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https://github.com/jaffar-hussein/neurone-models

These are models that are used to study the spiking of the neurones organized according to their complexity from just considering the voltage to doing the ADEX model
https://github.com/jaffar-hussein/neurone-models

brian brian2 matplotlib neuron neuron-model neuron-simulations neuroscience pyhon3

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These are models that are used to study the spiking of the neurones organized according to their complexity from just considering the voltage to doing the ADEX model

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README 

        
**GURA Jaffar**



**REPORT**



**Modelling of neuronal interactions at the claustrum level**



**LABORATORY: UMR9197 [NEUROPSI SACLAY FRANCE](https://neuropsi.cnrs.fr)**



**LABORATORY DIRECTOR: Mr. ROUYER Francois**



**TEAM: Computational Neuroscience**



**ACADEMIC SUPERVISOR: Prof. JACQUIR Sabir**



**INTERNSHIP SUPERVISOR: Prof. PANANCEAU Marc**



**ADDRESSEE: 151 Centre CEA Saclay 91400 SACLAY FRANCE**



**2021/2022**



# Table of Contents



[Abbreviations](#abbreviations)



[Abstract](#abstract)



[I) INTRODUCTION](#introduction)



[II) Methods](#methods)



[1. Adaptive Exponential Integrate Model

](#adaptive-exponential-integrate-model)



[2. Testing the relative effects of variables to the Adex Model

](#testing-the-relative-effects-of-variables-to-the-adex-model)



[3. Modelling Spike Trains from Experimental Data

](#modelling-spike-trains-from-experimental-data)



[III) Results and Discussions

](#results-and-discussions)



[I) Interspike Intervals with a variation of the τ ω

](#interspike-intervals-with-a-variation-of-the-τ-ω)



[II) Interspike Intervals with a variation of the values of b](#interspike-intervals-with-a-variation-of-the-values-of-b)



[III) Interspike Intervals with a variation of the a

](#interspike-intervals-with-a-variation-of-the-a)



[IV) Interspike Intervals with the variation of the injected current

](#interspike-intervals-with-the-variation-of-the-injected-current)



[V) Models from Experimental Data

](#models-from-experimental-data)



[VI) Conclusions ](#conclusions)



[Bibliography ](#Bibliography)



# Abbreviations



VIP -- Vasoactive Intestinal Peptides



PV - Parvalbumin



SOM - Somatostatin



NPY - Neuropeptide Y



ADEX -- Adaptive Exponential Integrate and Fire Model



ISI -- Interspike interval



tau- Membrane time constant



# Abstract



Several studies have modelled the dynamics of neurons and not a lot

specifically target the neurons of the claustrum. The claustrum neurons

are hampered by not having an agreed defined boundary. In our

internship, we study several models for neurons in general and see the

effect of the modulation of their parameters. We then simulate

experimental data to reproduce the neuron dynamics observed.



# INTRODUCTION



The claustrum is a thin sheet of grey matter located in the forebrain,

extending rostrocaudally along with the striatum and situated between

the insula and putamen (Smith, Lee and Jackson, 2020). It is the most

densely interconnected region of the brain (Graf *et al.*, 2020). The

claustrum is composed of both the spiny stellate projection neurons and

a variety of aspiny interneurons that can be differentiated by the

expression of various peptides and calcium-binding proteins such as PV,

VIP, SOM, NPY and others (Smith, Lee and Jackson, 2020). Due to the high

connection of the claustrum and other parts of the brain, it is thought

to take part in higher cognitive functions where it integrates

information and hence supports the consciousness (Crick and Koch, 2005).

The claustrum is also believed to take part in attention and resilience

from distraction (Atlan *et al.*, 2018). It has also been linked to

sleep (Liu *et al.*, 2019) and impulsivity(Norimoto *et al.*, 2020).



The claustrum projection neurons and interneurons can be distinguished

from each other based on their intrinsic electrical properties. The

projection neurons can be subdivided into 5 subclasses based on their

intrinsic electrical properties. This makes a total of 8 subclasses of

claustrum neurons(Graf *et al.*, 2020).



A neuron fires when it gets input from other sources. The firing of a

neuron produces an action potential (spike), which is an abrupt

transient change of the membrane voltage that propagates to other

neurons(Izhikevich, 2007). There are several models with different

parameters allowing the simulation of neuron dynamics. In the team, we

worked with the Adex model which is a relatively simple model with two

differential equations one for the voltage with respect to time and the

other for the adaptation variable with respect to time. The model shows

the evolution of the voltage in time when a current I is injected (Naud

*et al.*, 2008).



This internship aims to reproduce the dynamics of claustrum neurons

observed in the experimental works (Graf *et al.*, 2020). First, we

simulated the ADEX model in order to understand the influence of

different parameters on the Interspike interval then we reproduced

qualitatively some parameters of the neurons observed experimentally.



# Methods



All simulations were done in the Brian2 neural simulator and Python 3

programming language.



### Adaptive Exponential Integrate Model



This is a model of two differential equations that model the evolution

of membrane potential V when a certain current I is injected into the

system.



$$C\frac{dV}{dt} = \  - g_{l}\left( V - E_{L} \right) + g_{L}*\ \mathrm{\Delta}_{T}\exp\left( \frac{V - V_{T}}{\mathrm{\Delta}_{T}} \right) - \omega + Ι$$



Equation Adaptation



$$\tau_{\omega}\frac{d\omega}{dt} = a\left( V - E_{L} \right) - \omega$$



Equation Adaptation Current



Where :



$C$ = Membrane Capacitance



V = Membrane Potential



g~L~ = Leak Conductance



E~L~ = Resting Potential



V~T~ = Threshold Potential



ω = Adaptation Variable



I = Synaptic Current



τ ~ω~ = Time constant



∆~T\ =~ Threshold Slope Factor



a = Subthreshold Adaptation



When the current drives the potential beyond the threshold V~T~ this

leads to the positive feedback that drives an upswing of the action

potential. The upswing is stopped by a reset threshold that we fix, and

the action potential is replaced by a reset condition (Equation 1)(Naud

*et al.*, 2008).



$$if\ V > V_{T}\ then\ \begin{Bmatrix}

V \rightarrow V_{r} \\

\omega\  \rightarrow {\omega\ }_{r} = \omega\  + b \\

\end{Bmatrix}$$



Equation Reset Condition for the ADEX Model



Where:



b = Spike triggered adaptation



V~r~ = Reset Potential



The membrane potential is reset to V reset whereas the adaptation

variable is reset to the w~r~ which is the adaptation variable plus a

fixed amount b. The adaptation variable accumulates during the spike

train whereas the membrane potential does not.



The nine parameters can be divided into bifurcation and scaling

parameters. The scaling parameters are involved for scaling the time

axis. The five scaling parameters are the total capacitance (C), total

leak conductance (g~L~ ), effective rest potential (E~L~ ), threshold

slope factor (∆~T~ ), effective threshold potential (V~T~ ).



The remaining four parameters are bifurcation parameters and are

directly related to the conductance a, the time constant τw,the spike

triggered adaptation b, and the rest potential Vr. The modification of

these four parameters results in changes in the firing patterns.



### Testing the relative effects of variables to the Adex Model



To test the effect of different parameters on the evolution of the spike

train we simulated the firing of a neuron while adjusting for the value

of interest. While this was happening, we fixed the rest of the

variables to pre-defined control in which was our starting point for the

experiment as :



C = 200 pF



g~L~ = 10 nS



E~L~ = -65mV



V~T~ = -55 mV



I = .120nA



τ ~ω~ = 500 ms



dt = 5 mV



a = 2 pA



b = 10 pA



V~r~ = -52 mV



We varied the $a,\ b\ ,input\ current\  tau$.We recorded the spike

train and the ISI for the variable parameters while leaving the rest of

the parameters to remain the same as the control. We set the threshold

at -40mV and the refractory period to be 5ms. The experiment ran for 4s

for each simulation, and we took the value from 500ms to 4000ms to avoid

any bias at the beginning of the spike train.



### Modelling Spike Trains from Experimental Data



We modelled the neurons according to the intrinsic electrical properties

that we fixed into the Adex model derived from the classification of the

rat claustrum (Graf *et al.*, 2020). The Adex model (Figure 1), has 9

variables and we got 4 variables from the experimental data, that is the

membrane potential, the input current, the threshold, and the leak

conductance.



We fixed the variables that we got from the paper into the model and

modulated the rest of the variables to try and simulate the experimental

spike trains.



# Results and Discussions



The Adex model has been simulated with a variation of these parameters :



a , b , synaptic current , and τ ~ω~ ,Then the Interspike intervals have

been computed in order to look at the influence of these different

parameters on the frequency of the spikes.



### Interspike Intervals with a variation of the τ ~ω~



image1



Figure Change of ISI for variation of tau (ms)



In Figure 3 we vary the τ ~ω~ from 0ms to 1000ms and where a is 10 nS, b

is fixed at 10nS, and synaptic current is fixed at .120nA.



At point a in the graph the τ ~ω~ is 200ms we observe spike train with a

high frequency and regular ISI. With increase to point b of τ ~ω~ is

600ms we observe six values of ISI and hence an irregular spike train.

The third mark is at 1000ms we observe three distinct values of ISI and

hence more regular than b.



### Interspike Intervals with a variation of the values of b



In Figure 4 we vary the b from 0 pA to 25 pA and where a is 10 nS, τ ~ω~

is fixed at 500ms, and synaptic current is fixed at .120nA.



At point a in the graph the b is at 7 pA we observe spike train with a

high frequency and regular ISI. With increase to point b of b is 17 pA

we observe 4 values of ISI and hence an irregular spike train. The third

mark is at 27 pA we observe two distinct values of ISI and hence more

regular than b.



image2



Figure Variation of ISI with b (pA)



### Interspike Intervals with a variation of the a



In Figure 5 we vary the a from 0nS to 10nS and where b is 2nS, τ ~ω~ is

fixed at 500ms, and synaptic current is fixed at .120nA.



At point (a) in the graph the a is at 1 nS we observe spike train with a

high frequency and regular ISI. With increase to point (b) of b is 4nS

we observe 4 values of ISI and hence an irregular spike train. The third

mark is at 6 nS we observe three distinct values of ISI and hence more

regular than (b).

![image3](https://user-images.githubusercontent.com/57854451/232287845-6ccc4473-3da7-44f4-98aa-deb6dd18aa1d.png)



Figure Variation of ISI for a (nS)



### Interspike Intervals with the variation of the injected current



![image4](https://user-images.githubusercontent.com/57854451/232287755-e1eddb00-0f2b-4973-9cce-da6ab4b39fe5.png)



Figure Variation of ISI (s) with Injected current (pA)



In Figure 6 we vary the synaptic current from 0.05pA to 0.250pA and

where b is 2nS, τ ~ω~ is fixed at 500ms, and a is 10 nS.



At point (a) in the graph the synaptic current is at 0.08 pA we observe

spike train with a low frequency and an irregular spike train. With

increase to point (b) with synaptic current as 0.150 pA we a high

frequency spike train compared to (a) with a regular ISI. The third mark

is at 0.250 pA the frequency increases from the one at (b) and the ISI

remains regular.



## Models from Experimental Data



The data divides the neurons of the claustrum into the two major groups

interneurons and projection neurons and further subdivides the

projection neurons into five subgroups according to the shape of their

spike trains.(Graf *et al.*, 2020). The data in figure on the left are

the five sib-divisions of projections and one interneuron whereas the

figures on the right are the pre-liminary results obtained from our

simulations. They show a bit of difference but don't much up exactly to

the experimental data, this discrepancy is caused by lack of majority of

the variables considered in the ADEX model from the experimental data.



Screenshot 2023-04-16 at 10 57 30



image6



Figure Classification of claustrum neurons

(a) the experimental spike trains (Graf et al., 2020) (b) the

values of our simulations with data from experiments on mice (Graf et

al., 2020)



# Conclusions



We grouped the neurons of the claustrum according to their electrical

properties and their expression of different peptides. In total we

arrived at 8 distinct subgroups of the claustrum inter-neurons and also

obtained preliminary results in our simulations from experimental data.

In addition, I learnt different neuron models with increased complexity

till I arrived to the Adex model that our team was using for modelling

of the claustrum neurons.



The rest of the experimental data and all simulations can be accessed

through the GitHub repository



# Bibliography



Sciences Atlan, G. *et al.* (2018) 'The Claustrum Supports Resilience to

Distraction', *Current Biology*, 28(17), pp. 2752-2762.e7.

doi:10.1016/j.cub.2018.06.068.



Crick, F.C. and Koch, C. (2005) 'What is the function of the

claustrum?', *Philosophical transactions of the Royal Society of London.

Series B, Biological sciences*, 360(1458), pp. 1271--1279.

doi:10.1098/rstb.2005.1661.



Graf, M. *et al.* (2020) 'Identification of Mouse Claustral Neuron Types

Based on Their Intrinsic Electrical Properties', *eneuro*, 7(4), p.

ENEURO.0216-20.2020. doi:10.1523/ENEURO.0216-20.2020.



Izhikevich, E.M. (2007) *Dynamical systems in neuroscience: the geometry

of excitability and bursting*. Cambridge, Mass: MIT press (Computational

neuroscience).



Liu, J. *et al.* (2019) 'The Claustrum-Prefrontal Cortex Pathway

Regulates Impulsive-Like Behavior', *The Journal of Neuroscience*,

39(50), pp. 10071--10080. doi:10.1523/JNEUROSCI.1005-19.2019.



Naud, R. *et al.* (2008) 'Firing patterns in the adaptive exponential

integrate-and-fire model', *Biological Cybernetics*, 99(4--5), pp.

335--347. doi:10.1007/s00422-008-0264-7.



Norimoto, H. *et al.* (2020) 'A claustrum in reptiles and its role in

slow-wave sleep', *Nature*, 578(7795), pp. 413--418.

doi:10.1038/s41586-020-1993-6.



Smith, J.B., Lee, A.K. and Jackson, J. (2020) 'The claustrum', *Current

Biology*, 30(23), pp. R1401--R1406. doi:10.1016/j.cub.2020.09.069.



[^1]: The experimental spike trains obtained from (Graf *et al.*, 2020)