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BME 502, Spring 2001
Assignment 1
Name:_____________
Student ID:______________
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1. Which of the following statements are true?
a) In the resting neuron, the tendency for the concentration gradient of K to move K ions out
of the cell is slightly stronger than the tendency of the membrane potential to pull them in.
b) In the resting neuron, as far as Na Ions are concerned, the membrane potential and
concentration gradient act in the same direction.
c) A sodium-potassium pump expels Na ions from the inside of the neuron and retrieves K ions
from the outside.
d) Both Na and K ions carry a positive charge.
Answer: a, b, c, d
2. Enter in the following table the ratio of the intracellular to the extracellular ion
concentration for K, Na and Cl ions.
Ions
Internal/External
K
__/1
Na
1/__
Cl
1/__
Answer: K 20/1; Na 1/12; Cl 1/30
3. Which of the following variables are in balance at the equilibrium potential for an ion?
a) The intracellular and the extracellular concentrations of the ion.
b) Osmotic pressure and electric field.
c) Influx and efflux of the ion through the cell membrane.
d) The Na concentration outside the cell and the K concentration inside the cell.
Answer: b, c
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4. Which of the folowing statements indicate that, apart from K and Cl ions, Na ions also
influence the resting potential?
a) The resting potential is less negative than Ek.
b) The resting potential changes approximately in proportion to the logarithm of the
extracellular K concentration.
c) In the absence of extracellular Na the resting potential and Ek are the same.
d) The sodium equilibrium potential is positive while the potassium equilibrium potential is
negative.
Answer: a, c
5. Which of the following statements show why the resting membrane potential is made more
postive by the inflow of Na?
a) There are more Na ions outside the cell than inside.
b) The cell loses K ions because of the inflow of Na ions.
c) The negative charge on the inner side of the membrane is reduced by the influx of Na ions.
d) THe cell also picks up chloride as a result of the Na inflow.
Answer: b, c, d
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6. The Na efflux from the cell is "active" because:
a) The driving potential for the Na efflux is large.
b) No passive net Na efflux can take place against the driving potential.
c) Metabolic energy is required for the Na efflux.
d) The sodium conductance of the membrane is much higher than the potassium conductance.
e) The sodium conductance of the membrane is much lower than the postssum conductance.
Answer: b, c
7. Active Na transport can be blocked or greatly reduced by:
a) Lowering the extracellular K concentration.
b) Lowering the intracellular K concentration.
c) Increasing the intracellular Na concentration.
d) Cooling the cell.
Answer: a, d
8. At constant resting potential the passive sodium inflow is equal to the:
a) Passive potassium inflow.
b) Passive net potassium flow.
c) Active sodium outflow.
d) Active potassium outflow.
Answer: c
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9. For the following linear model of a cell, derive the steady state value of Vm.
Answer:
I=gNa(Vm-Ena)+gK(Vm-Ek)+gCl(Vm-Ecl)+gleak*Vm
I  ( gNa  gK  gCl  gleak )(Vm 
gNa  ENa  gK  EK  gCl  ECl
)
gNa  gK  gCl  gleak
 steady  state, I  0
gNa  ENa  gK  EK  gCl  ECl
Vm  Vrest 
gNa  gK  gCl  gleak
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10. Assume that the following typical conditions apply to an animal cell at rest in its normal
steady-state:
-the surface membrane contains a 3:2 Na/K pump;
-the surface membrane contains passive permeabilityk pathways for K, Cl and Na(ie. Leaking
happens);
-the cytosol contains impermeant, negatively-charged phosphates and proteins (P-);
-Vm (the cell membrane potential) satisfies: Vm = ECl; Vm > Ek; Vm < ENa;
-the cell membrane contains no other pumps or channels that need be considered here.
1). Specify the direction, if any, of the net passive flux of:
a) Cl-:
b) K+:
c) Na+:
Answer: Cl-: None
K+: Outward
Na+: Inward
2). Now assume that ouabain (a blocker of the Na/K pump is applied at a saturating
concentration).
a) What, if anything, do you expect to happen to Vm immediately (e.g. within one second)
after application of ouabain? Explain.
Answer: There would be a small depolarization.
Before, Na/K pump sustained a outward current. After application of ouabain, charge
would accumulate inside. So small depolarization.
b) How has the passive flux of Cl changed with respect to your answer in part A:
Answer: Should be not much changed. There would be some net Cl move inward, but the
amount is small.
This is because the depolarization in A is small and therefor the driving force for Cl is
small.
c) What will happen to cell volume in the long run? Explain briefly.
Answer: Charge will accumulate within cell. More water would be brought in by osmotic
pressure. Evetually the cell would blow out.
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11. You are examining the electrical characteristics of a cell’s membrane. You have a cell
immersed in a bath of extracellular fluid. You have measured the intracellular and extracellular
K+ concentrations, which are show as below:
Extracellular potassium concentration
Intracellular potassium concentration
3 mM
90 mM
What you also know is that the extracellular and intracellular concentrations of other ions are
pretty much the same with the case of normal neuron cell. And you recall following statement
from Dr. Berger’s handout #1:
"Membrane is largely permeable to K+;
Membrane is slightly permeable to Cl-;
Membrane is impermeable to Na+ and Ca2+;"
1) Which one of the following is true according to above? (Think about the immediate
electrochemical effects, and ignore any contribution of Na+/K+-ATPase or other pump
mechanisms.)
a. If you double the extracellular Na+ concentration, the membrane resting potential
would change;
b. If you double the extracellular K+ concentration, the membrane resting potential would
change;
c. The membrane’s resting potential is equal to the reversal potential of the Cl -;
d. The membrane’s resting potential is equal to the reversal potential of the Na+.
Answer: b
2) Estimate the cell’s membrane resting potential. Explain your reasoning and show your
calculation. (If you use ‘log’ in Nernst equation, the const RT/ZF=58)
Answer: The membrane is mainly permeable to K+. So when Na+ and Cl- are not considered,
the membrane resting potential is roughly the reversal potential of the K+ ions, which is
Em=Ek=RT/ZF*log([K+]o/[K+]i)=58*log(3/90)= -85.7mV
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3) Now you begin to change the extracellular K+ concentration with following procedure: First
keep the cell in the extracellular fluid with 3mM K+ for a long time, then suddenly change the
extracellular K+ concentration and record the resting potential at the same time. Then change
the extracellular K+ concentration back to 3mM and wait for a long time. Repeat the procedure
and you get a series of extracellular K+ concentration and the corresponding resting potential.
If you plot extracellular K+ concentration vs. corresponding resting potential with these values,
which of the following is most likely the result? Hint: The x-axis is log(extracellular K+
concentration)
Answer: b
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12. The graph below represents the I/V curve of a newly discovered channel.
1) According to the above I/V curve, what is this channel most likely gated by? Explain.
Answer: Voltage-gated, since the I-V curve is non-linear.
2) Assuming this is from a mammalian nerve cell, which of the following statements is
most likely to be true?
a) This channel is permeable only to Na + ions
b)This channel is permeable only to K+ ions
c)This channel is permeable only to Ca2+ ions
d)This channel is permeable only to Cl - ions
e)This channel is permeable to a lot of ions
f)This channel is NOT permeable to any ions
Answer: e
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