CA3 pyramidal cell: rhythmogenesis in a reduced Traub model (Pinsky, Rinzel 1994)

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Accession:35358
Fig. 2A and 3 are reproduced in this simulation of Pinsky PF, Rinzel J (1994).
References:
1 . Pinsky PF, Rinzel J (1994) Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. J Comput Neurosci 1:39-60 [PubMed]
2 . Pinsky PF, Rinzel J (1995) Erratum for Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. J Comput Neurosci 2:275-275
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): Hippocampus CA3 pyramidal cell;
Channel(s): I Na,t; I L high threshold; I K,Ca;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON; XPP;
Model Concept(s): Active Dendrites;
Implementer(s): Lytton, William [billl at neurosim.downstate.edu];
Search NeuronDB for information about:  Hippocampus CA3 pyramidal cell; I Na,t; I L high threshold; I K,Ca;
: $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()

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