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Neuroscience 201A Exam “Key”, October 7, 2014

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Neuroscience 201A Exam “Key”, October 7, 2014 Name: _____KEY_________________________ Neuroscience 201A Exam “Key”, October 7, 2014 Question #1 7.5 pts Consider a spherical neuron with a diameter of 20 µm and a resting potential of -70 mV. If the net negativity on the inside of the cell (all of the “excess” anions) were uniformly distributed within the volume of the cell rather than being “glommed” onto the inner surface of the plasma membrane, what would the concentration of these ions be (in M)? Assume that these are all univalent ions. Assume that the capacitance of the plasma membrane is the standard 1 µF/cm2. Page 1 Name: _____KEY_________________________ Question #2 12.5 pts Imagine that you have a squid neuron with a single population of leak channels, which are cation channels with permeability to only Na+ and K+. The concentrations of permeant ions on each side of the membrane are as follows: Ion Na+ K+ Outside 550 mM 20 mM Inside 55 mM 440 mM a) If the resting membrane potential of the cell is -63 mV, calculate gNa/gK for the leak channels. (You are encouraged to use conductances for this problem (not permeabilities). b) If the squid neuron is spherical with a diameter of 200 µm, if the leak conductance of its membrane is 0.3 mS/cm2, and if the conductance of a single leak channel is 10 pS, calculate the average density of leak channels in the membrane, as # per µm2. Page 2 Name: _____KEY_________________________ Question #3 12.5 pts The above figure illustrates a set of current responses (a, lower traces) to voltage steps (a, top traces) for a population of channels in a neuron with physiological solutions bathing the inside and outside of the cell. (Conventional graphics – inward current is downward and negative in sign). There are leak channels in this cell’s membrane in addition to the voltage dependent channels. a) What is the leakage conductance of this cell (the conductance attributable to all of the leak channels)? Assume that the resting potential is -50 mV. The leak channels are the ones open at rest. If you step the membrane potential to a value different than rest (rest = Erev for the leak channels), then you will see an immediate current (immediate because the channels are already open). The arrow in (a) points to this current. The current is about -0.075 x 10- 9 A, and the driving force, Vm – Erev, is -140-(-50) mV = -90 mV. From Ohm’s law, gL = is about 0.8 nS. This is a LOT smaller than the conductance due to the cation channels that open in response to hyperpolarization (which can be calculated from the slope of the straight line in (b)), which is about 13 nS. b) In part b is shown an IV curve for the early current after the potential is stepped from -140 mV to the indicated value in the graph. What is the reversal potential for this channel? To what ion or ions do you suspect that this channel is permeable? How would you test your hypothesis? If you think that this channel is permeable to multiple ions, how would you measure the permeability ratios (P1:P2, where 1 and 2 represent different ions). Reversal potential is about -35 mV. This does not match the equilibrium potential for any single ion, except perhaps that for chloride when the chloride transporters are not yet fully expressed during early development. The best guess is that it’s a cation channel with a slightly different gNa/gK than the AMPA Page 3 Name: _____KEY_________________________ or nicotinic receptor channels that we have discussed. How do you test whether any particular hypothesis about the permeability of an ion channel is correct? You change the concentration of the hypothesized permeant ions on one or the other side of the membrane and look to see if this shifts Erev for the channel. If a channel is permeable to a single ion, then a 10-fold change in the concentration of that ion on either side of the membrane will produce a ~60 mV shift in Erev. If, alternatively, the channel is permeable to multiple ions, such as sodium and potassium, then a 10-fold change in one of them will produce less than a ~60 mV shift in Erev. (In fact, the sum of the changes to a 10-fold change in each ion’s concentration gradient will be ~60 mV.) Note that by clamping the cell at ENa and looking for outward currents does NOT guarantee that these currents are potassium currents, and correspondingly, clamping at EK does not insure that the remaining inward currents are sodium currents. You’ve got to change concentrations and look for shifts in Erev to make this assessment. Once you have established which ions flow across the channel, you can use the GHK equation (P or G version) to calculate the ratio of permeabilities or conductances. Page 4 Name: _____KEY_________________________ Question #4 15 pts The following figure is taken from a paper on voltage-dependent calcium channels and shows the peak current- voltage relation for a single population of channels. a) Data shown as squares were collected under control conditions. From these data, construct a curve of peak conductance vs. voltage for this channel, over the range of -60 mV to +60 mV. b) The data shown in circles were collected using a drug (the “circle drug”). Provide a plausible hypothesis about what the “circle drug” does to alter the IV curve for this channel. What sort of evidence (obtained in an experiment of your choosing) would support this hypothesis? The data shown in triangles were collected in the presence of a different drug (the “triangle drug”). c) The figure supports the possibility that one of the two drugs (circle, triangle) alters the ion selectivity of the channels. Which drug is this, and on what do you base your assertion? a) Here the idea is to do what H&H did in their second 1952 paper (116:449-472) and convert from current to conductance using Ohm’s Law. From the data, we can assume that Erev for the channel is +50 mV. The data is below. Note that the closer you get to Erev, the greater the error, since you are dividing by a number, the driving force, that is approaching zero. The point at +60 mV has a lower conductance that those at +30-+40 mV. This is not likely to signify that fewer channels open with a stronger depolarization (which would require a much more complicated model for how the channel works) but rather just that there’s more error. Most conductance curves like this one will reach a maximum and stay there with stronger and stronger depolarizations (or hyperpolarizations, if that’s what opens the channel). Page 5 Name: _____KEY_________________________ b) The circle drug does not change Erev, but it greatly increases total current. Either there are more channels opening (more likely), or the conductance of the open channel is larger (less likely, since this might be expected to change selectivity and allow more potassium to pass, which would shift Erev to more negative values). One way to get more channels to open in response to a depolarization is to remove inactivation. If this drug removed inactivation of some of the calcium channels, more would be available to open and more would open, without necessarily changing the activation sensitivity of the channels. One way to test for this possibility is to see if you can eliminate the effect of the drug by delivering a pre-pulse to a large negative membrane potential, which should remove all inactivation from the channels. Upon stepping the membrane potential to, say, 0 mV, you will get a very large current, and the circle drug should not further enhance the current. Another possibility is that the drug makes the channel more sensitive to voltage, such that more open in response to a depolarization of any magnitude. This would help explain the apparent shift in voltage sensitivity of the channel, such that the clamp potential at which the current peaks is shifted from +10 mV to 0 mV. However (and I might be wrong about this), simply increasing the voltage sensitivity would not be expected to increase the maximal conductance, and in this instance, the maximal conductance is 2-3x times greater in the presence of the circle drug. The other possibility is that the circle drug increases the conductance of a single channel; the same number of channels open, but each passes more current. One challenge is to do this without changing selectivity, which is not changed (Erev). If, somehow, Nature could manage this, then you would expect to find that the open channel conductance would be increased. c) The triangle drug is likely to be the one that alters the selectivity of the channel, since Erev is changed from about +50 mV to a bit less than +40 mV. This drug might, for example, reduce the calcium selectivity of the channel and introduce some potassium (out) movement. If the conductance of an open channel were constant, it’s unlikely that the modest change in selectivity could explain the reduction of current that is observed. Page 6 Name: _____KEY_________________________ Question #5 12.5 pts The following passage recently appeared in the “News & Views” section of one of the journals with a one word name. “Gliomas, a common brain tumor, frequently induce epileptic seizures as they grow, but it is not clear why. LastName et al. (XXXX) show that the epileptic activity in the brain around gliomas happens because neurons respond anomalously to the neurotransmitter g-aminobutyric acid (GABA).
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