100% tevredenheidsgarantie Direct beschikbaar na betaling Zowel online als in PDF Je zit nergens aan vast
logo-home
Assignments week 5 €3,99   In winkelwagen

Case uitwerking

Assignments week 5

 8 keer bekeken  0 keer verkocht

Case of 8 pages for the course Introduction To Computational Neuroscience at UM (Score 80/100 points)

Voorbeeld 2 van de 8  pagina's

  • 21 juni 2022
  • 8
  • 2021/2022
  • Case uitwerking
  • M. senden
  • 7-8
Alle documenten voor dit vak (6)
avatar-seller
kikiboumans
Before you turn this problem in, make sure everything runs as expected. First, restart the
kernel (in the menubar, select Kernel→Restart) and then run all cells (in the menubar,
select Cell→Run All).
Make sure you fill in any place that says YOUR CODE HERE or "YOUR ANSWER HERE", as
well as your name and collaborators below:
NAME = Kiki
COLLABORATORS =



Assignments week 5
Complete the assignments below, save the notebook and submit them on canvas.

Assignment 5.1
What type of neuron is the leaky integrate-and-fire neuron according to the Hodgkin
classification? What type of neuron would this be according to the Izhikveich classification?
Justify your choice.
The leaky integrate-and-fire neuron is a model which uses only one single differential
equation for its membrane potential. It describes a model in which ions are leaking or
diffusing through the membrane. Each input pulse that is received by the leaky integrate-
and-firing neuron causes a short current pulse. When this pulse is strong enough to reach
the treshold, it will produce and output spike and the voltage will instantly be reset.
According to the Hodgkin classification this neuron would belong to the class 1
(excitability) neurons. This means that the neuron can produce spikes at low firing rates
depending on the strength of the input current and that the F-I curve will be continuous.
Izhikveich uses mathematical equations in his model, compared to the biophysics of
neurons that is used in the Hodgkin-Huxley model. With these mathematical equations the
model computes wide ranges of spiking (and bursting) patterns. The model does not have a
'fixed' treshold, but instead whether the neuron fires depends on the history of the
membrane potential prior to a spike. Meaning the recovery variable of the membrane plays
a big role (in causing sub-treshold fluctuations of the membrane potential). Thus, according
to the Izhikveich classification, the leaky integrate-and-fire neuron is a resonator, because
it displays a certain subtreshold in its firing rate. Also, the LIF neuron is bistable, because it
shows both resting and spiking states (resting after a recent membrane potential). This
indicates that, according to the classification of Izhikveich, the LIF neuron is a class 2
neuron (a bistable resonator), also referred to as a subcritical Adronov-Hopf.

Assignment 5.2
Whenever the membrane potential of a leaky integrate-and-fire neuron reaches the
threshold, a spike is emmitted and the membrane potential is reset to a specific value
( V r es et ) . How does the value we choose for this parameter affect the spiking (in particular

, the firing rate) of the neuron? Specifically, what is the difference in firing rate when we
choose V r e s e t to be larger than the resting potential as compared to when we choose it to be
smaller than the resting potential?
When we choose the V r e s e t to be smaller than the V L (the resting potential), namely a V r e s e t
of -90, it shows regular spiking followed by a refractory period. After every spike, the
membrane potential returns to the reset potential which is lower than the resting potential.
In that way it stimulates the membrane to hyperpolarize, which can be seen in the
refractory period. This correlates with the original code in the notebook in which the V r e s e t
is -80 and V L is -70.

However, if we choose a value for the V r e s e t that is larger than the V L of -70, specifically if
we choose -55, you can see that the neuron does not reutrn to its resting potential once the
spiking begins and it continuously stays in a depolarized state so there will not occur a
refractory period. You can see this because after 100 ms the line (which shows the resting
potential) is lower than the continuous depolarized state of the first 100 ms.
Finally, if we take a V r e s e t that is equal to the V t r e s h o l d (Vth) of -50, it will not show any
individual action potential spikes anymore. In this case, the neuron will stay depolarized
and will not enter a refractory period.
import numpy as np
import matplotlib.pyplot as pl

C = 0.5
gL = 0.025
VL = -70
Vth = -50
V_reset = -90
A_spike = 30
spike_times =[]

dt = 0.001
t_0 = 0
t_end = 200
t_stim = 100
t_steps = int((t_end-t_0)/dt)+1
T = np.linspace(t_0,t_end,t_steps)

I = 1.

V = np.zeros(t_steps)
V[0] = VL

for t in range(t_steps-1):
if (dt*t>t_stim):
I = 0.
if V[t] > Vth:
V[t] = V_reset

Voordelen van het kopen van samenvattingen bij Stuvia op een rij:

Verzekerd van kwaliteit door reviews

Verzekerd van kwaliteit door reviews

Stuvia-klanten hebben meer dan 700.000 samenvattingen beoordeeld. Zo weet je zeker dat je de beste documenten koopt!

Snel en makkelijk kopen

Snel en makkelijk kopen

Je betaalt supersnel en eenmalig met iDeal, creditcard of Stuvia-tegoed voor de samenvatting. Zonder lidmaatschap.

Focus op de essentie

Focus op de essentie

Samenvattingen worden geschreven voor en door anderen. Daarom zijn de samenvattingen altijd betrouwbaar en actueel. Zo kom je snel tot de kern!

Veelgestelde vragen

Wat krijg ik als ik dit document koop?

Je krijgt een PDF, die direct beschikbaar is na je aankoop. Het gekochte document is altijd, overal en oneindig toegankelijk via je profiel.

Tevredenheidsgarantie: hoe werkt dat?

Onze tevredenheidsgarantie zorgt ervoor dat je altijd een studiedocument vindt dat goed bij je past. Je vult een formulier in en onze klantenservice regelt de rest.

Van wie koop ik deze samenvatting?

Stuvia is een marktplaats, je koop dit document dus niet van ons, maar van verkoper kikiboumans. Stuvia faciliteert de betaling aan de verkoper.

Zit ik meteen vast aan een abonnement?

Nee, je koopt alleen deze samenvatting voor €3,99. Je zit daarna nergens aan vast.

Is Stuvia te vertrouwen?

4,6 sterren op Google & Trustpilot (+1000 reviews)

Afgelopen 30 dagen zijn er 73918 samenvattingen verkocht

Opgericht in 2010, al 14 jaar dé plek om samenvattingen te kopen

Start met verkopen
€3,99
  • (0)
  Kopen