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

 Download zip file   Auto-launch 
Help downloading and running models
"... 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 Computation 27(4):898-924 [PubMed]
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 cell; Hippocampus CA3 pyramidal cell; Neocortex V1 pyramidal corticothalamic L6 cell; Neocortex V1 pyramidal intratelencephalic L2-5 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 [samn at]; McDougal, Robert [robert.mcdougal at]; Sherif, Mohamed [ at];
Search NeuronDB for information about:  Hippocampus CA1 pyramidal cell; Hippocampus CA3 pyramidal cell; Neocortex V1 pyramidal corticothalamic L6 cell; Neocortex V1 pyramidal intratelencephalic L2-5 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 * *
: $Id:,v 1.6 2004/02/04 21:04:15 billl Exp $  
TITLE Kevins Cvode modified Generalized Hodgkin-Huxley eqn Channel Model 


Each channel has activation and inactivation particles as in the original
Hodgkin Huxley formulation.  The activation particle mm and inactivation
particle hh go from on to off states according to kinetic variables alpha
and beta which are voltage dependent.
Allows exponential, sigmoid and linoid forms (flags 0,1,2)
See functions alpha() and beta() for details of parameterization



	RANGE gmax, g, i
	GLOBAL erev, Inf, Tau, vrest
} : end NEURON

	  FARADAY = 96489.0	: Faraday's constant
	  R= 8.31441		: Gas constant

} : end CONSTANT

	(mA) = (milliamp)
	(mV) = (millivolt)
	(umho) = (micromho)
} : end UNITS

** Parameter values should come from files specific to particular channels

	erev 		= 0    (mV)
	gmax 		= 0    (mho/cm^2)

	maflag 		= 0
	malphaA 	= 0
	malphaB		= 0
	malphaV0	= 0
	mbflag 		= 0
	mbetaA 		= 0
	mbetaB		= 0
	mbetaV0		= 0
	exptemp		= 0
	mq10		= 3
	mexp 		= 0

	haflag 		= 0
	halphaA 	= 0
	halphaB		= 0
	halphaV0	= 0
	hbflag 		= 0
	hbetaA 		= 0
	hbetaB		= 0
	hbetaV0		= 0
	hq10		= 3
	hexp 		= 0

  cao                (mM)
  cai                (mM)
  celsius			   (degC)
  dt 				   (ms)
  v 			       (mV)

	i (mA/cm^2)		
	g (mho/cm^2)
	Inf[2]		: 0 = m and 1 = h
	Tau[2]		: 0 = m and 1 = h
} : end ASSIGNED 

STATE { m h }

	m = Inf[0] h = Inf[1]


  LOCAL hexp_val, index, mexp_val, mexp2

  SOLVE states METHOD cnexp

  hexp_val = 1
  mexp_val = 1

  : Determining h's exponent value
  if (hexp > 0) {
    FROM index=1 TO hexp {
      hexp_val = h * hexp_val

  : Determining m's exponent value
  if (mexp > 0) {
    FROM index = 1 TO mexp {
      mexp_val = m * mexp_val
  } else if (mexp<0) {
    FROM index = 1 TO mexp2 {
      mexp_val = Inf[0] * mexp_val

  :			       mexp			    hexp
  : Note that mexp_val is now = m      and hexp_val is now = h 
  g = gmax * mexp_val * hexp_val


: Must be given by a user routines in parameters.multi
: E.G.:
:   PROCEDURE iassign () { i = g*(v-erev) ina=i }
:   PROCEDURE iassign () { i = g*ghkca(v) ica=i }


  m' = (-m + Inf[0]) / Tau[0] 
  h' = (-h + Inf[1]) / Tau[1]

: NOTE : 0 = m and 1 = h
PROCEDURE mh (v) {
  LOCAL a, b, j, qq10[2]

  qq10[0] = mq10^((celsius-exptemp)/10.)	
  qq10[1] = hq10^((celsius-exptemp)/10.)	

  : Calculater Inf and Tau values for h and m
  FROM j = 0 TO 1 {
    a = alpha (v, j)
    b = beta (v, j)

    if (j==1 && hexp==0) { Tau[j] = 1. Inf[j] = 1.
    } else {
      Inf[j] = a / (a + b)
      Tau[j] = 1. / (a + b) / qq10[j]
} : end PROCEDURE mh (v)

FUNCTION alpha(v,j) {
  LOCAL flag, A, B, V0
  if (j==1 && hexp==0) {
	  alpha = 0
  } else {

     if (j == 1) {
	  A = halphaA B = halphaB V0 = halphaV0+vrest flag = haflag
     } else {
	  A = malphaA B = malphaB V0 = malphaV0+vrest flag = maflag

     if (flag == 1) { :  EXPONENTIAL
	 alpha = A*exp((v-V0)/B)	
     } else if (flag == 2) { :  SIGMOID
	 alpha = A/(exp((v-V0)/B)+1)
     } else if (flag == 3) { :  LINOID
	 if(v == V0) {
           alpha = A*B
         } else {
           alpha = A*(v-V0)/(exp((v-V0)/B)-1) }
} : end FUNCTION alpha (v,j)

FUNCTION beta (v,j) {
  LOCAL flag, A, B, V0
  if (j==1 && hexp==0) {
	  beta = 1
  } else {

     if (j == 1) {
	  A = hbetaA B = hbetaB V0 = hbetaV0+vrest flag = hbflag
     } else {
	  A = mbetaA B = mbetaB V0 = mbetaV0+vrest flag = mbflag

    if (flag == 1) { :  EXPONENTIAL
	 beta = A*exp((v-V0)/B)
     } else if (flag == 2) { :  SIGMOID
	 beta = A/(exp((v-V0)/B)+1)
     } else if (flag == 3) { :  LINOID
	 if(v == V0) {
            beta = A*B 
         } else {
            beta = A*(v-V0)/(exp((v-V0)/B)-1) }
} : end FUNCTION beta (v,j)

FUNCTION FRT(temperature) {
	FRT = FARADAY * 0.001 / R / (temperature + 273.15)
} : end FUNCTION FRT (temperature)

 FUNCTION ghkca (v) { : Goldman-Hodgkin-Katz eqn
       LOCAL nu, efun

       nu = v*2*FRT(celsius)
       if(fabs(nu) < 1.e-6) {
               efun = 1.- nu/2.
       } else {
               efun = nu/(exp(nu)-1.) }

       ghkca = -FARADAY*2.e-3*efun*(cao - cai*exp(nu))
 } : end FUNCTION ghkca()

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 Computation 27(4):898-924[PubMed]

References and models cited by this paper

References and models that cite this paper

Allbritton NL, Meyer T, Stryer L (1992) Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate. Science 258:1812-5 [PubMed]

Berridge MJ (1998) Neuronal calcium signaling. Neuron 21:13-26 [PubMed]

Blackwell KT (2013) Approaches and tools for modeling signaling pathways and calcium dynamics in neurons. J Neurosci Methods 220:131-40 [PubMed]

Busa WB, Nuccitelli R (1985) An elevated free cytosolic Ca2+ wave follows fertilization in eggs of the frog, Xenopus laevis. J Cell Biol 100:1325-9 [PubMed]

Carnevale NT, Hines ML (2006) The NEURON Book

De Schutter E (2008) Why are computational neuroscience and systems biology so separate? PLoS Comput Biol 4:e1000078 [Journal] [PubMed]

De Schutter E, Smolen P (1998) Calcium dynamics in large neuronal models Methods In Neuronal Modeling: From Ions To Networks, Koch C:Segev I, ed. pp.211

De Young GW, Keizer J (1992) A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proc Natl Acad Sci U S A 89:9895-9 [PubMed]

Fall CP, Rinzel J (2006) An intracellular Ca2+ subsystem as a biologically plausible source of intrinsic conditional bistability in a network model of working memory J Comput Neurosci 20:97-107 [Journal] [PubMed]

Fall CP, Wagner JM, Loew LM, Nuccitelli R (2004) Cortically restricted production of IP3 leads to propagation of the fertilization Ca2+ wave along the cell surface in a model of the Xenopus egg. J Theor Biol 231:487-96

Fitzpatrick JS, Hagenston AM, Hertle DN, Gipson KE, Bertetto-D'Angelo L, Yeckel MF (2009) Inositol-1,4,5-trisphosphate receptor-mediated Ca2+ waves in pyramidal neuron dendrites propagate through hot spots and cold spots. J Physiol 587:1439-59 [Journal] [PubMed]

Fontanilla RA, Nuccitelli R (1998) Characterization of the sperm-induced calcium wave in Xenopus eggs using confocal microscopy. Biophys J 75:2079-87 [Journal] [PubMed]

Green KN, LaFerla FM (2008) Linking calcium to Abeta and Alzheimer's disease. Neuron 59:190-4 [Journal] [PubMed]

Gunter TE, Yule DI, Gunter KK, Eliseev RA, Salter JD (2004) Calcium and mitochondria. FEBS Lett 567:96-102 [Journal] [PubMed]

Harris K (1994) Dendritic Spines

Hartsfield J () A quantitative study of neuronal calcium signaling Ph.D. diss., Baylor College of Medicine

Hines ML, Morse T, Migliore M, Carnevale NT, Shepherd GM (2004) ModelDB: A Database to Support Computational Neuroscience. J Comput Neurosci 17:7-11 [Journal] [PubMed]

Hong M, Ross WN (2007) Priming of intracellular calcium stores in rat CA1 pyramidal neurons. J Physiol 584:75-87 [PubMed]

Iftinca M, McKay BE, Snutch TP, McRory JE, Turner RW, Zamponi GW (2006) Temperature dependence of T-type calcium channel gating. Neuroscience 142:1031-42 [PubMed]

Kay AR, Wong RK (1987) Calcium current activation kinetics in isolated pyramidal neurones of the Ca1 region of the mature guinea-pig hippocampus. J Physiol 392:603-16 [PubMed]

Kotaleski JH, Blackwell KT (2010) Modelling the molecular mechanisms of synaptic plasticity using systems biology approaches. Nat Rev Neurosci 11:239-51 [PubMed]

Kretsinger RH (1980) Structure and evolution of calcium-modulated proteins. CRC Crit Rev Biochem 8:119-74 [PubMed]

LaFerla FM (2002) Calcium dyshomeostasis and intracellular signalling in Alzheimer's disease. Nat Rev Neurosci 3:862-72 [Journal] [PubMed]

Lechleiter J, Girard S, Peralta E, Clapham D (1991) Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes. Science 252:123-6 [PubMed]

Li YX, Rinzel J (1994) Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. J Theor Biol 166:461-73 [PubMed]

Lipton P (1999) Ischemic cell death in brain neurons. Physiol Rev 79:1431-568 [PubMed]

Lytton WW, Neymotin SA, Kerr CC (2014) Multiscale modeling for clinical translation in neuropsychiatric disease. J Comput Surg [Journal] [PubMed]

Martone ME, Zhang Y, Simpliciano VM, Carragher BO, Ellisman MH (1993) Three-dimensional visualization of the smooth endoplasmic reticulum in Purkinje cell dendrites. J Neurosci 13:4636-46 [PubMed]

McCormick DA, Huguenard JR (1992) A model of the electrophysiological properties of thalamocortical relay neurons. J Neurophysiol 68:1384-400 [Journal] [PubMed]

McDougal RA, Hines ML, Lytton WW (2013) Water-tight membranes from neuronal morphology files Journal of Neuroscience Methods 220(2):167-78 [Journal] [PubMed]

   Constructed Tessellated Neuronal Geometries (CTNG) (McDougal et al. 2013) [Model]

McDougal RA, Hines ML, Lytton WW (2013) Reaction-diffusion in the NEURON simulator. Front Neuroinform 7:28 [Journal] [PubMed]

   Reaction-diffusion in the NEURON simulator (McDougal et al 2013) [Model]

Nakamura T, Barbara JG, Nakamura K, Ross WN (1999) Synergistic release of Ca2+ from IP3-sensitive stores evoked by synaptic activation of mGluRs paired with backpropagating action potentials. Neuron 24:727-37 [PubMed]

Neymotin S,McDougal R,Hines M,Lytton W (2014) Calcium regulation of HCN supports persistent activity associated with working memory: a multiscale model of prefrontal cortex. BMC Neuroscience 15:108

Neymotin SA, Hilscher MM, Moulin TC, Skolnick Y, Lazarewicz MT, Lytton WW (2013) Ih Tunes Theta/Gamma Oscillations and Cross-Frequency Coupling In an In Silico CA3 Model PLoS ONE 8(10):e76285 [Journal] [PubMed]

   Ih tunes oscillations in an In Silico CA3 model (Neymotin et al. 2013) [Model]

Orrenius S, Zhivotovsky B, Nicotera P (2003) Regulation of cell death: the calcium-apoptosis link. Nat Rev Mol Cell Biol 4:552-65 [Journal] [PubMed]

Peercy BE (2008) Initiation and propagation of a neuronal intracellular calcium wave. J Comput Neurosci 25:334-48 [PubMed]

Peterson BE, Healy MD, Nadkarni PM, Miller PL, Shepherd GM (1996) ModelDB: an environment for running and storing computational models and their results applied to neuroscience. J Am Med Inform Assoc 3:389-98 [Journal] [PubMed]

Pozzo-Miller LD, Pivovarova NB, Leapman RD, Buchanan RA, Reese TS, Andrews SB (1997) Activity-dependent calcium sequestration in dendrites of hippocampal neurons in brain slices. J Neurosci 17:8729-38 [PubMed]

Ross WN, Nakamura T, Watanabe S, Larkum M, Lasser-Ross N (2005) Synaptically activated ca2+ release from internal stores in CNS neurons. Cell Mol Neurobiol 25:283-95 [PubMed]

Rowan MS, Neymotin SA, Lytton WW (2014) Electrostimulation to reduce synaptic scaling driven progression of Alzheimer's disease. Front Comput Neurosci 8:39 [Journal] [PubMed]

   Electrostimulation to reduce synaptic scaling driven progression of Alzheimers (Rowan et al. 2014) [Model]

Rowan MS,Neymotin SA (2013) Synaptic Scaling Balances Learning in a Spiking Model of Neocortex Adaptive and Natural Computing Algorithms, Tomassini M, Antonioni A, Daolio F, Buesser P, ed. pp.20 [Journal]

   Synaptic scaling balances learning in a spiking model of neocortex (Rowan & Neymotin 2013) [Model]

Safiulina VF, Caiati MD, Sivakumaran S, Bisson G, Migliore M, Cherubini E (2010) Control of GABA release at mossy fiber-CA3 connections in the developing hippocampus Front Synaptic Neurosci 2:1 [Journal] [PubMed]

   CA3 pyramidal neuron (Safiulina et al. 2010) [Model]

Shemer I, Brinne B, Tegner J, Grillner S (2008) Electrotonic signals along intracellular membranes may interconnect dendritic spines and nucleus. PLoS Comput Biol 4:e1000036 [PubMed]

Spacek J, Harris KM (1997) Three-dimensional organization of smooth endoplasmic reticulum in hippocampal CA1 dendrites and dendritic spines of the immature and mature rat. J Neurosci 17:190-203

Stern MD (1992) Buffering of calcium in the vicinity of a channel pore. Cell Calcium 13:183-92 [PubMed]

Storm JF (1987) Intracellular injection of a Ca2+ chelator inhibits spike repolarization in hippocampal neurons. Brain Res 435:387-92 [PubMed]

Stutzmann GE (2005) Calcium dysregulation, IP3 signaling, and Alzheimer's disease. Neuroscientist 11:110-5 [Journal] [PubMed]

Taxin ZH, Neymotin SA, Mohan A, Lipton P, Lytton WW (2014) Modeling molecular pathways of neuronal ischemia. Prog Mol Biol Transl Sci 123:249-75 [Journal] [PubMed]

Taylor CW, Tovey SC (2010) IP(3) receptors: toward understanding their activation. Cold Spring Harb Perspect Biol 2:a004010 [Journal] [PubMed]

Terasaki M, Slater NT, Fein A, Schmidek A, Reese TS (1994) Continuous network of endoplasmic reticulum in cerebellar Purkinje neurons. Proc Natl Acad Sci U S A 91:7510-4 [PubMed]

Thibault O, Porter NM, Chen KC, Blalock EM, Kaminker PG, Clodfelter GV, Brewer LD, Landfield (1998) Calcium dysregulation in neuronal aging and Alzheimer's disease: history and new directions. Cell Calcium 24:417-33 [PubMed]

Wagner J, Fall CP, Hong F, Sims CE, Allbritton NL, Fontanilla RA, Moraru II, Loew LM, Nuccite (2004) A wave of IP3 production accompanies the fertilization Ca2+ wave in the egg of the frog, Xenopus laevis: theoretical and experimental support. Cell Calcium 35:433-47 [Journal] [PubMed]

West AE, Chen WG, Dalva MB, Dolmetsch RE, Kornhauser JM, Shaywitz AJ, Takasu MA, Tao X, Green (2001) Calcium regulation of neuronal gene expression. Proc Natl Acad Sci U S A 98:11024-31 [PubMed]

Winograd M, Destexhe A, Sanchez-Vives MV (2008) Hyperpolarization-activated graded persistent activity in the prefrontal cortex. Proc Natl Acad Sci U S A 105:7298-303 [Journal] [PubMed]

   Hodgkin-Huxley model of persistent activity in prefrontal cortex neurons (Winograd et al. 2008) [Model]
   Hodgkin-Huxley model of persistent activity in PFC neurons (Winograd et al. 2008) (NEURON python) [Model]

Zündorf G, Reiser G (2011) Calcium dysregulation and homeostasis of neural calcium in the molecular mechanisms of neurodegenerative diseases provide multiple targets for neuroprotection. Antioxid Redox Signal 14:1275-88 [Journal] [PubMed]

Alturki A, Feng F, Nair A, Guntu V, Nair SS (2016) Distinct current modules shape cellular dynamics in model neurons. Neuroscience 334:309-331 [Journal] [PubMed]

   Distinct current modules shape cellular dynamics in model neurons (Alturki et al 2016) [Model]

McDougal RA, Bulanova AS, Lytton WW (2016) Reproducibility in computational neuroscience models and simulations IEEE Trans Biomed Eng 63(10):2021-2035 [Journal] [PubMed]

Neymotin SA, Dura-Bernal S, Lakatos P, Sanger TD, Lytton WW (2016) Multitarget Multiscale Simulation for Pharmacological Treatment of Dystonia in Motor Cortex. Front Pharmacol 7:157 [Journal] [PubMed]

   Multitarget pharmacology for Dystonia in M1 (Neymotin et al 2016) [Model]

Neymotin SA, McDougal RA, Bulanova AS, Zeki M, Lakatos P, Terman D, Hines ML, Lytton WW (2016) Calcium regulation of HCN channels supports persistent activity in a multiscale model of neocortex Neuroscience 316:344-366 [Journal] [PubMed]

   Ca+/HCN channel-dependent persistent activity in multiscale model of neocortex (Neymotin et al 2016) [Model]

Neymotin SA, Suter BA, Dura-Bernal S, Shepherd GM, Migliore M, Lytton WW (2017) Optimizing computer models of corticospinal neurons to replicate in vitro dynamics. J Neurophysiol 117(1):148-162 [Journal] [PubMed]

   Computer models of corticospinal neurons replicate in vitro dynamics (Neymotin et al. 2017) [Model]

(60 refs)