def model(time, time_stim, rate_stim, w_e, w_i, w_ie, I_e, I_i_sigma=0.01,
seed=None):
"""Model some BRAINS!"""
time = time * second
time_stim = time_stim * second
# Network
N = 1000
N_e = int(N * 0.8)
N_i = int(N * 0.2)
N_stim = int(N * 0.2)
r_e = 10 * Hz
r_i = r_e
cdelay = 2 * ms
w_e = w_e * msiemens
w_i = w_i * msiemens
w_ie = w_ie / N_i * msiemens
w_ee = 0 / N_e * msiemens
w_ii = 0.1 / N_i * msiemens
w_m = 0 / N_e * msiemens # Read ref 47 to get value
# --
# Model
np.random.seed(seed)
time_step = 0.1 * ms
decimals = 4
# --
# cell biophysics
# WB (I)
I_i = 1.1 # * uamp
I_i = np.random.normal(I_i, I_i_sigma, N_i) * uamp
if I_e is None:
I_e = (0.25, .25)
# After-hyperpolaization (AHP)
ahp = 5
area_wb = 1 * cm ** 2
Cm_wb = (1 * ufarad * cm ** -2) * area_wb
Cm = 1 * uF # /cm2
gL_wb = (0.1 * msiemens * cm ** -2) * area_wb
EL_wb = -70 * mV
Vt_wb = -52 * mV
ENa_wb = 55 * mV
gNa_wb = (35 * msiemens * cm ** -2) * area_wb
EK_wb = -90 * mV
gK_wb = 9 * msiemens
ESyn_wb = -75 * mV
gSyn_wb = (0.1 / N_i) * msiemens
# E
taue_hh = 5 * ms
taui_hh = 10 * ms
win_hh = 26 * nsiemens
# HH (E)
Cm = 1 * uF # /cm2
g_Na = 100 * msiemens
g_K = 80 * msiemens
g_l = 0.1 * msiemens
V_Na = 50 * mV
V_K = -100 * mV
V_l = -67 * mV
V_thresh = 20 * mV
# synapse biophysics
tau_r_ampa = 0.2 * ms
tau_d_ampa = 2 * ms
tau_r_gaba = 0.5 * ms
tau_d_gaba = 10 * ms
tau_r_nmda = 1 * ms
tau_d_nmda = 100 * ms
V_i = -80 * mV
V_e = 0 * mV
# --
# Eqs
wb = """
dv/dt = (-INa - IK - IL - I_syn + I) / Cm_wb : volt
""" + """
INa = gNa_wb * m**3 * h * (v-ENa_wb) : amp
m = alpham / (alpham + betam) : 1
dh/dt = ahp * (alphah * (1 - h) - betah * h) : 1
alpham = (-0.1/mV) * (v + 35*mV) /
(exp(-0.1/mV * (v + 35*mV)) - 1)/ms : Hz
betam = 4 * exp(-(v + 60*mV) / (18*mV))/ms : Hz
alphah = 0.07 * exp(-(v + 58*mV) / (20*mV))/ms : Hz
betah = 1.0 / (exp(-0.1/mV * (v + 28*mV)) + 1)/ms : Hz
""" + """
IK = gK_wb * n**4 * (v - EK_wb) : amp
dn/dt = ahp * (alphan * (1 - n) - (betan * n)) : 1
alphan = -0.01/mV * (v + 34*mV) /
(exp(-0.1/mV * (v + 34*mV)) - 1)/ms : Hz
betan = 0.125 * exp(-(v + 44*mV) / (80*mV))/ms : Hz
""" + """
IL = gL_wb * (v - EL_wb) : amp
""" + """
I_syn = g_e * (v - V_e) +
g_i * (v - ESyn_wb) : amp
g_e : siemens
g_i : siemens
""" + """
I : amp
theta : 1
"""
hh = """
dV/dt = (I_Na + I_K + I_l + I_m + I_syn + I) / Cm : volt
""" + """
I_Na = g_Na * (m ** 3) * h * (V_Na - V) : amp
m = a_m / (a_m + b_m) : 1
a_m = (0.32 * (54 + V/mV)) /
(1 - exp(-0.25 * (V/mV + 54))) / ms : Hz
b_m = (0.28 * (27 + V/mV)) / (exp(0.2 * (V/mV + 27)) - 1) / ms : Hz
h = clip(1 - 1.25 * n, 0, inf) : 1
""" + """
I_K = g_K * n ** 4 * (V_K - V) : amp
dn/dt = (a_n - (a_n * n)) - b_n * n : 1
a_n = (0.032 * (52 + V/mV)) /
(1 - exp(-0.2 * (V/mV + 52))) / ms : Hz
b_n = 0.5 * exp(-0.025 * (57 + V/mV)) / ms : Hz
""" + """
I_l = g_l * (V_l - V) : amp
""" + """
I_m = w_m * w * (V_K - V) : amp
dw/dt = (w_inf - w) / tau_w/ms : 1
w_inf = 1 / (1 + exp(-1 * (V/mV + 35) / 10)) : 1
tau_w = 400 / ((3.3 * exp((V/mV + 35)/20)) +
(exp(-1 * (V/mV + 35) / 20))) : 1
""" + """
I_syn = g_e * (V_e - V) +
g_i * (V_i - V) : amp
g_e : siemens
g_i : siemens
""" + """
I_stim = g_s * (V_e - V) : amp
g_s : siemens
""" + """
I : amp
"""
syn_e_in = """
dg/dt = -g / tau_d_ampa : siemens
g_e_post = g : siemens (summed)
"""
syn_e_stim = """
dg/dt = -g / tau_d_ampa : siemens
g_s_post = g : siemens (summed)
"""
syn_e = """
dg/dt = -g * 1 / (tau_d_ampa - tau_r_ampa): siemens
g_e_post = g : siemens (summed)
"""
syn_i = """
dg/dt = -g * 1 / (tau_d_gaba - tau_r_gaba) : siemens
g_i_post = g : siemens (summed)
"""
# --
# Build networks
P_i = NeuronGroup(
N_i,
model=wb,
threshold='v >= V_thresh',
refractory=2 * ms,
method='exponential_euler'
)
P_e = NeuronGroup(
N_e, model=hh,
threshold='V >= V_thresh',
refractory=3 * ms,
method='exponential_euler'
)
P_i.I = I_i
P_e.I = np.random.uniform(I_e[0], I_e[1], N_e) * uamp
P_e.V = V_l
P_i.v = EL_wb
P_e_back = PoissonGroup(N_e, rates=r_e)
# --
# Stimulus
time_stim = time_stim / second
window = 500 / 1000.
t_min = time_stim - window / 2
t_max = time_stim + window / 2
stdev = 100 / 1000. # 100 ms
# rate = 5 # Hz
k = N_stim * int(rate_stim / 2)
ts, idxs = gaussian_impulse(time_stim, t_min,
t_max, stdev, N_stim, k,
decimals=decimals)
P_stim = SpikeGeneratorGroup(N_stim, idxs, ts * second)
# --
# Connections
# External
C_stim_e = Synapses(
P_stim, P_e, model=syn_e_stim,
pre='g += w_e', connect='i == j'
)
C_back_e = Synapses(
P_e_back, P_e, model=syn_e_in,
pre='g += w_e', connect='i == j'
)
# Internal
C_ie = Synapses(P_i, P_e, model=syn_i, pre='g += w_ie', delay=cdelay)
C_ie.connect(True, p=0.4)
C_ii = Synapses(P_i, P_i, model=syn_i, pre='g += gSyn_wb', connect=True)
# --
# Record
spikes_i = SpikeMonitor(P_i)
spikes_e = SpikeMonitor(P_e)
spikes_stim = SpikeMonitor(P_stim)
pop_e = PopulationRateMonitor(P_e)
pop_i = PopulationRateMonitor(P_i)
voltages_e = StateMonitor(P_e, ('V', 'g_e', 'g_i', 'g_s'), record=range(11, 31))
voltages_i = StateMonitor(P_i, ('v', 'g_i'), record=range(11, 31))
# --
# Go!
defaultclock.dt = time_step
run(time, report='text')
return {
'spikes_i': spikes_i,
'spikes_e': spikes_e,
'spikes_stim': spikes_stim,
'pop_e': pop_e,
'pop_i': pop_i,
'voltages_e': voltages_e,
'voltages_i': voltages_i
}
def model(time, time_stim, rate_stim, w_e, w_i, w_ei, w_ie, seed=None):
# def model(time, stim, w_e, w_i, w_ei, w_ie, seed=None):
"""Model some BRAINS!"""
time = time * second
time_stim = time_stim * second
# Network
N = 1000
N_e = int(N * 0.8)
N_i = int(N * 0.2)
N_stim = int(N * 0.2)
r_e = 10 * Hz
r_i = r_e
delay = 2 * ms
p_ei = 0.4
p_ie = 0.4
p_ii = 1.0
w_e = w_e * msiemens
w_i = w_i * msiemens
w_ei = w_ei / (p_ei * N_e) * msiemens
w_ie = w_ie / (p_ie * N_i) * msiemens
w_ii = 0.0 / N_i * msiemens
w_m = 0.0 * msiemens # Read ref 47 to get value
# --
# Model
np.random.seed(seed)
time_step = 0.1 * ms
decimals = 4
# --
# cell biophysics
I_e = [0.01, 0.1]
I_i = [0.01, 0.1]
Cm = 1 * uF # /cm2
g_Na = 100 * msiemens
g_K = 80 * msiemens
g_l = 0.1 * msiemens
V_Na = 50 * mV
V_K = -100 * mV
V_l = -67 * mV
V_thresh = 20 * mV
# synapse biophysics
tau_r_ampa = 0.2 * ms
tau_d_ampa = 2 * ms
tau_r_gaba = 0.5 * ms
tau_d_gaba = 10 * ms
tau_r_nmda = 1 * ms
tau_d_nmda = 100 * ms
V_i = -80 * mV
V_e = 0 * mV
# --
# Eqs
hh = """
dV/dt = (I_Na + I_K + I_l + I_m + I_syn + I) / Cm : volt
""" + """
I_Na = g_Na * (m ** 3) * h * (V_Na - V) : amp
m = a_m / (a_m + b_m) : 1
a_m = (0.32 * (54 + V/mV)) / (1 - exp(-0.25 * (V/mV + 54))) / ms : Hz
b_m = (0.28 * (27 + V/mV)) / (exp(0.2 * (V/mV + 27)) - 1) / ms : Hz
h = clip(1 - 1.25 * n, 0, inf) : 1
""" + """
I_K = g_K * n ** 4 * (V_K - V) : amp
dn/dt = (a_n - (a_n * n)) - b_n * n : 1
a_n = (0.032 * (52 + V/mV)) / (1 - exp(-0.2 * (V/mV + 52))) / ms : Hz
b_n = 0.5 * exp(-0.025 * (57 + V/mV)) / ms : Hz
""" + """
I_l = g_l * (V_l - V) : amp
""" + """
I_m = w_m * w * (V_K - V) : amp
dw/dt = (w_inf - w) / tau_w/ms : 1
w_inf = 1 / (1 + exp(-1 * (V/mV + 35) / 10)) : 1
tau_w = 400 / ((3.3 * exp((V/mV + 35)/20)) + (exp(-1 * (V/mV + 35) / 20))) : 1
""" + """
I_syn = g_e * (V_e - V) +
g_i * (V_i - V) : amp
g_e : siemens
g_i : siemens
""" + """
I_stim = g_s * (V_e - V) : amp
g_s : siemens
""" + """
I : amp
"""
syn_e_in = """
dg/dt = -g / tau_d_ampa : siemens
g_e_post = g : siemens (summed)
"""
syn_e_stim = """
dg/dt = -g / tau_d_ampa : siemens
g_s_post = g : siemens (summed)
"""
syn_e = """
dg/dt = -g * 1 / (tau_d_ampa - tau_r_ampa): siemens
g_e_post = g : siemens (summed)
"""
syn_i = """
dg/dt = -g * 1 / (tau_d_gaba - tau_r_gaba) : siemens
g_i_post = g : siemens (summed)
"""
# --
# Build networks
P_e = NeuronGroup(
N_e, model=hh,
threshold='V >= V_thresh',
refractory=3 * ms,
method='exponential_euler'
)
P_i = NeuronGroup(
N_i,
model=hh,
threshold='V >= V_thresh',
refractory=3 * ms,
method='exponential_euler'
)
P_e.V = V_l
P_i.V = V_l
P_e.I = np.random.uniform(I_e[0], I_e[1], N_e) * uamp
P_i.I = np.random.uniform(I_i[0], I_i[1], N_i) * uamp
P_e_back = PoissonGroup(N_e, rates=r_e)
P_i_back = PoissonGroup(N_i, rates=r_i)
# --
# Stimulus
time_stim = time_stim / second
window = 500 / 1000.
t_min = time_stim - window / 2
t_max = time_stim + window / 2
stdev = 100 / 1000. # 100 ms
rate = 5 # Hz
k = N_stim * int(rate / 2)
ts, idxs = gaussian_impulse(time_stim, t_min, t_max, stdev, N_stim, k,
decimals=decimals)
P_stim = SpikeGeneratorGroup(N_stim, idxs, ts * second)
# --
# Connections
# External
C_stim_e = Synapses(P_stim, P_e, model=syn_e_stim,
pre='g += w_e', connect='i == j')
C_back_e = Synapses(P_e_back, P_e, model=syn_e_in, pre='g += w_e',
connect='i == j')
C_back_i = Synapses(P_i_back, P_i, model=syn_e_in, pre='g += w_i',
connect='i == j')
# Internal
C_ei = Synapses(P_e, P_i, model=syn_e, pre='g += w_ei', delay=delay)
C_ei.connect(True, p=p_ei)
C_ie = Synapses(P_i, P_e, model=syn_i, pre='g += w_ie', delay=delay)
C_ie.connect(True, p=p_ie)
C_ii = Synapses(P_i, P_i, model=syn_i, pre='g += w_ii', delay=delay)
C_ii.connect(True, p=p_ii)
# --
# Record
spikes_i = SpikeMonitor(P_i)
spikes_e = SpikeMonitor(P_e)
spikes_stim = SpikeMonitor(P_stim)
pop_e = PopulationRateMonitor(P_e)
pop_i = PopulationRateMonitor(P_i)
voltages_e = StateMonitor(
P_e, ('V', 'g_e', 'g_i', 'g_s'), record=range(11, 31))
voltages_i = StateMonitor(P_i, ('V', 'g_e', 'g_i'), record=range(11, 31))
# --
# Go!
defaultclock.dt = time_step
run(time, report='text')
return {
'spikes_i': spikes_i,
'spikes_e': spikes_e,
'spikes_stim': spikes_stim,
'pop_e': pop_e,
'pop_i': pop_i,
'voltages_e': voltages_e,
'voltages_i': voltages_i
}
def model(time, time_stim, rate_stim,
w_e, w_i, w_ei, w_ie, w_ee, w_ii,
I_e, I_i, I_i_sigma, I_e_sigma,
stdp, seed=None):
"""Model some BRAINS!"""
time = time * second
time_stim = time_stim * second
# Network
N = 400
N_e = int(N * 0.8)
N_i = int(N * 0.2)
N_stim = N_e # int(N * 0.2)
r_e = 0 * Hz
r_i = r_e
delay = 2 * ms
p_ei = 0.1
p_ie = 0.1
p_ee = 0.1
p_ii = 0.6
w_e = w_e / (p_ee * N_e) * msiemens
w_i = w_i * msiemens
w_ei = w_ei / (p_ei * N_e) * msiemens
w_ie = w_ie / (p_ie * N_i) * msiemens
w_ee = w_ee / (p_ee * N_e) * msiemens
w_ii = w_ii / (p_ii * N_i) * msiemens
w_m = 0 / N_e * msiemens # Read ref 47 to get value
# --
# Model
np.random.seed(seed)
time_step = 0.01 * ms
decimals = 4
# --
# Fixed
# cell
Cm = 1 * uF # /cm2
g_Na = 100 * msiemens
g_K = 80 * msiemens
g_l = 0.1 * msiemens
V_Na = 50 * mV
V_K = -100 * mV
V_l = -67 * mV
# syn
tau_r_ampa = 0.2 * ms
tau_d_ampa = 2 * ms
tau_r_gaba = 0.5 * ms
tau_d_gaba = 10 * ms
tau_r_nmda = 1 * ms
tau_d_nmda = 100 * ms
V_thresh = 20 * mV
V_i = -80 * mV
V_e = 0 * mV
hh = """
dV/dt = (I_Na + I_K + I_l + I_m + I_syn + I) / Cm : volt
""" + """
I_Na = g_Na * (m ** 3) * h * (V_Na - V) : amp
m = a_m / (a_m + b_m) : 1
a_m = (0.32 * (54 + V/mV)) / (1 - exp(-0.25 * (V/mV + 54))) / ms : Hz
b_m = (0.28 * (27 + V/mV)) / (exp(0.2 * (V/mV + 27)) - 1) / ms : Hz
h = clip(1 - 1.25 * n, 0, inf) : 1
""" + """
I_K = g_K * n ** 4 * (V_K - V) : amp
dn/dt = (a_n - (a_n * n)) - b_n * n : 1
a_n = (0.032 * (52 + V/mV)) / (1 - exp(-0.2 * (V/mV + 52))) / ms : Hz
b_n = 0.5 * exp(-0.025 * (57 + V/mV)) / ms : Hz
""" + """
I_l = g_l * (V_l - V) : amp
""" + """
I_m = w_m * w * (V_K - V) : amp
dw/dt = (w_inf - w) / tau_w/ms : 1
w_inf = 1 / (1 + exp(-1 * (V/mV + 35) / 10)) : 1
tau_w = 400 / ((3.3 * exp((V/mV + 35)/20)) + (exp(-1 * (V/mV + 35) / 20))) : 1
""" + """
I_syn = g_e * (V_e - V) +
g_ee * (V_e - V) +
g_i * (V_i - V) +
g_s * (V_e - V) : amp
dg_e/dt = -g_e / tau_d_ampa : siemens
dg_ee/dt = -g_ee / tau_d_ampa : siemens
dg_i/dt = -g_i / tau_d_gaba : siemens
dg_s/dt = -g_s / tau_d_ampa : siemens
I : amp
"""
P_e = NeuronGroup(
N_e, model=hh,
threshold='V >= V_thresh',
refractory=3 * ms
)
P_i = NeuronGroup(
N_i,
model=hh,
threshold='V >= V_thresh',
refractory=3 * ms
)
P_e.V = 'randn() * 0.1 * V_l'
P_i.V = 'randn() * 0.1 * V_l'
P_e.g_e = 'randn() * 0.1 * w_e'
P_e.g_ee = 'randn() * 0.1 * w_ee'
P_e.g_i = 'randn() * 0.1 * w_ie'
P_i.g_i = 'randn() * 0.1 * w_ii'
if np.allclose(I_e_sigma, 0.0):
P_e.I = I_e * uamp
else:
P_e.I = np.random.normal(I_e, I_e_sigma, N_e) * uamp
if np.allclose(I_i_sigma, 0.0):
P_i.I = I_i * uamp
else:
P_i.I = np.random.normal(I_i, I_i_sigma, N_i) * uamp
P_e_back = PoissonGroup(N_e, rates=r_e)
P_i_back = PoissonGroup(N_i, rates=r_i)
# --
# Stimulus
time_stim = time_stim / second
window = 500 / 1000.
t_min = time_stim - window / 2
t_max = time_stim + window / 2
stdev = 100 / 1000. # 100 ms
k = N_stim * int(rate_stim / 2)
ts, idxs = gaussian_impulse(
time_stim, t_min,
t_max, stdev, N_stim, k,
decimals=decimals
)
P_stim = SpikeGeneratorGroup(N_stim, idxs, ts * second)
# --
# Syn
# External
C_stim_e = Synapses(P_stim, P_e, pre='g_s += w_e')
C_stim_e.connect(True, p=p_ee)
# Internal
C_ei = Synapses(P_e, P_i, pre='g_e += w_ei', delay=delay)
C_ei.connect(True, p=p_ei)
C_ie = Synapses(P_i, P_e, pre='g_i += w_ie', delay=delay)
C_ie.connect(True, p=p_ie)
C_ii = Synapses(P_i, P_i, pre='g_i += w_ii', delay=delay)
C_ii.connect(True, p=p_ii)
C_ee = Synapses(P_e, P_e, pre='g_ee += w_ee', delay=delay)
C_ee.connect(True, p=p_ee)
if stdp:
# params
tau_pre = 20 * ms
tau_post = tau_pre
gmax = w_ee * 10
delta_pre = 0.005
delta_post = -delta_pre * tau_pre / tau_post * 1.05
delta_pre *= gmax
delta_post *= gmax
C_ee = Synapses(
P_e, P_e,
"""
w_stdp : siemens
dApre/dt = -Apre / tau_pre : siemens (event-driven)
dApost/dt = -Apost / tau_post : siemens (event-driven)
""",
pre="""
g_ee += w_stdp
Apre += delta_pre
w_stdp = clip(w_stdp + delta_pre, 0, gmax)
""",
post="""
Apost += delta_post
w_stdp = clip(w_stdp + delta_pre, 0, gmax)
"""
)
C_ee.connect(True, p=p_ee)
# --
# Record
spikes_i = SpikeMonitor(P_i)
spikes_e = SpikeMonitor(P_e)
spikes_stim = SpikeMonitor(P_stim)
pop_stim = PopulationRateMonitor(P_stim)
pop_e = PopulationRateMonitor(P_e)
pop_i = PopulationRateMonitor(P_i)
voltages_e = StateMonitor(P_e,
('V', 'g_e', 'g_i', 'g_s', 'g_ee'), record=True)
voltages_i = StateMonitor(P_i, ('V', 'g_e', 'g_i'), record=range(11, 31))
# --
# Go!
defaultclock.dt = time_step
run(time, report='text')
return {
'spikes_i': spikes_i,
'spikes_e': spikes_e,
'spikes_stim': spikes_stim,
'pop_e': pop_e,
'pop_stim' : pop_stim,
'pop_i': pop_i,
'voltages_e': voltages_e,
'voltages_i': voltages_i
}
