biexp synapse documentation not matching implementation?

[felix11h]

A biexponential synapse, as per the Brian 2 documentation, should implement a current/conductance as g(t)=(tau2/(tau2-tau1))*(exp(-t/tau1)-exp(-t/tau2)).

When playing around with the biexponential synapse concept, I found that maybe the above description might need to be updated. Consider

import matplotlib as mpl
mpl.use('Agg')
import pylab as pl

import numpy as np
from brian2 import *

fig, ax = pl.subplots()

xmin, xmax = 0,100
xs = np.linspace(xmin, xmax, 10000)

# biexp as implemented in library/synapses.py
model = '''
        dx/dt = (invpeak*y-x)*invtau1 : 1
        dy/dt = -y*invtau2            : 1
        '''

tau1, tau2 = 1.5*ms, 10*ms

invtau1, invtau2 = 1./tau1, 1./tau2
invpeak = (tau2 / tau1) ** (tau1 / (tau2 - tau1))

N = NeuronGroup(1, model)
N.y = 1

mon = StateMonitor(N, 'x', record=True)
run(xmax*ms)
ax.plot(mon.t/ms, mon.x.T)


# --------------------------

# g(t) of biexp as explained in documentation
def g(t, tau1, tau2):
    return (tau2/(tau2-tau1))*(np.exp(-t/tau1)-np.exp(-t/tau2))

ax.plot(xs, g(xs, tau1/ms, tau2/ms))

fig.savefig('figure.png')

which gives

I expected to see identical curves.

Note that it doesn't simply seem to be a matter of a missing minus sign as the amplitudes also don't seem to match. Any thoughts on this? Am I missing something? Thanks!

[mstimberg]

Hi Felix. I'm a bit confused, but where do you see the description in the documentation? In Brian 2, this function does not exist any more, so we only mention it in the conversion guide where we don't show the actual equation. In the Brian 1 documentation it mentions that the equation is valid "up to a normalizing factor". The model used by Brian makes sure that the peak equals 1. Now, I agree I would not have expected that the equation gives a negative curve, even though strictly speaking it does not make the statement incorrect (the normalizing factor could be negative...). But then again, I don't see where in the Brian 2 documentation we mention anything like this, so where would the documentation have to be corrected?

[felix11h]

Hi Marcel, thanks for the speedy reply! Oh, I see, I must admit I didn't pay attention to the version I'm looking at. You're right, one of the references I mention is from Brian 1.

I got the idea of using biexponential synapses from the Brian 2 documentation here https://brian2.readthedocs.io/en/stable/user/converting_from_integrated_form.html and it still seems to mention the equation for V(t), maybe a pointer to the missing normalization factor could be helpful here.

Thanks also for the reference to the Brian 1 documentation, that clears up things for me a lot!

[mstimberg]

Oh, I did not think of this page! I guess one could say its equation for V(t) is not wrong but simply a bit vague, given that it does not refer to the initial value V(0) (or w later in the code/equation). It would certainly be better to make this unambiguous.

[wilhelmbraun]

Hi Felix and Marcel,
I want to add that defining an additional function for the maximum of g and then exchanging tau1 and tau2 in the difference of exponentials for g makes the two definitions equivalent, as g does not have its peak at 1, but at g_peak.

def g_peak(tau1, tau2):

    return (tau2/(tau2-tau1))*((tau1/tau2)**(tau1/(tau2-tau1)) - (tau1/tau2)**(tau2/(tau2-tau1)))

def g(t, tau1, tau2):

    return (1./g_peak(tau1, tau2))*(tau2/(tau2-tau1))*(np.exp(-t/tau2)-np.exp(-t/tau1))

Now both the sign (because of the exchange) and the peak (because of g_peak)
are correct, which one can also show directly by solving the coupled system for (x,y) above. Here's a plot:

[felix11h]

Thanks @wilhelmbraun, this looks great!

[mstimberg]

If anyone is up for updating the documentation: pull requests welcome 😄

[Syed-Osama-Hussain]

Hello. @mstimberg, can I try it?

[mstimberg]

Hello. @mstimberg, can I try it?

Sure, please go ahead.

[Syed-Osama-Hussain]

Just to be sure, I have to replace the existing biexponential synapse equation to the one provided by @wilhelmbraun ?

[wilhelmbraun]

Hi Syed, the point is that the function g(t) as defined in my post reflects the implementation currently given in the documentation (Felix also mentioned it in his original post). So the setup is correct, if one considers the right g. Best, Wilhelm

…

On 2020-04-13 6:08 p.m., Syed Osama Hussain wrote: Just to be sure, I have to replace the existing biexponential synapse equation to the one provided by @wilhelmbraun <https://github.com/wilhelmbraun> ? — You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub <#1179 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACIIBZ4X25UPYDQ3HFVGWHTRMM2I5ANCNFSM4MCKQESA>.

[Syed-Osama-Hussain]

Thanks for the explanation!