A fast model of voltage-dependent NMDA Receptors (Moradi et al. 2013)

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Accession:145836
These are two or triple-exponential models of the voltage-dependent NMDA receptors. Conductance of these receptors increase voltage-dependently with a "Hodgkin and Huxley-type" gating style that is also depending on glutamate-binding. Time course of the gating of these receptors in response to glutamate are also changing voltage-dependently. Temperature sensitivity and desensitization of these receptor are also taken into account. Three previous kinetic models that are able to simulate the voltage-dependence of the NMDARs are also imported to the NMODL. These models are not temperature sensitive. These models are compatible with the "event delivery system" of NEURON. Parameters that are reported in our paper are applicable to CA1 pyramidal cell dendrites.
Reference:
1 . Moradi K, Moradi K, Ganjkhani M, Hajihasani M, Gharibzadeh S, Kaka G (2013) A fast model of voltage-dependent NMDA receptors J Comput Neurosci 34(3):521-531 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Synapse;
Brain Region(s)/Organism: Neocortex; Hippocampus;
Cell Type(s): Hippocampus CA1 pyramidal cell;
Channel(s):
Gap Junctions:
Receptor(s): NMDA; Glutamate;
Gene(s): NR2B GRIN2B;
Transmitter(s): Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Ion Channel Kinetics; Simplified Models; Long-term Synaptic Plasticity; Methods;
Implementer(s): Moradi, Keivan [k.moradi at gmail.com];
Search NeuronDB for information about:  Hippocampus CA1 pyramidal cell; NMDA; Glutamate; Glutamate;
TITLE Triple-exp model of NMDAR has (HH-type gating) (temp. sensitivity) (voltage-dependent time constants) (desensitization)

COMMENT
This is a Triple-exponential model of an NMDAR 
that has a slow voltage-dependent gating component in its conductance
time constants are voltage-dependent and temperature sensitive

Mg++ voltage dependency from Spruston95 -> Woodhull, 1973 

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

ENDCOMMENT

NEURON {
	POINT_PROCESS Exp5NMDA
	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, tau_D1, d1
	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 desensitization of the channel
	: these values are from Fig.3 in Varela et al. 1997
	: the (1) is needed for the range limits to be effective
	d1 = 0.2 	  	(1)		< 0, 1 >     : fast depression
	tau_D1 = 2500 	(ms)	< 1e-9, 1e9 >
: 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
: 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
}

BREAKPOINT {
	SOLVE state METHOD runge : derivimplicit : 
	: we found acceptable results with "runge" integration method
	: However, M. Hines encouraged us to use "derivimplicit" method instead - which is slightly slower than runge - 
	: to avoid probable unstability 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, D1, tsyn (ms)) {
	INITIAL {
	: these are in NET_RECEIVE to be per-stream
	: this header will appear once per stream
		D1 = 1
		tsyn = t
	}

	D1 = 1 - (1-D1)*exp(-(t - tsyn)/tau_D1)
	tsyn = t

	wf = weight*factor*D1
	A = A + wf
	B = B + wf
	C = C + wf

	D1 = D1 * d1
}

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
	}
}

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