Medial vestibular neuron models (Quadroni and Knopfel 1994)

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Accession:53876
The structure and the parameters of the model cells were chosen to reproduce the responses of type A and type B MVNns as described in electrophysiological recordings. The emergence of oscillatory firing under these two specific experimental conditions is consistent with electrophysiological recordings not used during construction of the model. We, therefore, suggest that these models have a high predictive value.
Reference:
1 . Quadroni R, Knöpfel T (1994) Compartmental models of type A and type B guinea pig medial vestibular neurons. J Neurophysiol 72:1911-24 [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): Vestibular neuron;
Channel(s): I Na,p; I Na,t; I L high threshold; I T low threshold; I A; I K; I h;
Gap Junctions:
Receptor(s): NMDA;
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Oscillations; Action Potentials; Calcium dynamics;
Implementer(s): Morse, Tom [Tom.Morse at Yale.edu];
Search NeuronDB for information about:  NMDA; I Na,p; I Na,t; I L high threshold; I T low threshold; I A; I K; I h;
COMMENT
This file, ca_soma_cylind_shells.mod, for Quadroni and Knopfel 1994, was modified from
cadifus.mod from Chapter 9 Hines and Carnevale NEURON
This file is identical to the other ca_*.mod files except has
the number of annulli, Nannuli (number of compartments) set to 25.
ENDCOMMENT
: Calcium ion accumulation with radial and longitudinal diffusion
NEURON {
SUFFIX ca_soma_cyl
USEION ca READ cai, ica WRITE cai
GLOBAL vrat : vrat must be GLOBAL --see INITIAL block
: however B which in cadifus.mod was called TotalBuffer may be and is here RANGE
RANGE K2f_ex, K2f_ATPase, B
RANGE i_Na_Ca_ex, i_ATPase, I	: Na Ca exchanger can pump one Ca out for 3 Na's 
				: that enter the cell.
				: the ATPase current pumps Ca out of the cell by
				: using up ATP
}
DEFINE Nannuli 50 : must be >=2 (i.e. at least shell and core)
UNITS {
	(molar) = (1/liter)
	(mM) = (millimolar)
	(um) = (micron)
	(mA) = (milliamp)
	(mV) = (millivolt)
	FARADAY = (faraday) (10000 coulomb)
	PI = (pi) (1)
}

PARAMETER {
	DCa = 0.6 (um2/ms)
	: Ca buffer reaction rates :
	k1buf = 30  (/mM ms)  : these rates from Sala and Hernandez-Cruz 1990
	k2buf = 0.03 (/ms) : and are labeled f and b in 
		   : Quadroni and Knopfel 1994 p. 1916
	B = 0.025 (mM) : this is [B] in Quadroni and Knopfel 94 Table 4
	: compare above with these rates from
	: k1buf = 100 (/mM ms) : Yamada et al. 1989
	: k2buf = 0.1 (/ms)
	: B = 0.003 (mM)

	K2f_ex = 0 : should be 2*FARADAY*3.3e-13 (mA/cm2mM2): Quadroni and Knopfel 94 
	: K2f_ex = 5e-6 (mA/cm2mM2): a value from Lytton and Sejnowski's (LS '91) 5e-6
			: (Soma value only - dendrites are different)
	cao = 2 (mM) : [Ca]_outside is set constant because it
		   :	doesn't change in this simulation.
	E_1  = 0.01315 (/mV) : Quadroni and Knopfel 94
	E_2 = 0.0255 (/mV)   :  "	
	nai = 7.6 (mM)	     :  "	: (LS's '91 = 10  mM)
	nao = 152 (mM)	     :  "	: (LS's '91 = 140 mM)
	K2f_ATPase = 0 : 2*FARADAY*2.65e-9 (mA/cm2)  : type A soma only : dendrites and type B cell different
	f_ATPase = 100 (/mM ms)	: simply called f for forward rate in Quadroni Knopfel
	b_ATPase = 0.005 (/ms)	: 1994 - this one is just called b for backward
}

ASSIGNED {
	v (mV)
	diam (um)
	ica (mA/cm2)
	I (mA/cm2)	: same as ica but used for diagnostic purposes
	i_Na_Ca_ex (mA/cm2)
	i_ATPase (mA/cm2)
	cai (mM)
	vrat[Nannuli] (1) : dimensionless
	: numeric value of vrat[i] equals the volume
	: of annulus iof a 1um diameter cylinder
	: multiply by diam^2 to get volume per um length
	Kd (/mM)
	B0 (mM)
}
STATE {
	: ca[0] is equivalent to cai
	: ca[] are very small, so specify absolute tolerance
	ca[Nannuli] (mM) <1e10>
	CaBuffer[Nannuli] (mM)
	Buffer[Nannuli] (mM)
	n (1)
}
BREAKPOINT { 
	SOLVE states METHOD cnexp
	i_Na_Ca_ex = -K2f_ex * (nai^3 * cao * exp(E_1 * v) - nao^3 * cai * exp(-E_2*v))
	i_ATPase = K2f_ATPase * n
	I= ica	: diagnostic purposes only
	SOLVE state METHOD sparse
}

DERIVATIVE states {
	: compute state variable n at present v and t
	n' = f_ATPase * cai * (1 - n) - b_ATPase * n
}

LOCAL factors_done
INITIAL {
	if (factors_done == 0) { : flag becomes 1 in the first segment
		factors_done = 1 : all subsequent segments will have
		factors() : vrat = 0 unless vrat is GLOBAL
	}

	n = f_ATPase * cai / (f_ATPase * cai + b_ATPase)

	Kd = k1buf/k2buf
	B0 = B/(1 + Kd*cai)
	FROM i=0 TO Nannuli-1 {
		cai = 5e-5	: arbitrary initialization 
		ca[i] = cai
		Buffer[i] = B0
		CaBuffer[i] = B - B0
	}
}
LOCAL frat[Nannuli] : scales the rate constants for model geometry
PROCEDURE factors() {
	LOCAL r, dr2
	r = 1/2 : starts at edge (half diam)
	dr2 = r/(Nannuli-1)/2 : full thickness of outermost annulus,
	: half thickness of all other annuli
	vrat[0] = 0
	frat[0] = 2*r
	FROM i=0 TO Nannuli-2 {
		vrat[i] = vrat[i] + PI*(r-dr2/2)*4*dr2 : interior half
		r = r - dr2
		frat[i+1] = 2*PI*r/(2*dr2) : outer radius of annulus
		: div by distance between centers
		r = r - dr2
		vrat[i+1] = PI*(r+dr2/2)*2*dr2 : outer half of annulus
	}
}
LOCAL dsq, dsqvol : can't define local variable in KINETIC block
: or use in COMPARTMENT statement
KINETIC state {
	COMPARTMENT i, diam*diam*vrat[i] {ca CaBuffer Buffer}
	: LONGITUDINAL_DIFFUSION i, DCa*diam*diam*vrat[i] {ca}
	~ ca[0] << ( (-ica - i_Na_Ca_ex - i_ATPase)*PI*diam/(2*FARADAY)) 
			: ica is Ca current from hva or lva or both
			: i_Na_Ca_ex is the current from Na-Ca exhanger
			: i_ATPase is the current from Ca-ATPase
	FROM i=0 TO Nannuli-2 {
		~ ca[i] <-> ca[i+1] (DCa*frat[i+1], DCa*frat[i+1])
	}
	dsq = diam*diam
	FROM i=0 TO Nannuli-1 {
		dsqvol = dsq*vrat[i]
		~ ca[i] + Buffer[i] <-> CaBuffer[i] (k1buf*dsqvol, k2buf*dsqvol)
	}
	cai = ca[0]
}

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