def __init__(self, n, equations, **parameters):
threshold = brian.EmpiricalThreshold(threshold=-40*mV, refractory=2*ms)
reset = 0*mV
refractory = 0*ms
BaseNeuronGroup.__init__(self, n, equations,
threshold, reset, refractory,
implicit=True,
**parameters)
def threshold(self):
return brian.EmpiricalThreshold(threshold=-40 * mV, refractory=2 * ms)
def make_gbc_group(num, celsius=37):
''' Creates a sbc neuron group
Parameters:
-----------
num : int
Number of neurons in the neuron group.
celsius : float
Temperatur in degree celsius, Default = 37
Output
------
A brian NeuronGroup
'''
C = 12 * pF
Eh = -43 * mV
EK = -77 * mV # -70mV in orig py file, but -77*mV in mod file
El = -65 * mV
ENa = 50 * mV
nf = 0.85 # proportion of n vs p kinetics
zss = 0.5 # steady state inactivation of glt
q10 = 3.**((celsius - 22) / 10.)
T10 = 10.**((celsius - 22) / 10.)
q10_gbar = 1.5
gnabar = calc_tf(q10_gbar, celsius) * 2500 * nS
gkhtbar = calc_tf(q10_gbar, celsius) * 150 * nS
gkltbar = calc_tf(q10_gbar, celsius) * 200 * nS
ghbar = calc_tf(q10_gbar, celsius) * 20 * nS
gl = calc_tf(q10_gbar, celsius) * 2 * nS
eqs = """
i_stim : amp
dvm/dt = (ileak + ina + ikht + iklt + ih + i_syn +i_stim) / C : volt
vu = vm/mV : 1 # unitless v
"""
# Rothman 1993 Na channel
eqs_na = """
ina = gnabar*m**3*h*(ENa-vm) : amp
dm/dt = malpha * (1. - m) - mbeta * m : 1
dh/dt = halpha * (1. - h) - hbeta * h : 1
malpha = (0.36 * q10 * (vu+49.)) / (1. - exp(-(vu+49.)/3.)) /ms : 1/ms
mbeta = (-0.4 * q10 * (vu+58.)) / (1. - exp((vu+58)/20.)) /ms : 1/ms
halpha = 2.4*q10 / (1. + exp((vu+68.)/3.)) /ms + 0.8*T10 / (1. + exp(vu + 61.3)) /ms : 1/ms
hbeta = 3.6*q10 / (1. + exp(-(vu+21.)/10.)) /ms : 1/ms
"""
eqs += eqs_na
# KHT channel (delayed-rectifier K+)
eqs_kht = """
ikht = gkhtbar*(nf*n**2 + (1-nf)*p)*(EK-vm) : amp
dn/dt=q10*(ninf-n)/ntau : 1
dp/dt=q10*(pinf-p)/ptau : 1
ninf = (1 + exp(-(vu + 15) / 5.))**-0.5 : 1
pinf = 1. / (1 + exp(-(vu + 23) / 6.)) : 1
ntau = ((100. / (11*exp((vu+60) / 24.) + 21*exp(-(vu+60) / 23.))) + 0.7)*ms : ms
ptau = ((100. / (4*exp((vu+60) / 32.) + 5*exp(-(vu+60) / 22.))) + 5)*ms : ms
"""
eqs += eqs_kht
# Ih channel (subthreshold adaptive, non-inactivating)
eqs_ih = """
ih = ghbar*r*(Eh-vm) : amp
dr/dt=q10*(rinf-r)/rtau : 1
rinf = 1. / (1+exp((vu + 76.) / 7.)) : 1
rtau = ((100000. / (237.*exp((vu+60.) / 12.) + 17.*exp(-(vu+60.) / 14.))) + 25.)*ms : ms
"""
eqs += eqs_ih
# KLT channel (low threshold K+)
eqs_klt = """
iklt = gkltbar*w**4*z*(EK-vm) : amp
dw/dt=q10*(winf-w)/wtau : 1
dz/dt=q10*(zinf-z)/wtau : 1
winf = (1. / (1 + exp(-(vu + 48.) / 6.)))**0.25 : 1
zinf = zss + ((1.-zss) / (1 + exp((vu + 71.) / 10.))) : 1
wtau = ((100. / (6.*exp((vu+60.) / 6.) + 16.*exp(-(vu+60.) / 45.))) + 1.5)*ms : ms
ztau = ((1000. / (exp((vu+60.) / 20.) + exp(-(vu+60.) / 8.))) + 50)*ms : ms
"""
eqs += eqs_klt
# Leak
eqs_leak = "ileak = gl*(El-vm) : amp"
eqs += eqs_leak
### Excitatory synapse
# Q10 for synaptic decay calculated from \cite{Postlethwaite2007}
Tf = calc_tf(q10=0.75, celsius=celsius, ref_temp=37)
taue_syn = 0.2 * Tf * ms
taui_syn = 9.03 * calc_tf(q10=0.75, celsius=celsius,
ref_temp=34) * ms # \cite{Xie2013}
eqs_syn = """
i_syn = ge_syn*(0*mV - vm) + gi_syn*(-77*mV - vm): amp
dge_syn/dt = -ge_syn/taue_syn : siemens
dgi_syn/dt = -gi_syn/taui_syn : siemens
"""
eqs += eqs_syn
if celsius < 37:
refractory = 0.7 * ms
else:
refractory = 0.5 * ms
group = brian.NeuronGroup(
N=num,
model=eqs,
threshold=brian.EmpiricalThreshold(threshold=-20 * mV,
refractory=refractory),
implicit=True,
)
### Set initial conditions
group.vm = El
group.r = 1. / (1 + np.exp((El / mV + 76.) / 7.))
group.m = group.malpha / (group.malpha + group.mbeta)
group.h = group.halpha / (group.halpha + group.halpha)
group.w = (1. / (1 + np.exp(-(El / mV + 48.) / 6.)))**0.25
group.z = zss + ((1. - zss) / (1 + np.exp((El / mV + 71.) / 10.)))
group.n = (1 + np.exp(-(El / mV + 15) / 5.))**-0.5
group.p = 1. / (1 + np.exp(-(El / mV + 23) / 6.))
return group
def make_mso_group(num,
gbar_na=3900,
gbar_klt=650,
gbar_h=520,
gbar_leak=13,
e_rest=-55.8,
voltage_clamp=False):
''' Creates a sbc neuron group
Parameters:
-----------
num : int
Number of neurons in the neuron group.
celsius : float
Temperatur in degree celsius, Default = 37
Output
------
A brian NeuronGroup
'''
C = 70 * pF # [Couchman2010]
e_h = -35 * mV # [Baumann2013]
e_k = -90 * mV
e_e = -0 * mV #[Colbourne2005]
e_i = -70 * mV #[Coulboure2005]
e_na = 56.2 * mV
e_rest = e_rest * mV # Between -60 and -55
nf = 1 # proportion of n vs p kinetics
zss = 0.4 # steady state inactivation of glt
gbar_na = gbar_na * nS
gbar_klt = gbar_klt * nS
gbar_h = gbar_h * nS
gbar_leak = gbar_leak * nS
if not voltage_clamp:
eqs = """
i_stim : amp
dvm/dt = - (-i_stim + i_leak + i_na + i_klt + i_h + i_syn) / C : volt
vu = vm/mV : 1 # unitless v
"""
else:
eqs = """
i_stim : amp
vm : volt
vu = vm/mV : 1 # unitless v
"""
eqs_na = """
g_na = gbar_na * m**3 * h : nsiemens
i_na = g_na * (vm - e_na) : amp
m_inf = 1 / (1 + exp((vu + 38) / -7)) :1
h_inf = 1 / (1 + exp((vu + 65) / 6)) :1
tau_m = (0.48 / (5 * exp((vu + 60) / 18) + 36 * exp((vu + 60) / -25)) ) * ms : ms
tau_h = (19.23 / (7 * exp((vu + 60) / 11) + 10 * exp((vu + 60) / -25)) + 0.12) * ms : ms
dm/dt = (m_inf - m) / tau_m :1
dh/dt = (h_inf - h) / tau_h :1
"""
eqs += eqs_na
# [Baumann2013] (Dorsal Cells)
eqs_h = """
g_h = gbar_h * a :nsiemens
i_h = g_h * (vm - e_h) : amp
a_inf = 1 / (1 + exp(0.1 * (vu + 80.4))) :1
tau_a = (79 + 417 * exp(-(vu + 61.5)**2 / 800)) *ms :ms
da/dt = (a_inf - a) / tau_a :1
"""
eqs += eqs_h
# Potassium low threshold [Khurana2011]
eqs_klt = """
g_klt = gbar_klt * w**4 * z : nsiemens
i_klt = g_klt * (vm - e_k) : amp
z_inf = zss + ((1-zss) / (1 + exp((vu + 57) / 5.44))) : 1
w_inf = 1 / (1 + exp(-(vu + 57.3) / 11.7)) :1
tau_w = 0.46 * (100. / (6. * exp((vu + 75.) / 12.15) + 24. * exp(-(vu + 75.) / 25) + 0.55)) * ms : ms
tau_z = 0.24 * ((1000 / (exp((vu + 60) / 20) + exp(-(vu + 60) / 8))) + 50) * ms : ms
dw/dt =( w_inf - w) / tau_w :1
dz/dt = (z_inf - z) / tau_z :1
"""
eqs += eqs_klt
# leak
eqs_leak = """
g_leak = gbar_leak * 1 : nsiemens
i_leak = g_leak * (vm - e_rest) : amp
"""
eqs += eqs_leak
#Synaptic Current
eqs_syn = """
ex_syn_i :1
ex_syn_c :1
in_syn_i :1
in_syn_c :1
i_syn = i_syn_ii + i_syn_ic + i_syn_ei + i_syn_ec : amp
#inhibitory currents
i_syn_ii = in_syn_i * siemens * (vm - e_i) : amp
i_syn_ic = in_syn_c * siemens * (vm - e_i) : amp
#exitatory currents
i_syn_ei = ex_syn_i * siemens * (vm - e_e) : amp
i_syn_ec = ex_syn_c * siemens * (vm - e_e) : amp
"""
eqs += eqs_syn
group = brian.NeuronGroup(
N=num,
model=eqs,
threshold=brian.EmpiricalThreshold(threshold=-30 * mV,
refractory=0.5 * ms),
implicit=True,
)
### Set initial conditions
group.vm = e_rest
group.m = group.m_inf
group.h = group.h_inf
group.w = group.w_inf
group.z = group.z_inf
group.a = group.a_inf
return group