GURA Jaffar

REPORT

Modelling of neuronal interactions at the claustrum level

LABORATORY: UMR9197 NEUROPSI SACLAY FRANCE

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

Abstract

I) INTRODUCTION

II) Methods

1. Adaptive Exponential Integrate Model

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

3. Modelling Spike Trains from Experimental Data

III) Results and Discussions

I) Interspike Intervals with a variation of the τ ω

II) Interspike Intervals with a variation of the values of b

III) Interspike Intervals with a variation of the a

IV) Interspike Intervals with the variation of the injected current

V) Models from Experimental Data

VI) Conclusions

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

gL = Leak Conductance

EL = Resting Potential

VT = 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 VT 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

Vr = Reset Potential

The membrane potential is reset to V reset whereas the adaptation variable is reset to the wr 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 (gL ), effective rest potential (EL ), threshold slope factor (∆T ), effective threshold potential (VT ).

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

gL = 10 nS

EL = -65mV

VT = -55 mV

I = .120nA

τ ω = 500 ms

dt = 5 mV

a = 2 pA

b = 10 pA

Vr = -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

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.

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).

Figure Variation of ISI for a (nS)

Interspike Intervals with the variation of the injected current

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.

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 https://github.com/Jaffar-Hussein/Neurone-Models

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.