2) The following circuit represents an excitable cell at equilibrium. The three resistors GNa, GK and Gc? represent Na+, K+ and Cl channels; the three batteries VNa, VK and VCI represent the reversal potentials for Na+, K+ and Cl.
gna
6k
gk
1k
gcl
10k
+ vna
vk
+ vcl
55mV
-85mV
-65mV
0
a) If the membrane potential Vm can be measured from the node at the top of this circuit, write an expression for the ionic currents Ina, Ik and Ic? through each resistor. Assume the quantities GNa, GK and Gc? are conductances, which is the inverse of resistance. For example, Gc? = 1/10 ?? or 0.1 mS in the circuit above.
b) Using your answers from part A, at what membrane potential Vm will INa = 0? At what membrane potential Vm will IK = 0? At what membrane potential Vm will Ic? = 0?
c) Use your answers from part A to derive the following relationship for the resting membrane potential Vm in terms of the conductances GNa, Gk and Gc and the reversal potentials VNa, VK and VCI:
Vm = \frac{G_{Na} \cdot V_{Na} + G_{K} \cdot V_{K} + G_{Cl} \cdot V_{Cl}}{G_{Na} + G_{K} + G_{Cl}}
HINT: use nodal analysis to write an expression for the sum of INa, Ik and Ic?.
