Circuit model of a cell membrane

8.5.P29

 

A cell membrane is electrically active as a result of ion pumps in the membrane that act as batteries and resistors. A structural model and an equivalent circuit model* are shown in the figures below. V₀ is the potential difference between the inside and the outside of the cell.

 

*Model adapted (simplified slightly) from Medical Physiology, 3^rdEd.E. L. Boulpaep & W. F. Boron (https://doctorlib.info/physiology/medical/) 

 

A. Assuming that the currents are stable (not changing), how do the currents flowing in the K, Na, and Cl channels relate? (Take I_K, I_Na , and I_Cl as positive quantities.)

 

1. I_K + I_Na = I_Cl 
2. I_K = I_Na + I_Cl 
3. I_K = I_Na - I_Cl 
4. I_K + I_Na + I_Cl = 0
5. None of these work. 

 

B. Assuming the currents are stable (not changing), how does the current through the capacitor, I_C, compare to the currents in the resistors? (Take I_C as a positive quantity.)

 

1. I_C = I_Cl + I_K - I_Na 
2. I_C = I_Cl + I_K + I_Na 
3. I_C = I_Cl -I_K - I_Na 
4. I_C = 0
5. None of these work. 

 

C. Which of the following relations hold among the magnitudes of the voltage drops, ΔV across the K, Na, and Cl resistors and the magnitudes of the voltages V maintained by the K, Na, and Cl batteries? (Take V_K, V_Na, V_Cl, ΔV_K, ΔV_Na, and ΔV _Cl as positive quantities.)

 

1. V_K + V_Na = ΔV_K + ΔV_Na
2. V_K - V_Na = ΔV_K + ΔV_Na
3. V_K + V_Cl = ΔV_K - ΔV_Cl 
4. V_K - V_Cl = ΔV_K + ΔV_Cl
5. None of these work. 

 

D. The potential drop across the capacitor is equal to

 

1. V_K - V_Na + V_Cl
2. V_K + V_Na + V_Cl
3. V₀ 
4. 0
5. None of these work. 

 

 

_{Joe Redish and Bill Dorland 5/18/18}