Altered complexity in layer 2/3 pyramidal neurons (Luuk van der Velden et al. 2012)

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" ... Our experimental results show that hypercomplexity of the apical dendritic tuft of layer 2/3 pyramidal neurons affects neuronal excitability by reducing the amount of spike frequency adaptation. This difference in firing pattern, related to a higher dendritic complexity, was accompanied by an altered development of the afterhyperpolarization slope with successive action potentials. Our abstract and realistic neuronal models, which allowed manipulation of the dendritic complexity, showed similar effects on neuronal excitability and confirmed the impact of apical dendritic complexity. Alterations of dendritic complexity, as observed in several pathological conditions such as neurodegenerative diseases or neurodevelopmental disorders, may thus not only affect the input to layer 2/3 pyramidal neurons but also shape their firing pattern and consequently alter the information processing in the cortex."
1 . van der Velden L, van Hooft JA, Chameau P (2012) Altered dendritic complexity affects firing properties of cortical layer 2/3 pyramidal neurons in mice lacking the 5-HT3A receptor. J Neurophysiol 108:1521-8 [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): Neocortex spiking regular (RS) neuron;
Channel(s): Ca pump;
Gap Junctions:
Receptor(s): 5-HT3;
Transmitter(s): Serotonin;
Simulation Environment: NEURON;
Model Concept(s): Influence of Dendritic Geometry;
Implementer(s): van der Velden, Luuk [l.j.j.vandervelden at];
Search NeuronDB for information about:  5-HT3; Ca pump; Serotonin;
ca.mod *
cad.mod *
kca.mod *
km.mod *
kv.mod *
L_HVA_Ca.mod *
TITLE Calcium ion accumulation with longitudinal and radial diffusion

PROCEDURE factors_cadifus() sets up the scale factors 
needed to model radial diffusion.
These scale factors do not have to be recomputed
when diam or DFree is changed.
The amount of calcium in an annulus is ca[i]*diam^2*vol[i] 
with ca[0] being the 2nd order correct concentration at the exact edge
and ca[NANN-1] being the concentration at the exact center.
Buffer concentration and rates are based on Yamada et al. 1989
model of bullfrog sympathetic ganglion cell.

	SUFFIX cadifus
	USEION ca READ cai, ica WRITE cai
	GLOBAL vol, TotalBuffer
	RANGE cai0


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

	DCa = 0.6		(um2/ms)
	: to change rate of buffering without disturbing equilibrium
	: multiply the following two by the same factor
	k1buf	= 100			(/mM-ms)
	k2buf	= 0.1			(/ms)
	TotalBuffer = 0.004	(mM)
	cai0 = 50e-6 (mM)	: Requires explicit use in INITIAL block

	diam		(um)
	ica		(mA/cm2)
	cai		(mM)
	vol[NANN]	(1)	: gets extra um2 when multiplied by diam^2
	Kd		(/mM)
	B0		(mM)

	ca[NANN]		(mM) <1e-6>	: ca[0] is equivalent to cai
	CaBuffer[NANN]	(mM)
	Buffer[NANN]	(mM)

	SOLVE state METHOD sparse

LOCAL factors_done

	if (factors_done == 0) {
		factors_done = 1

	cai = cai0
	Kd = k1buf/k2buf
	B0 = TotalBuffer/(1 + Kd*cai)

	FROM i=0 TO NANN-1 {
		ca[i] = cai
		Buffer[i] = B0
		CaBuffer[i] = TotalBuffer - B0

factors() sets up factors needed for radial diffusion 
modeled by NANN concentric compartments.
The outermost shell is half as thick as the other shells 
so the concentration is spatially second order correct 
at the surface of the cell.
The radius of the cylindrical core 
equals the thickness of the outermost shell.
The intervening NANN-2 shells each have thickness = r/(NANN-1)
(NANN must be >= 2).

ca[0] is at the edge of the cell, 
ca[NANN-1] is at the center of the cell, 
and ca[i] for 0 < i < NANN-1 is 
midway through the thickness of each annulus.


PROCEDURE factors() {
	LOCAL r, dr2
	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 in COMPARTMENT

KINETIC state {
	COMPARTMENT i, diam*diam*vol[i] {ca CaBuffer Buffer}
	LONGITUDINAL_DIFFUSION i, DCa*diam*diam*vol[i] {ca}
	~ ca[0] << (-ica*PI*diam/(2*FARADAY))
	FROM i=0 TO NANN-2 {
		~ ca[i] <-> ca[i+1] (DCa*frat[i+1], DCa*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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