def set_conductance_monitor(self):
"""yep"""
self.mon_econd_e = bb.StateMonitor(self.Pe,
'ge',
record=self.nrn_meas_e)
self.mon_icond_e = bb.StateMonitor(self.Pe,
'gi',
record=self.nrn_meas_e)
self.mon_econd_i = bb.StateMonitor(self.Pi,
'ge',
record=self.nrn_meas_i)
self.mon_icond_i = bb.StateMonitor(self.Pi,
'gi',
record=self.nrn_meas_i)
self.network.add(self.mon_econd_e, self.mon_icond_e, self.mon_econd_i,
self.mon_icond_i)
def simulate_WORM_neuron(input_current,
simulation_time=5 * b2.ms,
v_leak=V_LEAK,
g_leak=G_LEAK,
c_m=C_M,
rest_pot=R_POT,
tau=MEMBRANE_TIME_SCALE,
f_t=FIRING_THRESHOLD):
# differential equation of neuron model
eqs = """
dv/dt =
( g_leak * (v_leak - v) + input_current(t,i) ) / c_m : volt
"""
# LIF neuron using Brian2 library
neuron = b2.NeuronGroup(2, model=eqs, threshold='v>f_t', method="linear")
neuron.v = rest_pot # set initial value
# monitoring membrane potential of neuron and injecting current
state_monitor = b2.StateMonitor(neuron, ["v"], record=True)
S = b2.Synapses(neuron, neuron, model='w : volt', on_pre='v += w')
S.connect(i=0, j=1)
S.w = 0.01 * b2.mV
# run the simulation
b2.run(simulation_time)
return state_monitor
def main3():
# Adding Spikes
bs.start_scope()
tau = 10 * bs.ms
eqs = '''
dv/dt = (1-v)/tau : 1
'''
# conditions for spiking models
threshold = 'v>0.8'
reset = 'v = -0.8'
G = bs.NeuronGroup(1, eqs, threshold=threshold, reset=reset, method='exact')
M = bs.StateMonitor(G, 'v', record=0)
bs.run(50 * bs.ms)
plt.plot(M.t / bs.ms, M.v[0])
plt.xlabel('Time (ms)')
plt.ylabel('v')
plt.show()
# you can also add spike monitor
spike_monitor = bs.SpikeMonitor(G)
bs.run(50 * bs.ms)
print(f"Spike Times: {spike_monitor.t[:]}")
def main1():
bs.start_scope()
tau = 10 * bs.ms
# equations must end with : unit
# unit is the SI unit of that variable
# the unit is 1 since the number "1" is unitless
# v represents voltage, but we just keep it unitless for simplicity
# 1/s not part of the unit since the unit represents the unit of the variable itself
# rather than the unit of the equation
eqs = '''
dv/dt = (1-v)/tau: 1
'''
G = bs.NeuronGroup(1, model=eqs, method='exact')
# record : bool, sequence of ints
# Which indices to record, nothing is recorded for ``False``,
# everything is recorded for ``True`` (warning: may use a great deal of
# memory), or a specified subset of indices.
M = bs.StateMonitor(G, 'v', record=0)
print('Before v = %s' % G.v[0])
bs.run(100 * bs.ms) # runs the simulation for 100ms
print('After v = %s' % G.v[0])
plt.plot(M.t / bs.ms, M.v[0])
plt.xlabel('Time (ms)')
plt.ylabel('v')
plt.show()
def main4():
# Incorporation of refractory period
bs.start_scope()
tau = 10 * bs.ms
# the (unless refractory) is necessary
# refer to the documentation for more detail
eqs = '''
dv/dt = (1-v)/tau : 1 (unless refractory)
'''
equation = bs.Equations(eqs)
# conditions for spiking models
threshold = 'v>0.8'
reset = 'v = -0.8'
refractory = 5 * bs.ms
G = bs.NeuronGroup(1, eqs, threshold=threshold, reset=reset, method='exact', refractory=refractory)
state_monitor = bs.StateMonitor(G, 'v', record=0)
spike_monitor = bs.SpikeMonitor(G)
bs.run(50 * bs.ms)
plt.plot(state_monitor.t / bs.ms, state_monitor.v[0])
plt.xlabel('Time (ms)')
plt.ylabel('v')
plt.show()
def make_classification_network(self, number_of_stimuli, network_name):
if network_name not in self.networks:
network_size = number_of_stimuli * self.number_of_neurons
count_mat = np.zeros((int(self.stimulus_duration / ms * 10), network_size), int)
target = b2.NeuronGroup(N=number_of_stimuli, model=self.eqs, threshold='v>threshold', reset='v=0',
namespace={'tau': self.tau, 'threshold': self.threshold})
driving = b2.SpikeGeneratorGroup(N=network_size,
indices=[0], times=[0 * ms])
# counts = b2.TimedArray(values=_count_mat, dt=b2.defaultclock.dt)
synapses = b2.Synapses(source=driving, target=target,
model='w: 1', on_pre='v+=w*counts(t, i)')
i = np.arange(network_size)
j = np.repeat(range(number_of_stimuli), self.number_of_neurons)
synapses.connect(j=j, i=i)
synapses.w = np.tile(self.weights, reps=number_of_stimuli)
spikes = b2.SpikeMonitor(target, record=True)
voltage = b2.StateMonitor(target, 'v', record=True)
net = b2.Network([target, driving, synapses, spikes, voltage])
net.store()
self.networks[network_name] = dict(net=net,
count_mat=count_mat,
synapses=synapses,
v_mon=voltage,
spike_mon=spikes,
number_of_stimuli=number_of_stimuli,
driving=driving)
else:
self.networks[network_name]['synapses'].w = np.tile(self.weights, reps=number_of_stimuli)
def run_brian_sim(stim, dt, init_values, param_dict, method = 'exact'):
# Model specification
eqs = brian2.Equations("")
eqs += brian2.Equations("dV/dt = 1 / C * (Ie(t) + I_0 + I_1 - G * (V - El)) : volt (unless refractory)")
eqs += brian2.Equations("dTh_s/dt = -b_s * Th_s : volt (unless refractory)")
eqs += brian2.Equations("dTh_v/dt = a_v * (V - El) - b_v * (Th_v - Th_inf) : volt (unless refractory)")
eqs += brian2.Equations("dI_0/dt = -k_0 * I_0 : amp (unless refractory)")
eqs += brian2.Equations("dI_1/dt = -k_1 * I_1 : amp (unless refractory)")
reset = ""
reset = "\n".join([reset, "V = a_r * V + b_r"])
reset = "\n".join([reset, "Th_s = Th_s + a_s"])
reset = "\n".join([reset, "Th_v = Th_v"])
reset = "\n".join([reset, "I_0 = R_0 * I_0 * exp(-k_0 * (t_ref - dt)) + A_0"])
reset = "\n".join([reset, "I_1 = R_1 * I_1 * exp(-k_1 * (t_ref - dt)) + A_1"])
threshold = "V > Th_v + Th_s"
refractory = param_dict['t_ref']
Ie = brian2.TimedArray(stim, dt=dt)
nrn = brian2.NeuronGroup(1, eqs, method=method, reset=reset, threshold=threshold, refractory=refractory, namespace=param_dict)
nrn.V = init_values['V'] * brian2.units.volt
nrn.Th_s = init_values['Th_s'] * brian2.units.volt
nrn.Th_v = init_values['Th_v'] * brian2.units.volt
nrn.I_0 = init_values['I_0'] * brian2.units.amp
nrn.I_1 = init_values['I_1'] * brian2.units.amp
monvars = ['V','Th_s','Th_v','I_0','I_1',]
mon = brian2.StateMonitor(nrn, monvars, record=True)
num_step = len(stim)
brian2.defaultclock.dt = dt
brian2.run(num_step * dt)
return (mon.t / brian2.units.second, mon.V[0] / brian2.units.volt, mon.Th_s[0] / brian2.units.volt, mon.Th_v[0] / brian2.units.volt, mon.I_0[0] / brian2.units.amp, mon.I_1[0] / brian2.units.amp, )
def set_current_monitor(self):
"""yep"""
self.mon_ecurr_e = bb.StateMonitor(self.Pe,
'Ie',
record=self.nrn_meas_e)
self.mon_icurr_e = bb.StateMonitor(self.Pe,
'Ii',
record=self.nrn_meas_e)
self.mon_ecurr_i = bb.StateMonitor(self.Pi,
'Ie',
record=self.nrn_meas_i)
self.mon_icurr_i = bb.StateMonitor(self.Pi,
'Ii',
record=self.nrn_meas_i)
self.network.add(self.mon_ecurr_e, self.mon_icurr_e, self.mon_ecurr_i,
self.mon_icurr_i)
def neuron_sim(stim_V=0.8):
"""simulating the neuron using brian2 library"""
# initiate stimuli timing
stimulus = br2.TimedArray(
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, stim_V, 0, 0, 0, 0, 0, 0, 0, 0, 0],
dt=100 * br2.ms)
# initiating neurons
eqs = '''
dv/dt = (-v + stimulus(t)-0.1*rand()) / tau : 1
tau : second
'''
# creating neuron group
G = br2.NeuronGroup(10, eqs, dt=0.2 * br2.ms)
# creating different tau's for the neuron model
G.tau = np.linspace(10, 100, 10) * br2.ms
# defining state monitor to record voltage
M = br2.StateMonitor(G, 'v', record=True)
# creating network
net = br2.Network(G, M)
# storing initial state
net.store()
# np array to contain data
data = np.zeros(shape=(10, 10000, 4))
# producing four repetitions
for trial in range(4):
net.restore() # Restore the initial state
net.run(2 * br2.second)
# store the results
data[:, :, trial] = M.v
return data
def simulate_GPe_cell(par_g, par_sim):
num = par_g['num']
input_current = par_g['i_ext']
b2.defaultclock.dt = par_sim['dt']
eqs = '''
i_extg = input_current(t, i): amp
ainfg = 1 / (1 + exp(-(vg - thetaag*mV) / (sigag*mV))) : 1
sinfg = 1 / (1 + exp(-(vg - thetasg*mV) / (sigsg*mV))) : 1
rinfg = 1 / (1 + exp(-(vg - thetarg*mV) / (sigrg*mV))) : 1
minfg = 1 / (1 + exp(-(vg - thetamg*mV) / (sigmg*mV))) : 1
ninfg = 1 / (1 + exp(-(vg - thetang*mV) / (signg*mV))) : 1
hinfg = 1 / (1 + exp(-(vg - thetahg*mV) / (sighg*mV))) : 1
taung = taun0g + taun1g / (1 + exp(-(vg - thngt*mV) / (sng*mV))) : second
tauhg = tauh0g + tauh1g / (1 + exp(-(vg - thhgt*mV) / (shg*mV))) : second
itg = gtg * (ainfg ** 3) * rg * (vg - vcag) : amp
inag = gnag * (minfg ** 3) * hg * (vg - vnag) : amp
ikg = gkg * (ng ** 4) * (vg - vkg) : amp
iahpg = gahpg * (vg - vkg) * cag / (cag + k1g) : amp
icag = gcag * (sinfg ** 2) * (vg - vcag) : amp
ilg = glg * (vg - vlg) : amp
membrane_Im = -(itg + inag + ikg + iahpg + icag + ilg) + i_extg : amp
dhg/dt = phihg*(hinfg-hg)/tauhg : 1
dng/dt = phing*(ninfg-ng)/taung : 1
drg/dt = phig*(rinfg-rg)/taurg : 1
dcag/dt= epsg*((-icag-itg)/pA - kcag*cag) : 1 #! pA
dvg/dt = membrane_Im / C : volt
'''
neuron = b2.NeuronGroup(
num,
eqs,
method=par_sim['integration_method'],
dt=par_sim['dt'],
threshold='vg>-20*mV',
refractory='vg>-20*mV',
namespace=par_g,
)
neuron.vg = par_g['v0']
neuron.hg = "hinfg"
neuron.ng = "ninfg"
neuron.rg = "rinfg"
neuron.cag = 0
# neuron.i_extg = par_g['iapp']
st_mon = b2.StateMonitor(neuron, ["vg", 'i_extg'], record=True)
net = b2.Network(neuron)
net.add(st_mon)
net.run(par_sim['simulation_time'])
return st_mon
def simulate_STN_cell(par, par_sim):
num = par['num']
input_current = par['i_ext']
eqs = '''
I_ext = input_current(t, i): amp
minf = 1/(1+exp(-(vs-thetam*mV)/(sigmam*mV))) : 1
hinf = 1/(1+exp(-(vs-thetah*mV)/(sigmah*mV))) : 1
ninf = 1/(1+exp(-(vs-thetan*mV)/(sigman*mV))) : 1
ainf = 1/(1+exp(-(vs-thetaa*mV)/(sigmaa*mV))) : 1
binf = 1/(1+exp((r-thetab)/sigmab))-1/(1+exp(-thetab/sigmab)) : 1
rinf = 1/(1+exp(-(vs-thetar*mV)/(sigmar*mV))) : 1
sinf = 1/(1+exp(-(vs-thetas*mV)/(sigmas*mV))) : 1
taun = taun0+taun1/(1+exp(-(vs-thn*mV)/(sigmant*mV))) : second
tauh = tauh0+tauh1/(1+exp(-(vs-thh*mV)/(sigmaht*mV))) : second
taur = taur0+taur1/(1+exp(-(vs-thr*mV)/(sigmart*mV))) : second
il = gl * (vs - vl) : amp
ina = gna * minf ** 3 * h * (vs - vna) : amp
ik = gk * n ** 4 * (vs - vk) : amp
iahp = gahp * ca / (ca + k1) * (vs - vk) : amp
ica = gca * sinf ** 2 * (vs - vca) : amp
it = gt * ainf ** 3 * binf ** 2 * (vs - vca) : amp
dh/dt = phi * (hinf - h) / tauh : 1
dn/dt = phi * (ninf - n) / taun : 1
dr/dt = phir * (rinf - r) / taur : 1
dca/dt = eps * ((-ica - it)/pA - kca* ca) : 1 #! pA
membrane_Im = -(il + ina + ik + it + ica + iahp) + I_ext : amp
dvs/dt = membrane_Im/C : volt
'''
neuron = b2.NeuronGroup(
num,
eqs,
method=par_sim['integration_method'],
dt=par_sim['dt'],
threshold='vs>-20*mV',
refractory='vs>-20*mV',
namespace=par,
)
neuron.vs = par['v0']
neuron.h = "hinf"
neuron.n = "ninf"
neuron.r = "rinf"
neuron.ca = 0
st_mon = b2.StateMonitor(neuron, ["vs", "I_ext"], record=True)
net = b2.Network(neuron)
net.add(st_mon)
net.run(par_sim['simulation_time'])
return st_mon
def make_model(self):
# Determine the simulation
if self.clamp_type == 'current':
eqs_input = '''I_inj = inj_input(t) : amp'''
elif self.clamp_type == 'dynamic':
eqs_input = '''I_exc = g_exc(t) * (Er_e - v) : amp
I_inh = g_inh(t) * (Er_i - v) : amp
I_inj = I_exc + I_inh : amp'''
tracking = ['v', 'I_inj']
# Model the neuron with differential equations
eqs = '''
# Activation gates Na channel
m = 1. / (1. + exp(-(v - Vh) / k)) : 1
Vh = 3.223725 * k - 62.615488*mV : volt
# Inactivation gates Na channel
dh/dt = 5. * (alpha_h * (1 - h)- beta_h * h) : 1
alpha_h = 0.07 * exp(-(v + 58.*mV) / (20.*mV))/ms : Hz
beta_h = 1. / (exp(-0.1/mV * (v + 28.*mV)) + 1.)/ms : Hz
# Activation gates K channel
dn/dt = 5. * (alpha_n * (1. - n) - beta_n * n) : 1
alpha_n = 0.01/mV * 10*mV / exprel(-(v + 34.*mV) / (10.*mV))/ms : Hz
beta_n = 0.125 * exp(-(v + 44.*mV) / (80.*mV))/ms : Hz
# Activation gates K3.1 channel
dn3/dt = alphan3 * (1. - n3) - betan3 * n3 : 1
alphan3 = (1. / exp(((param * ((-0.029 * v + (1.9*mV))/mV)))))/ms : Hz
betan3 = (1. / exp(((param * ((0.021 * v + (1.1*mV))/mV)))))/ms : Hz
# Currents
I_leak = -gL * (v - EL) : amp
I_Na = -gNa * m**3 * h * (v - ENa) : amp
I_K = -gK * n**4 * (v - EK) : amp
I_K3 = -gK3 * n3**4 * (v - EK) : amp
dv/dt = (I_leak + I_Na + I_K + I_K3 + I_inj) / Cm : volt
'''
# Neuron & parameter initialization
neuron = b2.NeuronGroup(1,
model=eqs + eqs_input,
method='exponential_euler',
threshold='m > 0.5',
refractory=2 * b2.ms,
reset=None,
dt=self.dt * b2.ms)
neuron.v = -65 * b2.mV
# Track the parameters during simulation
self.M = b2.StateMonitor(neuron, tracking, record=True)
self.S = b2.SpikeMonitor(neuron, record=True)
self.neuron = neuron
net = b2.Network(neuron)
net.add(self.M, self.S)
self.network = net
def init_monitors(neurons, connections, monitor_params):
"""
Initialise Brian objects monitoring state variables in the network.
"""
monitors = {
'spikes': {},
'neurons': {},
'connections': {}
}
for layer in ['input', 'layer1e']:
monitors['spikes'][layer] = b2.SpikeMonitor(neurons[layer])
if 'monitors_dt' not in monitor_params:
timestep = None
else:
timestep = monitor_params['monitors_dt']
monitors['neurons']['layer1e'] = b2.StateMonitor(
neurons['layer1e'],
['v', 'ge', 'max_ge', 'theta'],
# record=True is currently broken for standalone simulations
record=range(len(neurons['layer1e'])),
dt=timestep
)
if 'layer1vis' in neurons:
monitors['neurons']['layer1vis'] = b2.StateMonitor(
neurons['layer1vis'],
['v'],
# record=True is currently broken for standalone simulations
record=range(len(neurons['layer1vis'])),
dt=b2.second/60
)
conn = connections['input-layer1e']
n_connections = len(conn.target) * len(conn.source)
monitors['connections']['input-layer1e'] = b2.StateMonitor(
connections['input-layer1e'],
['w', 'post', 'pre'],
record=range(n_connections),
dt=timestep
)
return monitors
def StateMonitors(neuron_groups, index_str, index_record=0):
index = _neuron_group_index(index_str)
if index_str == 'input':
M = br.StateMonitor(neuron_groups[index], 'v', record=index_record, \
name=(index_str + '_v'))
return M
elif index_str == 'hidden':
Mge = br.StateMonitor(neuron_groups[index][0], 'ge', record=index_record, \
name=(index_str + '_ge' + str(index_record)))
Mv = br.StateMonitor(neuron_groups[index][0], 'v', record=index_record, \
name=(index_str + '_v' + str(index_record)))
Mu = br.StateMonitor(neuron_groups[index][0], 'u', record=index_record, \
name=(index_str + '_u' + str(index_record)))
else:
Mge = br.StateMonitor(neuron_groups[index], 'ge', record=index_record, \
name=(index_str + '_ge' + str(index_record)))
Mv = br.StateMonitor(neuron_groups[index], 'v', record=index_record, \
name=(index_str + '_v' + str(index_record)))
Mu = br.StateMonitor(neuron_groups[index], 'u', record=index_record, \
name=(index_str + '_u' + str(index_record)))
return Mv, Mu, Mge
def simulate_Thl_cell_fig3(par, par_sim):
num = par_sim['num']
i_sensory_motor = par_sim['I_sm']
# b2.set_device('cpp_standalone')
b2.start_scope()
eqs = b2.Equations('''
minfthl = 1/(1+exp(-(vt-thtmthl*mV)/(sigmthl*mV))): 1
hinfthl = 1/(1+exp((vt-thththl*mV)/(sighthl*mV))): 1
pinfthl = 1/(1+exp(-(vt-thtpthl*mV)/(sigpthl*mV))) :1
rinfthl = 1/(1+exp((vt-thtrthl*mV)/(sigrthl*mV))) :1
ahthl = ah0thl*exp(-(vt-thtahthl*mV)/(sigahthl*mV)) :1
bhthl = bh0thl/(1+exp(-(vt-thtbhthl*mV)/(sigbhthl*mV))) :1
tauhthl = 1/(ahthl+bhthl) *ms :second
taurthl = taur0thl+taur1thl*exp(-(vt-thtrtauthl*mV)/(sigrtauthl*mV)) :second
ilthl=glthl*(vt-vlthl):amp
inathl=gnathl*minfthl*minfthl*minfthl*hthl*(vt-vnathl) :amp
ikthl=gkthl*((0.75*(1-hthl))**4)*(vt-vkthl) :amp
itthl=gtthl*pinfthl*pinfthl*rthl*(vt-vtthl) :amp
iextthl:amp
tmp_thl1 = sin(2*pi*(t-dsmthl)/tmsmthl) :1
tmp_thl2 = sin(2*pi*(t-dsmthl+wsmthl)/tmsmthl) :1
ym_thl1=1/(1+exp(-tmp_thl1/sigym)):1
ym_thl2=1/(1+exp(-tmp_thl2/sigym)):1
ithl_sm=imsmthl*ym_thl1*(1-ym_thl2) :amp
membrane_Ithl = -(ilthl+inathl+ikthl+itthl)+iextthl+ithl_sm:amp
drthl/dt=phirthl*(rinfthl-rthl)/taurthl :1
dhthl/dt=phihthl*(hinfthl-hthl)/tauhthl :1
dvt/dt = membrane_Ithl/cmthl : volt
''')
neuron = b2.NeuronGroup(
num,
eqs,
method=par_sim['integration_method'],
dt=par_sim['dt'],
threshold='vt>-55*mV',
refractory='vt>-55*mV',
namespace=par,
)
neuron.vt = par['v0']
neuron.hthl = "hinfthl"
neuron.rthl = "rinfthl"
neuron.iextthl = par['iext']
state_monitor = b2.StateMonitor(neuron, ["vt", "ithl_sm"], record=True)
net = b2.Network(neuron)
net.add(state_monitor)
net.run(par_sim['simulation_time'])
return state_monitor
def simulate_HH_neuron(I_e, simulation_time):
"""A Hodgkin-Huxley neuron implemented in Brian2.
Args:
I_e: Input current injected into the HH neuron
simulation_time (float): Simulation time [seconds]
Returns:
StateMonitor: Brian2 StateMonitor with recorded field "vm"
"""
# neuron parameters
El = -59. * b2.mV
EK = -82. * b2.mV
ENa = 45. * b2.mV
gl = 0.3 * b2.msiemens
gK = 36. * b2.msiemens
gNa = 120. * b2.msiemens
C = 1. * b2.ufarad
# forming HH model with differential equations
eqs = """
membrane_Im = I_e + gNa*m**3*h*(ENa-vm) + \
gl*(El-vm) + gK*n**4*(EK-vm) : amp
alphan = 0.01/mV * (-60.0*mV - vm) / (exp((-60.0*mV - vm) / (10.0*mV)) - 1.0)/ms: Hz
alpham = (vm + 45.0*mV) / (10.0*mV) / (1.0 - exp(-(vm + 45.0*mV) / (10.0*mV)))/ms : Hz
alphah = 0.07*exp(-(vm + 70.*mV)/(20.*mV))/ms : Hz
betan = 0.125 * exp(-(vm + 70.0*mV) / (80.0*mV))/ms: Hz
betam = 4.0 * exp(-(vm + 70.0*mV) / (18.0*mV))/ms: Hz
betah = 1. / (exp(-(vm + 40.0*mV) / (10.0*mV)) + 1.0)/ms : Hz
dn/dt = alphan*(1-n)-betan*n : 1
dm/dt = alpham*(1-m)-betam*m : 1
dh/dt = alphah*(1-h)-betah*h : 1
dvm/dt = membrane_Im/C : volt
"""
neuron = b2.NeuronGroup(1, eqs, method="exponential_euler")
# parameter initialization [come from x_inf(v) {x:m,n,h}]
neuron.vm = -70. * b2.mV
neuron.m = 0.05
neuron.h = 0.60
neuron.n = 0.32
# tracking parameters
st_mon = b2.StateMonitor(neuron, "vm", record=True)
# running the simulation
hh_net = b2.Network(neuron)
hh_net.add(st_mon)
hh_net.run(simulation_time)
return st_mon
def simulate_FSI_cell(par, par_sim):
pid = os.getpid()
b2.set_device('cpp_standalone', directory=join(
"output", f"standalone-{pid}"))
b2.get_device().reinit()
b2.get_device().activate(
directory=join("output", f"standalone-{pid}"))
num = par['num']
input_current = par['i_ext']
eqs = '''
Iapp = input_current(t, i): amp
m_inf = 1.0/(1.0+exp(-(vf+24*mV)/(11.5*mV))):1
h_inf = 1.0/(1.0+exp(-(vf+58.3*mV)/(-6.7*mV))):1
n_inf = 1.0/(1.0+exp(-(vf+12.4*mV)/(6.8*mV))):1
a_inf = 1.0/(1.0+exp(-(vf+50*mV)/(20.*mV))):1
b_inf = 1.0/(1.0+exp(-(vf+70*mV)/(-6.*mV))):1
tau_h=0.5*ms+14.0*ms/(1.0+exp(-(vf+60*mV)/(-12.*mV))):second
tau_n=(0.087*ms+11.4*ms/(1.0+exp(-(vf+14.6*mV)/(-8.6*mV))))
*(0.087+11.4/(1.0+exp(-(vf-1.3*mV)/(18.7*mV)))) :second
membrain_Im = -gNa*m_inf**3 *h*(vf-50*mV)
-gK*(n**power_n)*(vf+90*mV)
-gL*(vf+70*mV)-gA*a**3*b*(vf+90*mV)+Iapp:amp
dh/dt=(h_inf-h)/tau_h :1
dn/dt=(n_inf-n)/tau_n :1
da/dt=(a_inf-a)/(2.*ms) :1
db/dt=(b_inf-b)/(150.*ms) :1
dvf/dt=membrain_Im/Cm :volt
'''
neuron = b2.NeuronGroup(num,
eqs,
method=par_sim['integration_method'],
dt=par_sim['dt'],
threshold='vf>-20*mV',
refractory='vf>-20*mV',
namespace=par,
)
neuron.vf = par['v0']
neuron.h = "h_inf"
neuron.n = "n_inf"
neuron.a = "a_inf"
neuron.b = "b_inf"
st_mon = b2.StateMonitor(neuron, ["vf", "Iapp"], record=True)
net = b2.Network(neuron)
net.add(st_mon)
net.run(par_sim['simulation_time'])
return st_mon
def simulate_HH_neuron(input_current, simulation_time):
"""A Hodgkin-Huxley neuron implemented in Brian2.
Args:
input_current (TimedArray): Input current injected into the HH neuron
simulation_time (float): Simulation time [seconds]
Returns:
StateMonitor: Brian2 StateMonitor with recorded fields
["vm", "I_e", "m", "n", "h"]
"""
# neuron parameters
El = 10.6 * b2.mV
EK = -12 * b2.mV
ENa = 115 * b2.mV
gl = 0.3 * b2.msiemens
gK = 36 * b2.msiemens
gNa = 120 * b2.msiemens
C = 1 * b2.ufarad
# forming HH model with differential equations
eqs = """
I_e = input_current(t,i) : amp
membrane_Im = I_e + gNa*m**3*h*(ENa-vm) + \
gl*(El-vm) + gK*n**4*(EK-vm) : amp
alphah = .07*exp(-.05*vm/mV)/ms : Hz
alpham = .1*(25*mV-vm)/(exp(2.5-.1*vm/mV)-1)/mV/ms : Hz
alphan = .01*(10*mV-vm)/(exp(1-.1*vm/mV)-1)/mV/ms : Hz
betah = 1./(1+exp(3.-.1*vm/mV))/ms : Hz
betam = 4*exp(-.0556*vm/mV)/ms : Hz
betan = .125*exp(-.0125*vm/mV)/ms : Hz
dh/dt = alphah*(1-h)-betah*h : 1
dm/dt = alpham*(1-m)-betam*m : 1
dn/dt = alphan*(1-n)-betan*n : 1
dvm/dt = membrane_Im/C : volt
"""
neuron = b2.NeuronGroup(1, eqs, method="exponential_euler")
# parameter initialization
neuron.vm = 0
neuron.m = 0.05
neuron.h = 0.60
neuron.n = 0.32
# tracking parameters
st_mon = b2.StateMonitor(neuron, ["vm", "I_e", "m", "n", "h"], record=True)
# running the simulation
hh_net = b2.Network(neuron)
hh_net.add(st_mon)
hh_net.run(simulation_time)
return st_mon
def current_pulse_sim_with_opto(args, params=None):
if params is None:
params = get_neuron_params(args['NRN'])
params['Vclamp'] = -80
neurons, eqs = get_membrane_equation(params, [],\
return_equations=True)
if args['verbose']:
print(eqs)
fig, ax = brian2.subplots(figsize=(5,3))
# V value initialization
neurons.V = params['El']*brian2.mV
trace = brian2.StateMonitor(neurons, 'V', record=0)
spikes = brian2.SpikeMonitor(neurons)
# rest run
brian2.run(args['delay'] * brian2.ms)
# first pulse
neurons.I0 = args['amp']*brian2.pA
brian2.run(args['duration']/3. * brian2.ms)
neurons.Gclamp = 1e3*brian2.nS
brian2.run(args['duration']/3. * brian2.ms)
neurons.Gclamp = 0*brian2.nS
brian2.run(args['duration']/3. * brian2.ms)
# second pulse
neurons.I0 = 0
brian2.run(args['delay'] * brian2.ms)
# We draw nicer spikes
Vm = trace[0].V[:]
for t in spikes.t:
ax.plot(t/brian2.ms*np.ones(2),
[Vm[int(t/brian2.defaultclock.dt)]/brian2.mV,-10],
'--', color=args['color'])
ax.plot(trace.t / brian2.ms, Vm / brian2.mV, color=args['color'])
if 'NRN' in args.keys():
ax.set_title(args['NRN'])
ax.annotate(str(int(params['El']))+'mV', (-50,params['El']-5))
ax.plot([-20], [params['El']], 'k>')
ax.plot([0,50], [-50, -50], 'k-', lw=4)
ax.plot([0,0], [-50, -40], 'k-', lw=4)
ax.annotate('10mV', (-50,-38))
ax.annotate('50ms', (0,-55))
# set_plot(ax, [], xticks=[], yticks=[])
# show()
if 'save' in args.keys():
fig.savefig(args['save'])
return fig
def main2():
# setting synaptic weight
bs.start_scope()
n_neurons = 3
eqs = '''
dv/dt = (I-v)/tau : 1 (unless refractory)
I : 1
tau: second
'''
threshold = 'v>1'
reset = 'v = 0'
refractory = 10 * bs.ms
G = bs.NeuronGroup(N=n_neurons,
model=eqs,
threshold=threshold,
reset=reset,
method='exact',
refractory=refractory)
G.I = [2, 0, 0] # represents the I in eqs
# driving current should be bigger than the threshold, otherwise it wont spike at all
# I = 0 means that the voltage wont change since there is no driving current
G.tau = [10, 100, 100] * bs.ms # represents the tau in eqs
# unlike last time, the tau is defined with the neuron so we see the effects of different values
# model : `str`, `Equations`, optional
# The model equations for the synapses.
# you need to set this as model= in Synapses in order to incorporate weight
synapse_model = 'w : 1'
# So in total, what this model says is that whenever two neurons in G are connected by a synapse,
# when the source neuron fires a spike the target neuron will have its value of v increased by 0.2.
S = bs.Synapses(source=G,
target=G,
model=synapse_model,
on_pre='v_post += w')
S.connect(i=0, j=[1, 2])
# So this will give a synaptic connection from 0 to 1 with weight 0.2=0.2*1 and from 0 to 2 with weight 0.4=0.2*2.
S.w = 'j*0.2'
state_monitor = bs.StateMonitor(G, 'v', record=True)
bs.run(100 * bs.ms)
plt.plot(state_monitor.t / bs.ms, state_monitor.v[0], label='Neuron 0')
plt.plot(state_monitor.t / bs.ms, state_monitor.v[1], label='Neuron 1')
plt.plot(state_monitor.t / bs.ms, state_monitor.v[2], label='Neuron 2')
plt.xlabel('Time (ms)')
plt.ylabel('v')
plt.legend()
plt.show()
def simulate(runtime=0.5*b2.second, N=1):
b2.start_scope()
namespace['sigma'] = 2 * b2.mV
namespace['tau_m_E'] = namespace['C_m_E'] / namespace['g_m_E']
# I_1 = -2*b2.namp
# I_2 = -20*b2.namp
I_1 = namespace['g_m_E'] * (namespace['V_L'] - (2.5*b2.mV + namespace['V_thr']))
I_2 = namespace['g_m_E'] * (namespace['V_L'] - (-2.5*b2.mV + namespace['V_thr']))
eqn = """
dV/dt = (- g_m_E * (V - V_L) - I) / C_m_E + sigma*xi*tau_m_E**-0.5: volt (unless refractory)
I : amp
"""
N1 = b2.NeuronGroup(
N, eqn, threshold='V>V_thr',
reset='V = V_reset',
refractory=namespace['tau_rp_E'],
method='euler')
N1.V = namespace['V_reset']
N1.I = I_1
N2 = b2.NeuronGroup(
N, eqn, threshold='V>V_thr',
reset='V = V_reset',
refractory=namespace['tau_rp_E'],
method='euler')
N2.V = namespace['V_reset']
N2.I = I_2
st1 = b2.StateMonitor(N1, variables='V', record=True, name='st1')
st2 = b2.StateMonitor(N2, variables='V', record=True, name='st2')
sp1 = b2.SpikeMonitor(N1, name='sp1')
sp2 = b2.SpikeMonitor(N2, name='sp2')
net = b2.Network(b2.collect())
net.run(runtime, namespace=namespace, report='stdout')
return net
def main1():
bs.start_scope()
# Parameters
area = 20000 * bs.umetre**2
Cm = 1 * bs.ufarad * bs.cm**-2 * area
gl = 5e-5 * bs.siemens * bs.cm**-2 * area
El = -65 * bs.mV
EK = -90 * bs.mV
ENa = 50 * bs.mV
g_na = 100 * bs.msiemens * bs.cm**-2 * area
g_kd = 30 * bs.msiemens * bs.cm**-2 * area
VT = -63 * bs.mV
# HH stands for Hudgkin-Huxley
eqs_HH = '''
dv/dt = (gl*(El-v) - g_na*(m*m*m)*h*(v-ENa) - g_kd*(n*n*n*n)*(v-EK) + I)/Cm : volt
dm/dt = 0.32*(mV**-1)*(13.*mV-v+VT)/
(exp((13.*mV-v+VT)/(4.*mV))-1.)/ms*(1-m)-0.28*(mV**-1)*(v-VT-40.*mV)/
(exp((v-VT-40.*mV)/(5.*mV))-1.)/ms*m : 1
dn/dt = 0.032*(mV**-1)*(15.*mV-v+VT)/
(exp((15.*mV-v+VT)/(5.*mV))-1.)/ms*(1.-n)-.5*exp((10.*mV-v+VT)/(40.*mV))/ms*n : 1
dh/dt = 0.128*exp((17.*mV-v+VT)/(18.*mV))/ms*(1.-h)-4./(1+exp((40.*mV-v+VT)/(5.*mV)))/ms*h : 1
I : amp
'''
group = bs.NeuronGroup(1,
eqs_HH,
threshold='v > -40*mV',
refractory='v > -40*mV',
method='exponential_euler')
group.v = El
state_monitor = bs.StateMonitor(group, 'v', record=True)
spike_monitor = bs.SpikeMonitor(group, variables='v')
plt.figure(figsize=(9, 4))
for l in range(5):
group.I = bs.rand() * 50 * bs.nA
bs.run(10 * bs.ms)
bs.axvline(l * 10, ls='--', c='k')
bs.axhline(El / bs.mV, ls='-', c='lightgray', lw=3)
state_time = state_monitor.t
spike_time = spike_monitor.t
plt.plot(state_time / bs.ms, spike_monitor.v[0] / bs.mV, '-b')
plt.plot(spike_time / bs.ms, spike_monitor.v / bs.mV, 'ob')
plt.xlabel('Time (ms)')
plt.ylabel('v (mV)')
plt.show()
def _create_device(self, group, variable):
"""Create a Brian2 recording device."""
# Brian2 records in the 'start' scheduling slot by default
if variable == 'spikes':
self._devices[variable] = brian2.SpikeMonitor(group, record=self.recorded)
else:
varname = self.population.celltype.state_variable_translations[variable]['translated_name']
neurons_to_record = np.sort(np.fromiter(
self.recorded[variable], dtype=int)) - self.population.first_id
self._devices[variable] = brian2.StateMonitor(group, varname,
record=neurons_to_record,
when='end',
dt=self.sampling_interval * ms)
simulator.state.network.add(self._devices[variable])
def simulate(self,
current=input_factory.get_zero_current(),
time=10 * b2.ms,
rheo_threshold=None,
v_rest=None,
v_reset=None,
delta_t=None,
time_scale=None,
resistance=None,
threshold=None,
adapt_volt_c=None,
adapt_tau=None,
adapt_incr=None):
if (v_rest == None):
v_rest = self.rest_pot
if (v_reset == None):
v_reset = self.reset_pot
if (rheo_threshold == None):
rheo_threshold = self.rheo_threshold
if (delta_t == None):
delta_t = self.delta_t
if (time_scale == None):
time_scale = self.time_scale
if (resistance == None):
resistance = self.resistance
if (threshold == None):
threshold = self.threshold
if (adapt_volt_c == None):
adapt_volt_c = self.adapt_volt_c
if (adapt_tau == None):
adapt_tau = self.adapt_tau
if (adapt_incr == None):
adapt_incr = self.adapt_incr
v_spike_str = "v>{:f}*mvolt".format(threshold / b2.mvolt)
eqs = """
dv/dt = (-(v-v_rest) +delta_t*exp((v-rheo_threshold)/delta_t)+ resistance * current(t,i) - resistance * w)/(time_scale) : volt
dw/dt=(adapt_volt_c*(v-v_rest)-w)/adapt_tau : amp
"""
neuron = b2.NeuronGroup(1,
model=eqs,
threshold=v_spike_str,
reset="v=v_reset;w+=adapt_incr",
method="euler")
neuron.v = v_rest
neuron.w = 0.0 * b2.pA
state_monitor = b2.StateMonitor(neuron, ["v", "w"], record=True)
spike_monitor = b2.SpikeMonitor(neuron)
b2.run(time)
return state_monitor, spike_monitor
def simulate_neuron(self,
I_stim=input_factory.get_zero_current(),
simulation_time=1000 * ms,
**kwargs):
"""
Simulate/stimulate the neuron
:param I_stim: input stimulus (use the input_factory to create the stimulus)
:param simulation_time: duration (usually in milliseconds, eg. 3000*ms)
:param kwargs: custom neuron parameters can be given as arguments
:return: b2.StateMonitor, b2.SpikeMonitor
"""
neuron_parameters = dict(
self.neuron_parameters
) # Make a copy of parameters; otherwise will change object params
neuron_parameters.update(kwargs)
refractory_period = neuron_parameters['refractory_period']
stim_string = '+ I_stim(t,i)'
old_model_defns = dict(self.full_model_defns)
self.add_model_definition('EXT_CURRENTS', stim_string)
eqs = self.get_membrane_equation()
self.full_model_defns = old_model_defns
# Create a neuron group
neuron = b2.NeuronGroup(1,
model=eqs,
namespace=neuron_parameters,
reset=self.reset_statements,
threshold=self.threshold_condition,
refractory=refractory_period,
method=self.integration_method)
# Set initial values
initial_values = self.get_initial_values()
neuron.set_states(initial_values)
# Set what to monitor
state_monitor = b2.StateMonitor(neuron,
self.get_states_to_monitor(),
record=True)
spike_monitor = b2.SpikeMonitor(neuron)
# Run the simulation
net = b2.Network(neuron, state_monitor, spike_monitor)
net.run(simulation_time)
return state_monitor, spike_monitor
def main2():
tau = 10 * bs.ms
eqs = '''
dv/dt = (sin(2*pi*100*Hz*t)-v)/tau : 1
'''
G = bs.NeuronGroup(1, eqs, method="euler")
G.v = 5 # we can set the initial value
M = bs.StateMonitor(G, 'v', record=0)
bs.run(60 * bs.ms)
plt.plot(M.t / bs.ms, M.v[0])
plt.xlabel('Time (ms)')
plt.ylabel('v')
plt.show()
def main3():
# introducing delay
bs.start_scope()
n_neurons = 3
eqs = '''
dv/dt = (I-v)/tau : 1 (unless refractory)
I : 1
tau: second
'''
threshold = 'v>1'
reset = 'v = 0'
refractory = 10 * bs.ms
G = bs.NeuronGroup(N=n_neurons,
model=eqs,
threshold=threshold,
reset=reset,
method='exact',
refractory=refractory)
G.I = [2, 0, 0] # represents the I in eqs
# driving current should be bigger than the threshold, otherwise it wont spike at all
# I = 0 means that the voltage wont change since there is no driving current
G.tau = [10, 100, 100] * bs.ms # represents the tau in eqs
# unlike last time, the tau is defined with the neuron so we see the effects of different values
synapse_model = 'w : 1'
# So in total, what this model says is that whenever two neurons in G are connected by a synapse,
# when the source neuron fires a spike the target neuron will have its value of v increased by 0.2.
S = bs.Synapses(source=G,
target=G,
model=synapse_model,
on_pre='v_post += w')
S.connect(i=0, j=[1, 2])
S.w = 'j*0.2'
S.delay = 'j*2*ms'
state_monitor = bs.StateMonitor(G, 'v', record=True)
bs.run(100 * bs.ms)
plt.plot(state_monitor.t / bs.ms, state_monitor.v[0], label='Neuron 0')
plt.plot(state_monitor.t / bs.ms, state_monitor.v[1], label='Neuron 1')
plt.plot(state_monitor.t / bs.ms, state_monitor.v[2], label='Neuron 2')
plt.xlabel('Time (ms)')
plt.ylabel('v')
plt.legend()
plt.show()
def main6():
# neurons with parameters
n_neurons = 100
tau = 10 * bs.ms
v0_max = 3.0
duration = 1000 * bs.ms
# v0: 1 declares a new per-neuron parameter v0
eqs = """
dv/dt = (v0-v)/tau: 1 (unless refractory)
v0 : 1
"""
# conditions for spiking models
threshold = 'v>1'
reset = 'v = 0'
refractory = 5 * bs.ms
G = bs.NeuronGroup(N=n_neurons, model=eqs, threshold=threshold, reset=reset, method='exact', refractory=refractory)
state_monitor = bs.StateMonitor(G, 'v', record=True)
spike_monitor = bs.SpikeMonitor(G)
"""
The line G.v0 = 'i*v0_max/(N-1)' initialises the value of v0 for each neuron varying from 0 up to v0_max.
The symbol i when it appears in strings like this refers to the neuron index.
"""
G.v0 = 'i*v0_max/(N-1)'
bs.run(duration=duration)
plt.figure(figsize=(12, 4))
plt.subplot(121)
plt.plot(spike_monitor.t / bs.ms, spike_monitor.i, '.k')
plt.xlabel('Time (ms)')
plt.ylabel('Neuron index')
plt.subplot(122)
plt.plot(G.v0, spike_monitor.count / duration)
plt.xlabel('v0')
plt.ylabel('Firing rate (sp/s)')
plt.show()
plt.clf()
# plt.plot(state_monitor.t / bs.ms, state_monitor.v[0])
# plt.plot(state_monitor.t / bs.ms, state_monitor.v[10])
# plt.plot(state_monitor.t / bs.ms, state_monitor.v[50])
plt.plot(state_monitor.t / bs.ms, state_monitor.v[30])
plt.plot(state_monitor.t / bs.ms, state_monitor.v[40])
plt.plot(state_monitor.t / bs.ms, state_monitor.v[70])
plt.xlabel('Time (ms)')
plt.ylabel('v')
plt.show()
def simulate_exponential_IF_neuron(tau=MEMBRANE_TIME_SCALE_tau,
R=MEMBRANE_RESISTANCE_R,
v_rest=V_REST,
v_reset=V_RESET,
v_rheobase=RHEOBASE_THRESHOLD_v_rh,
v_spike=FIRING_THRESHOLD_v_spike,
delta_T=SHARPNESS_delta_T,
I_stim=input_factory.get_zero_current(),
simulation_time=200 * b2.ms):
"""
Implements the dynamics of the exponential Integrate-and-fire model
Args:
tau (Quantity): Membrane time constant
R (Quantity): Membrane resistance
v_rest (Quantity): Resting potential
v_reset (Quantity): Reset value (vm after spike)
v_rheobase (Quantity): Rheobase threshold
v_spike (Quantity) : voltage threshold for the spike condition
delta_T (Quantity): Sharpness of the exponential term
I_stim (TimedArray): Input current
simulation_time (Quantity): Duration for which the model is simulated
Returns:
(voltage_monitor, spike_monitor):
A b2.StateMonitor for the variable "v" and a b2.SpikeMonitor
"""
eqs = """
dv/dt = (-(v-v_rest) +delta_T*exp((v-v_rheobase)/delta_T)+ R * I_stim(t,i))/(tau) : volt
"""
neuron = b2.NeuronGroup(1,
model=eqs,
reset="v=v_reset",
threshold="v>v_spike",
method="euler")
neuron.v = v_rest
# monitoring membrane potential of neuron and injecting current
voltage_monitor = b2.StateMonitor(neuron, ["v"], record=True)
spike_monitor = b2.SpikeMonitor(neuron)
# run the simulation
net = b2.Network(neuron, voltage_monitor, spike_monitor)
net.run(simulation_time)
return voltage_monitor, spike_monitor
def make_model(self):
# Determine the simulation
if self.clamp_type == 'current':
eqs_input = '''I_inj = inj_input(t) : amp'''
elif self.clamp_type == 'dynamic':
eqs_input = '''I_exc = g_exc(t) * (Er_e - v) : amp
I_inh = g_inh(t) * (Er_i - v) : amp
I_inj = I_exc + I_inh : amp'''
tracking = ['v', 'I_inj']
# Model the neuron with differential equations
eqs = '''
Vh_m = 3.583881 * k_m - 53.294454*mV : volt
m = 1 / (1 + exp(-(v - Vh_m) / k_m)) : 1
h = 1 / (1 + exp((v - Vh_h) / k_h)) : 1
alpha_n = (0.032 * 5. / exprel((15. -v/mV + VT/mV) / 5.))/ms : Hz
beta_n = (0.5 * exp((10. - v/mV + VT/mV) / 40.))/ms : Hz
dn/dt = alpha_n * (1 - n) - beta_n * n : 1
I_leak = -gL * (v - EL) : amp
I_Na = -gNa * m**3 * h * (v - ENa) : amp
I_K = -gK * n**4 * (v - EK) : amp
dv/dt = (I_leak + I_Na + I_K + I_inj) / Cm : volt
'''
# Neuron & parameter initialization
neuron = b2.NeuronGroup(1,
model=eqs + eqs_input,
method='exponential_euler',
threshold='m > 0.5',
refractory=2 * b2.ms,
reset=None,
dt=self.dt * b2.ms)
neuron.v = -65 * b2.mV
# Track the parameters during simulation
self.M = b2.StateMonitor(neuron, tracking, record=True)
self.S = b2.SpikeMonitor(neuron, record=True)
self.neuron = neuron
net = b2.Network(neuron)
net.add(self.M, self.S)
self.network = net
