Problem Set #2: Action Potential Initiation in Neocortical Pyramidal Neurons

Despite the presence of voltage-gated Na⁺ channels in the dendrites of neurocortical neurons, action potentials do not initiate there, but rather initiate exclusively at the axon hillock/initial segment. Mainen et al. (1995) proposed that this apparent contradiction resulted from a very high density of Na⁺ channels in the axon and hillock of the neuron, such that depolarization near threshold resulted in a much larger number of open Na⁺ channels there. This followed from similar ideas in early studies in motoneurons by Westerfield and Moore. Later Colbert and Pan (2002) failed to show higher Na⁺ channel density in axons of pyramidal neurons, but rather showed that the properties of the Na⁺ channels were different, with a lower voltage threshold for activation than somatic Na⁺ channels. The problem set this week is to explore this question using modeling with NEURON. Zach Mainen has made available to us the neuron code for the simulations in Mainen et al. (1995), and this can be used as a starting point for the simulations. Print out the results of each of these simulations, and indicate how you implemented each of the steps below.

1) Using the Mainen-provided model, reproduce the Stuart and Sakmann (1994) results (figure 2a bottom) through a manipulation of just the axonal Na⁺ channel density. Plot the amplitude of the back propagating spike as a function of axonal Na⁺ conductance, highlighting the point where the Stuart and Sakmann (1994) results are reproduced. Does your estimate of where the Stuart and Sakmann results are reproduced match what was found by Mainen et al. (1995)? Indicate on your plot the density which they concluded would reproduce the result.

2) Implement the Colbert and Pan (2002) finding (-7 mV shift in Na⁺ channel activation voltage dependence) and generate a new plot, again highlighting the point where the Stuart and Sakmann results are reproduced. You may want to edit the .mod file for the Na⁺ channels to achieve this. Does it matter whether or not the shift is implemented only in the axonal segments (axon, hillock, and initial segment), or is it sufficient to just shift the voltage dependence in the whole cell? Explain your answer.

3) Use the model of Colbert and Pan (2002), from step 2, but instead of injecting current into the soma, inject it directly into the initial segment. Under the conditions you found in question one to reproduce the Stuart and Sakmann (1994) results, can you generate a fully back-propagating spike? Under the conditions you found in question two to reproduce the Stuart and Sakmann (1994) results, can you generate a back-propagating spike? If you can, are there any conditions you can find or manipulations you can make such that an action potential is generated at the initial segment but does NOT back-propagate to the dendrite?

References

(N.B. that you do NOT need to read these references thoroughly to complete the problem set, though you will need to consult Mainen et al. for question #1.)

Colbert, CM, Pan, E (2002) Ion channel properties underlying axonal action potential initiation in pyramidal neurons. Nature neuroscience, 5:533–538.

Mainen, ZF, Joerges, J, Huguenard, JR, Sejnowski, TJ (1995) A model of spike initiation in neocortical pyramidal neurons. Neuron, 15:1427–1439.

Stuart, GJ, Sakmann, B (1994) Active propagation of somatic action potentials into neocortical pyramidal cell dendrites. Nature, 367:69–72.