A network of AOB mitral cells that produces infra-slow bursting (Zylbertal et al. 2017)

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Infra-slow rhythmic neuronal activity with very long (> 10 s) period duration was described in many brain areas but little is known about the role of this activity and the mechanisms that produce it. Here we combine experimental and computational methods to show that synchronous infra-slow bursting activity in mitral cells of the mouse accessory olfactory bulb (AOB) emerges from interplay between intracellular dynamics and network connectivity. In this novel mechanism, slow intracellular Na+ dynamics endow AOB mitral cells with a weak tendency to burst, which is further enhanced and stabilized by chemical and electrical synapses between them. Combined with the unique topology of the AOB network, infra-slow bursting enables integration and binding of multiple chemosensory stimuli over prolonged time scale. The example protocol simulates a two-glomeruli network with a single shared cell. Although each glomerulus is stimulated at a different time point, the activity of the entire population becomes synchronous (see paper Fig. 8)
1 . Zylbertal A, Yarom Y, Wagner S (2017) Synchronous Infra-Slow Bursting in the Mouse Accessory Olfactory Bulb Emerge from Interplay between Intrinsic Neuronal Dynamics and Network Connectivity. J Neurosci 37:2656-2672 [PubMed]
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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 (accessory) mitral cell;
Channel(s): I CAN; Na/Ca exchanger; Na/K pump; I Calcium; I Na,t;
Gap Junctions: Gap junctions;
Simulation Environment: NEURON; Python;
Model Concept(s): Bursting; Synchronization; Activity Patterns; Oscillations; Persistent activity; Olfaction;
Implementer(s): Zylbertal, Asaph [asaph.zylbertal at mail.huji.ac.il];
Search NeuronDB for information about:  I Na,t; I CAN; I Calcium; Na/Ca exchanger; Na/K pump;
26 Ago 2002 Modification of original channel to allow variable time step and to correct an initialization error.
    Done by Michael Hines(michael.hines@yale.e) and Ruggero Scorcioni(rscorcio@gmu.edu) at EU Advance Course in Computational Neuroscience. Obidos, Portugal


Sodium channel, Hodgkin-Huxley style kinetics.  

Kinetics were fit to data from Huguenard et al. (1988) and Hamill et
al. (1991)

qi is not well constrained by the data, since there are no points
between -80 and -55.  So this was fixed at 5 while the thi1,thi2,Rg,Rd
were optimized using a simplex least square proc

voltage dependencies are shifted approximately from the best
fit to give higher threshold

Author: Zach Mainen, Salk Institute, 1994, zach@salk.edu

May 2006: set the tha -28 mV, vshift 0 and thinf -55 mV to comply with measured 
Somatic Na+ kinetics in neocortex. Kole, ANU, 2006



	SUFFIX nat : renenamed to account for transient behaviour (Armin, Jul 09)
	RANGE m, h, gna, gbar, vshift, vshift2, timefactor_m, timefactor_h,gbarfactor, ina
	GLOBAL tha, thi1, thi2, qa, qi, qinf, thinf
	RANGE minf, hinf, mtau, htau
	GLOBAL Ra, Rb, Rd, Rg
	GLOBAL q10, temp, tadj, vmin, vmax


	gbar = 0   	(S/cm2)	: 0.12 mho/cm2
	vshift = 0	(mV)		: voltage shift
	vshift2 = 0	(mV)		: voltage shift 2
	tha  = -28	(mV)		: v 1/2 for act		(-42)
	qa   = 9	(mV)			: act slope		
	Ra   = 0.182	(/ms)	: open (v)		
	Rb   = 0.124	(/ms)	: close (v)		

	thi1  = -50	(mV)		: v 1/2 for inact 	
	thi2  = -75	(mV)		: v 1/2 for inact 	
	qi   = 5	(mV)	        	: inact tau slope
	thinf  = -55	(mV)		: inact inf slope	
	qinf  = 6.2	(mV)		: inact inf slope
	Rg   = 0.0091	(/ms)	: inact (v)	
	Rd   = 0.024	(/ms)	: inact recov (v) 

	temp = 23	(degC)		: original temp 
	q10  = 2.3			: temperature sensitivity

	v 		(mV)
	dt		(ms)
	celsius		(degC)
	vmin = -120	(mV)
	vmax = 1000	(mV)
	gbarfactor = 1
	timefactor_m = 1		: increase, decrease the speed of the the activation of the channels
	timefactor_h = 1		: increase, decrease the speed of the the activation of the channels

	(mA) = (milliamp)
	(mV) = (millivolt)
	(pS) = (picosiemens)
	(um) = (micron)

	ina 		(mA/cm2)
	gna		(S/cm2)
	ena		(mV)
	minf 		hinf
	mtau (ms)	htau (ms)

STATE { m h }

	m = minf
	h = hinf


	SOLVE states METHOD cnexp
    gna = gbarfactor*tadj*gbar*m*m*m*h
	ina = gna * (v - ena)

LOCAL mexp, hexp 

DERIVATIVE states {   :Computes state variables m, h, and n 
        trates(v-vshift-vshift2)      :             at the current v and dt.
        m' =  (minf-m)/(timefactor_m*mtau)
        h' =  (hinf-h)/(timefactor_h*htau)

PROCEDURE trates(v) {  
    TABLE minf,  hinf, mtau, htau
	DEPEND  celsius, temp, Ra, Rb, Rd, Rg, tha, thi1, thi2, qa, qi, qinf
	FROM vmin TO vmax WITH 1600

	rates(v): not consistently executed from here if usetable == 1

:        tinc = -dt * tadj

:        mexp = 1 - exp(tinc/mtau)
:        hexp = 1 - exp(tinc/htau)

PROCEDURE rates(vm) {  
        LOCAL  a, b

	a = trap0(vm,tha,Ra,qa)
	b = trap0(-vm,-tha,Rb,qa)

        tadj = q10^((celsius - temp)/10)

	mtau = 1/tadj/(a+b)
	if (mtau<1e-7) {mtau=1e-7}

	minf = a/(a+b)

		:"h" inactivation 

	a = trap0(vm,thi1,Rd,qi)
	b = trap0(-vm,-thi2,Rg,qi)
	htau = 1/tadj/(a+b)
	if (htau<1e-7) {htau=1e-7}
	hinf = 1/(1+exp((vm-thinf)/qinf))

FUNCTION trap0(v,th,a,q) {
	if (fabs(v/th) > 1e-6) {
	        trap0 = a * (v - th) / (1 - exp(-(v - th)/q))
	} else {
	        trap0 = a * q