Spine fusion and branching effects synaptic response (Rusakov et al 1996, 1997)

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This compartmental model of a hippocampal granule cell has spinous synapses placed on the second-order dendrites. Changes in shape and connectivity of the spines usually does not effect the synaptic response of the cell unless active conductances are incorporated into the spine membrane (e.g. voltage-dependent Ca2+ channels). With active conductances, spines can generate spike-like events. We showed that changes like fusion and branching, or in fact any increase in the equivalent spine neck resistance, could trigger a dramatic increase in the spine's influence on the dendritic shaft potential.
1 . Rusakov DA, Richter-Levin G, Stewart MG, Bliss TV (1997) Reduction in spine density associated with long-term potentiation in the dentate gyrus suggests a spine fusion-and-branching model of potentiation. Hippocampus 7:489-500 [PubMed]
2 . Rusakov DA, Stewart MG, Korogod SM (1996) Branching of active dendritic spines as a mechanism for controlling synaptic efficacy. Neuroscience 75:315-23 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Synapse;
Brain Region(s)/Organism:
Cell Type(s): Dentate gyrus granule GLU cell;
Channel(s): I Na,t; I K; I K,Ca; I Sodium; I Calcium; I Potassium;
Gap Junctions:
Receptor(s): AMPA; NMDA;
Simulation Environment: NEURON;
Model Concept(s): Dendritic Action Potentials; Active Dendrites; Influence of Dendritic Geometry; Detailed Neuronal Models; Synaptic Plasticity; Long-term Synaptic Plasticity;
Implementer(s): Rusakov, DA [D.Rusakov at ion.ucl.ac.uk];
Search NeuronDB for information about:  Dentate gyrus granule GLU cell; AMPA; NMDA; I Na,t; I K; I K,Ca; I Sodium; I Calcium; I Potassium;
TITLE Calcium ion accumulation with longitudinal and radial diffusion

: The internal coordinate system is set up in PROCEDURE coord_cadifus()
: The scale factors set up in this procedure do not have to be recomputed
: when diam or DFree are changed.
: The amount of calcium in an annulus is ca[i]*diam^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 cadifus
	USEION ca READ cao, cai, ica WRITE cai, ica
	RANGE icabar
	GLOBAL vol, Buffer0


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

	DFree = .6	(um2/ms)
	diam		(um)
	cao		(mM)
	ica		(mA/cm2)
	k1buf		(/mM-ms)
	k2buf		(/ms)
	icabar		(mA/cm2)

	cai		(mM)
	vol[NANN]	(1)	: gets extra cm2 when multiplied by diam^2

	ca[NANN]	(mM) : ca[0] is equivalent to cai
	CaBuffer[NANN]  (mM)
	Buffer[NANN]    (mM)

	SOLVE state METHOD sparse
	ica = icabar

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

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] {ca CaBuffer Buffer}
	LONGITUDINAL_DIFFUSION j, DFree*diam*diam*vol[j] {ca}
	~ ca[0] << (-ica*PI*diam*frat[0]/(2*FARADAY))
	FROM i=0 TO NANN-2 {
		~ ca[i] <-> ca[i+1] (DFree*frat[i+1], DFree*frat[i+1])
	dsq = diam*diam
	FROM i=0 TO NANN-1 {
		dsqvol = dsq*vol[i]
		~ ca[i] + Buffer[i] <-> CaBuffer[i] (k1buf*dsqvol,k2buf*dsqvol)
	cai = ca[0]

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