CA1 pyramidal neuron: as a 2-layer NN and subthreshold synaptic summation (Poirazi et al 2003)

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Accession:20212
We developed a CA1 pyramidal cell model calibrated with a broad spectrum of in vitro data. Using simultaneous dendritic and somatic recordings, and combining results for two different response measures (peak vs. mean EPSP), two different stimulus formats (single shock vs. 50 Hz trains), and two different spatial integration conditions (within vs. between-branch summation), we found the cell's subthreshold responses to paired inputs are best described as a sum of nonlinear subunit responses, where the subunits correspond to different dendritic branches. In addition to suggesting a new type of experiment and providing testable predictions, our model shows how conclusions regarding synaptic arithmetic can be influenced by an array of seemingly innocuous experimental design choices.
References:
1 . Poirazi P, Brannon T, Mel BW (2003) Arithmetic of subthreshold synaptic summation in a model CA1 pyramidal cell. Neuron 37:977-87 [PubMed]
2 . Poirazi P, Brannon T, Mel BW (2003) Pyramidal neuron as two-layer neural network. Neuron 37:989-99 [PubMed]
3 . Poirazi P, Brannon T, Mel BW (2003ab-sup) Online Supplement: About the Model Neuron 37 Online:1-20
4 . Polsky A, Mel BW, Schiller J (2004) Computational subunits in thin dendrites of pyramidal cells. Nat Neurosci 7:621-7 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Hippocampus CA1 pyramidal cell;
Channel(s): I Na,p; I Na,t; I L high threshold; I T low threshold; I A; I K; I M; I h; I K,Ca; I Calcium;
Gap Junctions:
Receptor(s): GabaA; GabaB; NMDA; Glutamate;
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Action Potential Initiation; Activity Patterns; Dendritic Action Potentials; Active Dendrites; Influence of Dendritic Geometry; Detailed Neuronal Models; Action Potentials; Depression; Delay;
Implementer(s): Poirazi, Panayiota [poirazi at imbb.forth.gr];
Search NeuronDB for information about:  Hippocampus CA1 pyramidal cell; GabaA; GabaB; NMDA; Glutamate; I Na,p; I Na,t; I L high threshold; I T low threshold; I A; I K; I M; I h; I K,Ca; I Calcium;
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CA1_multi
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VClamp.omod *
                            
TITLE Low threshold calcium current
:
:   Ca++ current responsible for low threshold spikes (LTS)
:   Differential equations
:
:   Model of Huguenard & McCormick, J Neurophysiol 68: 1373-1383, 1992.
:   The kinetics is described by Goldman-Hodgkin-Katz equations,
:   using a m2h format, according to the voltage-clamp data
:   (whole cell patch clamp) of Huguenard & Prince, J. Neurosci. 
:   12: 3804-3817, 1992.
:
:   This model is described in detail in:
:   Destexhe A, Neubig M, Ulrich D and Huguenard JR.  
:   Dendritic low-threshold calcium currents in thalamic relay cells.  
:   Journal of Neuroscience 18: 3574-3588, 1998.
:   (a postscript version of this paper, including figures, is available on
:   the Internet at http://cns.fmed.ulaval.ca)
:
:    - shift parameter for screening charge
:    - empirical correction for contamination by inactivation (Huguenard)
:    - GHK equations
:
:
:   Written by Alain Destexhe, Laval University, 1995
:

INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}

NEURON {
	SUFFIX itGHK
	USEION ca READ cai,cao WRITE ica
	RANGE pcabar, m_inf, tau_m, h_inf, tau_h, shift, actshift
	GLOBAL qm, qh
}

UNITS {
	(molar) = (1/liter)
	(mV) =	(millivolt)
	(mA) =	(milliamp)
	(mM) =	(millimolar)

	FARADAY = (faraday) (coulomb)
	R = (k-mole) (joule/degC)
}

PARAMETER {
	v		(mV)
	celsius	= 36	(degC)
	pcabar	=.2e-3	(cm/s)	: Maximum Permeability
	shift	= 2 	(mV)	: corresponds to 2mM ext Ca++
	actshift = 0 	(mV)	: shift of activation curve (towards hyperpol)
	cai	= 2.4e-4 (mM)	: adjusted for eca=120 mV
	cao	= 2	(mM)
	qm	= 5		: q10's for activation and inactivation
	qh	= 3		: from Coulter et al., J Physiol 414: 587, 1989
}

STATE {
	m h
}

ASSIGNED {
	ica	(mA/cm2)
	m_inf
	tau_m	(ms)
	h_inf
	tau_h	(ms)
	phi_m
	phi_h
}

BREAKPOINT {
	SOLVE castate METHOD euler
	ica = pcabar * m*m*h * ghk(v, cai, cao)
}

DERIVATIVE castate {
	evaluate_fct(v)

	m' = (m_inf - m) / tau_m
	h' = (h_inf - h) / tau_h
}


UNITSOFF
INITIAL {
	phi_m = qm ^ ((celsius-24)/10)
	phi_h = qh ^ ((celsius-24)/10)

	evaluate_fct(v)

	m = m_inf
	h = h_inf
}

PROCEDURE evaluate_fct(v(mV)) {
:
:   The kinetic functions are taken as described in the model of 
:   Huguenard & McCormick, and corresponds to a temperature of 23-25 deg.
:   Transformation to 36 deg assuming Q10 of 5 and 3 for m and h
:   (as in Coulter et al., J Physiol 414: 587, 1989).
:
:   The activation functions were estimated by John Huguenard.
:   The V_1/2 were of -57 and -81 in the vclamp simulations, 
:   and -60 and -84 in the current clamp simulations.
:
:   The activation function were empirically corrected in order to account
:   for the contamination of inactivation.  Therefore the simulations 
:   using these values reproduce more closely the voltage clamp experiments.
:   (cfr. Huguenard & McCormick, J Neurophysiol, 1992).
:
	m_inf = 1.0 / ( 1 + exp(-(v+shift+actshift+57)/6.2) )
	h_inf = 1.0 / ( 1 + exp((v+shift+81)/4.0) )

	tau_m = ( 0.612 + 1.0 / ( exp(-(v+shift+actshift+132)/16.7) + exp((v+shift+actshift+16.8)/18.2) ) ) / phi_m
	if( (v+shift) < -80) {
		tau_h = exp((v+shift+467)/66.6) / phi_h
	} else {
		tau_h = ( 28 + exp(-(v+shift+22)/10.5) ) / phi_h
	}
}

FUNCTION ghk(v(mV), ci(mM), co(mM)) (.001 coul/cm3) {
	LOCAL z, eci, eco
	z = (1e-3)*2*FARADAY*v/(R*(celsius+273.15))
	eco = co*efun(z)
	eci = ci*efun(-z)
	:high cao charge moves inward
	:negative potential charge moves inward
	ghk = (.001)*2*FARADAY*(eci - eco)
}

FUNCTION efun(z) {
	if (fabs(z) < 1e-4) {
		efun = 1 - z/2
	}else{
		efun = z/(exp(z) - 1)
	}
}
FUNCTION nongat(v,cai,cao) {	: non gated current
	nongat = pcabar * ghk(v, cai, cao)
}
UNITSON

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