COMMENT
Two state kinetic scheme synapse described by rise time taur,
and decay time constant taud. The normalized peak condunductance is 1.
Decay time MUST be greater than rise time.
The solution of A->G->bath with rate constants 1/taur and 1/taud is
A = a*exp(-t/taur) and
G = a*taud/(taud-taur)*(-exp(-t/taur) + exp(-t/taud))
where taur < taud
If taud-taur -> 0 then we have a alphasynapse.
and if taur -> 0 then we have just single exponential decay.
The factor is evaluated in the
initial block such that an event of weight 1 generates a
peak conductance of 1.
Because the solution is a sum of exponentials, the
coupled equations can be solved as a pair of independent equations
by the more efficient cnexp method.
ENDCOMMENT
NEURON {
POINT_PROCESS ghknmda
USEION na WRITE ina
USEION k WRITE ik
USEION ca READ cai, cao WRITE ica
RANGE taur, taud
RANGE inmda
RANGE P, mg, Pmax
GLOBAL mgb
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(uS) = (microsiemens)
(molar) = (1/liter)
(mM) = (millimolar)
FARADAY = (faraday) (coulomb)
R = (k-mole) (joule/degC)
}
PARAMETER {
taur=5 (ms) <1e-9,1e9>
taud = 50 (ms) <1e-9,1e9>
cai = 100e-6(mM) : 100nM
cao = 2 (mM)
nai = 18 (mM) : Set for a reversal pot of +55mV
nao = 140 (mM)
ki = 140 (mM) : Set for a reversal pot of -90mV
ko = 5 (mM)
celsius (degC)
mg = 2 (mM)
Pmax=1e-6 (cm/s) : According to Canavier, PNMDA's default value is
: 1e-6 for 10uM, 1.4e-6 cm/s for 30uM of NMDA
}
ASSIGNED {
ina (nA)
ik (nA)
ica (nA)
v (mV)
P (cm/s)
factor
mgb (1)
inmda (nA)
Area (cm2)
}
STATE {
A (cm/s)
B (cm/s)
}
INITIAL {
LOCAL tp
if (taur/taud > .9999) {
taur = .9999*taud
}
A = 0
B = 0
tp = (taur*taud)/(taud - taur) * log(taud/taur)
factor = -exp(-tp/taur) + exp(-tp/taud)
factor = 1/factor
Area=1
}
BREAKPOINT {
SOLVE state METHOD cnexp
P=B-A
mgb = mgblock(v)
: Area is just for unit conversion of ghk output
ina = P*mgb*ghk(v, nai, nao,1)*Area
ica = P*10.6*mgb*ghk(v, cai, cao,2)*Area
ik = P*mgb*ghk(v, ki, ko,1)*Area
inmda = ica + ik + ina
}
DERIVATIVE state {
A' = -A/taur
B' = -B/taud
}
FUNCTION ghk(v(mV), ci(mM), co(mM),z) (0.001 coul/cm3) {
LOCAL arg, eci, eco
arg = (0.001)*z*FARADAY*v/(R*(celsius+273.15))
eco = co*efun(arg)
eci = ci*efun(-arg)
ghk = (0.001)*z*FARADAY*(eci - eco)
}
FUNCTION efun(z) {
if (fabs(z) < 1e-4) {
efun = 1 - z/2
}else{
efun = z/(exp(z) - 1)
}
}
FUNCTION mgblock(v(mV)) (1){
TABLE
DEPEND mg
FROM -140 TO 80 WITH 1000
: from Jahr & Stevens, JNS, 1990
mgblock = 1 / (1 + exp(0.062 (/mV) * -v) * (mg / 3.57 (mM)))
}
NET_RECEIVE(weight (uS)) { : No use to weight, can be used instead of Pmax,
: if you want NetCon access to the synaptic
: conductance.
state_discontinuity(A, A + Pmax*factor)
state_discontinuity(B, B + Pmax*factor)
}