STDP promotes synchrony of inhibitory networks in the presence of heterogeneity (Talathi et al 2008)

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"Recently Haas et al. (J Neurophysiol 96: 3305–3313, 2006), observed a novel form of spike timing dependent plasticity (iSTDP) in GABAergic synaptic couplings in layer II of the entorhinal cortex. Depending on the relative timings of the presynaptic input at time tpre and the postsynaptic excitation at time tpost, the synapse is strengthened (delta_t = t(post) - t(pre) > 0) or weakened (delta_t < 0). The temporal dynamic range of the observed STDP rule was found to lie in the higher gamma frequency band (> or = 40 Hz), a frequency range important for several vital neuronal tasks. In this paper we study the function of this novel form of iSTDP in the synchronization of the inhibitory neuronal network. In particular we consider a network of two unidirectionally coupled interneurons (UCI) and two mutually coupled interneurons (MCI), in the presence of heterogeneity in the intrinsic firing rates of each coupled neuron. ..."
1 . Talathi SS, Hwang DU, Ditto WL (2008) Spike timing dependent plasticity promotes synchrony of inhibitory networks in the presence of heterogeneity. J Comput Neurosci 25:262-81 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Entorhinal cortex;
Cell Type(s):
Channel(s): I Na,t; I K;
Gap Junctions:
Receptor(s): GabaA; Gaba;
Simulation Environment: C or C++ program;
Model Concept(s): STDP;
Implementer(s): Talathi Sachin [talathi at];
Search NeuronDB for information about:  GabaA; Gaba; I Na,t; I K;
readme * *
CN_absynapse.h * *
CN_absynapseECplast1.h * *
CN_absynapseECplast2.h * *
CN_absynapseECplast3.h * *
CN_DCInput.h * *
CN_ECneuron.h * *
CN_HHneuron.h * *
CN_inputneuron.h * *
CN_LPneuronAstrid.h * *
CN_LPneuronRafi4.h * *
CN_multifire_inputneuron.h * *
CN_neuron.h * *
CN_NeuronModel.h * *
CN_Poissonneuron.h * *
CN_Rallsynapse.h * *
CN_rk65n.h * *
CN_synapse.h * *
CN_synapseAstrid.h * *
CN_TimeNeuron.h * *
CN_Valneuron.h * *
CN_Valneuron2.h *
ids.h *
Makefile *
testCN * *
   Author: Thomas Nowotny
   Institute: Institute for Nonlinear Dynamics
              University of California San Diego
              La Jolla, CA 92093-0402
   email to:
   initial version: 2005-08-19


#include ""

LPAneuron::LPAneuron(int inlabel, double *the_p= LPA_p):
  neuron(inlabel, LPA_IVARNO, LPANEURON, the_p, LPA_PNO)

LPAneuron::LPAneuron(int inlabel, tnvector<int> inpos, double *the_p= LPA_p):
  neuron(inlabel, LPA_IVARNO, LPANEURON, inpos, the_p, LPA_PNO)

inline double LPAneuron::E(double *x)
  return x[idx];

#define efunc(X,Y,Z) (1.0/(1.0+expl(((X)+(Y))/(Z))))
#define E x[idx]

#define Capacit p[0]
#define tau_Ca p[1]
#define f p[2]
#define C_Ca_0 p[3]
#define E_Na p[4]
#define E_K p[5]
#define E_H p[6]
#define E_leak p[7]
#define g_H p[8]
#define g_leak p[9]
#define g_Na p[10]
#define g_CaT p[11]
#define g_CaS p[12]
#define g_A p[13]
#define g_KCa p[14]
#define g_Kd p[15]
#define Area p[16]

void LPAneuron::currents(ostream &os, double *x)
  I_Na=  g_Na*ipower(x[idx+1],3)*x[idx+2]*(E-E_Na)*Area;
  I_CaT= g_CaT*ipower(x[idx+3],3)*x[idx+4]*(E-_E_Ca)*Area;
  I_CaS= g_CaS*ipower(x[idx+5],3)*x[idx+6]*(E-_E_Ca)*Area;
  I_A=   g_A*ipower(x[idx+7],3)*x[idx+8]*(E-E_K)*Area;
  I_KCa= g_KCa*ipower(x[idx+9],4)*(E-E_K)*Area;
  I_Kd=  g_Kd*ipower(x[idx+10],4)*(E-E_K)*Area;
  I_H=   g_H*x[idx+11]*(E-E_H)*Area;
  I_leak= g_leak*(E-E_leak)*Area;
  os << I_Na << " ";
  os << I_CaT << " ";
  os << I_CaS << " ";
  os << I_A << " ";
  os << I_KCa << " ";
  os << I_Kd << " ";
  os << I_H << " ";
  os << I_leak << " ";

void LPAneuron::derivative(double *x, double *dx)
  Isyn= 0.0;
  forall (den_it) {
    Isyn+= den_it->c_value()->Isyn(x);

  I_Na=  g_Na*ipower(x[idx+1],3)*x[idx+2]*(E-E_Na);
  I_CaT= g_CaT*ipower(x[idx+3],3)*x[idx+4]*(E-_E_Ca);
  I_CaS= g_CaS*ipower(x[idx+5],3)*x[idx+6]*(E-_E_Ca);
  I_A=   g_A*ipower(x[idx+7],3)*x[idx+8]*(E-E_K);
  I_KCa= g_KCa*ipower(x[idx+9],4)*(E-E_K);
  I_Kd=  g_Kd*ipower(x[idx+10],4)*(E-E_K);
  I_H=   g_H*x[idx+11]*(E-E_H);
  I_leak= g_leak*(E-E_leak);
  dx[idx]= Isyn/Capacit -(I_Na + I_Kd + I_CaT + I_CaS + I_A + I_KCa +
			       I_H + I_leak)*Area/Capacit;
  // differential eqn for mNa
  // differential eqn for hNa
  _hinf= efunc(E,48.9,5.18);
  _tauh= (1.34*efunc(E,62.9,-10.0))*(1.5+efunc(E,34.9,3.6));
  if (_tauh < 1e-2) _tauh= 1e-2; // this is a horrible numerical instability
  // if the neuron is hyperpolarized, _tauh goes to 0 amplifying the already
  // clear disadvantageous rounding errors in (order of 1 - order of 1)
  // in mNa *a lot*. This leads to an explosion and eventually nan ...
  //  cerr << _hinf << " " << _tauh << " ";

  // differential eqn for mCa1
  _minf= efunc(E,27.1,-7.2);
  _taum= 43.4-42.6*efunc(E,68.1,-20.5);
  // differential eqn for hCa1
  _hinf= efunc(E,32.1,5.5);
  _tauh= 210.0-179.6*efunc(E,55.0,-16.9);

  // differential eqn for mCa2
  _minf= efunc(E,33.0,-8.1);
  _taum= 2.8+(14.0/(exp((E+27.0)/10.0)+exp((E+70.0)/-13.0)));
  // differential eqn for hCa2
  _hinf= efunc(E,60,6.2);
  _tauh= 120+(300.0/(exp((E+55.0)/9.0)+exp((E+65.0)/-16)));

  // differential eqn for mA
  _minf= efunc(E,27.2,-8.7);
  _taum= 23.2-20.8*efunc(E,32.9,-15.2);
  // differential eqn for hA
  _hinf= efunc(E,56.9,4.9);
  _tauh= 77.2-58.4*efunc(E,38.9,-26.5);

  // differential eqn for mKCa
  _minf= (x[idx+12]/(x[idx+12]+3.0))*efunc(E,28.3,-12.6);
  _taum= 180.6-150.2*efunc(E,46.0,-22.7);
  // differential eqn for mKd
  _minf= efunc(E,12.3,-11.8);
  _taum= 14.4-12.8*efunc(E,28.3,-19.2);
  // differential eqn for mh
  _minf= efunc(E,75.0,5.5);
  _taum= 2.0/(exp((E+169.7)/-11.6)+exp((E-26.7)/14.3));
  if (_taum < 1e-2) _taum= 1e-2; // same instability as for _tauh_Na ...

  // differential eqn for o, prob. of Ca mediated K channel activation 

  // the Isyn is calculated elsewhere
  dx[idx+13]= 0.0; 

#undef efunc
#undef E
#undef Capacit
#undef tau_Ca
#undef f
#undef C_Ca_0
#undef E_Na
#undef E_K
#undef E_H
#undef E_leak
#undef g_H
#undef g_leak
#undef g_Na
#undef g_CaT
#undef g_CaS
#undef g_A
#undef g_KCa
#undef g_Kd
#undef Area