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/cm 2. Page 1
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 g Na /g K 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/cm 2, and if the conductance of a single leak channel is 10 ps, calculate the average density of leak channels in the membrane, as # per µm 2. Page 2
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. Page 3 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 = E rev 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, V m E rev, is -140-(-50) mv = -90 mv. From Ohm s law, g L = 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 (P 1 :P 2, 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 g Na /g K than the AMPA
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 E rev 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 E rev. 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 E rev. (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 E Na and looking for outward currents does NOT guarantee that these currents are potassium currents, and correspondingly, clamping at E K does not insure that the remaining inward currents are sodium currents. You ve got to change concentrations and look for shifts in E rev 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
Question #4 15 pts The following figure is taken from a paper on voltage-dependent calcium channels and shows the peak currentvoltage relation for a single population of channels. Page 5 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 E rev for the channel is +50 mv. The data is below. Note that the closer you get to E rev, 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).
b) The circle drug does not change E rev, 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 E rev 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 (E rev ). 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 E rev 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
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). Usually GABA turns neurons off, but when gliomas are nearby, it turns them on instead. What do you hypothesize that gliomas are doing to neurons that would allow GABA to depolarize them enough to fire them? Describe an experimental test of your prediction. Assume that you can whole cell record/clamp from neurons in slices with gliomas nearby and that you can activate GABAergic inputs onto these cells. Nearly all of you suggested that GABA is acting by driving the membrane of neurons near gliomas towards a E rev that is more positive than in the control case: more positive than threshold. There are two possibilities here: the first is that GABA gates a Cl - with a E Cl that is less negative than normal. This is the actual explanation for the work cited in the News & Views article. If E Cl is less negative than normal, then the Cl - gradient must be more shallow than normal, and this may occur either because intracellular Cl - is higher than normal or because extracellular is lower than normal. The second possibility is not very likely, since it would require that in the same general volume there are two different concentrations of extracellular Cl -. More likely is the possibility that intracellular Cl - is elevated, and this may occur because the chloride potassium (KCC2) symporter (which carries Cl - out of the cell using the K + electrochemical gradient) is inhibited or down regulated. How would you test for this? The simplest way would be to activate the GABA synaptic input while clamping the postsynaptic cell and to measure E rev for the input. E GABA (E rev ) should be more positive for neurons nearer gliomas in the slice. But how would you know that this was because of a change in E Cl and not simply a change in the selectivity of the GABA receptor (the second possible explanation for why E rev might be more positive near gliomas)? The cleanest approach here would be to measure E rev before and after changing the Cl - equilibrium (Nernst) potential. If the channel is selective entirely for Cl -, then a 10-fold change in E Cl will produce a ~60 mv shilft in E rev(gaba). You could also propose measuring Cl - concentration directly inside the cell, and I think that there are some fluorescent indicators dyes that allow you do to that (not sure whether they are proven to be useful in this situation). If E rev is more depolarized because the channel is no longer selective to Cl - but has cation or sodium permeability as well, then when you change E Cl - by 10 fold, you should get less than a 60 mv shift in E rev. Likewise, in this case you will get a shift in E rev when you change, for example, E Na. Note that it would be difficult to increase extracellular Cl - above its normal level, since the outside of the cell is approximately isotonic NaCl: an additional increase would produce a hypertonic solution and make the cell swell. Page 7
Question #6 10 pts The figure above, taken from the slide set on synaptic transmission, illustrates an example of a result in which N, the physiologically measured number of releasable quanta, was equal to the number of synaptic boutons (each of which is thought to contain a single active zone). The data above is interpreted as supporting a univesicular release model for this synapse. a) An alternative possible explanation for the data above is that release is multivesicular, but that a single quantum of transmitter saturates the AMPA receptors at the synaptic site. The data shown on the left (Fig. 4) argue against this possibility. Explain why. b) What sources of intersite quantal variance are likely to be at play in this experimental arrangement? Page 8
Suggested answer to question #6 (previous page): (a) The data shown in the top part of the previous page is equally compatible with a univesicular model of release, with or without saturation of AMPARs with a single quantum of transmitter, or with a multivesicular model of release, with saturation of AMPARs with a single quantum of transmitter. What result in the lower figure suggests that there is not multivesicular release? The finding that the efficacy (% block) with DGG is the same at two different extracellular calcium concentrations, which produce very different sized EPSCs, suggests that release is not multivesicular. Had it been multivesicular, one would have expected DGG to more effectively better at the lower extracellular calcium concentration. (b) We covered several possible sources of intersite quantal variability in class, including variability in the amount of glutamate packaged in a vesicle (assuming no saturation of glurs with a quantum), variability in the number of glurs postsynaptically or in their properties, variability in the anatomy of the synapse (escape routes for glu, glial cells nearby with glu transporters). To get full credit, you had to add that another source of variability is the distance between the recording site (the cell body) and each of the sites (see figure, top of previous page, lower left panel). Sites that are more distant may produce smaller and slower responses, or maybe not (now that you know about things like synaptic scaling). Note that variations in N or p are not sources of quantal variability, since we are talking about single quantalresponses and not about trial-to-trial variability in the number of quanta released. Question #7 (Please write your response to this question on a separate page, if you are completing the exam in paper format.) How are high selectivity and high rate of transport through ion channels achieved simultaneously? Do you think Na + can permeate through a Ca 2+ -selective ion channel? If yes, under what conditions? Please explain your answers. 15 pts High selectivity of ion channels is achieved with high-affinity binding sites for the permeant ion in the selectivity filter. The high rate of transport is achieved by placing several such binding sites in close proximity to each other, so that when all or majority of the binding sites are occupied by permeant ions, the electrostatic repulsion between the ions reduces binding affinity and significantly shortens the time the ions dwell in pore. Na + can permeate through Ca 2+ selective channels in the absence of Ca 2+. Under these conditions Na + can occupy Ca 2+ -binding sites in the pore and go through the channel. When Ca 2+ is present, it outcompetes Na + and does not allow it to bind in the pore. Page 9
Question #8 (Please write your response to this question on a separate page, if you are completing the exam in paper format.) What is the role of S1, S2 and S3 transmembrane helices of the voltage-gated ion channels in the mechanism of voltage sensitivity? Do you think it would be possible to construct a simpler voltage-sensor domain that would consist of S4 domain only? Please explain your answers. 15 pts S4 helix has several positively charged amino acid residues that must be stabilized within the hydrophobic environment of the lipid membrane. S1 S3 helixes provide negatively charged/polar residues that form a transmembrane translocation pathway that allows S4 helix to exist and move within the lipid membrane. There are additional benefits of S1-S3 helixes. Specific states of the S4 helix (such as open and closed) can be stabilized as compared to intermediate states. Also, S1-S3 helixes form a foundation that S4 helix uses to apply force to the pore domain. All the factors mentioned above make it very unlikely that a VSD can be constructed of S4 helix only. Page 10