CMM5311
HOMEWORK #1
SEPTEMBER 4, 2008
COORDINATOR: DR. J.M. RENAUD
DUE DATE: SEPTEMBER 11, 2008
1. Discuss the significance of each parameter of the Nernst equation. (15 marks).
Ion fluxes across the cell membrane are driven by two forces: the concentration gradient,
which is unique to each ion, and the electrical gradient that is generated by Em. When all
ions are permeable to the cell membrane, then an equilibrium will be reached when all
ions have equal concentrations on both side of the membrane. However, if some ions are
impermeable and a concentration gradient exists for some ions, then as the permeable
ions diffuse down their concentration gradient, they leave behind a countercharge
creating in the same process a membrane potential. In this situation, the effects of the
concentration and electrical gradient are in opposite direction. Now, an equilibrium is
reached for an ion when the influx down one gradient is equal but opposite to the efflux
down the other gradient; i.e., the net flux of that ion is zero.
The Nernst equation calculates the potential of the membrane at which an ion is at
equilibrium. Since membrane potential is a diffusion potential, energy is required for the
ion to diffuse across the cell membrane. The energy component of the Nernst equation is
‘RT’ where R is the gas constant with the unit of joule/mole/°K and T is the temperature
in °K. So the term ‘RT’ defines the amount of energy the system has at a given
temperature. A potential involves the movement of charges where 1 joule is required to
move 1 Coulomb of charges from point A to B. The term ‘nF’ define the charges where F
is the Faraday constant with the unit of Coulomb/mole and n is the charge or valency of
the ion. Finally, the equilibrium potential is a function of the natural log of the
concentration gradient of the ion. The larger the concentration gradient, then the greater
the potential must be to overcome (or oppose) the diffusion down the concentration
gradient.
2. According to the table below
A

What are the expected membrane potentials (Em) at 37°C? (10 marks)

What is the expected flux direction of Na+, K+ and Cl- for each condition? (10
marks)
B
C
D
E
[Na ]e
145
145
145
[ION] (mM)
145
145
[Na+]i
10
10
10
10
+
10
F
G
H
I
145
145
145
40
10
10
10
10
[K+]e
5
5
5
5
5
20
5
5
5
[K+]i
180
180
180
180
180
180
165
180
180
[Cl-]e
125
125
125
125
125
125
125
60
125
[Cl-]i
5
5
5
5
5
5
5
20
5
0.01
0.01
0.01
0.01
Ion Permability
200
0.01
PNa
0.01
200
0.01
PK
1
1
50
50
1
1
1
1
1
PCl
2
2
2
2
0.05
2
2
2
2
3. Based on the results obtained in #2, discuss how Em affects ionic fluxes (10 marks)
Em generates an electrical gradient across the cell membrane. The greater Em is, the
greater the electrical gradient and thus the greater the ion fluxes down that gradient. For
example in condition A, Em is -86.7 mV. If for whatever reason Em increases to -90 mV,
it will then increases the Na+ and K+ influxes (down the electrical gradient) into the cell,
which is more negative, while increasing Cl- efflux (down the electrical gradient).
Note: no mention here of the net flux and the concentration gradient
4. Based on the results obtained in #2, discuss how changes in ion concentration affect Em.
(10 marks)
Em is a diffusion potential, which means that a membrane potential is created when the
diffusion of an ion across the cell membrane generates a current. When the concentration
of an ion is changed, it affects the flux of that ion down its concentration gradient. For
example, in condition A, Em is -86.7 mV while EK is -95.2 mV. So in the resting state,
there is a net efflux of K+, which tends to bring Em toward EK. If [K+]e increases then the
efflux of K+ down its concentration gradient decreases. As less K+ is moving out of the
cell, it reduces the rate at which positive charges leaves the cell. Consequently, Em
becomes less negative or depolarizes. Another example is a decrease in [Cl-]e. In this
case, it is the Cl- influx down its concentration gradient that is reduced. As less Cl- comes
in the cell, the membrane depolarizes.
5. Based on the results obtained in #2, explain how an increase in GK can lower action
potential amplitude (10 marks).
In condition A, Em is -86.7 mV while EK is -95.2 mV. So in the resting state, there is a
net efflux of K+, which tends to bring Em toward EK.
During an action potential the membrane is depolarized from -86 mV to +30 mV. As the
membrane depolarizes, the K+ efflux constantly increases as EK – Em increases.
Consequently, the K+ influx counteracts the Na+-induced membrane depolarization.
When GK increases, it allows for more K+ efflux further counteracting the Na+
depolarization; i.e., it lowers action potential amplitude.
6. What do you predict an increase in GCl will do on action potential amplitude? (10 marks)
In condition A, Em is -86.7 mV while ECl is -85.6 mV. So in the resting state, there is
only a very small efflux of Cl-, which tends to bring Em toward ECl. An increase in GCl, is
not expected to have a large effect on Em because the driving force (ECl-Em) is very
small.
However, during an action potential the membrane is depolarized from -86 mV to +30
mV. As the membrane depolarizes, the net flux of Cl- will switch from efflux to influx as
Em becomes less negative than ECl. Furthermore, the influx constantly increases as the
membrane depolarizes or as ECl – Em increases. Consequently, the Cl- influx counteracts
the Na+-induced membrane depolarization. When GCl increases, it allows for more Clinflux further counteracting the Na+ depolarization; i.e., it lowers action potential
amplitude.