Modelling Paper Lindietal

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1

Hello, I am having some issues modelling this paper (Lindi, https://doi.org/10.1101/2023.03.07.531640) in Brian2
The paper has the following equations:
(see equations 4, 5, 6 on image eqs_4_5_6.png)

Where j denotes the j-th neuron in population beta (post synaptic spike population) and i denotes the i-th neuron in population alpha (pre synaptic spike population). In the paper there are 5 populations and there 8 possible synapses connections between populations.
populations: “D2”, “STN”, “Arky”, “Proto”, “FSI”
synapses: Proto-D2, STN-Proto, Proto-STN, Proto-Proto, Arky-Proto, D2-FSI, FSI-Proto, D2-Arky

I am having some issues modelling the delta function (for the synaptic spikes) from different Neurongroups in Brian2.

eqs_4_5_6
eqs_4_5_6760×828 180 KB

2

Hi. Do you really need to model the delta function? It only tells you that when there is a presynaptic spike (with a delay \Delta), I_{rj} will be incremented. So you can do this as usual in Brian with on_pre declaration and connection delays.

3

Thanks for your reply,

You do not necessary need a delta function just an instant increment at a certain timestip. Like the way you said
I implemented a solution like that. However than there is an issue because for each subgroup from neurons from group alpha (e.g. Proto) to neurons from group beta (e.g. FSI) you need a different tau_r_j^(beta_alpha) for each subgroup. Which is with which I am struggling.

4

I see. Why don’t you use multiple postsynaptic currents (each could have a different \tau_{rj}^{\beta\alpha}) and sum them on the postsynaptic neuron? I pasted an example from the documentation below. They have a nice explanation of what summed variables are and how to use them.

neurons = NeuronGroup(1, model='''dv/dt=(gtot-v)/(10*ms) : 1
                                  gtot = gtot1 + gtot2: 1
                                  gtot1 : 1
                                  gtot2 : 1''')
S1 = Synapses(neuron_input, neurons,
              model='''dg/dt=-a1*g+b1*x*(1-g) : 1
                       gtot1_post = g : 1  (summed)
                       dx/dt=-c1*x : 1
                       w : 1 # synaptic weight
                    ''', on_pre='x+=w')
S2 = Synapses(neuron_input, neurons,
              model='''dg/dt=-a2*g+b2*x*(1-g) : 1
                       gtot2_post = g : 1  (summed)
                       dx/dt=-c2*x : 1
                       w : 1 # synaptic weight
                    ''', on_pre='x+=w')
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