neuroscience questions help needed

need help with question 2 to 5 , 7

Neuroscience3600 Problem Set 2

For full credit, show your thought process. In quantitative problems, work out the intermediate steps in

the math. For other questions, be sure to provide justification for your answer. Point credit for each

problem shown to the left (total of 20 pts).

1. (3 pts) In the first homework assignment, you demonstrated that the resting potential of a cell is

−71.5 mV assuming conductance ratios of gK:gNa:gCl = 1: 0.02: 0.03 and equilibrium potentials of EK=-

70mV, ENa=+50mV, ECl=-55mV.

a. Assume that the conductance ratios change to gK:gNa:gCl = 1:40:0, as might happen at the peak

of the action potential. What is the membrane voltage under this condition?

b. Calculate the peak of a Calcium-based spike. Assume gK:gNa:gCl: gCa = 1:0:0:40. Is this more or

less than the peak of the Sodium-based spike? Given that both conductances are the same,

explain the discrepancy (1 sentence). Use ECa=+125mV. The following formula may be of help:

c. Draw the balance model for i) the peak of the sodium based action potential and ii) the peak of

the calcium based action potential.

2. (2 pts) Epileptic seizures are caused by rhythmic firing of large groups of neurons, often triggered by

a hyperexcitable region of the brain. Most of the drugs developed to treat epilepsy appear to work

by making it harder for neurons to fire an action potential.

a) One group of anti-epileptic drugs are GABA agonists (they enhance activity of the inhibitory

neurotransmitter GABA). GABA channels are typically selective for Chloride ions (Cl-). Explain

how and why tonically increased Cl- conductance might influence spike rate. How will it affect

the resting potential?

b) A second group of anti-epileptic drugs, including dilantin and carbamazepine, acts to inhibit

voltage-sensitive sodium channels. Complete block of all voltage-gated Na+ channels obviously

prevents an action potential and would be lethal. If some of the voltage gated channels were

blocked, how would the cell’s activity be affected? Explain. Consider its effect on spike

threshold and action potential height.

3. (2 pts) If you take an intact neuron in a dish and increase extracellular K+ so that it equals the

intracellular K+

a) what is the impact on the K+ equilibrium potential?

b) What is the impact on the Na+ equilibrium potential?

c) Assume the cell starts at the resting potential and has only Na+ and K+ channels (both voltage-

gated and those supporting leak currents). Sketch a graph of the cell’s electrical potential versus

time after adding extracellular K+. Provide an explanation for your graph.

4. (1 pt) What is the voltage clamp technique and why is it such an important breakthrough in the

study of the action potential?

Neuroscience 3600 Problem Set 2

5. (2 pt) Batrachotoxin is a poison secreted from the skin of a South American frog. Its primary effect

is to eliminate the inactivation gate of Na+ channels. Draw a voltage trace for a typical action

potential and, on the same graph using a dotted line, indicate what the action potential would look

like were the cell affected by batrachotoxin. Explain the effect.

6. (3 pt) Current is injected into a passive axon at one point, raising the potential by 55 mV. The

membrane resistance is rm = 225 Ωmm (that’s Ohms x mm) and internal resistance is ri=100 Ω/mm

(Ohms per mm). Assume the axon has no voltage-sensitive conductances (it’s passive) and started

with a membrane potential of 0 mV. Use the gridlines below (or your own computer generated

plot) to plot the voltage as a function of distance for the following distances from the injection site

(in mm): 0, .5, 1, 2, 3, 4, 5, 6. Put appropriate labels and units on axes. (Hint: Consult lecture notes

for formula for length constant). At what distance does the voltage reach 37% of the starting

voltage?

7. (3 pt) You are recording currents using an intracellular electrode and voltage-clamp from a squid

giant axon. You change the membrane voltage from resting potential to 0 mV and manipulate

external Na+. Sketch both the Na & K currents on a current (I) vs. time plot under three

conditions (outward current up, inward current down):

a) Extracellular Na+ concentration normal

b) Extracellular Na+ concentration equal to the interior concentration

c) Extracellular Na+ concentration at zero

8. (1 pt) If you started an action potential simultaneously at both the soma and at the axon

terminal simultaneously, what would happen when the two collide? Why?

Neuroscience 3600 Problem Set 2

9. (2 pt) Explain how myelin helps increase the speed of propagation of the action potential.

Explanation should include effects on internal resistance, membrane resistance, and

capacitance.

10. (1 pts) Why do larger axons conduct electrical signals faster? (Hint: both internal resistance and

membrane resistance change with the radius of the cell. Which changes faster? What does this

mean for signal speed?)