mspt7a - Medical Student Education

Problem Set #7
1.) If you were patch clamping a single channel in a Xenopus oocyte and observed that
the current delivered by the clamp amplifier during the voltage pulse to + 20 mV
was outward, what would be your guess as to the type of channel which was being
studied? Note: assume standard intracellullar and extracellular ion concentrations.
Answer: Since the clamp amplifier maintains the membrane voltage constant, it delivers
current in the opposite directions of positive ionic flow. In this case, it delivers and
outward current, in order to counter-act the inward current caused by Na influx during
the depolarization.
2.) Upon depolarization, an inward current is first observed, followed by and outward
current. What ion is responsible for the inward current? Can you determine a reason
for this current to be maximized at 0 mV as opposed to more hyper-polarized or
depolarized potentials?
Answer: The inward current is attributed to sodium influx. The reason that the sodium
influx is maximized at 0 mV is because at this potential there is sufficient membrane
depolarization such that the open probability is relatively large while the driving force
(50 mV) is still appreciable. At more hyperpolarized potentials, the open probability is
too small to result in appreciable macroscopic ion current (although driving force is
larger). At more depolarized potentials, the opposite situation occurs; namely, the
driving force is small, although the open probability is large.
3.) Ion channels are typically described in terms of their conductance which is the inverse
of the resistance. Please briefly explain how the macroscopic potassium conductance
can be a non-linear function of voltage if ohmic resistors demonstrate linear current
flow as a function of voltage.
Answer: For ohmic resistors: I = V/R = V * g (conductance). However, in a population
of channels gp (conductance) = Po * gsc(single channel conductance))*NK(density). It’s
important to distinguish single channel conductance which is linear with voltage from a
population conductance which is non-linear with voltage primarily due to the nonlinearity of Po.
4. Seeking to escape the basic science rigors of medical school, you register for an
introductory Greek class. As you begin to nod off in class one day, the professor
notices and says, “You might think that the greek alphabet is too simple for your
brilliant mind, but I’ll have you know that greek letters are of huge significance in the
world of science. Since you obviously need some extra motivation, perhaps you could
tell us the meaning and importance of the time constant m and the space constant 
with respect to neuronal action potentials.” Everyone knows you are a medical student
(because you told them) and awaits your answer...
m = Rm * Cm and is indicative of how long it takes to charge the capacitive
neuronal membrane.
 = the square root of (rm/ri), or the square root of (aRm/2Ri)
(little r is resistance, big R is area)
the space constant indicates how far a current pulse or voltage change can
travel/spread before it decays to 0.37 or 1/e of the original value.
Both constants are important in determining the speed of AP propagation or
conduction velocity. (Faster with small tau and big lambda)
5. A classmate of yours decides to make flash cards to learn the sequence of events in a
typical action potential, starting with a neuronal membrane at resting potential. But
one stress-filled day, as your friend attempts to catch a Netter atlas before it hits the
ground, everything goes flying. As scalpels and histo slides fly through the air, the
flash cards get scrambled, and your friend yells for help. Because you are an MSP
student, you have no trouble putting the flashcards into the correct order:
5. Current flows in a loop between the Na and K resistors.
2. The capacitor is slightly charged, current flows through the Na resistor
and the capacitor .
6. Current flows through K resistor and capacitor.
3. gNa decreases as gK increases.
1. There is no current flowing through the capacitor, the sum of the Na, K,
and leakage currents are zero.
4. Once again, the sum of the Na, K, and leakage currents are zero.
6. When an electrode is impaled into a normal axon (no voltage clamps) and a current is
supplied with respect to another electrode located on the outside of the axon, the
measured membrane voltage is greatest near the penetrating electrode and gets
progressively smaller as you move away from the electrode in any given direction.
Describe the two main membrane factors responsible for this observed voltage drop.
1. Axon membranes have a finite permeability, thus, as the current flows along
the axon, some current will flow perpendicularly through the membrane and
diminish the membrane potential. This finite permeability yields the
membrane resistance (rm).
2. The internal cytoplasmic resistance (axoplasmic) also produces a voltage
drop (V= iri) which diminishes the membrane potential as the current flows
along the inner cell membrane.
7. Given that the intrinsic membrane properites (capacitance, resistance, etc.) of all
nerve fibers are the same, explain why it is that action potentials propagate faster in
fibers with larger diameters.
The effectiveness of voltage spread along the axon depends on how much current
goes through the axon (a fuction of membrane resistance, rm) as compared to how
much moves along the axon (function of internal longitudinal resistance, ri).
Quantitatively, this is given by the space constant ().
In technical terms, the space constant represents the distance that one must move
away from the site of the stimulating current to record a voltage that is 0.37 (1/e) the
value of the voltage at the injection site.
But in practical terms this simply means that by increasing the radius (a), the
electrical disurbance in the membrane will travel farther and initiate the next action
potential further away  faster AP propagation.
2 Ri
Where a = axon radius.
8. What is the sodium reversal potential (numerically) and what does it signify?
According to the current traces on page 28 the reversal potential is 50 mV which
coincides with the sodium Nernst potential as computed with the known
concentrations of sodium inside and outside the fiber. The current is inward for all
potentials negative of 50 mV and outward when the potential is more positive than
50 mV.
9. The main ingredient in lethal injections is KCl. Discuss the mechanism which a
massive dose potassium extracellularly will kill a person (think of the membrane
potential in cardiac myocytes).
Potassium normally resides in much greater concentrations intracellularly. An
elevated concentration of potassium extracellularly depolarizes the cardiac
myocytes. This may cause an initial depolarization, but more importantly would
result in eventual inactivation of the sodium channels. Once the channels are
inactivated, they are unable to propogate an electric potential through the myocytes.
The membrane must repolarize to end the inactivation. The graph on page 30
shows that the membrane must be repolarized for at least 10 ms.
10. Suppose you could stimulate a nerve in the middle of its axon. How would you
expect this to effect the propagation of the action potential?
The impulse would travel in both directions anterograde and retrograde (towards
the terminal and towards the dendrites). Normally retrograde propagation is
inhibited by the inactivation of the sodium channels. In any given patch positive
charges influx—these then diffuse along the longitudinal resistivity of the axon.
Anterograde this increase in membrane potential allows the opening of the sodium
channel. Retrograde, normally, the increase in membrane potential does not affect
the sodium channels because they are inactivated. When you start the stimulus in
the middle, the retrograde channels are not already inactivated, so the increase in
positive charges causes the sodium channels to open.
11. What are strategies used by nerves to increase the speed of action potentials?
Increasing the diameter increases the conductance velocity. Hence the huge giant
axon of the squid. However for higher mammals like humans, we would need to
have huge necks just to coordinate the movement of our feet. Vertebrates in order
to have small necks myelinate their axons. The activation of the Na conductance
occurs in the exposed axon at the nodes of Ranvier. This is called saltatory