BCM-like synaptic plasticity with conductance-based models (Narayanan Johnston, 2010)

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Accession:147538
" ... Although the BCM-like plasticity framework has been a useful formulation to understand synaptic plasticity and metaplasticity, a mechanism for the activity-dependent regulation of this modification threshold has remained an open question. In this simulation study based on CA1 pyramidal cells, we use a modification of the calcium-dependent hypothesis proposed elsewhere and show that a change in the hyperpolarization-activated, nonspecific-cation h current is capable of shifting the modification threshold. ..."
Reference:
1 . Narayanan R, Johnston D (2010) The h current is a candidate mechanism for regulating the sliding modification threshold in a BCM-like synaptic learning rule. J Neurophysiol 104:1020-33 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Synapse; Channel/Receptor;
Brain Region(s)/Organism: Hippocampus;
Cell Type(s): Hippocampus CA1 pyramidal GLU cell;
Channel(s): I Na,t; I A; I h; I Potassium;
Gap Junctions:
Receptor(s): AMPA; NMDA;
Gene(s):
Transmitter(s): Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Active Dendrites; Synaptic Plasticity; Calcium dynamics;
Implementer(s): Narayanan, Rishikesh [rishi at iisc.ac.in];
Search NeuronDB for information about:  Hippocampus CA1 pyramidal GLU cell; AMPA; NMDA; I Na,t; I A; I h; I Potassium; Glutamate;
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/(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.

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 BCM-like synaptic 
learning rule.  J Neurophysiol. 2010 Aug;104(2):1020-33.

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 = (k-mole) (joule/degC)
}

PARAMETER {
	taur=2 		(ms) <1e-9,1e9>
	taud = 10 	(ms) <1e-9,1e9>
	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=1e-6   (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=B-A

: 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) < 1e-4) {
		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*1e-4	: There was a slip in the paper, which says P2=P1/1e-4
	P4=1e3
	P3=3		: Cube, directly multiplying, see below.

	ci=(ci-1e-4)*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=(ci-1e-4)*1e3	: The function takes uM, and we get mM.
	Omega=0.25+1/(1+exp(-(ci-alpha2)*beta2))-0.25/(1+exp(-(ci-alpha1)*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)
}

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