# Biexponential synapce eqation

**URL:** <https://brian.discourse.group/t/biexponential-synapce-eqation/389>\
**Category:** Support\
**Created:** [20 May 2021 11:53 UTC](https://brian.discourse.group/t/biexponential-synapce-eqation/389 "2021-05-20T11:53:16Z")\
**Posts on this page:** 1\
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**Author:** ![Ziaeemehr](https://yyz2.discourse-cdn.com/free1/user_avatar/brian.discourse.group/ziaeemehr/32/12_2.png) [@Ziaeemehr](https://brian.discourse.group/u/Ziaeemehr)\
**Post date:** [20 May 2021 16:17 UTC](https://brian.discourse.group/t/biexponential-synapce-eqation/389/2 "2021-05-20T16:17:23Z")

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Hi,  
Did you see this? It may help.

> [@Biexponential synapse](https://brian.discourse.group/t/biexponential-synapse/244):
>
> I am trying to implement a Biexponential shape conductance base synapse: I\_{syn} = g\_{syn} (V-V\_{ref})\sum\_j s\_j \\ \dot{s\_j} = \alpha H\_{\infty}(v\_j-\theta) (1-s) - \beta s\\ H\_{\infty} = \frac{1}{1+\exp(-(v-\theta^H)/\sigma^H)} \theta, \theta\_H and \sigma are constants. Adding H\_{\infty} is the question. Following the [documentation](https://brian2.readthedocs.io/en/stable/user/converting_from_integrated_form.html) I came up to this : I skipped the H\_{\infty} for now: I think this should be : g\_{syn}(t) = g\_{peak} \frac{e^{-t/\tau\_1}-e^{-t/\tau\_2}}{e^{-t\_{peak}/\tau…

I also recommend chapter 20 of Modeling neural dynamics, Borgers  
[this](https://github.com/ITNG/ModelingNeuralDynamics/tree/master/python/20_Chemical_Synapses/RTM_PLOT_S_TWO_VARIABLES) is a python implementation and also [Brain](https://github.com/ITNG/ModelingNeuralDynamics/blob/master/brian/chapter20.ipynb).

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