COMMENT
Updated Exp2Syn synapse with Mg-blocked nmda channel.
Defaul values of parameters (time constants etc) set to match synaptic channels in
striatal medium spiny neurons (Du et al., 2017; Chapman et al., 2003; Ding et al., 2008).
Robert . Lindroos @ ki . se
original comment:
________________
Two state kinetic scheme synapse described by rise time tau1,
and decay time constant tau2. The normalized peak condunductance is 1.
Decay time MUST be greater than rise time.
The solution of A->G->bath with rate constants 1/tau1 and 1/tau2 is
A = a*exp(-t/tau1) and
G = a*tau2/(tau2-tau1)*(-exp(-t/tau1) + exp(-t/tau2))
where tau1 < tau2
If tau2-tau1 -> 0 then we have a alphasynapse.
and if tau1 -> 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 glutamate
RANGE tau1_ampa, tau2_ampa, tau1_nmda, tau2_nmda
RANGE erev, g, i
RANGE i_ampa, i_nmda, g_ampa, g_nmda, ratio, I, G, mg, q, block, alpha, beta
RANGE ampa_scale_factor, nmda_scale_factor
RANGE damod, maxModNMDA,max2NMDA,maxModAMPA,max2AMPA,l1NMDA,l2NMDA,l1AMPA,l2AMPA
NONSPECIFIC_CURRENT i
USEION cal WRITE ical VALENCE 2
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(uS) = (microsiemens)
}
PARAMETER {
erev = 0.0 (mV)
tau1_ampa = 1.9 (ms)
tau2_ampa = 4.8 (ms) : tau2 > tau1
tau1_nmda = 5.52 (ms) : Chapman et al 2003; table 1, adult rat (rise time, rt = 12.13. rt ~= 2.197*tau (wiki;rise time) -> tau = 12.13 / 2.197 ~= 5.52
tau2_nmda = 231 (ms) : Chapman et al 2003 (table 1; adult)
ratio = 1 (1) : both components give same maximal amplitude of current
mg = 1 (mM)
alpha = 0.062
beta = 3.57
q = 2 : approx room temp ->
nmda_scale_factor = 1
ampa_scale_factor = 1
ca_ratio_ampa = 0.005
ca_ratio_nmda = 0.1
maxModNMDA = 1
max2NMDA = 1
maxModAMPA = 1
max2AMPA = 1
damod = 0
l1NMDA = 0
l2NMDA = 0
l1AMPA = 0
l2AMPA = 0
}
ASSIGNED {
v (mV)
i (nA)
g (uS)
factor_nmda
factor_ampa
i_ampa
i_nmda
g_ampa
g_nmda
block
I
G
ical (nA)
}
STATE {
A (uS)
B (uS)
C (uS)
D (uS)
}
INITIAL {
LOCAL tp
if (tau1_nmda/tau2_nmda > .9999) {
tau1_nmda = .9999*tau2_nmda
}
if (tau1_ampa/tau2_ampa > .9999) {
tau1_ampa = .9999*tau2_ampa
}
: NMDA
A = 0
B = 0
tp = (tau1_nmda*tau2_nmda)/(tau2_nmda - tau1_nmda) * log(tau2_nmda/tau1_nmda)
factor_nmda = -exp(-tp/tau1_nmda) + exp(-tp/tau2_nmda)
factor_nmda = 1/factor_nmda
: AMPA
C = 0
D = 0
tp = (tau1_ampa*tau2_ampa)/(tau2_ampa - tau1_ampa) * log(tau2_ampa/tau1_ampa)
factor_ampa = -exp(-tp/tau1_ampa) + exp(-tp/tau2_ampa)
factor_ampa = 1/factor_ampa
}
BREAKPOINT {
SOLVE state METHOD cnexp
: NMDA
g_nmda = (B - A) * modulation(maxModNMDA,max2NMDA,l1NMDA,l2NMDA)
block = MgBlock()
i_nmda = g_nmda * (v - erev) * block * nmda_scale_factor
: AMPA
g_ampa = (D - C) * modulation(maxModAMPA,max2AMPA,l1AMPA,l2AMPA)
i_ampa = g_ampa * (v - erev) * ampa_scale_factor
: total current
G = g_ampa + g_nmda
I = i_ampa + i_nmda
: splitting in ca and non ca currents
ical = i_ampa*ca_ratio_ampa + i_nmda*ca_ratio_nmda
i = i_ampa*(1-ca_ratio_ampa) + i_nmda*(1-ca_ratio_nmda)
}
DERIVATIVE state {
A' = -A/tau1_nmda*q
B' = -B/tau2_nmda*q
C' = -C/tau1_ampa*q
D' = -D/tau2_ampa*q
}
NET_RECEIVE(weight (uS)) {
A = A + weight*factor_nmda
B = B + weight*factor_nmda
C = C + weight*factor_ampa*ratio
D = D + weight*factor_ampa*ratio
}
FUNCTION MgBlock() {
MgBlock = 1 / (1 + mg * exp(-alpha * v) / beta )
}
FUNCTION modulation(m1,m2,l1,l2) {
: returns modulation factor
modulation = 1 + damod * ( (m1-1)*l1 + (m2-1)*l2 )
if (modulation < 0) {
modulation = 0
}
}