kact = 0.4
ip3rtau = 2000
h.CVode().active(1)
h.cvode.atol(1e-10)
# define the regions for the rxd
cyt = rxd.Region(h.allsec(),
nrn_region='i',
geometry=rxd.FractionalVolume(fc, surface_fraction=1))
er = rxd.Region(h.allsec(), geometry=rxd.FractionalVolume(fe))
cyt_er_membrane = rxd.Region(h.allsec(), geometry=rxd.FixedPerimeter(1))
# the species and other states
ca = rxd.Species([cyt, er], d=caDiff, name='ca', charge=2, initial=cac_init)
ip3 = rxd.Species(cyt, d=ip3Diff, initial=ip3_init)
ip3r_gate_state = rxd.State(cyt_er_membrane, initial=0.8)
h_gate = ip3r_gate_state[cyt_er_membrane]
# pumps and channels between ER and Cytosol
serca = rxd.MultiCompartmentReaction(ca[cyt] > ca[er],
gserca / ((kserca /
(1000. * ca[cyt]))**2 + 1),
membrane=cyt_er_membrane,
custom_dynamics=True)
leak = rxd.MultiCompartmentReaction(ca[er] != ca[cyt],
gleak,
gleak,
membrane=cyt_er_membrane)
minf = ip3[cyt] * 1000. * ca[cyt] / (ip3[cyt] + kip3) / (1000. * ca[cyt] +
def __init__(self, x, y, z, rec=False):
self.x = x
self.y = y
self.z = z
self.soma = h.Section(name="soma", cell=self)
# add 3D points to locate the neuron in the ECS
self.soma.pt3dadd(x, y, z + somaR, 2.0 * somaR)
self.soma.pt3dadd(x, y, z - somaR, 2.0 * somaR)
# Where? -- define the intracellular space and membrane
self.cyt = rxd.Region(self.soma, name="cyt", nrn_region="i")
self.mem = rxd.Region(self.soma, name="mem", geometry=rxd.membrane())
cell = [self.cyt, self.mem]
# Who? -- the relevant ions and gates
self.k = rxd.Species(cell, name="k", d=2.62, charge=1, initial=125)
self.na = rxd.Species(cell, name="na", d=1.78, charge=1, initial=10)
self.n = rxd.State(cell, name="n", initial=0.25512)
self.ki, self.nai = self.k[self.cyt], self.na[self.cyt]
# What? -- gating variables and ion currents
self.n_gate = rxd.Rate(self.n, phin * (ninf - self.n) / taun)
# Nernst potentials
ena = 1e3 * h.R * (h.celsius + 273.15) * log(
nao / self.nai) / h.FARADAY
ek = 1e3 * h.R * (h.celsius + 273.15) * log(ko / self.ki) / h.FARADAY
# Persistent Na current
self.nap_current = rxd.MultiCompartmentReaction(
self.nai,
nao,
gnap * nap_minf * nap_hinf * (v - ena),
mass_action=False,
membrane=self.mem,
membrane_flux=True,
)
# Na current
self.na_current = rxd.MultiCompartmentReaction(
self.nai,
nao,
gna * minf**3 * (1.0 - self.n) * (v - ena),
mass_action=False,
membrane=self.mem,
membrane_flux=True,
)
# K current
self.k_current = rxd.MultiCompartmentReaction(
self.ki,
ko,
gk * self.n**4 * (v - ek),
mass_action=False,
membrane=self.mem,
membrane_flux=True,
)
# K leak
self.k_leak = rxd.MultiCompartmentReaction(
self.ki,
ko,
gl * (v - ek),
mass_action=False,
membrane=self.mem,
membrane_flux=True,
)
# passive leak
self.soma.insert("pas")
self.soma(0.5).pas.g = pas_gl
self.soma(0.5).pas.e = pas_el
if rec: # record membrane potential (shown in figure 1C)
self.somaV = h.Vector()
self.somaV.record(self.soma(0.5)._ref_v, rec)
k[ecs],
na[cyt],
na[ecs],
cl[cyt],
cl[ecs],
glial_na[gcyt],
glial_k[gcyt],
)
# i = in cytosol (cyt) o = in extracellular (ecs)
# extracellular oxygen concentration
o2ecs = rxd.Species([ecs], name="o2ecs", initial=oa_bath)
# STATES-------------------------------------------------------------------------------------------------------------------------
# gating variables (m, h, n)
mgate = rxd.State([cyt, mem], name="mgate", initial=0.00787013592322398)
hgate = rxd.State([cyt, mem], name="hgate", initial=0.9981099795551048)
ngate = rxd.State([cyt, mem], name="ngate", initial=0.02284760152971809)
# ALL EQUATIONS------------------------------------------------------------------------------------------------------------------
gna = gnabar * mgate**3 * hgate
gk = gkbar * ngate**4
fko = 1.0 / (1.0 + exp(16.0 - ko))
nkcc1 = unkcc1 * fko * (log((ki * cli) / (ko * clo)) + log(
(nai * cli) / (nao * clo)))
kcc2 = ukcc2 * log((ki * cli) / (ko * clo))
ena = 26.64 * log(nao / nai) # nerst equation - reversal potentials
ek = 26.64 * log(ko / ki) # ^^^^^
ecl = 26.64 * log(cli / clo) # ^^^
p = p_max / (1.0 + exp((20.0 - oa_bath * alpha) / 3))
ca = rxd.Species([cyt, er],
d=caDiff,
name='ca',
charge=2,
initial=dconf['cacytinit'])
caexinit = dconf['caexinit']
caextrude = rxd.Rate(ca, (caexinit - ca[cyt]) / taurcada,
regions=cyt,
membrane_flux=False)
ip3 = rxd.Species(cyt, d=0.283, name='ip3', initial=0.0)
# action of IP3 receptor
Kip3 = 0.13
Kact = 0.4
minf = ip3[cyt] * 1000. * ca[cyt] / (ip3[cyt] + Kip3) / (1000. * ca[cyt] +
Kact)
ip3r_gate_state = rxd.State(cyt_er_membrane, initial=0.8)
h_gate = ip3r_gate_state[cyt_er_membrane]
k = dconf['gip3'] * (minf * h_gate)**3
ip3r = rxd.MultiCompartmentReaction(ca[er] <> ca[cyt],
k,
k,
membrane=cyt_er_membrane)
# IP3 receptor gating
ip3rg = rxd.Rate(h_gate,
(1. / (1 + 1000. * ca[cyt] / (0.4)) - h_gate) / 400.0)
# IP3 degradation - moves towards baseline level (ip3_init)
ip3degTau = 1000 # 1000 ms
ip3deg = rxd.Rate(ip3, (0.0 - ip3[cyt]) / ip3degTau,
regions=cyt,
membrane_flux=False)
### RYR - based on Sneyd et al, 2003
