Neuroscience 201A Problem Set #1, 27 September 2016 1. The figure above was obtained from a paper on calcium channels expressed by dentate granule cells. The whole-cell Ca 2+ currents in (A) were measured in response to voltage steps from a holding potential of 60 mv to test potentials of 10, 0, and + 10 mv. The external solution contained normal saline (2 mm Ca 2+ ) plus tetrodotoxin to block Na + channels, and the internal solution in the patch electrode contained 150 mm KCl. The lines through the current traces are the fit to a single exponential function with time constants of 40-50 ms. Design an experiment using only voltage clamp steps that would reveal whether the decline in the amplitude of the whole cell current during the test pulse is due to (a) inactivation of the calcium current or (b) activation of a calcium-dependent potassium current that is superimposed on a non-inactivating calcium current. Page 1
2. Consider a spherical neuron, with a diameter of 25 µm and with the following concentrations of ions on both sides of the membrane: Ion Intracellular (mm) Extracellular (mm) Potassium 135 4 Sodium 18 145 Chloride 8 105 (other ions not listed) Assume that the cell s membrane has a C m (specific membrane capacitance) of 10-6 F*cm -2 and a R m (specific membrane resistance) (at rest) of 10 5 ohm*cm 2. a) If the resting membrane is permeable to only Na + and K +, calculate the g K /g Na at rest if the membrane potential is -68 mv. b) Calculate the change in [Na + ] i that would be produced by a single action potential, assuming that V m at the peak of the action potential is 52 mv and assuming that only sodium ions cross the membrane during the rising phase of the action potential (i.e., no potassium moves until the peak potential is achieved). c) The assumption in part b (above) about the temporal separation of sodium and potassium currents is unrealistic. Why? What are the consequences, if any, of dropping this assumption on your calculation in part b concerning the increase in [Na + ] i? Page 2
3. The figure above is taken from the third paper from the Hodgkin and Huxley series ( 1952c ). This record shows potassium current in response to a step depolarization of 25 mv from rest. The two traces show current (above) and conductance (below). a) How did H&H eliminate sodium current in this experiment? (see the legend) b) How did H&H determine conductance? c) What is the cause of the large discontinuity in the current trace at the end of the voltage step? d) Calculate E K. Assume that the membrane potential at rest is -70 mv. Note that E K is given in the legend. Calculate it yourself and see if you agree with the legend. Page 3
4. This problem relates to the graph below, which shows four current responses of a rabbit node of Ranvier to -35 mv (A,B) or +60 mv (C,D) from a hyperpolarized holding potential of -110 mv. The sign conventions for this graph are post-h&h and correct inward current is downward deflecting. A. In A, what channels are responsible for the inward current that exists before the start of the pulse? Give your reasoning. B. The first part of the response in A following the voltage step to -35 mv (which begins about 1 ms after the start of the trace) is outward and brief. What is the basis of this transient current? C. At the time of the peak inward current in A, calculate the approximate values of g Na and g L (leak conductance). D. What is the purpose of the -110 mv hyperpolarizing prepulse in these traces? E. What is the purpose of depolarizing the membrane strongly in C (as compared to A)? F. What is the most obvious difference between the properties of ion channels at the rabbit node of Ranvier, as illustrated in this figure, and at the squid giant axon? What do you think will be the consequences of this difference on signaling in the rabbit? Page 4
5. In 1952, Alan Hodgkin and his colleagues published a paper in the Journal of Physiology in which they described the consequences of replacing the cytoplasm of a squid giant axon with a salt solution similar to that ordinarily found in the extracellular space outside the axon and of bathing the axon in a solution with the composition of one usually found in the interior of the axon. (Thus, they reversed the solutions on the two sides of the membrane.) The following were the solutions they used (note that the squid lives in sea water, which has a higher osmolarity than mammalian saline, and hence these numbers are higher than what we would expect for mammals) Na + K + Cl - Impermeant anions Solution perfusing the interior of the axon: Solution in which the axon was bathed: 525 mm 25 mm 550 mm 0 mm 50 mm 500 mm 50 mm 500 mm a) If the resting membrane is permeable only to potassium and chloride, and if the permeabilities (and conductances) to these two ions are equal, calculate the resting potential of this axon. b) Is this axon excitable? That is, if you were to make its membrane more positive by injecting current into the interior of the axon, would you be able to elicit an action potential? Justify your answer. Page 5
6. Consider the following chamber, separated by a semi-permeable membrane: I II A - 100 0 Cl 50 150 K + 150 150 The membrane is permeable to both Cl and K +, but not A (anions). The starting condition is that the concentrations are exactly as written (in mm, to 10 decimal places) and that there is no charge across the semipermeable membrane. Part A: Without considering the possibility of water movement, calculate how Cl and K + will move in order to bring each to electrochemical equilibrium. What will be the final concentrations of K + and Cl - on each side (I, II) of the membrane. Does your solution satisfy electroneutrality? What is the electrical potential across the membrane? Part B: Are the two sides osmotically balanced, meaning, is the concentration of osmotically active particles the same on both sides? If it is not, what will happen if water is allowed to move? Part C: Now do this again with Na+ on side II: I II Na + 100 A 100 0 Cl 50 150 K + 150 50 As before, the membrane is permeable to K + and to Cl- only. Calculate how Cl and K + will move in order to bring each to electrochemical equilibrium. Does your solution satisfy electroneutrality? What is the electrical potential across the membrane? Does water move? Page 6
7. The graphic below is taken from H&H1952e: the fifth and last of the 1952 H&H papers and the one containing the modeling. You will note that resting potential is set at 0 mv, for graphical purposes. Assuming that this cell has only sodium and potassium channels, calculate E Na. Assume that E K is 30 mv more negative than resting potential. Indicate any assumptions that you have to make to proceed. Page 7
8. Part 1: The records above (left) were obtained during voltage clamp to the indicated values of membrane potential of a patch of membrane. At 30 mv and 50 mv the zero current value is evident at the lower margin of the trace. To measure the probability that a channel is open, p open, would it be appropriate to analyze the trace at 30 mv? Why, or why not? Part 2: The two records on the right were taken from patches such as that shown for the left figure and show current records at two different [Ca 2+ ] o s (top, bottom) during a gradually changing ramp of voltage (see x-axis; HP is holding potential); thus, at the left margin of the graph, the holding potential is 0, and at the right margin, holding potential is 100 mv. What is the minimum number of channels in this patch (refer to the lower of the two graphs)? Part 3: Make a very rough calculation (from the right figures) of the single channel conductance and E rev of these channels? Page 8