Data-driven, HH-type model of the lateral pyloric (LP) cell in the STG (Nowotny et al. 2008)

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Accession:116957
This model was developed using voltage clamp data and existing LP models to assemble an initial set of currents which were then adjusted by extensive fitting to a long data set of an isolated LP neuron. The main points of the work are a) automatic fitting is difficult but works when the method is carefully adjusted to the problem (and the initial guess is good enough). b) The resulting model (in this case) made reasonable predictions for manipulations not included in the original data set, e.g., blocking some of the ionic currents. c) The model is reasonably robust against changes in parameters but the different parameters vary a lot in this respect. d) The model is suitable for use in a network and has been used for this purpose (Ivanchenko et al. 2008)
References:
1 . Nowotny T, Levi R, Selverston AI (2008) Probing the dynamics of identified neurons with a data-driven modeling approach. PLoS ONE 3:e2627 [PubMed]
2 . Ivanchenko MV, Nowotny T, Selverston AI, Rabinovich MI (2008) Pacemaker and network mechanisms of rhythm generation: cooperation and competition. J Theor Biol 253:452-61 [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): Hodgkin-Huxley neuron; Stomatogastric Ganglion (STG) Lateral Pyloric (LP) cell;
Channel(s): I A; I K; I M; I h; I K,Ca; I Sodium; I Calcium; I Potassium;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: C or C++ program;
Model Concept(s): Activity Patterns; Bursting; Parameter Fitting; Invertebrate; Methods; Parameter sensitivity;
Implementer(s): Nowotny, Thomas [t.nowotny at sussex.ac.uk];
Search NeuronDB for information about:  I A; I K; I M; I h; I K,Ca; I Sodium; I Calcium; I Potassium;
/*--------------------------------------------------------------------------
   Author: Thomas Nowotny
  
   Institute: Institute for Nonlinear Dynamics
              University of California San Diego
              La Jolla, CA 92093-0402
  
   email to:  tnowotny@ucsd.edu
  
   initial version: 2005-08-17
  
--------------------------------------------------------------------------*/

using namespace std;

#ifndef CN_RK65N_CC
#define CN_RK65N_CC

#include "CN_rk65n.h"
#include <iostream>

#define min(X,Y) (X<Y? X:Y)
#define max(X,Y) (X>Y? X:Y)

#define sixth 0.166666666666667



rk65n::rk65n(int dim, double inmaxdt, double ineps, double inabseps,
	     double inreleps)
{
  N= dim;
  maxdt= inmaxdt;
  eps= ineps;
  abseps= inabseps;
  releps= inreleps;
  for (int i= 0; i < 9; i++) {
    Y[i]= new double[N];
    F[i]= new double[N];
    for (int j= i; j < 8; j++) {
      a[i][j]= 0.0;
    }
  }
  y5= new double[N];
  
  a[1][0]= 0.111111111111111;
  a[2][0]= 0.555555555555556e-1;
  a[2][1]= 0.555555555555556e-1;
  a[3][0]= 0.416666666666667e-1;
  a[3][1]= 0.0;
  a[3][2]= 0.125;
  a[4][0]= 0.166666666666667;
  a[4][1]= 0.0;
  a[4][2]= -0.5;
  a[4][3]= 0.666666666666667;
  a[5][0]= 0.1875e+1;
  a[5][1]= 0.0;
  a[5][2]= -0.7875e+1;
  a[5][3]= 0.7e+1;
  a[5][4]= -0.5;
  a[6][0]= -0.4227272727272727e+1;
  a[6][1]= 0.0;
  a[6][2]= 0.176995738636364e+2;
  a[6][3]= -0.142883522727273e+2;
  a[6][4]= 0.522017045454545;
  a[6][5]= 0.104403409090909e+1;
  a[7][0]= 0.840622673179752e+1;
  a[7][1]= 0.0;
  a[7][2]= -0.337303717185049e+2;
  a[7][3]= 0.271460231129622e+2;
  a[7][4]= 0.342046929709216;
  a[7][5]= -0.184653767923258e+1;
  a[7][6]= 0.577349465373733;
  a[8][0]= 0.128104575163399;
  a[8][1]= 0.0;
  a[8][2]= 0.0;
  a[8][3]= -0.108433734939759;
  a[8][4]= 0.669375;
  a[8][5]= -0.146666666666667;
  a[8][6]= 0.284444444444444;
  a[8][7]= 0.173176381998583;

  b[0]= 0.567119155354449e-1;
  b[1]= 0.0;
  b[2]= 0.0;
  b[3]= 0.210909572355356;
  b[4]= 0.141490384615385;
  b[5]= 0.202051282051282;
  b[6]= 0.253186813186813;
  b[7]= 0.843679809736684e-1;
  b[8]= 0.512820512820513e-1;
}

rk65n::~rk65n()
{
  for (int i= 0; i < 9; i++) {
    delete[] Y[i];
    delete[] F[i];
  }
  delete[] y5;
}

double rk65n::integrate(double *y, double *yn,
			NeuronModel *model, double dt)
{
  // calculate iterative terms rk65_Y[__i] and rk65_F[__i] (to sixth order)
  for (i= 0; i < 9; i++)
  {
    for (k= 0; k < N; k++)
    {
      aF= 0.0;
      for (j= 0; j < i; j++)
	aF+= a[i][j]*F[j][k];
      Y[i][k]= y[k]+dt*aF;
    }
    model->derivative(Y[i], F[i]);
  }

  // sum up rk65_Y[__i] and rk65_F[__i] to build 5th order scheme -> rk65_y5
  for (k= 0; k < N; k++)
  {
    aF= 0.0;
    for (j= 0; j < 8; j++) aF+= a[8][j]*F[j][k];
    y5[k]= y[k]+ dt*aF;
  }

  // sum up rk65_Y[__i] and rk65_F[__i] to build 6th order scheme -> yn
  for (k= 0; k < N; k++)
  {
    aF= 0.0;
    for (j= 0; j < 9; j++) aF+= b[j]*F[j][k];
    yn[k]= y[k]+ dt*aF;
  }

  // determine minimal necessary new dt to get error < theEps based on the
  // difference between results rk65_y5 and yn
  dtx= maxdt;
#ifdef DEBUG
  int min_var= -1;
#endif
  for (k= 0; k < N; k++)
  {
    theEps= max(abseps, min(eps, fabs(releps*yn[k])));
    delta= abs(yn[k]-y5[k]);
    if (delta > DBL_MIN) {
      newdt= exp(sixth*(log(theEps)-log(delta)))*dt;
      if (newdt < dtx) {
#ifdef DEBUG
	min_var= k;
#endif
	dtx= newdt;
      }
    }
  }
#ifdef DEBUG
  cerr << min_var << " " << dtx << endl;
#endif
  return dtx;
}

#undef min
#undef max

#endif

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