AP back-prop. explains threshold variability and rapid rise (McCormick et al. 2007, Yu et al. 2008)

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Accession:135839
This simple axon-soma model explained how the rapid rising phase in the somatic spike is derived from the propagated axon initiated spike, and how the somatic spike threshold variance is affected by spike propagation.
References:
1 . McCormick DA, Shu Y, Yu Y (2007) Neurophysiology: Hodgkin and Huxley model--still standing? Nature 445:E1-2; discussion E2-3 [PubMed]
2 . Yu Y, Shu Y, McCormick DA (2008) Cortical action potential backpropagation explains spike threshold variability and rapid-onset kinetics. J Neurosci 28:7260-72 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Axon;
Brain Region(s)/Organism: Neocortex;
Cell Type(s): Neocortex V1 L6 pyramidal corticothalamic cell; Neocortex V1 L2/6 pyramidal intratelencephalic cell;
Channel(s): I Na,t; I L high threshold; I T low threshold; I A; I K; I M; I h; I K,Ca; I_AHP;
Gap Junctions:
Receptor(s): GabaA; NMDA;
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Action Potential Initiation; Detailed Neuronal Models;
Implementer(s):
Search NeuronDB for information about:  Neocortex V1 L6 pyramidal corticothalamic cell; Neocortex V1 L2/6 pyramidal intratelencephalic cell; GabaA; NMDA; I Na,t; I L high threshold; I T low threshold; I A; I K; I M; I h; I K,Ca; I_AHP;
/
McCormickEtAl2007YuEtAl2008
readme.txt
ca.mod *
cad.mod *
caL3d.mod *
capump.mod
gabaa5.mod *
Gfluct.mod *
ia.mod *
iahp.mod *
iahp2.mod *
ih.mod
im.mod *
kca.mod *
km.mod *
kv.mod *
na.mod *
NMDA_Mg.mod *
nmda5.mod *
release.mod *
for_plot_spike.m
mosinit.hoc
neuron_soma.dat
Rapid_rising_somatic_spike_soma_axon.hoc
                            
COMMENT

High threshold Ca2+ channel

2-state kinetics with sigmoidal voltage-dependence

  C<->O

Goldman-Hodgkin-Katz equations

     # MODEL
    |   MODEL AUTHOR  : D.A. McCormick & J. Huguenard
    |   MODEL DATE    : 1992
    |   MODEL REF     : A model of the electrophysiological properties of 
thalamocortical relay neurons. J Neurophysiol, 1992 Oct, 68(4):1384-400.
 
    # EXPERIMENT
    |   EXP AUTHOR    : Kay AR; Wong RK
    |   EXP DATE      : 1987
    |   EXP REF       : Journal of Physiology, 1987 Nov, 392:603-16.
    |   ANIMAL        : guinea-pig
    |   BRAIN REGION  : hippocampus
    |   CELL TYPE     : Ca1 pyramidal
    |   TECHNIQUE     : slices, whole-cell
    |   RECORDING METHOD  : voltage-clamp
    |   TEMPERATURE   : 20-22
 
Reference:

   Destexhe, A., Mainen, Z.F. and Sejnowski, T.J. Synthesis of models for
   excitable membranes, synaptic transmission and neuromodulation using a 
   common kinetic formalism, Journal of Computational Neuroscience 1: 
   195-230, 1994.

  (electronic copy available at http://cns.iaf.cnrs-gif.fr)


ENDCOMMENT

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

NEURON {
	SUFFIX caL3d
	USEION ca READ cai, cao WRITE ica
	RANGE O, C, I
	RANGE a,b
	GLOBAL Ra, Rb, q, th, p
	GLOBAL q10, temp, tadj
}

UNITS {
	F = (faraday) (coulomb)
	R = (k-mole) (joule/degC)
	(mA) = (milliamp)
	(mV) = (millivolt)
	(pS) = (picosiemens)
	(um) = (micron)
	(mM) = (milli/liter)
} 

PARAMETER {
	p    = 0.2e-3  	(cm/s)		: max permeability
	v 		(mV)

	th   = 5	(mV)		: v 1/2 for on/off
	q   = 13	(mV)		: voltage dependence

	: max rates

	Ra   = 1.6	(/ms)		: open (v)
	Rb   = 0.2	(/ms)		: close (v)

	celsius		(degC)
	temp = 22	(degC)		: original temp
	q10  = 3			: temperature sensitivity
} 


ASSIGNED {
	ica 		(mA/cm2)
	cao		(mM)
	cai		(mM)
	a (/ms)	b (/ms)
	tadj
}
 

STATE { C O }

INITIAL { 
	C = 1 
}


BREAKPOINT {
	rates(v)
	SOLVE kstates METHOD sparse
	ica = O * p * ghk(v,cai,cao)
} 


KINETIC kstates {
	~ C <-> O 	(a,b)	
	CONSERVE C+O = 1
}	
	
PROCEDURE rates(v(mV)) {
	TABLE a, b
	DEPEND Ra, Rb, th, celsius, temp, q10
	FROM -100 TO 100 WITH 200

	tadj = q10 ^ ((celsius - temp)/10 (degC))

	a = Ra / (1 + exp(-(v-th)/q)) * tadj
	b = Rb / (1 + exp((v-th)/q)) * tadj
}

: Special gear for calculating the Ca2+ reversal potential
: via Goldman-Hodgkin-Katz eqn.
: [Ca2+]o "cao" and [Ca2+]i "cai" are assumed to be set elsewhere


FUNCTION ghk(v(mV), ci(mM), co(mM)) (0.001 coul/cm3) {
	LOCAL z

	z = (0.001)*2*F*v/(R*(celsius+273.15))
	ghk = (.001)*2*F*(ci*efun(-z) - co*efun(z))
}

FUNCTION efun(z) {
	if (fabs(z) < 1e-4) {
		efun = 1 - z/2
	}else{
		efun = z/(exp(z) - 1)
	}
}





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