Simulation of a particular STDP function

[henrymiller....@gmail.com]

I refer to the above example. I used the below code and got the following outputs:

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start_scope()

# Parameters

num_inputs = 100

input_rate = 10*Hz

# Parameters from STDP function 

taupre = taupost = 20*ms

wmax = 0.01

Apre = 0.01

Apost = -Apre*1.05

# Time constant

tau = 1*ms

# Construct the poisson neurons

P = PoissonGroup(num_inputs, rates=input_rate)

eqs = '''

    dv/dt = -v/tau : 1

    '''

# Construct the output neuron

G = NeuronGroup(1, eqs, threshold='v>0.04', reset='v=0', method='exact')

# Define the synapses

S = Synapses(P, G,

             '''

             w: 1

             dapre/dt = -apre/taupre : 1 (event-driven)

             dapost/dt = -apost/taupost : 1 (event-driven)

             ''',

             on_pre='''

             v_post += w

             apre += Apre

             w = clip(w+apost, 0, wmax)

             ''',

             on_post='''

             apost += Apost

             w = clip(w+apre, 0, wmax)

             ''', method='linear')

S.connect()

# Initialise the weights of the synapses

S.w = 0.01

# State monitor for synapses

M = StateMonitor(S,['w', 'apre', 'apost'], record=True)

# State monitor for output neuron

F = StateMonitor(G,'v',record=True)

# Run simulation for 2 second

run(2*second)

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Output:

Is this really the correct way to do this? Do the weights really represent the conductances or no? Someone please enlighten me on this. Thanks!

[Marcel Stimberg]

Hi Henry,

your model looks ok in general, but the weights do not correspond to conductances in the strict sense. You'll find more info on synaptic models in textbooks, but roughly:

1. if your synaptic event directly increases the post-synaptic membrane potential, you are using the simplest possible model of a synapse, which is often called "delta synapse" (the post-synaptic membrane potential increases instantaneously)
2. If your synaptic event increases a current (and additive term in the equation for v), you have a "current-based synapse" – the increase of the post-synaptic membrane potential is no longer instantaneous, but it is the same independent of the current value of the membrane potential
3. If your synaptic event increases a conductance (g in a term like g*(E_syn - v) that is added in the equation for v), you have a "conductance-based synapse" – the increase of the post-synaptic membrane potential now depends on the current value of the membrane potential (bigger effect of the synapse the further away you are from E_syn, the reversal potential of the synapse).

Only in 3) the synaptic weight is a conductance.

Hope that makes things clearer, best

  Marcel