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

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Accession:168874
"... 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. "
Reference:
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;
Gene(s):
Transmitter(s): Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Calcium waves; Reaction-diffusion;
Implementer(s): Neymotin, Sam [samn at neurosim.downstate.edu]; McDougal, Robert [robert.mcdougal at yale.edu]; Sherif, Mohamed [mohamed.sherif.md at gmail.com];
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;
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ca1dDemo
data
readme.txt
cagk.mod *
cal_mig.mod
can_mig.mod
cat_mig.mod
kaprox.mod *
kdrca1.mod *
km.mod *
misc.mod *
na3n.mod *
naf.mod
NMDA.mod
stats.mod *
vecst.mod *
AMPA0.cfg
AMPA150.cfg
analysisCode.py
batch.py
cawave.cfg
cawave.py
conf.py
geneval_cvode.inc *
misc.h *
netcon.inc *
nqs.hoc
nqs.py
plot_fig11.py
setup.hoc *
vector.py *
                            
: $Id: geneval_cvode.inc,v 1.6 2004/02/04 21:04:15 billl Exp $  
TITLE Kevins Cvode modified Generalized Hodgkin-Huxley eqn Channel Model 

COMMENT

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

ENDCOMMENT

INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}

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

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

} : end CONSTANT

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

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

PARAMETER {
	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
} : end PARAMETER
ENDCOMMENT

PARAMETER {
  cao                (mM)
  cai                (mM)
  celsius			   (degC)
  dt 				   (ms)
  v 			       (mV)
}

ASSIGNED {
	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 }

INITIAL { 
 	mh(v)
	m = Inf[0] h = Inf[1]
}

BREAKPOINT {

  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) {
    mexp2=-mexp
    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

  iassign()
} : end BREAKPOINT

: ASSIGNMENT PROCEDURES
: 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 }

:-------------------------------------------------------------------

DERIVATIVE states {
  mh(v)
  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]

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References and models that cite this paper

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