2. Leaky-integrate-and-fire model¶
Book chapters
See Chapter 1 Section 3 on general information about leaky-integrate-and-fire models.
Python classes
The leaky_integrate_and_fire.LIF
module contains all code required for this exercise.
At the beginning of your exercise solutions, import the contained functions by running
from neurodynex.leaky_integrate_and_fire.LIF import *
You can then simply run the exercise functions by executing
LIF_Step() # example Step
LIF_Sinus() # example Sinus
2.1. Exercise¶
Use the function LIF_Step()
to simulate a Leaky Integrate-And-Fire
neuron stimulated by a current step of a given amplitude. The goal of
this exercise is to modify the provided python functions and use the
numpy
and matplotlib
packages to answer the following questions.
2.1.1. Question¶
What is the minimum current step amplitude I_amp
to elicit a spike
with model parameters as given in LIF_Step()
? Plot the injected
values of current step amplitude against the frequency of the spiking
response (you can use the inter-spike interval to calculate this – let
the frequency be \(0Hz\) if the model does not spike, or emits only
a single spike) during a \(500ms\) current step.
2.2. Exercise¶
Use the function LIF_Sinus()
to simulate a Leaky Integrate-And-Fire
neuron stimulated by a sinusoidal current of a given frequency. The goal
of this exercise is to modify the provided python functions and use the
numpy
and matplotlib
packages to plot the amplitude and frequency
gain and phase of the voltage oscillations as a function of the input
current frequency.
2.2.1. Question¶
For input frequencies between \(0.1kHz\) and \(1.kHz\), plot the input frequency against the resulting amplitude of subthreshold oscillations of the membrane potential. If your neuron emits spikes at high stimulation frequencies, decrease the amplitude of the input current.
2.2.2. Question¶
For input frequencies between \(0.1kHz\) and \(1.kHz\), plot the input frequency against the resulting frequency and phase of subthreshold oscillations of the membrane potential. Again, keep your input amplitude in a regime, where the neuron does not fire action potentials.