Olfactory bulb network model of gamma oscillations (Bathellier et al. 2006; Lagier et al. 2007)

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Accession:91387
This model implements a network of 100 mitral cells connected with asynchronous inhibitory "synapses" that is meant to reproduce the GABAergic transmission of ensembles of connected granule cells. For appropriate parameters of this special synapse the model generates gamma oscillations with properties very similar to what is observed in olfactory bulb slices (See Bathellier et al. 2006, Lagier et al. 2007). Mitral cells are modeled as single compartment neurons with a small number of different voltage gated channels. Parameters were tuned to reproduce the fast subthreshold oscillation of the membrane potential observed experimentally (see Desmaisons et al. 1999).
References:
1 . Bathellier B, Lagier S, Faure P, Lledo PM (2006) Circuit properties generating gamma oscillations in a network model of the olfactory bulb. J Neurophysiol 95:2678-91 [PubMed]
2 . Lagier S, Panzanelli P, Russo RE, Nissant A, Bathellier B, Sassoè-Pognetto M, Fritschy JM, Lledo PM (2007) GABAergic inhibition at dendrodendritic synapses tunes gamma oscillations in the olfactory bulb. Proc Natl Acad Sci U S A 104:7259-64 [PubMed]
3 . Bathellier B, Lagier S, Faure P, Lledo PM (2006) Corrigendum for Bathellier et al., J Neurophysiol 95 (4) 2678-2691. J Neurophysiol 95:3961-3962
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Olfactory bulb;
Cell Type(s): Olfactory bulb main mitral GLU cell;
Channel(s): I Na,p; I Na,t; I A; I K;
Gap Junctions:
Receptor(s): GabaA;
Gene(s):
Transmitter(s):
Simulation Environment: C or C++ program;
Model Concept(s): Oscillations; Delay; Olfaction;
Implementer(s):
Search NeuronDB for information about:  Olfactory bulb main mitral GLU cell; GabaA; I Na,p; I Na,t; I A; I K;
/**************************************************************************

	StdForms.h													JJS 9/08/95
	
		part of CONICAL, the Computational Neuroscience Class Library
	
	This file does not define a class; rather, it defines some standard
	formulas which are frequently used to describe channel gating, etc.
	It also defines some constants and a front-end function for accessing
	compatible functions through a single call (StdFormula) if the format
	is only known at runtime.
	
	Requires:
		math			-- ANSI math functions (defined in <math.h>)
		
**************************************************************************/

#ifndef STDFORMS_H
#define STDFORMS_H

#ifndef real
#define real double
#endif

#include <math.h>

enum StdForm {
	kExpForm,
	kSigForm,
	kSioForm,
	kLinForm,
	kCstForm,
	kKftForm,
	kKslForm,
	kWangForm,
	kAmForm,
	kAh1Form,
	kAh2Form,
kQtyForms };

inline real ExpForm(real v, real A, real B, real V0)
{
	return A * exp((v-V0)/B);
}

inline real SigForm(real v, real A, real B, real V0)
{
	return A / (exp((v-V0)/B) + 1);
}

inline real LinForm(real v, real A, real B, real V0)
{
	return (v==V0 ? A : A * (v-V0) / (exp((v-V0)/B)  - 1) );
}

inline real CstForm( real A)
{
	return A ;
}

inline real SioForm(real v, real A, real B, real V0, real C)
{
	return C + A / (exp((v-V0)/B) + 1);
}

inline real WangForm(real v, real A, real B, real V0, real C)
{
	return A *exp(C*(v-V0)/B)/ (exp((v-V0)/B) + 1);
}

inline real KftForm(real v)
{
	if(v<-0.043) return 0.95889E-3 + 0.209E-3 * exp( v/0.03938 ) ;
	if(v>=-0.043 && v<-0.025) return 2.6597E-3 + 0.5108E-3* exp(-2*pow((v+34.559E-3)/14.031E-3 ,2));
	if(v>=-0.025 && v<0.032)  return 0.117E-3 + 3.2E-3/(exp((v+0.00309)/0.01361)+1);
    if(v>=0.032) return 0.34E-3;
}

inline real AmForm(real v)
{
    return 1E-3*(1/( exp((v+0.0358)/0.0197)+exp(-(v+0.0797)/0.0127) ) + 0.37); 
}

inline real Ah1Form(real v)
{
    if(v<-0.063) return 1E-3/( exp((v+0.046)/0.0197)+exp(-(v+0.238)/0.0375) ) ;
    if(v>=-0.063) return 19E-3; 
}

inline real Ah2Form(real v)
{
    if(v<-0.073) return 1E-3/( exp((v+0.046)/0.0197)+exp(-(v+0.238)/0.0375) ) ;
    if(v>=-0.073) return 60E-3; 
}

inline real StdFormula( StdForm pForm, real V, real A, real B, real V0, real C )
{
	switch (pForm) {
		case kExpForm: return ExpForm( V, A, B, V0 );
		case kSigForm: return SigForm( V, A, B, V0 );
		case kSioForm: return SioForm( V, A, B, V0, C);
		case kLinForm: return LinForm( V, A, B, V0 );
		case kCstForm: return CstForm( A );
		case kWangForm: return WangForm(V, A, B, V0, C);
        case kKftForm: return KftForm( V );
		case kKslForm: return 4*KftForm( V );
		case kAmForm: return AmForm(V);
		case kAh1Form: return Ah1Form(V);
		case kAh2Form: return Ah2Form(V);
	}
	return 0;
}

#endif

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