Neuronal dendrite calcium wave model (Neymotin et al, 2015)

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"... We developed a reaction-diffusion model of an apical dendrite with diffusible inositol triphosphate (IP3 ), diffusible Ca2+, IP3 receptors (IP3 Rs), endoplasmic reticulum (ER) Ca2+ leak, and ER pump (SERCA) on ER. ... At least two modes of Ca2+ wave spread have been suggested: a continuous mode based on presumed relative homogeneity of ER within the cell; and a pseudo-saltatory model where Ca2+ regeneration occurs at discrete points with diffusion between them. We compared the effects of three patterns of hypothesized IP3 R distribution: 1. continuous homogeneous ER, 2. hotspots with increased IP3R density (IP3 R hotspots), 3. areas of increased ER density (ER stacks). All three modes produced Ca2+ waves with velocities similar to those measured in vitro (~50 - 90µm /sec). ... The measures were sensitive to changes in density and spacing of IP3 R hotspots and stacks. ... An extended electrochemical model, including voltage gated calcium channels and AMPA synapses, demonstrated that membrane priming via AMPA stimulation enhances subsequent Ca2+ wave amplitude and duration. Our modeling suggests that pharmacological targeting of IP3 Rs and SERCA could allow modulation of Ca2+ wave propagation in diseases where Ca2+ dysregulation has been implicated. "
1 . Neymotin SA, McDougal RA, Sherif MA, Fall CP, Hines ML, Lytton WW (2015) Neuronal calcium wave propagation varies with changes in endoplasmic reticulum parameters: a computer model. Neural Comput 27:898-924 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Dendrite;
Brain Region(s)/Organism:
Cell Type(s): Hippocampus CA1 pyramidal GLU cell; Hippocampus CA3 pyramidal GLU cell; Neocortex L5/6 pyramidal GLU cell; Neocortex L2/3 pyramidal GLU cell;
Channel(s): I T low threshold; I A; I K; I K,Ca; I CAN; I Sodium; I Calcium; I_SERCA; I_KD; Ca pump;
Gap Junctions:
Receptor(s): AMPA;
Transmitter(s): Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Calcium waves; Reaction-diffusion;
Implementer(s): Neymotin, Sam [Samuel.Neymotin at]; McDougal, Robert [robert.mcdougal at]; Sherif, Mohamed [ at];
Search NeuronDB for information about:  Hippocampus CA1 pyramidal GLU cell; Hippocampus CA3 pyramidal GLU cell; Neocortex L5/6 pyramidal GLU cell; Neocortex L2/3 pyramidal GLU cell; AMPA; I T low threshold; I A; I K; I K,Ca; I CAN; I Sodium; I Calcium; I_SERCA; I_KD; Ca pump; Glutamate;
cagk.mod *
kaprox.mod *
kdrca1.mod *
km.mod *
misc.mod *
na3n.mod *
stats.mod *
vecst.mod *
cawave.cfg *
misc.h * *
setup.hoc * *
TITLE L-calcium channel
: L-type calcium channel with [Ca]i inactivation
: from Jaffe, D. B., Ross, W. N., Lisman, J. E., Laser-Ross, N., Miyakawa, H., and Johnston, D. A. A model for dendritic Ca2
: accumulation in hippocampal pyramidal neurons based on fluorescence imaging measurements. J. Neurophysiol. 71:1O65-1077 1994.
: conduction density estimate of 50-200 pS/mu2; 0.0025 S/cm2 (5-20 channels of 10 each)
: M. Migliore, E. Cook, D.B. Jaffe, D.A. Turner and D. Johnston, Computer simulations of morphologically reconstructed CA3
: hippocampal neurons, J. Neurophysiol. 73, 1157-1168 (1995). 
: adapted from\ca3_db\cal2.mod
: this version from\kv72-R213QW-mutations\cal2.mod
: Miceli F, Soldovieri MV, Ambrosino P, Barrese V, Migliore M, Cilio MR, Taglialatela M (2013) Genotype-phenotype
: correlations in neonatal epilepsies caused by mutations in the voltage sensor of Kv7.2 potassium channel subunits. PNAS 110:4386-4391

  (mA) = (milliamp)
  (mV) = (millivolt)

  FARADAY = 96520 (coul)
  R = 8.3134 (joule/degC)
  KTOMV = .0853 (mV/degC)

  v (mV)
  celsius 	(degC)
  gcalbar=.003 (mho/cm2)
  ki=.001 (mM)
  cai = 50.e-6 (mM)
  cao = 2 (mM)
  q10 = 5
  tfa = 1
  a0m =0.1
  zetam = 2
  vhalfm = 4

  SUFFIX cal
  USEION ca READ cai,cao WRITE ica
  RANGE gcalbar,cai, ica, gcal, ggk
  GLOBAL minf,tau


  ica (mA/cm2)
  gcal (mho/cm2)
  tau   (ms)

  m = minf
  gcal = gcalbar*m*m*h2(cai)
  ica = gcal*ggk

  SOLVE state METHOD cnexp
  gcal = gcalbar*m*m*h2(cai)
  ica = gcal*ggk

FUNCTION h2(cai(mM)) {
  h2 = ki/(ki+cai)

FUNCTION ghk(v(mV), ci(mM), co(mM)) (mV) {
  LOCAL nu,f
  f = KTF(celsius)/2
  nu = v/f
  ghk=-f*(1. - (ci/co)*exp(nu))*efun(nu)

FUNCTION KTF(celsius (DegC)) (mV) {
  KTF = ((25./293.15)*(celsius + 273.15))

FUNCTION efun(z) {
  if (fabs(z) < 1e-4) {
    efun = 1 - z/2
    efun = z/(exp(z) - 1)

FUNCTION alp(v(mV)) (1/ms) {
  alp = 15.69*(-1.0*v+81.5)/(exp((-1.0*v+81.5)/10.0)-1.0)

FUNCTION bet(v(mV)) (1/ms) {
  bet = 0.29*exp(-v/10.86)

FUNCTION alpmt(v(mV)) {
  alpmt = exp(0.0378*zetam*(v-vhalfm)) 

FUNCTION betmt(v(mV)) {
  betmt = exp(0.0378*zetam*gmm*(v-vhalfm)) 

DERIVATIVE state {  
  m' = (minf - m)/tau

PROCEDURE rate(v (mV)) { :callable from hoc
  LOCAL a, b, qt
  a = alp(v)
  b = 1/((a + bet(v)))
  minf = a*b
  tau = betmt(v)/(qt*a0m*(1+alpmt(v)))
  if (tau<mmin/qt) {tau=mmin/qt}