Hello, Marcel

Thanks for helping.

Here is complete code. There are PYR and PVN groups and four synaptic models. Running the code successfully executes, but gives a warning related to the problematic variable ‘u’:

“WARNING ‘u’ is an internal variable …. But also exists in the run namespace with the value 1. * nsiemens. The internal variable will be used:

As you can see from the plots, after a time delay caused by the initial value u=1, PYR[0] receives multiple EPSCs and IPSCs and fires action potentials, but u does not undergo +1 reset.

My guess is there is a simple solution that I am not seeing.

Mitch

```
import matplotlib.pyplot as plt
from brian2 import *
defaultclock.dt = 0.02*ms
seed(3)
from brian2.codegen import runtime
C_pyr = 115 * pF
C_pvn = 30 * pF
vr = -52.0 * mV
vpeak = 30.0 * mV
c = -53.0 * mV
N1 = 5000 # number of PYR neurons in network
N2 = 50 # number of PVN neurons in network
klow = 0.1 * nS/mV
khigh = 3.3 * nS/mV
a = 0.008 /ms
va = -65 * mV
vt = -49.0 * mV
Ishift= 0 * pA
# synaptic parameters
g_e = 0.285 * nS
g_i = 0.285 * nS
alpha = 2000 /second
Beta = 333.33 /second
s_inf =alpha/(alpha+Beta)
tau_s =1/(alpha+Beta)
Ee=-15 *mV
Ei=-68 *mV
eqs_pyr = """
Iext : amp
Isyn_e_pyr = g_e*(v-Ee)*s_sum_e_pyr : amp
Isyn_i_pyr = g_i*(v-Ei)*s_sum_i_pyr : amp
s_sum_e_pyr : 1
s_sum_i_pyr : 1
Iapp : amp
k = (int(v<vt) * klow) + (int(v>=vt) * khigh) : siemens/volt
du/dt = a*(-u) : siemens
dv/dt = (k*(v-vr)*(v-vt)+Ishift+Iext-Isyn_e_pyr-Isyn_i_pyr-u*(v-va))/C_pyr : volt
"""
reset = '''
u += 1
v = c
'''
eqs_pvn = """
Isyn_e_pvn = g_e*(v-Ee)*s_sum_e_pvn : amp
Isyn_i_pvn = g_i*(v-Ei)*s_sum_i_pvn : amp
s_sum_e_pvn : 1
s_sum_i_pvn : 1
k = (int(v<vt) * klow) + (int(v>=vt) * khigh) : siemens/volt
dv/dt = (k*(v-vr)*(v-vt)+Ishift-Isyn_e_pvn-Isyn_i_pvn)/C_pvn : volt
"""
reset = '''
v = c
'''
PYR = NeuronGroup(N1, model=eqs_pyr, reset= reset, threshold='v >= vpeak', method = 'euler')
# create subgroups
PYR1 = PYR[:4950]
PYR2 = PYR[50:]
PYR1.Iapp = 0.00000000000015 * amp
PYR2.Iapp = 0.00000000000015 * amp
PYR1.Iext = (randn(len(PYR1))*PYR1.Iapp*10 + PYR1.Iapp)
PYR2.Iext = (randn(len(PYR2))*PYR2.Iapp*10 + PYR2.Iapp)
print(PYR)
PVN = NeuronGroup(N2, model=eqs_pvn, reset= reset, threshold='v >= vpeak', method = 'euler')
print(PVN)
S_pyr_pyr=Synapses(PYR,PYR,
model="""
ds0/dt=-(s0-s_inf)/(tau_s) :1 (clock-driven)
ds1/dt=-s1*Beta :1 (clock-driven)
s_tot=clip(s0,0,s1) :1
s_sum_e_pyr_post = s_tot : 1 (summed)
""",
on_pre="""
s0=s1
s1=(s_inf*(1-exp(-0.001*second/tau_s))+s1*exp(-0.001*second/tau_s))*exp(0.001*Beta*second)
delay=0.001*second
""",
method = 'exact')
S_pvn_pyr=Synapses(PVN,PYR,
model="""
ds0/dt=-(s0-s_inf)/(tau_s) :1 (clock-driven)
ds1/dt=-s1*Beta :1 (clock-driven)
s_tot=clip(s0,0,s1) :1
s_sum_i_pyr_post = s_tot : 1 (summed)
""",
on_pre="""
s0=s1
s1=(s_inf*(1-exp(-0.001*second/tau_s))+s1*exp(-0.001*second/tau_s))*exp(0.001*Beta*second)
delay=0.001*second
""",
method = 'exact')
S_pyr_pvn=Synapses(PYR,PVN,
model="""
ds0/dt=-(s0-s_inf)/(tau_s) :1 (clock-driven)
ds1/dt=-s1*Beta :1 (clock-driven)
s_tot=clip(s0,0,s1) :1
s_sum_e_pvn_post = s_tot : 1 (summed)
""",
on_pre="""
s0=s1
s1=(s_inf*(1-exp(-0.001*second/tau_s))+s1*exp(-0.001*second/tau_s))*exp(0.001*Beta*second)
delay=0.001*second
""",
method = 'exact')
S_pvn_pvn=Synapses(PVN,PVN,
model="""
ds0/dt=-(s0-s_inf)/(tau_s) :1 (clock-driven)
ds1/dt=-s1*Beta :1 (clock-driven)
s_tot=clip(s0,0,s1) :1
s_sum_i_pvn_post = s_tot : 1 (summed)
""",
on_pre="""
s0=s1
s1=(s_inf*(1-exp(-0.001*second/tau_s))+s1*exp(-0.001*second/tau_s))*exp(0.001*Beta*second)
delay=0.001*second
""",
method = 'exact')
# set PYR to PYR connectivity to 0.2%
S_pyr_pyr.connect(condition='rand() < 0.002')
# set PYR to PVN connectivity to 5%
S_pyr_pvn.connect(condition='rand() < 0.05')
# set PVN to PVN connectivity to 5%
S_pvn_pvn.connect(condition='rand() < 0.05')
# set PVN to PYR connectivity to 5%
S_pvn_pyr.connect(condition='rand() < 0.05')
# set initial conditions
S_pyr_pyr.s0=0
S_pyr_pyr.s1=0
S_pyr_pvn.s0=0
S_pyr_pvn.s1=0
S_pvn_pyr.s0=0
S_pvn_pyr.s1=0
S_pvn_pvn.s0=0
S_pvn_pvn.s1=0
PYR.v = (rand(len(PYR))*0.002 * volt) - (0.052 * volt)
PVN.v = (rand(len(PVN))*0.002 * volt) - (0.052 * volt)
PYR.u = 1 * nS
#record PYR membrane potential, adaptive conductance, synaptic currents of cells and spike times in network
PYR_v = StateMonitor(PYR,'v',record = [0,1,2,3,4,995,996,997,998,999])
PYR_u = StateMonitor(PYR,'u',record = [0,1,2,3,4,995,996,997,998,999])
PYR_Isyn_e_pyr = StateMonitor(PYR,'Isyn_e_pyr',record= [4])
PYR_Isyn_i_pyr = StateMonitor(PYR,'Isyn_i_pyr',record= [4])
PYR_spktimes = SpikeMonitor(PYR, record=[0,1,2,3,4,995,996,997,998,999])
#record PVN membrane potential of cells and spike times in network
PVN_v = StateMonitor(PVN,'v',record = [0,1,2,3,4,5])
PVN_spktimes = SpikeMonitor(PVN, record=[0,1,2,3,4,5,6,7,8,9])
#run for x seconds of simulated time
duration = 1 * second
#include neuron groups, synapse groups, and monitors in our simulation
net = Network(PYR,PYR1,PYR2,PVN,S_pyr_pyr,S_pyr_pvn,S_pvn_pyr,S_pvn_pvn,PYR_v,PYR_spktimes,PYR_u,PYR_Isyn_e_pyr,PYR_Isyn_i_pyr,PVN_v,PVN_spktimes)
net.run(duration)
# plot PYR membrane potential
plt.figure(0)
plt.plot(PYR_v.t/ms,PYR_v.v[0]/mV)
plt.xlabel("Time (ms)")
plt.ylabel("PYR Membrane Potential (mV)")
plt.title('PYR network Cell 1 Vm')
plt.show()
# plot PYR Adaptive Conductance u
plt.figure(1)
plt.plot(PYR_u.t/ms,PYR_u.u[0]/nsiemens)
plt.xlabel("Time (ms)")
plt.ylabel("PYR Adaptive Conductance u (nS)")
plt.title('PYR network Cell 1 Adaptive Conductance')
plt.show()
# plot PYR excitatory synaptic current Isyn_e_pyr
plt.figure(2)
plt.plot(PYR_Isyn_e_pyr.t/ms,PYR_Isyn_e_pyr.Isyn_e_pyr[0]/pA)
plt.xlabel("Time (ms)")
plt.ylabel("EPSCs (pA)")
plt.title('PYR network Cell 1 EPSCs')
plt.show()
# plot PYR inhibitory synaptic current Isyn_i_pyr
plt.figure(3)
plt.plot(PYR_Isyn_i_pyr.t/ms,PYR_Isyn_i_pyr.Isyn_i_pyr[0]/pA)
plt.xlabel("Time (ms)")
plt.ylabel("IPSCs (pA)")
plt.title('PYR network Cell 1 IPSCs')
plt.show()
```