Dear Tom,

Thanks for the time you spent answering my question and Sorry for not including enough details for the question.
I added a figure to describe the question. I’m using ‘oaf_cond_exp’ neuron model in a balanced network. I want to change the synaptic decay time while the area under the conductance curve remain a constant value as it has shown in the figure. Mentioning the synaptic conductance as synaptic current was definitely a mistake.


Nosratullah Mohammadi

On 07 May 2020 AD, at 00:54, Tom Tetzlaff <> wrote:

Dear Nosratullah,

sorry, can you perhaps rephrase your question? It is unclear what you
mean by "make the area under the synaptic current constant".

In networks with conductance based synapses, there is no such thing as
*the* synaptic current. For conductance based synapses, the current
I_ij(t)=g_ij(t)*(V_i(t)-E_j) at synapse j->i is determined by the
membrane potential V_i(t) of the target cell i, which, in turn, is
affected by the synaptic currents at all synapses of this neuron (for
point neurons). As the membrane potential V_i(t) is strongly fluctuating
in balanced networks, the synaptic-current responses I_ij(t) triggered
by input spikes from neuron j are different (in shape) for each incoming
spike, even if the weight and time constant of the conductance kernel
are fixed.

You can of course easily preserve the area

A = \int dt g_ij(t) = w_ij * tau

under the exponential conductance kernel

g_ij(t)=w_ij * exp(-t/tau) * H(t)

(with H(t)=Heaviside function) by compensating a change in its amplitude
w_ij ("weight") by the time constant tau = A/w_ij. But this won't make
I_ij(t) constant.


On 06.05.20 11:19, Nosratullah M wrote:
Dear all,

I hope you are in staying safe.
I'm working on a balanced network consisting of "iaf_cond_exp" neurone
I want to have the control over these parameters at the same time:
- increasing the synaptic decay time.
- reducing the synaptic weight.
The goal is to make the area under the synaptic current, constant. So
that we know that the only parameter that is affecting on the network,
is synaptic delay.
I wonder if you know of any furmula in mathematics or any algorithm,
that can help me, making this process automatic. And keeping the area
under the curve, a constant value.

Best wishes,

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Dr. Tom Tetzlaff
Institute of Neuroscience and Medicine (INM-6)
Computational and Systems Neuroscience &
Institute for Advanced Simulation (IAS-6)
Theoretical Neuroscience
Jülich Research Centre and JARA
Jülich, Germany

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