Biexponential synapce eqation

[ysj]

Hello BRIANs,

I know that the Brian can implement biexponential synapse and has the equation for the code implementation.
https://brian2.readthedocs.io/en/stable/user/converting_from_integrated_form.html?highlight=biexponential#converting-from-integrated-form-to-odes

I tried to derive the fomula used in the Brian implementation, but it made the different equation. I know my process is wrong, but after long time consideration, I want you to ask the hint to get collect equation for biexponential synapse model implementation. I believe that if we can understand the process, users can expand a lot of variety of synaptic equation by themselves, and can accelerate the potential of Brian for general choice of neuroscientific tool.

I’m very looking forward to hearing from you guys.

Best wishes,

ysj

[Ziaeemehr]

Hi,
Did you see this? It may help.

Biexponential synapse

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 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 is a python implementation and also Brain.

[ysj]

Hi Ziaeemehr,

Thanks a lot for your notification. To be honest, I saw the topic before, but unfortunately I am not sure the process that is not written the detail in the topic. That’s why I am asking it in current topic.

If you can point out what is the wrong and /or some hints to describe correct equation, I’m glad to know (or how you derived your implemented equation in former topic).

[Ziaeemehr]

Here there is more details but still need to drive the relations patiently.
I just used the documentation for the question I linked and did not drive the equations.

[ysj]

Hi Ziaeemehr,

Thanks a lot for sharing the paper, and also for explaining your case. That’s good information.
So, as you said, we still don’t get the answer of derivation, but hope we can get some hints further.
I’m also trying to find more detail in paper and/or books continuously.