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: 2002-01-25
  
--------------------------------------------------------------------------*/

#ifndef LPRNEURON_CC
#define LPRNEURON_CC

#include "CN_neuron.cc"

#define efunc(X,Y,Z) (1.0/(1.0+exp(((X)-(Y))/(Z))))
#define Eaxon x[idx]
#define Esoma x[idx+15]

#define gNa p[0]
#define ENa p[1] 
#define gCa1 p[2]
#define gCa2 p[3]
#define goCa p[4]
#define EK p[5]
#define gd p[6]
#define gA p[7]
#define gh p[8]
#define EIh p[9]
#define gleak p[10]
#define Eleak p[11]
#define Cmem p[12]
#define c_iCa p[13]
#define k_Ca p[14]
#define kfac p[15]
#define Vshift p[16]
#define IDC p[17]
#define kfacfast p[18]
#define gVV p[19]
#define Cs p[20]
#define gleaks p[21]
#define RTF p[22]
#define AreaAxon p[23]
#define Area p[24]

// ICa from my own fit
#define k_aCa1 p[25]
#define k_bCa1 p[26]
#define k_aCa2 p[27]
#define V_aCa1 p[28]
#define V_bCa1 p[29]
#define V_aCa2 p[30]
#define s_aCa1 p[31]
#define s_bCa1 p[32]
#define s_aCa2 p[33]
#define P_Ca p[34]
#define Ca_out p[35]
#define V_kbCa1 p[36]
#define s_kbCa1 p[37]

#define k_oa p[38]
#define k_ob p[39]
#define V_ao1 p[40]
#define V_ao2 p[41]
#define s_ao1 p[42]
#define s_ao2 p[43]
#define f p[44]
#define c1 p[45]
#define c2 p[46]
#define c3 p[47]
#define Ca_0 p[48]

#define k_aA p[49]
#define k_bA1 p[50]
#define c_A2 p[51]
#define V_aA p[52]
#define V_bA p[53]
#define V_kbA2 p[54]
#define V_x p[55]
#define s_aA p[56]
#define s_bA p[57]
#define s_kbA2 p[58]
#define s_x p[59]

// Ih from my own fit
#define c_r p[60]
#define V_r p[61]
#define V_kr p[62]
#define s_r p[63]
#define s_kr p[64]

#define I_scale p[65]

#define E_M p[66]
#define g_M p[67]
#define k_M p[68]
#define V_M p[69]
#define s_M p[70]
#define V_kM p[71]
#define s_kM p[72]

LPRneuron::LPRneuron(int inlabel, double *the_p= LPR_p):
  neuron(inlabel, LPR_IVARNO, LPRNEURON, the_p, LPR_PNO)
{
}

LPRneuron::LPRneuron(int inlabel, vector<int> inpos, double *the_p= LPR_p):
  neuron(inlabel, LPR_IVARNO, LPRNEURON, inpos, the_p, LPR_PNO)
{
}

inline double LPRneuron::E(double *x)
{
  return x[idx+15]+Vshift;
}

void LPRneuron::currents(ostream &os, double *x)
{
  static double INa, ICa, IoCa, Id, IA, Ih, Il, IM, IVV, sum;

  // differential eqn for the axon membrane potential
  INa= pw3(x[idx+1])*x[idx+2]*gNa*(Eaxon-ENa)*AreaAxon;
  Id= pw4(x[idx+8])*gd*(Esoma-EK)*AreaAxon;
  IM= g_M*x[idx+14]*(Eaxon-E_M)*AreaAxon;
  Il= gleak*(Eaxon-Eleak)*AreaAxon;
  IVV= gVV*(Esoma-Eaxon);
  
  os << INa << " ";
  os << Id << " ";
  os << IM << " ";
  os << Il << " ";
  sum= INa + Id + IM + Il - IVV;
  os << sum << " ";
  
  ICa= (x[idx+3]*x[idx+4]*gCa1+x[idx+5]*gCa2)*
    P_Ca*Esoma*(x[idx+13]*exp(Esoma/RTF)-Ca_out)/(exp(Esoma/RTF)-1.0)*Area;
  IoCa= x[idx+6]*x[idx+7]*goCa*(Esoma-EK)*Area;
  IA= pw3(x[idx+9])*gA*(Esoma-EK)*
    (efunc(Esoma,V_x,s_x)*x[idx+10]+(1.0-efunc(Esoma,V_x,s_x))*x[idx+11])*Area;
  Ih= x[idx+12]*gh*(Esoma-EIh)*Area;
  Il= gleaks*(Esoma-Eleak)*Area;

  sum= ICa + IoCa + IA + Ih + IVV + Il;
  os << ICa << " ";
  os << IoCa << " ";
  os << IA << " ";
  os << Ih << " ";
  os << IVV << " ";
  os << Il << " ";
  os << sum << endl;
}

void LPRneuron::derivative(double *x, double *dx)
{
  static double a, b, hinf, kh, minf, km;
  static double INa, Id, ICa, IoCa, IA, Ih, Il, IM, IVV;
  static double Isyn;
  
  Isyn= 0.0;
  forall(den, den_it) {
    Isyn+= (*den_it)->Isyn(x);
  }
  
  // differential eqn for the axon membrane potential
  INa= pw3(x[idx+1])*x[idx+2]*gNa*(Eaxon-ENa)*AreaAxon;
  Id= pw4(x[idx+8])*gd*(Eaxon-EK)*AreaAxon;
  IM= g_M*x[idx+14]*(Eaxon-E_M)*AreaAxon;
  Il= gleak*(Eaxon-Eleak)*AreaAxon;
  IVV= gVV*(Esoma-Eaxon);
  
  dx[idx]= (-INa - Id - IM - Il + IVV)/Cmem; 

  // soma compartment
  a= exp(Esoma/RTF);
  ICa= (x[idx+3]*x[idx+4]*gCa1+x[idx+5]*gCa2)*P_Ca*Esoma*(x[idx+13]*a-Ca_out)/(a-1.0)*Area;
  
  IoCa= x[idx+6]*x[idx+7]*goCa*(Esoma-EK)*Area;

  a= efunc(Esoma,V_x,s_x);
  IA= pw3(x[idx+9])*gA*(Esoma-EK)*(a*x[idx+10]+(1.0-a)*x[idx+11])*Area;

  Ih= x[idx+12]*gh*(Esoma-EIh)*Area;

  Il= gleaks*(Esoma-Eleak)*Area;

  dx[idx+15]= (-ICa - IoCa - IA - Ih - Il - IVV + (IDC+Isyn)*I_scale)/Cs;

  // differential eqn for mNa
  a= (-16.64-0.32*x[idx]) / (exp(-13.0-x[idx]/4.0)-1.0);
  b= (0.28*x[idx]+7.0) / (exp(x[idx]/5.0+5.0)-1.0);
  dx[idx+1]= a*(1.0-x[idx+1])-b*x[idx+1];
  // differential eqn for hNa
  a= 0.128*exp(-2.66666666667-x[idx]/18.0);
  b= 4.0 / (exp(-5.0-x[idx]/5.0)+1.0);
  dx[idx+2]= a*(1.0-x[idx+2])-b*x[idx+2];

  // differential eqn for md
  a=  (-1.6-0.032*x[idx]) / (exp(-10.0-x[idx]/5.0)-1.0);
  b= 0.5*exp(-1.375-x[idx]/40.0);
  dx[idx+8]= a*(1.0-x[idx+8])-b*x[idx+8];

  // differential eqn for mCa1
  minf= efunc(Esoma,V_aCa1,s_aCa1);
  km= k_aCa1*kfac;
  dx[idx+3]= (minf-x[idx+3])*km;
  // differential eqn for hCa1
  hinf= efunc(Esoma,V_bCa1,s_bCa1);
  kh= k_bCa1*efunc(Esoma,V_kbCa1,s_kbCa1)*kfac;
  dx[idx+4]= (hinf-x[idx+4])*kh;

  // differential eqn for mCa2
  minf= efunc(Esoma,V_aCa2,s_aCa2);
  km= k_aCa2*kfac;
  dx[idx+5]= (minf-x[idx+5])*km;

  // differential eqn for moCa
  a= V_ao1-f*x[idx+13];
  b= V_ao2-f*x[idx+13];
  minf= efunc(Esoma,a,s_ao1)*efunc(Esoma,b,s_ao2)*(x[idx+13]/(c1+x[idx+13]));
  km= k_oa*kfac;
  dx[idx+6]= (minf-x[idx+6])*km;
  // differential eqn for hoCa
  hinf= c2/(c3+x[idx+13]);
  kh= k_ob*kfac;
  dx[idx+7]= (hinf-x[idx+7])*kh;

  // differential eqn for mA
  minf= efunc(Esoma,V_aA,s_aA);
  km= k_aA*kfac;
  dx[idx+9]= (minf-x[idx+9])*km;
  // differential eqn for hA1
  hinf= efunc(Esoma,V_bA,s_bA);
  kh= k_bA1*kfac;
  dx[idx+10]= (hinf-x[idx+10])*kh;
  // differential eqn for hA2
  kh= c_A2*efunc(Esoma,V_kbA2,s_kbA2)*kfac;
  dx[idx+11]= (hinf-x[idx+11])*kh;
    
  // differential eqn for mh
  minf= efunc(Esoma,V_r,s_r); 
  km= c_r/efunc(Esoma,V_kr,s_kr)*kfac;
  dx[idx+12]= (minf-x[idx+12])*km;
     
  // differential eqn for Ca concentration 
  dx[idx+13]= -c_iCa*ICa - k_Ca*(x[idx+13]-Ca_0);

  // differential equn for M current activation var
  minf= efunc(Eaxon,V_M,s_M);
  km= k_M*efunc(Eaxon,V_kM,s_kM)*kfac;
  dx[idx+14]= (minf-x[idx+14])*km;
}

#undef efunc
#undef Eaxon
#undef Esoma

#undef gNa 
#undef ENa 
#undef gCa1 
#undef gCa2 
#undef goCa 
#undef EK 
#undef gd 
#undef gA 
#undef gh 
#undef EIh 
#undef gleak 
#undef Eleak 
#undef Cmem 
#undef c_iCa 
#undef k_Ca 
#undef kfac 
#undef Vshift 
#undef IDC 
#undef kfacfast 
#undef gVV 
#undef Cs 
#undef gleaks 
#undef RTF 
#undef Area
#undef AreaAxon

// ICa from my own fit
#undef k_aCa1 
#undef k_bCa1 
#undef k_aCa2 
#undef V_aCa1 
#undef V_bCa1 
#undef V_aCa2 
#undef s_aCa1 
#undef s_bCa1 
#undef s_aCa2 
#undef P_Ca 
#undef Ca_out 
#undef V_kbCa1 
#undef s_kbCa1 

#undef k_oa 
#undef k_ob 
#undef V_ao1 
#undef V_ao2 
#undef s_ao1 
#undef s_ao2 
#undef f 
#undef c1 
#undef c2 
#undef c3 
#undef Ca_0 

#undef c_n 
#undef V_n 
#undef V_kn 
#undef s_n 
#undef s_kn 

#undef k_aA 
#undef k_bA1 
#undef c_A2 
#undef V_aA 
#undef V_bA 
#undef V_kbA2 
#undef V_x 
#undef s_aA 
#undef s_bA 
#undef s_kbA2 
#undef s_x 

// Ih from my own fit
#undef c_r 
#undef V_r 
#undef V_kr 
#undef s_r 
#undef s_kr 

#undef I_scale 

#undef E_M 
#undef g_M 
#undef k_M 
#undef V_M 
#undef s_M 
#undef V_kM
#undef s_kM

#endif

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