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

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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).
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
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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;
Simulation Environment: C or C++ program;
Model Concept(s): Oscillations; Delay; Olfaction;
Search NeuronDB for information about:  Olfactory bulb main mitral GLU cell; GabaA; I Na,p; I Na,t; I A; I K;

	FirstOrderRk4.h												JJS 9/06/95
		modified from CONICAL, the Computational Neuroscience Class Library
	This header file does not declare a class, but rather, a general-
	purpose function for integrating first-order kinetic equations of 
	the form:
				dy/dt = alpha*(1-y) - beta*y
	This is equivalent to the kinetic reaction a <---> b, where y is the
	value of a (or b), 1-y is the value of the other, the forward reaction
	rate is alpha, and the backward rate is beta.  To use, write
				newy = FirstOrder( y, alpha, beta, dt )

		math library		-- ANSI math functions, defined in <math.h>


#include <math.h>

#ifndef real
#define real double

inline real FirstOrderRk4( real y, real alpha, real beta, real dt )
	real ratesum = alpha + beta;
	//Exp Euler 
    //return y + (alpha/ratesum - y) * (1 - exp(-ratesum*dt) );
    //Runge Kutta
    return  (alpha - ratesum*y)*dt;