Adaptative Integrate And Fire Model



In [11]:

    
%matplotlib inline

import brian2 as b2
import matplotlib.pyplot as plt
from neurodynex.hodgkin_huxley import HH
from neurodynex.tools import input_factory
import jupyterthemes as jt



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jt.get_themes()
jt.









    



  File "<ipython-input-13-ddd3be6a2c6b>", line 2
    jt -t grade3 -T -N
               ^
SyntaxError: invalid syntax



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HH.getting_started()

6.1. Exercise: step current response

We study the response of a Hodgkin-Huxley neuron to different input currents. Have a look at the documentation of the functions HH.simulate_HH_neuron() and HH.plot_data() and the module neurodynex.tools.input_factory.

6.1.1. Question

What is the lowest step current amplitude I_min for generating at least one spike? Determine the value by trying different input amplitudes in the code fragment:



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I_min = 2.30
current = input_factory.get_step_current(5, 100, b2.ms, I_min *b2.uA)
state_monitor = HH.simulate_HH_neuron(current, 120 * b2.ms)
HH.plot_data(state_monitor, title="HH Neuron, minimal current")

6.1.2. Question

What is the lowest step current amplitude to generate repetitive firing?



In [14]:

    
I_min = 6.32
current = input_factory.get_step_current(5, 400, b2.ms, I_min *b2.uA)
state_monitor = HH.simulate_HH_neuron(current, 500 * b2.ms)
HH.plot_data(state_monitor, title="HH Neuron, minimal current")

6.2. Exercise: slow and fast ramp current

The minimal current to elicit a spike does not just depend on the amplitude I or on the total charge Q of the current, but on the “shape” of the current. Let’s see why:

6.2.1. Question

Inject a slow ramp current into a HH neuron. The current has amplitude 0A at t in [0, 5] ms and linearly increases to an amplitude I_min_slow at t=50ms. At t>50ms, the current is set to 0A. What is the minimal amplitude I_min_slow to trigger one spike (vm>50mV)?



In [24]:

    
I_min_slow = 12.21
slow_ramp_current = input_factory.get_ramp_current(5, 50, b2.ms, 0.*b2.uA, I_min_slow *b2.uA)
state_monitor = HH.simulate_HH_neuron(slow_ramp_current, 100 * b2.ms)
HH.plot_data(state_monitor, title="HH Neuron, minimal current")

6.2.2. Question

Now inject a fast ramp current into a HH neuron. The current has amplitude 0 at t in [0, 5] ms and linearly increases to an amplitude I_min_fast at t=10ms. At t>10ms, the current is set to 0A. What is the minimal amplitude I_min_fast to trigger one spike? Note: Technically the input current is implemented using a TimedArray. For a short, steep ramp, the one milliseconds discretization for the current is not high enough. You can create a more fine resolution:



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I_min_fas = 12.21
fast_ramp_current = input_factory.get_ramp_current(50, 100, 0.1*b2.ms, 0.*b2.uA, I_min_fast *b2.uA)
state_monitor = HH.simulate_HH_neuron(slow_ramp_current, 100 * b2.ms)
HH.plot_data(state_monitor, title="HH Neuron, minimal current")

6.2.3. Question Compare the two previous results. By looking at the gating variables m,n, and h, can you explain the reason for the differences in that “current threshold”? Hint: have a look at Chapter 2 Figure 2.3 b

6.3. Exercise: Rebound Spike

A HH neuron can spike not only if it receives a sufficiently strong depolarizing input current but also after a hyperpolarizing current. Such a spike is called a rebound spike.

6.3.1. Question Inject a hyperpolarizing step current I_amp = -1 uA for 20ms into the HH neuron. Simulate the neuron for 50 ms and plot the voltage trace and the gating variables. Repeat the simulation with I_amp = -5 uA What is happening here? To which gating variable do you attribute this rebound spike?

6.4. Exercise: Brian implementation of a HH neuron In this exercise you will learn to work with the Brian2 model equations. To do so, get the source code of the function HH.simulate_HH_neuron() (follow the link to the documentation and then click on the [source] link). Copy the function code and paste it into your Jupyter Notebook. Change the function name from simulate_HH_neuron to a name of your choice, for example simulate_modified_HH_neuron(). Have a look at the source code and find the conductance parameters gK and gNa.

6.4.1. Question

In the source code of your function simulate_modified_HH_neuron, change the density of sodium channels. Increase it by a factor of 1.4. Stimulate this modified neuron with a step current.