5. Type I and type II neuron models

Book chapters

See Chapter 4 and especially Chapter 4 Section 4 for background knowledge on Type I and Type II neuron models.

Python classes

The neurodynex.neuron_type.typeXY module contains all classes required for this exercise. For the exercises you will need to import the classes NeuronX and NeuronY by running

from neurodynex.neuron_type.typeXY import NeuronX, NeuronY

Note

Both NeuronX and NeuronY inherit from a common base class neuron_type.neurons.NeuronAbstract and thus implement similar methods.

For those who are interested, here is more about classes and inheritance in Python.

5.1. Exercise: Probing Type I and Type II neuron models

This exercise deals not only with Python functions, but with python objects.

The classes NeuronX and NeuronY both are neurons, that have different dynamics: one is Type I and one is Type II. Finding out which class implements which dynamics is the goal of the exercise.

To run the exercises you will have to instantiate these classes. You can then plot step_current injections (using the step method) or extract the firing rate for a given step current (using the get_rate method):

from neurodynex.neuron_type.typeXY import NeuronX, NeuronY

n1 = NeuronX()  # instantiates a new neuron of type X

n1.step(do_plot=True)  # plot a step current injection

To check your results, you can use the get_neuron_type function, e.g.:

>> n1 = NeuronX()  # instantiates a new neuron of type X
>> n1.get_neuron_type()
neurodynex.neuron_type.neurons.NeuronTypeOne

5.1.1. Question: Estimating the threshold

What is the threshold current for repetitive firing for NeuronX and NeuronY?

Exploring various values of I_amp, find the range in which the threshold occurs, to a precision of 0.01.

Note

As shown abve, use the step functions to plot the responses to step current which starts after 100ms (to let the system equilibrate) and lasting at least 1000ms (to detect repetitive firing with a long period):

Already from the voltage response near threshold you might have an idea which is type I or II, but let’s investigate further.

5.1.2. Question: Pulse response

Plot the response to short current pulses near threshold, and interpret the results: which class is Type I, which is II?

For example:

import matplotlib.pyplot as plt
plt.figure()  # new figure
n1 = NeuronX()  # instantiates a new neuron of type X

t, v, w, I = n1.step(I_amp=1.05, I_tstart=100, I_tend=110, t_end=300)
plt.plot(t,v)

t, v, w, I = n1.step(I_amp=1.1, I_tstart=100, I_tend=110, t_end=300)
plt.plot(t,v)

# can you simplify this in a loop?

plt.show()

5.2. Exercise: f-I curves

During the questions of this exercise you will write a python script that plots the f-I curve for type I and type II neuron models.

5.2.1. Get firing rates from simulations

We provide you with a function get_spiketimes to determine the spike times from given timeseries t and v:

>> from neurodynex.neuron_type.neurons import get_spiketimes
>> t, v, w, I = n1.step(I_amp=1.0, I_tstart=100, I_tend=1000., t_end=1000.)
>> st = get_spiketimes(t, v)
>> print st
[ 102.9  146.1   189.1 ... ]

Use this function to write a Python function (in your own .py file) that calculates an estimate of the firing rate, given a neuron instance and an input current:

def get_firing_rate(neuron, I_amp):

    # run a step on the neuron via neuron.step()
    # get the spike times
    # calculate the firing rate f

    return f

Note

To calculate the firing rate, first calculate the inter-spike intervals (time difference between spikes) from the spike times using this elegant indexing idiom

isi = st[1:]-st[:-1]

Then find the mean and take the reciprocal (pay attention when converting from 1/ms to Hz) to yield the firing-rate:

f = 1000.0/mean(isi)

Note

You can check your results by calling:

# get firing rate and plot the dynamics for an injection of I_amp
n1.get_rate(I_amp, do_plot=True)

5.2.2. Plot the f-I curve

Now let’s use your function get_firing_rate to plot an f-vs-I curve for both neuron classes.

Add the following function skeleton to your code and complete it to plot the f-I curve, given the neuron class as an argument:

import matplotlib.pyplot as plt
import numpy as np

def plot_fI_curve(NeuronClass):

    plt.figure()  # new figure

    neuron = NeuronClass()  # instantiate the neuron class

    I = np.arange(0.0,1.05,0.1)  # a range of current inputs
    f = []

    # loop over current values
    for I_amp in I:

        firing_rate = # insert here a call to your function get_firing_rate( ... )

        f.append(firing_rate)

    plt.plot(I, f)
    plt.xlabel('Amplitude of Injecting step current (pA)')
    plt.ylabel('Firing rate (Hz)')
    plt.grid()
    plt.show()

• Call your plot_fI_curve function with each class NeuronX and NeuronY as argument.
• Change the I range to zoom in near the threshold, and try running it again for both classes.

Which class is Type I and which is Type II?