Stochastic Ih and Na-channels in pyramidal neuron dendrites (Kole et al 2006)

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Accession:64195
The hyperpolarization-activated cation current (Ih) plays an important role in regulating neuronal excitability, yet its native single-channel properties in the brain are essentially unknown. Here we use variance-mean analysis to study the properties of single Ih channels in the apical dendrites of cortical layer 5 pyramidal neurons in vitro. ... In contrast to the uniformly distributed single-channel conductance, Ih channel number increases exponentially with distance, reaching densities as high as approximately 550 channels/microm2 at distal dendritic sites. These high channel densities generate significant membrane voltage noise. By incorporating a stochastic model of Ih single-channel gating into a morphologically realistic model of a layer 5 neuron, we show that this channel noise is higher in distal dendritic compartments and increased threefold with a 10-fold increased single-channel conductance (6.8 pS) but constant Ih current density. ... These data suggest that, in the face of high current densities, the small single-channel conductance of Ih is critical for maintaining the fidelity of action potential output. See paper for more and details.
Reference:
1 . Kole MH, Hallermann S, Stuart GJ (2006) Single Ih channels in pyramidal neuron dendrites: properties, distribution, and impact on action potential output. J Neurosci 26:1677-87 [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): Neocortex V1 L6 pyramidal corticothalamic GLU cell;
Channel(s): I h;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Ion Channel Kinetics; Active Dendrites;
Implementer(s): Hallermann, Stefan [hallermann at medizin.uni-leipzig.de];
Search NeuronDB for information about:  Neocortex V1 L6 pyramidal corticothalamic GLU cell; I h;
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Stochastic
Stochastic_Na
README.txt
ca.mod *
cad.mod *
caT.mod
ih_stochastic.mod
ka.mod
kca.mod *
km.mod *
kv.mod *
na.mod
syn.mod *
fig6B.hoc
fig7D.hoc
mosinit.hoc
Ri18geo.hoc *
Ri18init.hoc
shortRun.hoc
                            
TITLE stochastic Ih-channels

COMMENT

Author: Stefan Hallermann 

Provides Ih-channel stochastics as described in Kole et al. (2006).

In the initiation the number of channels (N) and the number of open channels (N_open)
is calculated for each segment and stored as a range variable. For each dt the Procedure
noise() is evaluated once. In noise() each open channel has the chance to close according
to the closing rate beta(v) and each close channels has the chance to open according to
the opening rate alpha(v). After this "update" of the number of open channels the
resulting current through the open channels (i) is calculated depending on the local
driving force in the segment.
	
ENDCOMMENT


UNITS {
	(mA) = (milliamp)
	(mV) = (millivolt)

}

PARAMETER {
	v 			(mV)
	ehd=-45  		(mV) 		:ih-reversal potential			       
	ghdbar=0.00015 		(S/cm2)		:default Ih conductance; exponential distribution is set in Ri18init.hoc 
	gamma=680e-15		(S)		:single channel cond
	seed
}


NEURON {
	SUFFIX ih
	NONSPECIFIC_CURRENT i
	RANGE ghdbar,N,N_open
}

STATE {
	l
}

ASSIGNED {
	i (mA/cm2)
	dt			(ms)
	area			(um2)
	N			:number of channels
	N_open			:number of open channels
}

INITIAL {								:calculates the number of Ih-channel per segment and the number of open channels at the initial potential
	N=abs(((1e-8*area*ghdbar)/gamma)+0.5)				:area in um2; 1e-8*area in cm2; ghdbar in S/cm2; gamma in S
	N_open=abs(N*alpha(v)/(alpha(v)+beta(v)))
	l=0								:only needed for dummy diff.eq.

	set_seed(seed)
}


BREAKPOINT {
	SOLVE states METHOD cnexp					:only needed to make the proc noise() be evaluated once per dt (breakpoint() is evaluated twice per dt!)
	i = ((N_open*gamma)/(1e-8*area))*(v-ehd)			:cond/cm2 * delta_pot		(cond=N_open*gamma in S)
}


FUNCTION alpha(v(mV)) {
	:opening rate in 1/s
	alpha = 6.43*(v+154.9)/(exp((v+154.9)/11.9)-1)			:parameters are estimated by direct fitting of HH model to activation time constants and voltage activation curve recorded at 34C
}

FUNCTION beta(v(mV)) {
	:closing rate in 1/s
	beta = 193*exp(v/33.1)			
}


DERIVATIVE states {     						
	l' =  l			    					:dummy diff.eq.
	noise()
}

PROCEDURE noise() {
	LOCAL N_close,N_open_merk,N_close_merk,a,b,prob_open,prob_close
	a=alpha(v)
	b=beta(v)
	N_open_merk=N_open
	N_close_merk=N-N_open

	:activation	(all close channels have the chance to open with the probability prob_open depending on dt and the opening rate alpha(v))
	:(the approximation with the 1. and 2. element of exp. infinitive series is only little faster:  prob_open=dt*b/1000)
	prob_open=1-exp(-dt*a/1000)					:(/1000 since dt is in ms and rate beta in 1/s)
	FROM ii=1 TO N_close_merk {
		if (scop_random()<= prob_open)	{			:scop_random uniform between 0 and 1
			N_open=N_open+1
		}
	}

	:deactivation	(all open channels have the chance to close with the probability prob_close depending on dt and the closing rate beta(v))
	prob_close=1-exp(-dt*b/1000)	
	FROM ii=1 TO N_open_merk {
		if (scop_random()<= prob_close)	{		
			N_open=N_open-1
		}
	}
}





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