MSP Problem Set 6
1. An axonal cell membrane is found to have a charge separation of 5,000 ions per m2.
a. Given that the membrane capacitance (Cm) is 1F/cm2, calculate the membrane
potential that is needed to separate this amount of ion charge?
Answer: 80mV
(5000ions/m2 )(1.6 coulombs/ion) = 8 x 10–16 coulombs/m2
Conveting units:
(8 x 10–16 coulombs/m2)(1012m/104cm2)(106  coulombs/coulomb)
= 0.08  coulombs/ cm2
Now V=Q/C = (0.08  coulombs/ cm2) / (1F/ cm2) = 0.08  coulombs/F = .08 V
(note: 1 coulomb = 1F x 1V)
b. A typical resting neuron membrane potential is about –60mV (+/- 20). What does this
tell you about the the nature of the cell membrane in its ability to act as a capacitor?
Due to the very high specific capacitance of the cell membrane, very little charge
separation is needed to yield a relatively high membrane potential (eg 100mV).
2.
Experimental evidence shows that the propagation speed (conduction velocity) of
an action potential along an axon is directly proportional axon diameter.
Explain why this is so.
The basic idea here is that resistance (Rm) decreases as the access area
increases.
A greater surface area corresponds to more ion channels through which ion
conductance can occur (increased conductance = less resistance).
3.
Describe this diagram in terms of properties of a biological membrane.
Capacitance = the lipid bilayer
Resistance = channels (remember resistance is just the inverse of conductance)
Battery = ionic gradients (set up, usually, by the Na/K ATPase)
4.
A. What is driving force?
The membrane potential minus the reversal potential (equilibrium potential for
a given ion). If the membrane and reversal potentials are equal, the ion is at
equilibrium and there will be 0 current flow.
B. How does it relate to the flow of current?
I=g(driving force)
Driving force is directly proportional to the current flow.
C. Under what 2 conditions would there be no current flow through a
membrane?
(1) driving force = 0 (see 2a)
(2) conductance = 0
5.
The extracellular concentrations of K, Na, and Cl are 4, 145, and 114
respectively. The intracellular concentrations are 139, 12, and 9 respectively. K has a
permeablility of 3 and a conductance of 5.4. Na has a permeability of 30 and a
conductance of 35. Cl has a permeability and conductance of 1. Calculate the
membrane potential twice (once using permeabilities and once using conductances).
They should use the GHK equation Em=60log PK*Ko + PNa*Nao + PCl * Cli
PK*Ki + PNa*Nai +PCl*Clo
And the equation given in Bezanilla’s handout V=ENa*gNa +EK*gK +ECl*gCl
gNa + gK + gCl
The answer for both equations is: 41.4
6.
Due to your strong interest in structure-function relationships of voltage-gated
channels, you decide to participate in a research project studying potassium channels.
You are expecially interested in the role of the S4 segment as a voltage sensor, hence
decide to focus on this portion of the protein. You generate a mutant channel (via sitedirected mutagenesis) in which the positively charged residues are neutralized by
replacement with uncharged amino acids. Predict how the graph of Po Vs. Voltage for
the mutant channel will compare to that of the wild-type channel.
Answer: Since the S4 segment will have fewer number of positive charges, it will
not be as sensitive to changes in the membrane potential. For this reason, the Po
vs. Voltage graph for the mutant will be less steep in comparison to that of the
wild-type channel. Note: although some students may speculate that a shift in
the curve will also occur, this shift is not specific to the charge content of the S4
segment (i.e. mutations in non-voltage sensing portions of the channel may cause
a shift).
7.
Suppose that an atypical K+ channel is discovered which is comprised of three
gating subunits as opposed to the normal number of four. Each of the S4 segments in
this aberrant channel is identical to that found in normal potassium channels. How will
the latency to first opening in this channel compare to that in wild-type?
Answer: Po = n3, where n = the probability that any of the gating subunits are in the
open position. Since n<1, the graph of n3 vs. time is steeper than that of n4,
hence the lag time to first opening is shorter; on average, the mutant channel
opens quicker.
8.
What is the single channel conductance of K+ when the membrane potential
reaches 0mv? (Assume that the KI=139, Ko=4, conductance = 25pS)
I=(V-EK) Ek= 60 log (4/139) = -92 so…. I=25(0 - -92) = 2300
9.
What variables are important in determining the potassium current through a
nerve axon membrane?
IK=NKPo(V-EK). In words this could be described as the density of channels in
the membrane (N), the conductance of an individual channel (), the open
probability of a single channel (Po), the voltage of the membrane (V), and the
electrochemical potential of K+ (EK).
10.
Describe the difference between closed and inactivated. What kind of channel
inactivates?
Inactivation is the result of docking a region of the protein into the internal
mouth of the channel stopping ion flow (ball and chain). In this condition, the
channel is still open but unable to conduct. A channel can be inactivated and
have no current flow even though the membrane potential is favorable for an
open configuration. This occurs in sodium channels. Closed refers to the
position of the subunits (i.e. all in the down position). Being open or closed is
dependent on membrane potential. No current flow in either condition.
11.
If the probability of one subunit to be in the active position is 0.3 in resting
conditions in the K+ channel, why is the probability for the channel to be open so much
smaller?
In order for the channel to be open all four units of the K+ channel need to be
in the active position. To get that open probability you need to multiply the
open probability of each of them: (0.3)4 = .0081 = 0.81%.
12.
You’re watching old-school ‘80s Justice League of America cartoons on the
Cartoon Network, and you see the Atom shrink himself down to molecular size.
You begin to daydream about shrinking yourself down so you can see channels
up close. You approach two membranes at different voltages with identical Na+
channels in them. You notice that on one membrane, the channels are open
more often but allow less current to flow than the channels on the other
membrane, which are not open as often. How can this be?
Current depends on conductance (open probability) and driving
force. The second membrane must have a larger driving force for
Na+.
13.
On page 21 of Dr. Bezanilla’s reader, in the lower right hand corner there are a
family of Na+ current traces corresponding to different depolarization steps.
a. What does it mean to have a negative current?
For a cation, inward current is negative.
b. Notice that there is one positive current. Which voltage step does this
correspond to?
The most positive one: +50 mV
c. At approximately what voltage would the current switch/reverse from
negative to positive? Why?
At ENa (aka VNa), the reversal potential for Na+. At this
potential there is no driving force and therefore no current. At
a more positive potential, the driving force will reverse and
force Na+ out.