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) Hodgkin and Huxley model still standing? Nature 445:E1-E2 [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 pyramidal corticothalamic L6 cell; Neocortex V1 pyramidal intratelencephalic L2-6 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 pyramidal corticothalamic L6 cell; Neocortex V1 pyramidal intratelencephalic L2-6 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;
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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 *
kca.mod'A=0
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
                            
TITLE Slow Ca-dependent potassium current
:
:   Ca++ dependent K+ current IC responsible for slow AHP
:   Differential equations
:
:   Model based on a first order kinetic scheme
:
:      <closed> + n cai <-> <open>	(alpha,beta)
:
:   Following this model, the activation fct will be half-activated at 
:   a concentration of Cai = (beta/alpha)^(1/n) = cac (parameter)
:
:   The mod file is here written for the case n=2 (2 binding sites)
:   ---------------------------------------------
:
:   This current models the "slow" IK[Ca] (IAHP): 
:      - potassium current
:      - activated by intracellular calcium
:      - NOT voltage dependent
:
:   A minimal value for the time constant has been added
:
:   Ref: Destexhe et al., J. Neurophysiology 72: 803-818, 1994.
:
:   Modifications by Arthur Houweling for use in MyFirstNEURON


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

NEURON {
	SUFFIX iAHP2
	USEION k READ ek WRITE ik
	USEION ca READ cai
        RANGE gkbar, m_inf, tau_m
	GLOBAL beta, cac
	RANGE ik
}


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


PARAMETER {
	v		(mV)
	celsius		(degC)
        dt              (ms)
	ek		(mV)
	cai		(mM)	
	gkbar	= .03	(mho/cm2)
:	gkbar	= .01	(mho/cm2)
	beta	= 0.03	(1/ms)		: backward rate constant
	cac	= 0.025	(mM)		: middle point of activation fct
	taumin	= 0.1	(ms)		: minimal value of the time cst
}


STATE {
	m
}

ASSIGNED {
	ik	(mA/cm2)
	m_inf
	tau_m	(ms)
	tadj
}

BREAKPOINT { 
	SOLVE states :METHOD euler
	ik = gkbar * m*m * (v - ek)
}

:DERIVATIVE states {
:       evaluate_fct(v,cai)
:
:       m'= (m_inf-m) / tau_m 
:}
  
PROCEDURE states() {
        evaluate_fct(v,cai)

        m= m + (1-exp(-dt/tau_m))*(m_inf-m)
}

UNITSOFF
INITIAL {
:
:  activation kinetics are assumed to be at 22 deg. C
:  Q10 is assumed to be 3
:
	tadj = 3 ^ ((celsius-22.0)/10)

	evaluate_fct(v,cai)
	m = m_inf
}

PROCEDURE evaluate_fct(v(mV),cai(mM)) {  LOCAL car

	car = (cai/cac)^2

	m_inf = car / ( 1 + car )
	tau_m = 1 / beta / (1 + car) / tadj

        if(tau_m < taumin) { tau_m = taumin } 	: min value of time cst
}
UNITSON

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