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Bio 3411 Problem Set #7
Name:__________________________
TA Name:____________________
This Problem Set will be DUE: Nov. 15th at the beginning of class
1.(1 point) List3 differences between active and passive propagation, Why do passively
propagated signals only travel a short distance in neurons (please mention the length
constant, internal resistance, and membrane resistance in your answer) ?
active propagation: slow, doesn't decrement, energy distributed along length;
passive propagation:fast, decrements, energy enters at a single point
Passive propagated signal travel a short distance in neurons because voltage is lost to resistance
as the signal is propagated. The length constant, which is the distance is takes for the voltage to
drop down to 1/e of its original value, is defined as (Rm/Ri)1/2, where Rm is membrane resistance
and Ri is internal resistance. The Ri/Rm ratio is large, so the length constant is small.
2.(0.5 point)
i)__ Potassium channels are open at rest while Sodium___ channels are closed at rest.
ii)_concentration gradient__and __electrical gradient_are the two forces that are equal
and opposite at the equilibrium potential of an ion.
3. (0.5 point) Why does the resting membrane potential of some neurons deviate slightly
from the equilibrium potential of K+, while the resting potential of glial cells is almost
always EK?
This occurs because of the presence of sodium leak channels in some neurons. However, these
are not open in glial cells, so the resting potential is solely EK.
4. (4 points)The ion concentrations of a typical neuron in the squid axon are something
like:
K+
Na+
ClCa++
Inside (mM)
200
40
25
0.001
Outside (mM)
2
400
250
1
a. (0.5 point) What’s the definition of equilibrium potential for an ion? What’s the
definition of resting potential for a cell?
b. (1 point) Calculate the equilibrium potential for each ion in the squid axon.
Using a microelectrode, you measure this cell’s resting membrane potential at –90 mV.
c.(0.5 point) Is this cell permeable to only K+? If not, what else might it be permeable to?
d.(0.5 point)At this resting potential, is there a net flow of K+ and if so, which direction?
f. (1.5 points) If this same cell were to become permeable principally to Ca++, which
direction would the net flow of Ca++ ions be? What would the new resting membrane
potential be if the cell were to maintain a permeability only to Ca++? What would the new
intra- and extracellular concentrations of Ca++ be when this new equilibrium potential is
reached? Unchanged
5.(1 point) The equilibrium potential for K+ and Cl- are both within the range of the
observed resting potential, how to distinguish which one is responsible for the generation
of resting potential (hint: Salkoff handout)?
6. (3 points) For the sake of clarity, for calculation questions, please circle your final
answer.
Ion
K+
Na+
Ca++
Cl-
Inside neuron
250
40
0.0001
16
Outside neuron
25
400
1
160
Use the Nerst Equation and GHK Equation to solve the following problems.
At rest, a neuron is primarily permeable to K+, however there is some Na+ permeability
as well.
a. (0.5 point) What effect does additional Na+ permeability at rest have on the membrane
potential (as opposed to K+ permeability only)?
b.(1 point)If the conductance (g) of K+ and Na+ at rest is 25 and 1 Seimens respectively,
what is the actual resting potential of this neuron? (At no chloride and calcium
conductance)
c. (0.5 point) How does this compare to the resting potential for a neuron permeable to
K+ alone?
d.(1 points) Now let's add GABA to this neuron, which will open Cl- ion channels.
i. If the Cl- conductance (g) is 4 Siemens, what is the new resting potential?
(taking into account K+ and Na+ at conductances in part 1b.)
ii. At this resting potential, which direction will each permeable ion be flowing?