Cell Biology Problem Set: Membrane Potential Colin Nichols 10/06
1. Consider the following concentrations (all are given in mM) found in a typical mammalian cell.
Complete the table by calculating the equilibrium potential (Nernst Potential) for each ion. (2 pts) ion Extracellular Intracellular E ion
(mV)
Na
+
145 4
K
+
4 140
Ca
+2
2 1 X 10
-4
Cl
-
120 4
+93.6
-92.6
-88.6
+129 (remember z = 2 for Ca)
RT/zF = 60 mV @ 30 °C for z = 1
For Ca 2+ (the hardest one):
E
Ca
= (60 mV / 2) * log (2 mM / 1 x 10
-4
mM) = +129 mV
2. The relative permeabilities to K
PK
+
: PNa
+
: PCl
+
, Na
-
1 : 0.01 : 2
+
and Cl
-
are as follows (with PCa
2+
= 0) :
Vm
Estimate Vm using the GHK equation. (1 pt)
= 60 mV
*
log
1

4
1

140


0 .
01

145
0 .
01

4


2

4
2

120
= 60 mV
*
log (13.5 / 380) = -87.1 mV
3.
If the relative permeabilities suddenly became 0.1 : 5 : 2, how would Vm change? (1 pt)
Vm = 60 mV
*
log (733 /274) = +25.7 mV
4. The specific capacitance of most cell membranes is 1 µF / cm
2
. a) How many K
+
ions must cross the membrane of a spherical cell, 40 µm in diameter, to change the membrane potential by 10 millivolts. (1 pt)
Area = 4

r
2
= 4
*
3.1416
*
(20 x 10
-4
cm)
2
= 5 x 10
-5
cm
2
= 5 x 10
-11
Farads
Q = C
*
V = 5 x 10
-11
Farads
*
0.010 Volts = 5 x 10
-13
Coulombs
5 x 10
-13
Coulombs / 9.65 x 10
4
Coulombs / mole ~ 5.2 x 10
-18
moles
5.3 x 10
-18
moles x 6.02 x 10
23
ions / mole = 3.1 x 10 6 ions b) How many millimoles does this represent (1 pt) . 5.2 x 10 -15 mMoles c) What change in cytoplasmic K
+
concentration will occur? (1 pt)
Volume = 4

r
3
/ 3 = 4
*
3.1416
*
(20 x 10
-4
cm)
3
/ 3 = 3.3 x 10
-8
cm
3
or ml
5.2 x 10
-15
mMoles / 3.3 x 10
-8
ml = 1.55 x 10
-7
mMoles / ml or
0.155 µM

5. a) Sketch an action potential (voltage versus time) that approximates what is seen in a ventricular myocyte. b) Superimpose an action potential that might result if the number of voltage-gated K channels were substantially reduced, but all other conductances were unaffected.
AP prolonged, plateau maybe elevated, peak of AP elevated slightly c) Superimpose an action potential that might result if the number of Ca channels were substantially reduced, but all other conductances were unaffected.
AP shortened, plateau depressed
6.
If the pH outside of a cell is 7.4 and the pH inside the cell is 7.2 a) What is the Nernst potential for protons across the cell membrane? (1 pt)
E
H
= 60 (-7.4 - (-7.2)) = -12 mV a) b) In what direction will the net flow of protons occur through a surface membrane proton channel at the following membrane potentials: -80 mV? 0 mV? +80 mV? (1 pt) inward at -80 mV; outward at 0 mV and +80 mV