Description
1. (20 points) Please state whether each of the following statements is true or false. If it is false,
correct the statement to receive full credit. Each statement is worth one point.
(a) The human brain has on the order of 1012 neurons.
(b) The frontal lobe of the brain is posterior to the occipital lobe.
(c) The brain has folds which increase its surface area.
(d) The left hemisphere of the brain in general deals with the sensory and motor processing
of the left side of the body (more so than the right hemisphere of the brain).
(e) The monosynaptic circuit involed in the knee-jerk spinal reflex does not involve the
brain.
(f) A type of glial cell, called astrocytes, produce myelin to insulate neural axons.
(g) Neurons can convey electrical signals on the order of meters.
(h) At the synapse, neurons transmit information exclusively through electromagnetic transduction.
(i) The action potential shape does not convey information.
(j) Sodium ions are far more concentrated within the cytoplasmic side of a neuron (as
opposed to the extracellular side).
(k) It is possible for a neuron to fire action potentials at a rate of 10,000 Hz (10,000 in one
second).
(l) Consider measuring the membrane potential of a neuron (with the cytoplasmic side as
”+” and the extracellular side as ”-”). A depolarization corresponds to a decrease in
membrane potential.
(m) A depolarized cell increases the likelihood of an action potential.
(n) Na+ ions hold water more closely than K+ ions do.
(o) Increasing the thickness of myelin sheaths will decease action potential speed.
(p) Multiple sclerosis is caused by the demyelination of axons.
(q) Action potentials are all-or-nothing events.
(r) All action potentials have the same shape.
(s) The equation relating conductance (G) to current (I) and voltage (V) is I = V G.
(t) Anionic proteins residing in the cytoplasm are as permeable to the membrane as sodium
and potassium ions.
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2. (25 points) Consider an “alien” neuron that you have just measured as having: (1) an internal
concentration of 336 mM K+ and 50 mM Na+, and (2) an external concentration of 42 mM
K+ and 300 mM Na+. Your measurements also indicate that the membrane is not permeable
to any other ions.
(a) (10 points) What are the equilibrium membrane potentials EK and ENA, including the
appropriate sign?
(b) (5 points) A fellow researcher studying an identical neuron in a make-shift lab (there’s a
national emergency with many researchers scrambling to understand these cells because
alien neurons have fallen to Earth!) comes over to you and says that she is seeing action
potentials with a peak-to-peak amplitude of 110 mV. Do you say (i) ”that’s great, very
useful information,” or (ii) ”I don’t think so, why don’t you repeat your measurement
and check the calibration on your amplifier and oscilloscope”? Why?
(c) (10 points) Your colleague returns and she says, “Dear Moron – I’ve checked my experimental setup and even repeated the measurement on another setup, and these neurons
have action potentials with a peak-to-peak voltage of 110 mV.” You sheepishly remember that when you were originally measuring the cell concentrations you dropped your
meter on your Double Double burger from In-N-Out (thereby getting that really yummy
pinkish sauce all over your meter) just before measuring the external Na+ concentration. You measured the other three concentrations before this little mishap. Before
re-measuring the external Na+ concentration you think a moment and then say either
(i) that it will be higher than your original (and incorrect) measurement or (ii) lower
than your original (and incorrect) measurement? Why?
3. (20 points) After bonding over your practice of eating In-N-Out while conducting experiments, you two decide to team up to further characterize the same alien neuron. Your
colleague has made some measurements, but needs you to help her understand aspects of
the neuron’s signaling time course. Assume the properties of the alien neuron from question
(1) continue to hold. An additional property your colleague has noticed is that these alien
neurons are shaped like spheres, and that their radius is 10 µm.
(a) (5 points) Your colleague reports that she’s measured the change in voltage across
the membrane when she injects current into Na+ and K+ ion channels. She observes
the relationship is linear, so that these ion channels behave like resistors. When she
blocks K+ channels using tetraethylammonium and injects 1 pA of current into the
neuron, the membrane voltage changes by 45 mV. When she blocks Na+ channels using
tetrodotoxin and injects 1 pA of current into the neuron, the membrane voltage changes
by 50 mV. Assume that the Na+ ion channels only allow through Na+ ions, and that the
K+ ion channels only allow through K+ ions. What are the Na+ and K+ ion channel
conductances?
(b) (5 points) What is the membrane’s input resistance? (Hint: Assume no cytoplasmic
resistance. Also recall that at DC steady state, a capacitor looks like an open circuit.)
(c) (5 points) Assume that the membrane is well-modeled by a parallel plate capacitor, with
ends separated by a distance of 100 pm. What is the membrane’s input capacitance?
(Please use the permittivity of free space for this calculation.)
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(d) (5 points) If the input voltage ∆Vm and threshold to trigger a spike were the same for
the alien neuron and a human neuron (which have membrane potential time constants
of 20-50ms), will the alien neuron fire a spike more quickly or slowly than a human
neuron?
4. (15 points) Consider a neuron with (1) a (non-standard) membrane that is only permeable
to one ion, (2) the permeable ion has a concentration gradient, and (3) the overall system
eventually reaches an equilibrium where drift current and diffusion current are equal and
opposite.
Now, in contrast, consider a neuron with (1) a standard membrane that is permeable to
multiple ionic species, (2) each ion has a concentration gradient, and (3) the overall system
eventually reaches steady state.
(a) (10 points) In this multiple-species case, are the drift and diffusion currents for each
individual ionic species equal and opposite? Why or why not?
(b) (5 points) What do neurons do to maintain their concentration gradients?
5. (20 points) You are comparing the axons of neurons taken from two different species. In
species A, the cytoplasm has radius r = 490µm and the membrane is t = 10µm thick. In
species B, the cytoplasm has radius r = 250µm and the membrane is surrounded by a thick
layer of myelin, so that the total thickness of the membrane and myelin is t = 250µm. The
two neurons are otherwise identical in all other ways (e.g., ion concentrations, membrane
conductance, conductance of the axon’s intracellular fluid.)
(a) (10 points) You stimulate each neuron and measure the speed of the resulting action
potential. Which axon would you expect to have faster action potential conduction?
Please show calculations. (Hint: Ignore membrane resistance. A simple RC model is
sufficient.)
(b) (5 points) Myelin is widely known to increase speed of conduction, but it takes up room.
In a situation where many neurons must be packed into a limited space, is it worth it?
(Hint: The overall diameter for species A and B is the same.) Why (1 or 2 succinct
sentences is sufficient)?
(c) (5 points) Species B has Nodes of Ranvier. What is the purpose of these nodes, and
how do they function? Why (1 or 2 succinct sentences is sufficient)?
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