# Exponential LIF with alpha shape synaptic conductance **URL:** \ **Category:** Support\ **Created:** [16 December 2020 13:27 UTC](https://brian.discourse.group/t/exponential-lif-with-alpha-shape-synaptic-conductance/234 "2020-12-16T13:27:01Z")\ **Posts on this page:** 6\ **Page:** 1
**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:** [16 December 2020 13:27 UTC](https://brian.discourse.group/t/exponential-lif-with-alpha-shape-synaptic-conductance/234/1 "2020-12-16T13:27:01Z")
I am trying to connect two exponential LIF with alpha shape synapse. following the [documentation](https://brian2.readthedocs.io/en/stable/introduction/brian1_to_2/library.html?highlight=alpha_conductance#conductance-based-synapses) for brian2 equivalence of `alpha_conductance` ```auto tau = 2.5*ms; E = 0*mV syn_eqs = Equations('''dg_syn/dt = (s - g_syn)/tau : siemens ds/dt = -s/tau : siemens''') group = NeuronGroup(N, eqs, threshold='vm>-50*mV', reset='vm=-70*mV') syn = Synapses(source, group, on_pre='s += 10*nS') # ... connect synapses, etc. ``` I wrote this: \*\*Edited \*\* ```python eqs_e = """ Im = IX + gL * (EL - vm) + gL * DeltaT * exp((vm - VT) / DeltaT) : amp dvm/dt = (Im + I_syn_e) / C : volt VT : volt IX : amp I_syn_e : amp """ eqs_syn_e = """ dg_syn_e/dt = (s_e - g_syn_e) / Tau_e : siemens (event-driven) ds_e/dt = -s_e / Tau_e : siemens (event-driven) I_syn_e_post = g_syn_e * (Erev_e - vm): amp (summed) """ E_cells = b2.NeuronGroup(E_cell_params['Ncells'], model=eqs_e, dt=dt, method=integration_method, threshold="vm > 0.*mV", reset="vm=-65*mV"), refractory="vm > 0.*mV", namespace=param_E_syn) cEE = b2.Synapses(E_cells, E_cells, eqs_syn_e, on_pre='g_syn_e += 0.1*nsiemens'), namespace=param_E_syn) cEE.connect(i=0, j=1) ``` witch give me this error: ```auto KeyError: 'The identifier "g_syn_e" could not be resolved.' ``` I also want to integrate the synapse as `(event-driven)`. I am not sure whether it is possible here. Thanks for any guide. ---
**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:** [16 December 2020 13:45 UTC](https://brian.discourse.group/t/exponential-lif-with-alpha-shape-synaptic-conductance/234/2 "2020-12-16T13:45:34Z")
Oh It was just a typo `dg_syn_e/dt = ... ` is correct, Am I correct in the implementation of alpha shape synapse? ![Selection_001](https://global.discourse-cdn.com/free1/uploads/brian/original/1X/963657f4eb1cff6a2cf97b30dcc2a2db3e52a78d.png) 1 is connectoed to 2, I expected to see a bump on 2 as 1 spike as I was familiar from NEST or it may be just need tuning the parameters. ---
**Author:** ![mstimberg](https://yyz2.discourse-cdn.com/free1/user_avatar/brian.discourse.group/mstimberg/32/11_2.png) [@mstimberg](https://brian.discourse.group/u/mstimberg)\ **Post date:** [16 December 2020 15:21 UTC](https://brian.discourse.group/t/exponential-lif-with-alpha-shape-synaptic-conductance/234/3 "2020-12-16T15:21:14Z")
Hi. The implementation of the alpha synapse looks mostly correct, but you’ll have to increase `s` in the `on_pre` statement, instead of `g_syn_e`. Otherwise `s` will always be 0 and this will be an exponential synapse. Also, you cannot use `event-driven` here. The `event-driven` flags means that the value of the respective value is only updated whenever a spike arrives. This is not possible here, since you need the values of `g_syn_e` and `s_e` at every time step to calculate the synaptic current `I_syn_e_post`. Note that if you use the same time constant `Tau_e` for all synapses, then it is much more efficient to include all your equations in the `NeuronGroup` equations instead of in the `Synapses` object. This way, you will sum up the conductances/currents of all synapses before calculating the exponential decay only once per neuron. By including these equations in the `Synapses` object you are calculating the exponential decay once per synapse before summing it up. Mathematically both formulations are equivalent, but the `NeuronGroup` calculation is much more efficient. Of course, in your example with 2 neurons and 1 synapse this does not really matter… Regarding your plot, I don’t really see the effect of the synapse but that might be due to the issues mentioned above. To check what is going on in detail you could record and plot `g_syn_e` and `I_syn_e`. ---
**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:** [16 December 2020 16:17 UTC](https://brian.discourse.group/t/exponential-lif-with-alpha-shape-synaptic-conductance/234/4 "2020-12-16T16:17:26Z")
Hi, Thank you It seems the `g_syn_e` is updating properly but `I_syn_e` is not. ![Figure_1](https://global.discourse-cdn.com/free1/uploads/brian/original/1X/21ab75a5c3e9443a9440184afc7abd352eb32fc7.png) Excuse me the code is a bit long just in case to check. ```auto import os import time import pylab as plt import numpy as np from numpy.random import randn import brian2 as b2 from brian2.equations.equations import Equations b2.seed(2) np.random.seed(2) def simulate(): common_params = { # Parameters common to all neurons. 'C': 100*b2.pfarad, 'tau_m': 10*b2.ms, 'EL': -60*b2.mV, 'DeltaT': 2*b2.mV, 'Vreset': -65, # *b2.mV 'VTmean': -50*b2.mV, 'VTsd': 2*b2.mV } common_params['gL'] = common_params['C'] / common_params['tau_m'] param_E_syn = { "Erev_e": 0.0*b2.mV, "Tau_e": 4.0*b2.ms, "w_e": 1.1, # ! *b2.nsiemens 0.1 "p_e": 1.0, } E_cell_params = {'Ncells': num_E_cells, 'IXmean': 120*b2.pA, 'IXsd': 20*b2.pA} eqs_e = """ VT : volt IX : amp I_syn_e : amp Im = IX + gL * (EL - vm) + gL * DeltaT * exp((vm - VT) / DeltaT) : amp ds_e/dt = -s_e / Tau_e : siemens dg_syn_e/dt = (s_e - g_syn_e) / Tau_e : siemens dvm/dt = (Im + I_syn_e) / C : volt """ eqs_syn_e = """ I_syn_e_post = g_syn_e_pre * (Erev_e - vm): amp (summed) """ E_cells = b2.NeuronGroup(E_cell_params['Ncells'], model=eqs_e, dt=dt0, method=integration_method, threshold="vm > 0.*mV", reset="vm={}*mV".format(common_params['Vreset']), refractory="vm > 0.*mV", namespace={**common_params, **param_E_syn, }) cEE = b2.Synapses(E_cells, E_cells, eqs_syn_e, on_pre='s_e += {}*nsiemens'.format( param_E_syn["w_e"]), dt=dt0, method=integration_method, namespace={**common_params, **param_E_syn, }) cEE.connect(i=0, j=1) # Initialise random parameters. E_cells.VT = [common_params['VTmean']] * 2 E_cells.IX = (randn(len(E_cells)) * E_cell_params['IXsd'] + E_cell_params['IXmean']) E_cells.vm = randn(len(E_cells)) * 10 * b2.mV - 60 * b2.mV spike_monitor_E = b2.SpikeMonitor(E_cells) state_monitor_E = b2.StateMonitor(E_cells, ["vm", "g_syn_e", "I_syn_e"], record=True) net = b2.Network(E_cells) net.add(state_monitor_E) net.add(cEE) net.add(spike_monitor_E) b2.run(sim_duration*b2.ms) return spike_monitor_E, state_monitor_E def plot(spike_monitor_E, state_monitor_E, plot_voltages=False): fig, ax = plt.subplots(4, figsize=(10, 5), sharex=True) ax[0].plot(spike_monitor_E.t/b2.ms, spike_monitor_E.i, '.k', ms=3) if plot_voltages: for i in range(num_E_cells): ax[1].plot(state_monitor_E.t/b2.ms, state_monitor_E.vm[i]/b2.mV, label=str(i+1)) ax[2].plot(state_monitor_E.t/b2.ms, state_monitor_E.g_syn_e[1]/b2.nsiemens, lw=1, color="b", ls="--") ax[3].plot(state_monitor_E.t/b2.ms, state_monitor_E.I_syn_e[1]/b2.pA, lw=1, color="b", ls="--") ax[2].set_ylabel(r"$g_{syn}$(nS)") ax[3].set_ylabel(r"$I_{syn}$(pA)") ax[0].set_ylabel("E cells") ax[1].legend(loc="upper right") ax[1].set_ylabel("Voltages E") ax[-1].set_xlabel("time (ms)") plt.savefig("data/E_cell.png", dpi=150) plt.show() if __name__ == " __main__": num_E_cells = 2 dt0 = 0.1*b2.ms sim_duration = 200 stimulus = np.sin(np.arange(0, sim_duration)*2*np.pi/sim_duration) state = "beta" integration_method = "rk2" record_volrages = True plot_voltages = record_volrages sp_mon, st_mon = simulate() plot(sp_mon, st_mon, plot_voltages) ``` ---
**Author:** ![mstimberg](https://yyz2.discourse-cdn.com/free1/user_avatar/brian.discourse.group/mstimberg/32/11_2.png) [@mstimberg](https://brian.discourse.group/u/mstimberg)\ **Post date:** [16 December 2020 16:52 UTC](https://brian.discourse.group/t/exponential-lif-with-alpha-shape-synaptic-conductance/234/5 "2020-12-16T16:52:37Z")
> [@Ziaeemehr](#): > > `I_syn_e_post = g_syn_e_pre * (Erev_e - vm): amp (summed)` This calculates the synaptic current of the post-synaptic cell based on the synaptic conductance of the _pre_-synaptic cell and therefore gives zero in your example. But you don’t actually need a summed variable here. You can delete the equation from the synapses and define `I_syn_e` in the neuron equations: ```auto I_syn_e = g_syn_e * (Erev_e - vm) : amp ``` ---
**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:** [16 December 2020 17:03 UTC](https://brian.discourse.group/t/exponential-lif-with-alpha-shape-synaptic-conductance/234/6 "2020-12-16T17:03:25Z")
That solved the issue, I still need to think about it. thank you 🙂