PNB 2XB3 Homework Assignment 3
Due date: Monday, October 1, 2012 at 8:30 AM
Number of students submitting this paper (circle one): 1
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1. (2 points). We learned in class that the action potential (rising and falling
phases) lasts about 1 ms in a typical neuron, and the refractory period doesn't end
until about 1 ms later. Given this information, what is the maximal action potential
firing rate of a typical neuron? Give your answer in action potentials per second.
2. (2 points) A neuroscientist records the voltage of a neuron with an electrode
placed inside the axon hillock. As soon as a naturally occurring action potential
(blue) is detected, the neuroscientist injects Na+ ion into the axon with a
micropipette. As we learned in class, the sodium injection will produce two action
potentials moving with equal speed in opposite directions (red action potentials 1
and 2). Action potential 1 will reach the axon terminal and cause the release of
neurotransmitter. Action potential 2, however, is heading directly into the path of
the blue action potential. What will happen when action potential 2 and the blue
action potential meet? Explain your reasoning.
Drawing adapted from Purves et. al., Fig. 5.21A (4th Edition)
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3. You're explaining some fascinating neuroscience topics to an intelligent friend
who has not taken a neuroscience class, but who does know something about
chemistry and physics. Your friend has never been shy about questioning your
claims, and she gives you a pretty hard time, as described below:
a) (2 points) You explain to your friend that when the action potential reaches the
axon terminal, voltage-gated calcium channels open and calcium flows into the
cell. "But wait!" your friend interjects. "You just told me that at the peak of the
action potential the inside of the cell is, like, positive 30 mV, so it seems to me that
this should repel the calcium ions, since positive charges repel each other, right?
So I would think that the calcium would flow out of the cell, at least when the
action potential is at its peak value, not into the cell. I mean, I think that you're,
like, totally wrong!"
How would you respond to your friend? Be as specific as you can, and explain
your answer using any relevant neuroscience equations.
b) (2 points) In talking to your friend about neurotransmitters, you explain that
GABA causes an IPSP by opening a ligand-gated chloride channel. "Not to keep
doubting you," says your friend as she shakes her head impatiently, "but since the
inside of a resting neuron is at -65mV, and since chloride is a negatively charged
ion, why does GABA cause an IPSP? Shouldn't chloride be repelled from the
inside of the cell, so that when GABA binds its receptor chloride would leave the
cell? So wouldn't this make the intracellular potential more positive, not more
negative? I mean, it seems to me that GABA would cause an EPSP, not an IPSP."
How would you respond to your friend? Be as specific as you can, and explain
your answer using any relevant neuroscience equations. (Assume that the
intracellular chloride concentration is 5 mM, and the extracellular concentration is
110 mM).
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4. (2 points) The postsynaptic neuron shown below is initially at rest (-65 mV)
when two presynaptic pyramidal cells fire action potentials that cause simultaneous
EPSPs at the axon hillock. Each EPSP has an amplitude of 10 mV at the location
of its synapse on the dendrite. The distances of these synapses from the axon
hillock are 200 microns and 300 microns (i.e, 0.2 and 0.3 mm). Will the
postsynaptic neuron fire an action potential? (You may assume that the
postsynaptic neuron has an action potential threshold of -50 mV and a dendritic
length constant of 1 mm).
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5. (2 points) A presynaptic pyramidal cell fires two action potentials in a row,
separated by 7 ms. The first action potential causes a subthreshold EPSP of 8 mV
peak amplitude at the axon hillock of the postsynaptic neuron (i.e., the EPSP
depolarizes the axon hillock from -65 mV to -57 mV). Will the postsynaptic cell
fire an action potential when the second EPSP reaches its peak amplitude of 8 mV
at the axon hillock 7 ms later? (You may assume that the postsynaptic neuron has
an action potential threshold of -50 mV and a dendritic time constant of 5 ms).
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