TITLE Triple-exponential model of NMDA receptors
COMMENT
This is an espetial version of SynExp5NMDA.mod model, which do not have desesitization,
and also resets automatically 17 and 55 ms after start of simulation
We use it to fit tree different recordings of NMDA at the same time
Desensitization is introduced in this model. Actually, this model has 4 differential equations
becasue desensitization is solved analitically. It can be reduced to 3 by solving its A state analitically.
For more info read the original paper.
Keivan Moradi 2012
This provides a simple 5-exponential model of an NMDA originally written by Keivan Moradi 2011
Mg++ voltage dependency from Spruston95 -> Woodhull, 1973
ENDCOMMENT
NEURON {
POINT_PROCESS Exp5NMDA3
NONSPECIFIC_CURRENT i
RANGE tau1, tau2_0, a2, b2, wtau2, tau3_0, a3, b3, tauV, e, i, gVI, gVDst, gVDv0, Mg, K0, delta, tp, wf
GLOBAL inf, tau2, tau3
THREADSAFE
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(uS) = (microsiemens)
(mM) = (milli/liter)
(S) = (siemens)
(pS) = (picosiemens)
(um) = (micron)
(J) = (joules)
}
PARAMETER {
: Parameters Control Neurotransmitter and Voltage-dependent gating of NMDAR
tau1 = 1.69 (ms) <1e-9,1e9> : Spruston95 CA1 dend [Mg=0 v=-80 celcius=18] be careful: Mg can change these values
: parameters control exponential rise to a maximum of tau2
tau2_0 = 3.97 (ms)
a2 = 0.70 (ms)
b2 = 0.0243 (1/mV)
wtau2= 0.65 <1e-9,1> : Hestrin90
: parameters control exponential rise to a maximum of tau3
tau3_0 = 41.62 (ms)
a3 = 34.69 (ms)
b3 = 0.01 (1/mV)
: Hestrin90 CA1 soma [Mg=1 v=-40 celcius=30-32] the decay of the NMDA component of the EPSC recorded at temperatures above 30 degC
: the fast phase of decay, which accounted for 65%-+12% of the decay, had a time constant of 23.5-+3.8 ms,
: whereas the slow component had a time constant of 123-+83 ms.
: wtau2= 0.78 Spruston95 CA1 dend [Mg=0 v=-80 celcius=18] percentage of contribution of tau2 in deactivation of NMDAR
Q10_tau1 = 2.2 : Hestrin90
Q10_tau2 = 3.68 : Hestrin90 -> 3.5-+0.9, Korinek10 -> NR1/2B -> 3.68
Q10_tau3 = 2.65 : Korinek10
T0_tau = 35 (degC) : reference temperature
: Hestrin90 CA1 soma [Mg=1 v=-40 celcius=31.5->25] The average Q10 for the rising phase was 2.2-+0.5,
: and that for the major fast decaying phase was 3.5-+0.9
tp = 30 (ms) : time of the peack -> when C + B - A reaches the maximum value or simply when NMDA has the peack current
: tp should be recalculated when tau1 or tau2 or tau3 changes
: Parameters Control voltage-dependent gating of NMDAR
tauV = 7 (ms) <1e-9,1e9> : Kim11
: at 26 degC & [Mg]o = 1 mM,
: [Mg]o = 0 reduces value of this parameter
: Because TauV at room temperature (20) & [Mg]o = 1 mM is 9.12 Clarke08 & Kim11
: and because Q10 at 26 degC is 1.52
: then tauV at 26 degC should be 7
gVDst = 0.007 (1/mV) : steepness of the gVD-V graph from Clarke08 -> 2 units / 285 mv
gVDv0 = -100 (mV) : Membrane potential at which there is no voltage dependent current, from Clarke08 -> -90 or -100
gVI = 1 (uS) : Maximum Conductance of Voltage Independent component, This value is used to calculate gVD
Q10 = 1.52 : Kim11
T0 = 26 (degC) : reference temperature
celsius (degC) : actual temperature for simulation, defined in Neuron, usually about 35
: Parameters Control Mg block of NMDAR
Mg = 1 (mM) : external magnesium concentration from Spruston95
K0 = 4.1 (mM) : IC50 at 0 mV from Spruston95
delta = 0.8 (1) : the electrical distance of the Mg2+ binding site from the outside of the membrane from Spruston95
: The Parameter Controls Ohm haw in NMDAR
e = -0.7 (mV) : in CA1-CA3 region = -0.7 from Spruston95
}
CONSTANT {
T = 273.16 (degC)
F = 9.648e4 (coul) : Faraday's constant (coulombs/mol)
R = 8.315 (J/degC): universal gas constant (joules/mol/K)
z = 2 (1) : valency of Mg2+
}
ASSIGNED {
v (mV)
dt (ms)
i (nA)
g (uS)
factor
wf
q10_tau2
q10_tau3
inf (uS)
tau (ms)
tau2 (ms)
tau3 (ms)
wtau3
}
STATE {
A : Gating in response to release of Glutamate
B : Gating in response to release of Glutamate
C : Gating in response to release of Glutamate
gVD (uS): Voltage dependent gating
}
INITIAL {
Mgblock(v)
: temperature-sensitivity of the of NMDARs
tau1 = tau1 * Q10_tau1^((T0_tau - celsius)/10(degC))
q10_tau2 = Q10_tau2^((T0_tau - celsius)/10(degC))
q10_tau3 = Q10_tau3^((T0_tau - celsius)/10(degC))
: temperature-sensitivity of the slow unblock of NMDARs
tau = tauV * Q10^((T0 - celsius)/10(degC))
rates(v)
wtau3 = 1 - wtau2
: if tau3 >> tau2 and wtau3 << wtau2 -> Maximum conductance is determined by tau1 and tau2
: tp = tau1*tau2*log(tau2/(wtau2*tau1))/(tau2 - tau1)
factor = -exp(-tp/tau1) + wtau2*exp(-tp/tau2) + wtau3*exp(-tp/tau3)
factor = 1/factor
A = 0
B = 0
C = 0
gVD = 0
wf = 1
net_send(17, 1)
net_send(55, 1)
}
BREAKPOINT {
SOLVE state METHOD derivimplicit
: we found acceptable results with "runge" integration method
: However Hines encouraged us to use "derivimplicit" method instead - which is slightly slower than runge -
: to avoid probable problems
i = (wtau3*C + wtau2*B - A)*(gVI + gVD)*Mgblock(v)*(v - e)
}
DERIVATIVE state {
rates(v)
A' = -A/tau1
B' = -B/tau2
C' = -C/tau3
: Voltage Dapaendent Gating of NMDA needs prior binding to Glutamate Kim11
gVD' = ((wtau3*C + wtau2*B)/wf)*(inf-gVD)/tau
: gVD' = (inf-gVD)/tau
}
NET_RECEIVE(weight) {
if (flag == 1) {
: this reseting part is temporarily used to fit all recordings at the same time
gVD = 0
A = 0
B = 0
C = 0
} else {
wf = weight*factor
A = A + wf
B = B + wf
C = C + wf
}
}
FUNCTION Mgblock(v(mV)) {
: from Spruston95
Mgblock = 1 / (1 + (Mg/K0)*exp((0.001)*(-z)*delta*F*v/R/(T+celsius)))
}
PROCEDURE rates(v (mV)) {
inf = (v - gVDv0) * gVDst * gVI
tau2 = (tau2_0 + a2*(1-exp(-b2*v)))*q10_tau2
tau3 = (tau3_0 + a3*(1-exp(-b3*v)))*q10_tau3
if (tau1/tau2 > .9999) {
tau1 = .9999*tau2
}
if (tau2/tau3 > .9999) {
tau2 = .9999*tau3
}
} |