COMMENT
The kinetics part is obtained from Exp2Syn of NEURON.
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/(taudtaur)*(exp(t/taur) + exp(t/taud))
where taur < taud
If taudtaur > 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.
Added by Rishikesh Narayanan:
1. GHK based ionic currents for AMPA current
2. Weights, and their update, according Shouval et al., PNAS, 2002.
Details may be found in:
Narayanan R, Johnston D. The h current is a candidate mechanism for
regulating the sliding modification threshold in a BCMlike synaptic
learning rule. J Neurophysiol. 2010 Aug;104(2):102033.
ENDCOMMENT
NEURON {
POINT_PROCESS Wghkampa
USEION na WRITE ina
USEION k WRITE ik
USEION ca READ cai : Weight update requires cai
RANGE taur, taud
RANGE iampa,winit
RANGE P, Pmax, lr
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(uS) = (microsiemens)
(molar) = (1/liter)
(mM) = (millimolar)
FARADAY = (faraday) (coulomb)
R = (kmole) (joule/degC)
}
PARAMETER {
taur=2 (ms) <1e9,1e9>
taud = 10 (ms) <1e9,1e9>
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)
cai (mM)
celsius (degC)
Pmax=1e6 (cm/s)
alpha1=0.35 :Parameters for the Omega function.
beta1=80
alpha2=0.55
beta2=80
winit=1 (1)
}
ASSIGNED {
ina (nA)
ik (nA)
v (mV)
P (cm/s)
factor
iampa (nA)
lr
Area (cm2)
}
STATE {
A (cm/s)
B (cm/s)
w (1)
}
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
w=winit
}
BREAKPOINT {
SOLVE state METHOD cnexp
P=BA
: Area is just for unit conversion of ghk output
ina = P*w*ghk(v, nai, nao,1)*Area
ik = P*w*ghk(v, ki, ko,1)*Area
iampa = ik + ina
}
DERIVATIVE state {
lr=eta(cai)
w' = lr*(Omega(cai)w)
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) < 1e4) {
efun = 1  z/2
}else{
efun = z/(exp(z)  1)
}
}
FUNCTION eta(ci (mM)) { : when ci is 0, inv has to be 3 hours.
LOCAL inv, P1, P2, P3, P4
P1=100
P2=P1*1e4 : There was a slip in the paper, which says P2=P1/1e4
P4=1e3
P3=3 : Cube, directly multiplying, see below.
ci=(ci1e4)*1e3 : The function takes uM, and we get mM.
inv=P4 + P1/(P2+ci*ci*ci) :As P3 is 3, set ci^P3 as ci*ci*ci.
eta=1/inv
}
FUNCTION Omega(ci (mM)) {
ci=(ci1e4)*1e3 : The function takes uM, and we get mM.
Omega=0.25+1/(1+exp((cialpha2)*beta2))0.25/(1+exp((cialpha1)*beta1))
}
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)
}
