def test_simulation_theory(self):
reset_brian2()
t = 1000 * ms
dt = 0.01 * ms
defaultclock.dt = dt
pop = MFLinearPopulation(
100, {
PP.GM: 25. * nS,
PP.CM: 0.5 * nF,
PP.VL: -70. * mV,
PP.VTHR: -50. * mV,
PP.VRES: -55. * mV,
PP.TAU_RP: 2. * ms
})
pop.rate = 1 * Hz
noise = MFStaticInput(1000, 1 * Hz, pop, {
IP.GM: 2 * nS,
IP.VREV: 0 * volt,
IP.TAU: 2. * ms,
})
rec = MFLinearInput(pop, pop, {
IP.GM: 0.973 / 100 * nS,
IP.VREV: -70 * volt,
IP.TAU: 10. * ms,
})
system = MFSystem(pop)
solver = MFSolver.rates_voltages(system, solver='mse', maxiter=1)
sol = solver.run()
theory = sol.state[0]
rate = PopulationRateMonitor(pop.brian2)
net = system.collect_brian2_network(rate)
net.run(t)
#brian2_introspect(net, globals())
stable_t = int(t / dt * 0.1)
isolated = np.array(rate.rate)[stable_t:-stable_t]
print(isolated.mean())
if False:
plt.plot(rate.t / ms, rate.smooth_rate(width=25 * ms) / Hz)
plt.plot(np.ones(10000) * isolated.mean(), label='simulation mean')
plt.plot(np.ones(10000) * theory, label='theory mean')
plt.ylabel('Population rate (Hz) per 100')
plt.xlabel('Simulation time (ms)')
plt.title('Poisson noise 5 Hz per 1000')
plt.legend()
plt.show()
def with_rate(rate):
reset_brian2()
pop = MFLinearPopulation(n_pop, {
PP.GM: 25. * nS,
PP.CM: 0.5 * nF,
PP.VL: -70. * mV,
PP.VTHR: -50. * mV,
PP.VRES: -55. * mV,
PP.TAU_RP: 2. * ms
})
pop.rate = 10 * Hz
MFStaticInput(n_noise, rate * Hz, pop, {
IP.GM: 2.08 * nS,
IP.VREV: 0 * volt,
IP.TAU: 1.5 * ms,
})
system = MFSystem(pop)
rate = PopulationRateMonitor(pop.brian2)
net = system.collect_brian2_network(rate)
net.run(t)
margin = round(0.5 * second / defaultclock.dt)
stable = rate.smooth_rate(width=20 * ms)[margin:-margin]
mean_simu = np.mean(stable)
std_simu = np.reshape(stable, (samples, -1)).mean(axis=1).std() / np.sqrt(samples) * 1.96
print(std_simu)
solver = MFSolver.rates_voltages(system, solver='simplex', maxiter=1)
sol = solver.run()
mean_theo = sol.state[0]
return [mean_theo, mean_simu, std_simu]
def for_rate(rate):
reset_brian2()
pop = MFLinearPopulation(
n_pop, {
PP.GM: 25. * nS,
PP.CM: 0.5 * nF,
PP.VL: -70. * mV,
PP.VTHR: -50. * mV,
PP.VRES: -55. * mV,
PP.TAU_RP: 2. * ms
})
pop.rate = 1 * Hz
MFStaticInput(n_noise, rate * Hz, pop, {
IP.GM: 2 * nS,
IP.VREV: 0 * volt,
IP.TAU: 2. * ms,
})
t = 500 * ms
dt = 0.1 * ms
system = MFSystem(pop)
rate = PopulationRateMonitor(pop.brian2)
net = system.collect_brian2_network(rate)
net.run(t)
stable_t = int(t / dt * 0.1)
isolated = np.array(rate.rate)[stable_t:-stable_t]
sim = np.mean(isolated)
solver = MFSolver.rates_voltages(system,
solver='simplex',
maxiter=1)
sol = solver.run()
return [sol.state[0], sim]
def for_rate(rate):
pop = MFLinearPopulation(100, {
PP.GM: 25. * nS,
PP.CM: 0.5 * nF,
PP.VL: -70. * mV,
PP.VTHR: -50. * mV,
PP.VRES: -55. * mV,
PP.TAU_RP: 2. * ms
})
pop.rate = 10 * Hz
noise = MFStaticInput(1000, rate * Hz, pop, {
IP.GM: 2 * nS,
IP.VREV: 0 * volt,
IP.TAU: 2. * ms,
})
pop.add_noise(noise)
system = MFSystem(pop)
solver = MFSolver.rates_voltages(system, solver='mse', maxiter=1)
print(solver.state)
sol = solver.run()
return sol.state[0]
def one_subpopulation():
# populations
N = 250
N_E = int(N * 0.8) # pyramidal neurons
N_I = int(N * 0.2) # interneurons
# voltage
V_L = -70. * mV
V_thr = -50. * mV
V_reset = -55. * mV
V_E = 0. * mV
V_I = -70. * mV
# membrane capacitance
C_m_E = 0.5 * nF
C_m_I = 0.2 * nF
# membrane leak
g_m_E = 25. * nS
g_m_I = 20. * nS
# refractory period
tau_rp_E = 2. * ms
tau_rp_I = 1. * ms
# external stimuli
rate = 3 * Hz
C_ext = 800
# AMPA (excitatory)
g_AMPA_ext_E = 2.08 * nS
g_AMPA_rec_E = 0.104 * nS * 800. / N_E
g_AMPA_ext_I = 1.62 * nS
g_AMPA_rec_I = 0.081 * nS * 800. / N_E
tau_AMPA = 2. * ms
# NMDA (excitatory)
g_NMDA_E = 0.327 * nS * 800. / N_E
g_NMDA_I = 0.258 * nS * 800. / N_E
tau_NMDA_rise = 2. * ms
tau_NMDA_decay = 100. * ms
alpha = 0.5 / ms
beta = 0.062
gamma = 1. / 3.57
Mg2 = 1.
# GABAergic (inhibitory)
g_GABA_E = 1.25 * nS * 200. / N_I
g_GABA_I = 0.973 * nS * 200. / N_I
tau_GABA = 10. * ms
# subpopulations
f = 0.1
p = 1
N_sub = int(N_E * f)
N_non = int(N_E * (1. - f * p))
w_plus = 2.1
w_minus = 1. - f * (w_plus - 1.) / (1. - f)
# modeling
E_params = {
PP.GM: g_m_E,
PP.CM: C_m_E,
PP.VL: V_L,
PP.VTHR: V_thr,
PP.VRES: V_reset,
PP.TAU_RP: tau_rp_E
}
I_params = {
PP.GM: g_m_I,
PP.CM: C_m_I,
PP.VL: V_L,
PP.VTHR: V_thr,
PP.VRES: V_reset,
PP.TAU_RP: tau_rp_I,
}
pop_e1 = MFLinearPopulation(N_non, E_params, name="E")
pop_e2 = MFLinearPopulation(N_sub, E_params, name="Edown")
pop_i = MFLinearPopulation(N_I, I_params, name="I")
# noise pops
MFStaticInput(C_ext,
rate,
pop_e1, {
IP.GM: g_AMPA_ext_E,
IP.VREV: V_E,
IP.TAU: tau_AMPA,
},
name="E_noise1")
MFStaticInput(C_ext,
rate,
pop_e2, {
IP.GM: g_AMPA_ext_E,
IP.VREV: V_E,
IP.TAU: tau_AMPA,
},
name="E_noise2")
MFStaticInput(C_ext,
rate,
pop_i, {
IP.GM: g_AMPA_ext_I,
IP.VREV: V_E,
IP.TAU: tau_AMPA,
},
name="I_noise")
# E->E NMDA
ee_nmda = MFParameters({
IP.GM: g_NMDA_E,
IP.VREV: V_E,
IP.TAU: tau_NMDA_decay,
IP.TAU_NMDA_RISE: tau_NMDA_rise,
IP.ALPHA: alpha,
IP.BETA: beta,
IP.GAMMA: gamma,
IP.MG: Mg2,
})
MFNonLinearNMDAInput(pop_e1,
pop_e1,
ee_nmda + {IP.W: 1},
name='EE NMDA 1',
connection=Connection.all_to_others())
MFNonLinearNMDAInput(pop_e1,
pop_e2,
ee_nmda + {IP.W: w_minus},
name='EE NMDA 2')
MFNonLinearNMDAInput(pop_e2,
pop_e2,
ee_nmda + {IP.W: w_plus},
name='EE NMDA 3',
connection=Connection.all_to_others())
MFNonLinearNMDAInput(pop_e2, pop_e1, ee_nmda + {IP.W: 1}, name='EE NMDA 4')
# E->E AMPA
ee_ampa = MFParameters({
IP.GM: g_AMPA_rec_E,
IP.VREV: V_E,
IP.TAU: tau_AMPA,
})
MFLinearInput(pop_e1, pop_e1, ee_ampa + {IP.W: 1}, name='EE AMPA 1')
MFLinearInput(pop_e1,
pop_e2,
ee_ampa + {IP.W: w_minus},
name='EE AMPA 2',
connection=Connection.all_to_others())
MFLinearInput(pop_e2, pop_e1, ee_ampa + {IP.W: w_plus}, name='EE AMPA 3')
MFLinearInput(pop_e2,
pop_e2,
ee_ampa + {IP.W: 1},
name='EE AMPA 4',
connection=Connection.all_to_others())
# E->I NMDA
ei_nmda = {
IP.GM: g_NMDA_I,
IP.VREV: V_E,
IP.W: 1,
IP.TAU: tau_NMDA_decay,
IP.TAU_NMDA_RISE: tau_NMDA_rise,
IP.ALPHA: alpha,
IP.BETA: beta,
IP.GAMMA: gamma,
IP.MG: Mg2,
}
MFNonLinearNMDAInput(pop_e1, pop_i, ei_nmda, name='EI NMDA')
MFNonLinearNMDAInput(pop_e2, pop_i, ei_nmda, name='EI NMDA 2')
# E->I AMPA
ei_ampa = {
IP.GM: g_AMPA_rec_E,
IP.VREV: V_E,
IP.TAU: tau_AMPA,
}
MFLinearInput(pop_e1, pop_i, ei_ampa, name='EI AMPA')
MFLinearInput(pop_e2, pop_i, ei_ampa, name='EI AMPA 2')
# I->I GABA
MFLinearInput(pop_i,
pop_i, {
IP.GM: g_GABA_I,
IP.VREV: V_I,
IP.TAU: tau_GABA,
},
name='II GABA',
connection=Connection.all_to_others())
# I->E GABA
ie_gaba = {
IP.GM: g_GABA_E,
IP.VREV: V_I,
IP.TAU: tau_GABA,
}
MFLinearInput(pop_i, pop_e1, ie_gaba, name='IE GABA 1')
MFLinearInput(pop_i, pop_e2, ie_gaba, name='IE GABA 2')
return MFSystem(pop_e1, pop_e2, pop_i, name="Brunel Wang 2001")
def no_subpopulation():
# brunel 1999 system, one up state pop
initials = {'nu_e': 3 * Hz, 'nu_i': 9 * Hz}
pop_e = MFLinearPopulation(800, {
PP.GM: params_standard['E']['g_L'],
PP.VL: params_standard['E']['V_L'],
PP.CM: params_standard['E']['C_m'],
PP.VTHR: params_standard['E']['V_th'],
PP.VRES: params_standard['E']['V_reset'],
PP.TAU_RP: params_standard['E']['t_ref']
}, name='E')
pop_i = MFLinearPopulation(200, {
PP.GM: params_standard['I']['g_L'],
PP.VL: params_standard['I']['V_L'],
PP.CM: params_standard['I']['C_m'],
PP.VTHR: params_standard['I']['V_th'],
PP.VRES: params_standard['I']['V_reset'],
PP.TAU_RP: params_standard['I']['t_ref']
}, name='I')
pop_e.rate = initials['nu_e']
pop_e.v_mean = -51. * mV
pop_i.rate = initials['nu_i']
pop_i.v_mean = -55. * mV
system = MFSystem(pop_e, pop_i, name='EI')
# noise pops
source_e_noise = MFStaticInput(params_standard['E']['Cext'], params_standard['E']['nu_ext'], pop_e, {
IP.GM: params_standard['E']['gAMPA'],
IP.VREV: params_standard['E']['VE'],
IP.TAU: params_standard['E']['tau_AMPA'],
}, name='E_noise')
source_i_noise = MFStaticInput(params_standard['I']['Cext'], params_standard['I']['nu_ext'], pop_i, {
IP.GM: params_standard['I']['gAMPA'],
IP.VREV: params_standard['I']['VE'],
IP.TAU: params_standard['I']['tau_AMPA'],
}, name='I_noise')
# E->E NMDA
source_ee_nmda = MFLinearSTPNMDAInput(pop_e, pop_e, {
IP.BETA: params_standard['E']['beta'],
IP.GAMMA: params_standard['E']['gamma'],
IP.GM: params_standard['E']['gNMDA'],
IP.VREV: params_standard['E']['VE'],
IP.TAU: params_standard['E']['tau_NMDA'],
IP.W: 1,
IP.TAU_F: 1000 * ms,
IP.TAU_D: 150 * ms,
IP.U: 1,
}, name='EE Nmda')
# E->I NMDA
source_ie_nmda = MFLinearSTPNMDAInput(pop_e, pop_i, {
IP.BETA: params_standard['I']['beta'],
IP.GAMMA: params_standard['I']['gamma'],
IP.GM: params_standard['I']['gNMDA'],
IP.VREV: params_standard['I']['VE'],
IP.TAU: params_standard['I']['tau_NMDA'],
IP.W: 1,
IP.TAU_F: 1000 * ms,
IP.TAU_D: 150 * ms,
IP.U: 1,
}, name='IE Nmda')
# I->I GABA
source_ii_gaba = MFLinearInput(pop_i, pop_i, {
IP.GM: params_standard['I']['gGABA'],
IP.VREV:params_standard['I']['VI'],
IP.TAU: params_standard['I']['tau_GABA'],
}, name='II Gaba')
# I->E GABA
source_ei_gaba = MFLinearInput(pop_i, pop_e, {
IP.GM: params_standard['E']['gGABA'],
IP.VREV: params_standard['E']['VI'],
IP.TAU: params_standard['E']['tau_GABA'],
}, name='EI Gaba')
return system
def one_subpopulation(w_plus_val=2.5):
# brunel 1999 system, one up state pop
ff = .1
w_plus = w_plus_val
w_min = 1. - ff * (w_plus - 1.) / (1. - ff)
initials = {'nu_plus': 25 * Hz, 'nu_min': 1.5 * Hz, 'nu_i': 9 * Hz}
pop_e1 = MFLinearPopulation(800 * ff, {
PP.GM: params_standard['E']['g_L'],
PP.VL: params_standard['E']['V_L'],
PP.CM: params_standard['E']['C_m'],
PP.VTHR: params_standard['E']['V_th'],
PP.VRES: params_standard['E']['V_reset'],
PP.TAU_RP: params_standard['E']['t_ref']
}, name='Eup')
pop_e2 = MFLinearPopulation(800 * (1. - ff), {
PP.GM: params_standard['E']['g_L'],
PP.VL: params_standard['E']['V_L'],
PP.CM: params_standard['E']['C_m'],
PP.VTHR: params_standard['E']['V_th'],
PP.VRES: params_standard['E']['V_reset'],
PP.TAU_RP: params_standard['E']['t_ref']
}, name='Edown')
pop_i = MFLinearPopulation(200, {
PP.GM: params_standard['I']['g_L'],
PP.VL: params_standard['I']['V_L'],
PP.CM: params_standard['I']['C_m'],
PP.VTHR: params_standard['I']['V_th'],
PP.VRES: params_standard['I']['V_reset'],
PP.TAU_RP: params_standard['I']['t_ref']
}, name='I')
pop_e1.rate = initials['nu_plus']
pop_e1.v_mean = -51. * mV
pop_e2.rate = initials['nu_min']
pop_e2.v_mean = -55. * mV
pop_i.rate = initials['nu_i']
pop_i.v_mean = -55. * mV
system = MFSystem(pop_e1, pop_e2, pop_i, name='Brunel')
# noise pops
source_e_noise1 = MFStaticInput(params_standard['E']['Cext'], params_standard['E']['nu_ext'], pop_e1, {
IP.GM: params_standard['E']['gAMPA'],
IP.VREV: params_standard['E']['VE'],
IP.TAU: params_standard['E']['tau_AMPA'],
}, name='E_noise1')
source_e_noise2 = MFStaticInput(params_standard['E']['Cext'], params_standard['E']['nu_ext'], pop_e2, {
IP.GM: params_standard['E']['gAMPA'],
IP.VREV: params_standard['E']['VE'],
IP.TAU: params_standard['E']['tau_AMPA'],
}, name='E_noise2')
source_i_noise = MFStaticInput(params_standard['I']['Cext'], params_standard['I']['nu_ext'], pop_i, {
IP.GM: params_standard['I']['gAMPA'],
IP.VREV: params_standard['I']['VE'],
IP.TAU: params_standard['I']['tau_AMPA'],
}, name='I_noise')
# E->E NMDA
ee_nmda = MFParameters({
IP.BETA: params_standard['E']['beta'],
IP.GAMMA: params_standard['E']['gamma'],
IP.GM: params_standard['E']['gNMDA'],
IP.VREV: params_standard['E']['VE'],
IP.TAU: params_standard['E']['tau_NMDA'],
IP.TAU_F: 1000 * ms,
IP.TAU_D: 150 * ms,
IP.U: 1,
})
source_ee_nmda1 = MFLinearSTPNMDAInput(pop_e1, pop_e1, ee_nmda + {
IP.W: w_plus
}, name='EE Nmda1')
source_ee_nmda12 = MFLinearSTPNMDAInput(pop_e2, pop_e1, ee_nmda + {
IP.W: w_min
}, name='EE Nmda12')
source_ee_nmda2 = MFLinearSTPNMDAInput(pop_e1, pop_e2, ee_nmda + {
IP.W: w_min
}, name='EE Nmda2')
source_ee_nmda22 = MFLinearSTPNMDAInput(pop_e2, pop_e2, ee_nmda + {
IP.W: (w_plus * ff + (1. - 2. * ff) * w_min) / (1 - ff)
}, name='EE Nmda22')
# E->I NMDA
ei_nmda = {
IP.BETA: params_standard['I']['beta'],
IP.GAMMA: params_standard['I']['gamma'],
IP.GM: params_standard['I']['gNMDA'],
IP.VREV: params_standard['I']['VE'],
IP.TAU: params_standard['I']['tau_NMDA'],
IP.W: 1,
IP.TAU_F: 1000 * ms,
IP.TAU_D: 150 * ms,
IP.U: 1,
}
source_ie_nmda = MFLinearSTPNMDAInput(pop_e1, pop_i, ei_nmda, name='IE Nmda')
source_ie_nmda2 = MFLinearSTPNMDAInput(pop_e2, pop_i, ei_nmda, name='IE Nmda2')
# I->I GABA
source_ii_gaba = MFLinearInput(pop_i, pop_i, {
IP.GM: params_standard['I']['gGABA'],
IP.VREV: params_standard['I']['VI'],
IP.TAU: params_standard['I']['tau_GABA'],
}, name='II Gaba')
# I->E GABA
source_ei_gaba1 = MFLinearInput(pop_i, pop_e1, {
IP.GM: params_standard['E']['gGABA'],
IP.VREV: params_standard['E']['VI'],
IP.TAU: params_standard['E']['tau_GABA'],
}, name='EI Gaba')
source_ei_gaba2 = MFLinearInput(pop_i, pop_e2, {
IP.GM: params_standard['E']['gGABA'],
IP.VREV: params_standard['E']['VI'],
IP.TAU: params_standard['E']['tau_GABA'],
}, name='EI Gaba2')
return system