ‘shifts’ to the new equilibrium potential.

Note that in accordance with the Equivalent Circuit Model and the electrical behavior of R-C circuits, the new equilibrium V_m is not reached instantaneously (for this simulation, membrane capacitance was set to a value of 1.0 mf). At the completion of the simulation run, the numerical value of the new equilibrium V_m is displayed to the right of the line.

2. At least when first working with the simulation, just make changes in one parameter at a time. Do enough runs varying just that parameter until you’re sure you understand the effect of the changes you’re making……and can give a clear explanation to your lab partners. Then use the Reset button to return all settings to their default value and work with a different parameter, and so on. Wait until you have some experience – and have developed a good understanding of the effect of individual parameter changes – before you start experimenting with changes in more than one parameter at a time.

3. Before clicking the Go button after you’ve made a change in the value of any parameter(s), make a prediction about whether the change you’ve made will cause V_m to increase ( ), decrease ( ¯ ), or remain unchanged, and record your prediction in the appropriate column in the data sheet. Compare the result you get with your prediction. (you’ll note that I’ve done an example, just to get you started) If you consistently able to make correct predictions, congratulations! You understand the ionic basis for V_m. If you predicted incorrectly, figure out where you erred. The point of this simulation is to help you learn, not to trip you up!!

4. A data sheet is provided for your convenience. You’ll probably need to make several copies of it for use in the following exercises.

5. Remember: when working with membrane potentials, use the absolute value of V_m if you wish to compare to V_m values to determine which is larger. That is, unlike the relationship you learned in your math class, -70 mV represents a smaller V_m than –85 mV, and –50 mV is equal to +50 mV in terms of the potential difference across the membrane.

Exercises

1. Click the Go button to solve the Goldman Equation for the default parameter settings. Record the parameter settings and the resulting value for V_m on your data sheet. Now, increase g_Na+ to 3, predict the effect on V_m, ( , ¯ or no change), and click the Go button. (note the 1 ms delay before the new parameter values are applied and V_m changes to its new equilibrium value.) Was your prediction confirmed? Continue changing g_Na+ until you’re certain you understand and can explain the effect of g_Na+ on V_m.

2. Click Clear, then Reset to generate a cleaned-up display of the default V_m. Repeat Exercise #1, this time varying g_K+.

3. Click Reset, then Clear. Repeat Exercise #1, this time varying g_Cl-.

4. Click Reset, then Clear. Try various combinations of [Na⁺] (both external and internal) to quantify the relationship between ion concentration gradients and V_m.

5. Click Reset, then Clear. Try various combinations of [K⁺] (both external and internal) to quantify the relationship between ion concentration gradients and V_m.

6. Determine the equilibrium V_m for Na⁺ (e_Na+) by setting the conductances for K⁺ and Cl^- equal to 0 (why set the conductances to 0?). Vary g_Na+ to assess its effect on e_Na+. Now, repeat this exercise for K⁺, then Cl^-.

7. Set g_Na+ = g_K+ and note the resulting equilibrium V_m. Does the equilibrium V_m depend on the actual values for g_Na+ and g_K+, or on their relative values? Can you explain your results?

Questions

Basic Questions:

1. Compare the effects on V_m of changing g_K+ and g_Na+. Were the effects on V_m the same in each case?

2. If you increase g_Na+ by 10 units, say from its default value of 1 to a value of 11, does that have the same quantitative effect (ignoring the sign of the effect) on V_m as an increase in g_K+ from 75 to 85? Offer an explanation for your observation. What if you increase g_Na+ and g_K+ by the same relative amount (i.e., suppose you double them both relative to their respective resting values)?

3. If you double g_Cl-, what does that do to resting V_m? What impact does doubling g_Cl- have on the effect of doubling g_Na+ or g_K+? That is, does increasing g_Cl- make it more difficult to change V_m by changing g_K+ and/or g_Na+, or less difficult? Explain your results. (Hint: think in terms of the relative values of e_Na+, e_K+, and e_Cl-.

4. If you double [Na⁺]_ext, does that have the same quantitative effect (ignoring the sign of the effect) on V_m as doubling [K⁺]_ext? Why or why not? What if you make the same numerical changes in [Na⁺]_int or [K⁺] _int (i.e., increase each by 20 units)?

5. Does the value for equilibrium V_m for an individual ion species depend on its conductance? Explain why or why not.

Advanced Questions:

1. Construct graphs of equilibrium V_m versus [Na⁺]_ext, [Na⁺]_int, [K⁺]_ext, [K⁺] _int, g_Na+ , or g_K+ , and g_Cl-. Fill out the following table by entering whether the data are fit best by a straight line (linear model) or a curved line (non-linear model) and providing your interpretation of the meaning of each graph

Graph of Vm versus:	Best-fit Model (linear or non-linear)	Interpretation
[Na^+]ext
[Na^+]int
[K^+]ext
[K^+] int
gNa+
gK+
gCl-

2. In the context of these simulations, what is a reversal potential?

3. Suppose you doubled the membrane’s capacitance to 2 mf. What changes would you expect to observe in the graphs of V_m versus time? What if you reduced the capacitance to 0.5mf? (if necessary, you can review the electrical behavior of R-C circuits and run the associated simulation.)

Data Sheet For Goldman Equation Simulation

Run #	[Na^+]ext	[K^+]ext	[Na^+]int	[K^+]int	gNa+	gK+	gCl-	Predicted Effect on Vm (, ¯ or none)	Actual Vm ( mV )	Notes
Reset	120	3	10	140	1	75	75	n/a	n/a	Default Equilibrium Vm = -89 mV
1	²	²	²	²	2	²	²	¯	-83	-83 mV < -89 mV è Prediction confirmed!!