Sodium currents activate without a delay (Baranauskas and Martina 2006)

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Accession:62673
Hodgkin and Huxley established that sodium currents in the squid giant axons activate after a delay, which is explained by the model of a channel with three identical independent gates that all have to open before the channel can pass current (the HH model). It is assumed that this model can adequately describe the sodium current activation time course in all mammalian central neurons, although there is no experimental evidence to support such a conjecture. We performed high temporal resolution studies of sodium currents gating in three types of central neurons. ... These results can be explained by a model with two closed states and one open state. ... This model captures all major properties of the sodium current activation. In addition, the proposed model reproduces the observed action potential shape more accurately than the traditional HH model. See paper for more and details.
Reference:
1 . Baranauskas G, Martina M (2006) Sodium currents activate without a Hodgkin-and-Huxley-type delay in central mammalian neurons. J Neurosci 26:671-84 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Channel/Receptor;
Brain Region(s)/Organism:
Cell Type(s): Dentate gyrus granule GLU cell; Hippocampus CA1 pyramidal GLU cell; Neocortex L5/6 pyramidal GLU cell; Neocortex L2/3 pyramidal GLU cell;
Channel(s): I Na,t;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Action Potential Initiation; Ion Channel Kinetics; Action Potentials;
Implementer(s): Baranauskas, Gytis [baranauskas at elet.polimi.it];
Search NeuronDB for information about:  Dentate gyrus granule GLU cell; Hippocampus CA1 pyramidal GLU cell; Neocortex L5/6 pyramidal GLU cell; Neocortex L2/3 pyramidal GLU cell; I Na,t;
TITLE Two-closed one-open state sodium channel model 
: G Baranauskas November 2005, this model was developed by fitting
: voltage clamp data reported in J. Neurosci 26 pp 671-84 2006

NEURON {
     SUFFIX MCna1
     USEION na READ ena WRITE ina
     RANGE gna1bar, gna1, ina   
     GLOBAL cnt1, cnt2, Na_intern, Na_extern 
}

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

PARAMETER {

     gna1bar=.120 (mho/cm2) <0,1e9> : though this parameter has the
: same units as conductance because of the Goldman-Hodgkin-Katz
: formalism used here the real meaning of this value is
: P*[Na_extern]*F*F/RT. The conversion factor from this parameter to the
: conductance will depend on voltage and Na_inter and Na_extern defined
: in the BREAKPOINT fomula

     Na_intern = 15 (mM)
     Na_extern = 135 (mM)

}
STATE {
     C1 C2 O I1 I2 IO
}
ASSIGNED {
     v (mV)
     celsius (degC) : 6.3 
     ena (mV)
     cnt1 cnt2
     ina (mA/cm2)
     gna1 (mho/cm2)
}

ASSIGNED {  a1 (/ms)   b1 (/ms)  a2 (/ms)  b2 (/ms) a3 (/ms)  b3 (/ms)}

INITIAL {
	cnt1 = 0
	cnt2 = 0
     C1=1
     rate(v*1(/mV))
     SOLVE states STEADYSTATE sparse
}

BREAKPOINT {
     SOLVE states METHOD sparse
     gna1 = gna1bar*O

     ina = gna1*v*(Na_intern/Na_extern - exp(-v/25.4))/(1-exp(-v/25.4)) 
: the Goldman-Hodgkin-Katz equation was used to determine current 
: amplitude, in this case 15 mM Na_inter and 135 mM Na_extern was used

	cnt1 = cnt1 + 1
}

KINETIC states {
	cnt2 = cnt2 + 1
     rate(v*1(/mV))
:     CONSERVE I1 + I2 + IO + C1 + C2 + O = 1
     ~ I1 <-> I2 (a1, b1) 
     ~ C1 <-> C2 (a1, b1)         
   
     ~ I2 <-> IO (a2, b2)
     ~ C2 <-> O (a2, b2)

     ~ C1 <-> I1 (a3, b3)
     ~ C2 <-> I2 (a3, b3)      
     ~ O <-> IO (a3, b3)   
}

UNITSOFF

PROCEDURE rate(v) {LOCAL q10, q11 
     TABLE a1, a2, a3, b1, b2, b3 DEPEND celsius FROM -100 TO 100 WITH 200
     q10 = (2.8)^((celsius - 13)/10)  : the fit was performed at 13C
     q11 = (2.4)^((celsius - 13)/10) 
 
     a1 = q10*10*exp((v+6)/45) : a1 and b1 correspond to the fast
: transition and a2, b2 - the slow transition that determines kinetics

     a2 = q10*11/(0.4+exp(-(v+6)/12))
     b1 = q10*0.35*exp(-(v+6)/8)
     b2 = q10*0.035/(0.0015 + exp((v+6)/12))

     a3 = q11*2/(2+exp(-(v+6)/12))      : a3 and b3 are inactivation rates
     b3 = q11*0.00005*exp(-(v+6)/13)
}
UNITSON