Model of SK current`s influence on precision in Globus Pallidus Neurons (Deister et al. 2009)

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" ... In numerical simulations, the availability of both Na+ and A-type K+ channels during autonomous firing were reduced when SK channels were removed, and a nearly equal reduction in Na+ and K+ subthreshold-activated ion channel availability produced a large decrease in the neuron's slope conductance near threshold. This change made the neuron more sensitive to intrinsically generated noise. In vivo, this change would also enhance the sensitivity of GP (Globus Pallidus) neurons to small synaptic inputs."
1 . Deister CA, Chan CS, Surmeier DJ, Wilson CJ (2009) Calcium-activated SK channels influence voltage-gated ion channels to determine the precision of firing in globus pallidus neurons. J Neurosci 29:8452-61 [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): Globus pallidus neuron;
Channel(s): I Na,p; I Na,t; I A; I K; I K,Ca; I Sodium; I Potassium;
Gap Junctions:
Simulation Environment: NEURON;
Model Concept(s): Oscillations; Noise Sensitivity;
Implementer(s): Deister, Christopher [chris.deister at];
Search NeuronDB for information about:  I Na,p; I Na,t; I A; I K; I K,Ca; I Sodium; I Potassium;
: Modified by Chris Deister 1/7/2007 to make Ca2+ clearance a littel faster
:Migliore file Modify by Maciej Lazarewicz ( May/16/2001

TITLE Calcium ion accumulation and diffusion
: The internal coordinate system is set up in PROCEDURE coord_cadifus()
: and must be executed before computing the concentrations.
: The scale factors set up in this procedure do not have to be recomputed
: when diam1 or DFree are changed.
: The amount of calcium in an annulus is ca[i]*diam1^2*vol[i] with
: ca[0] being the second order correct concentration at the exact edge
: and ca[NANN-1] being the concentration at the exact center

	SUFFIX ca_gp
	USEION ca READ cao, cai, ica WRITE cai, ica
	RANGE ipump,last_ipump,test
	GLOBAL DFree, k1buf, k2buf, k1, k2, k3, k4, totpump, totbuf
	GLOBAL vol, Buffer0


        (mol)   = (1)
	(molar) = (1/liter)
	(mM)	= (millimolar)
	(um)	= (micron)
	(mA)	= (milliamp)
	FARADAY = (faraday)	(10000 coulomb)
	PI	= (pi) 		(1)

	DFree	= .6	(um2/ms)
	diam 	= 1	(um)
	cao		(mM)
	ica		(mA/cm2)
	k1buf 	= 100	(/mM-ms) :was 500
	k2buf 	= 0.5	(/ms)
        k1	= 1.05e10 (um3/s)
        k2	= 50.e7 (/s)	: k1*50.e-3
        k3	= 1.e10 (/s)	: k1
        k4	= 5.e5	(um3/s)	: k1*5.e-4, was 5e6
	totpump	= 8	(mol/cm2)	:was 2
	totbuf	= 0.1	(mM)

CONSTANT { volo=1  (liter)}

	area		(um2)
	cai		(mM)
	vol[NANN]	(1)	: gets extra cm2 when multiplied by diam^2
	ipump           (mA/cm2)
	last_ipump	(mA/cm2)

	ca[NANN]	(mM) <1.e-5> : ca[0] is equivalent to cai
	CaBuffer[NANN]  (mM)
	Buffer[NANN]    (mM)
        pump            (mol/cm2) <1.e-3>
        pumpca          (mol/cm2) <1.e-15>


	SOLVE state METHOD sparse
	ica = ipump
	test = 0

LOCAL coord_done

	if (coord_done == 0) {
		coord_done = 1
	: note Buffer gets set to Buffer0 automatically
	: and CaBuffer gets set to 0 (Default value of CaBuffer0) as well
	FROM i=0 TO NANN-1 {
		ca[i] = cai

       	ipump 	= 0
        pump 	= totpump
        pumpca 	= (1e-18)*pump*cao*k4/k3

        FROM i=0 TO NANN-1 {
               	ca[i] = cai
		CaBuffer[i] =(totbuf*ca[i])/(k2buf/k1buf+ca[i])
		Buffer[i] = totbuf - CaBuffer[i]

LOCAL frat[NANN] 	: gets extra cm when multiplied by diam

PROCEDURE coord() {
	LOCAL r, dr2
	: cylindrical coordinate system  with constant annuli thickness to
	: center of cell. Note however that the first annulus is half thickness
	: so that the concentration is second order correct spatially at
	: the membrane or exact edge of the cell.
	: note ca[0] is at edge of cell
	:      ca[NANN-1] is at center of cell
	r = 1/2					:starts at edge (half diam)
	dr2 = r/(NANN-1)/2			:half thickness of annulus
	vol[0] = 0
	frat[0] = 2*r
	FROM i=0 TO NANN-2 {
		vol[i] = vol[i] + PI*(r-dr2/2)*2*dr2	:interior half
		r = r - dr2
		frat[i+1] = 2*PI*r/(2*dr2)	:exterior edge of annulus
					: divided by distance between centers
		r = r - dr2
		vol[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
KINETIC state {
	COMPARTMENT i, diam*diam*vol[i]*1(um) {ca CaBuffer Buffer}
        COMPARTMENT (1.e10)*area {pump pumpca}
        COMPARTMENT (1.e15)*volo {cao}

	~ ca[0] << (-(ica-last_ipump)*PI*diam*frat[0]*1(um)/(2*FARADAY))

	FROM i=0 TO NANN-2 {
		~ ca[i] <-> ca[i+1] 	(DFree*frat[i+1]*1(um), DFree*frat[i+1]*1(um))

	dsq = diam*diam*1(um)
	FROM i=0 TO NANN-1 {
		dsqvol = dsq*vol[i]
		~ ca[i] + Buffer[i] <-> CaBuffer[i] (k1buf*dsqvol,k2buf*dsqvol)

        ~ca[0] + pump <-> pumpca 	((1.e-11)*k1*area, (1.e7)*k2*area)
        ~pumpca       <-> pump + cao 	((1.e7)*k3*area, (1.e-11)*k4*area)

        ipump = 2*FARADAY*(f_flux-b_flux)/area

	cai = ca[0]

At this time, conductances (and channel states and currents are
calculated at the midpoint of a dt interval.  Membrane potential and
concentrations are calculated at the edges of a dt interval.  With
secondorder=2 everything turns out to be second order correct.

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