Biophysical and phenomenological models of spike-timing dependent plasticity (Badoual et al. 2006)

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Accession:116096
"Spike-timing dependent plasticity (STDP) is a form of associative synaptic modification which depends on the respective timing of pre- and post-synaptic spikes. The biophysical mechanisms underlying this form of plasticity are currently not known. We present here a biophysical model which captures the characteristics of STDP, such as its frequency dependency, and the effects of spike pair or spike triplet interactions. ... A simplified phenomenological model is also derived..."
Reference:
1 . Badoual M, Zou Q, Davison AP, Rudolph M, Bal T, Fregnac Y, Destexhe A (2006) Biophysical and phenomenological models of multiple spike interactions in spike-timing dependent plasticity. Int J Neural Syst 16:79-97 [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):
Channel(s): I Na,t; I K; I M; I Calcium;
Gap Junctions:
Receptor(s): AMPA; NMDA;
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Simplified Models; Synaptic Plasticity; Long-term Synaptic Plasticity; STDP;
Implementer(s):
Search NeuronDB for information about:  AMPA; NMDA; I Na,t; I K; I M; I Calcium;
/* ----------------------------------------------------------------
   
   Cell model used in:
   
   M. Badoual, Q. Zou, A.P. Davison, M. Rudolph, T. Bal,
   Y. Frégnac and A. Destexhe (2006) Biophysical and phenomenological
   models of multiple spike interactions in spike-timing dependent
   plasticity.
   Int J. Neural Syst. 16: 79-97
   
   
   This file is a lightly modified version of the file "demofig1.hoc" in
   
   http://senselab.med.yale.edu/modeldb/ShowModel.asp?model=2488
   
   original author:  Zach Mainen (zach@salk.edu or zach@cshl.org)
   
   modifications by: Mathilde Badoual
  
---------------------------------------------------------------- */


create soma
access soma

tstop = 200
steps_per_ms = 40
dt = 0.025
celsius=37

pi=3.141593

// --------------------------------------------------------------
// passive & active membrane
// --------------------------------------------------------------

ra        = 150
global_ra = ra
// rm*2 and cm/2 to take into account the area of the spine
rm        = 12000
c_m       = 1.0
cm_myelin = 0.04
g_pas_node = 0.02

v_init    = -70
celsius   = 37

Ek = -90
Ena = 60


gna_soma = 35
gna_node = 30000
gna_iseg=3000
gna_dend = 35

gkv_axon = 500
gkv_soma = 30

gca = 0.8

gkm = .1
gkm_dend=0.1
gkca = 3

gca_soma = gca
gca_dend=gca
gkm_soma = gkm
gkca_soma = gkca
 

// --------------------------------------------------------------
// Axon geometry
//
// Similar to Mainen et al (Neuron, 1995)
// --------------------------------------------------------------

n_axon_seg = 5

create soma,iseg,hill,myelin[2],node[2]

proc create_axon() {

  create iseg,hill,myelin[n_axon_seg],node[n_axon_seg]

  soma {
    L=20
    equiv_diam = 20
    diam = equiv_diam
  }
  if (numarg()) equiv_diam = $1

  iseg {                // initial segment between hillock + myelin
     L = 15
     nseg = 5
     diam = equiv_diam/20        // see Sloper and Powell 1982, Fig.71
  }

  hill {                
    L = 10
    nseg = 5
    diam(0:1) = 4*iseg.diam:iseg.diam
  }

  // construct myelinated axon with nodes of ranvier

  for i=0,n_axon_seg-1 {
    myelin[i] {         // myelin element
      nseg = 5
      L = 100
      diam = iseg.diam         
    }
    node[i] {           // nodes of Ranvier
      nseg = 1
      L = 1.0           
      diam = iseg.diam*.75       // nodes are thinner than axon
    }
  }

  soma connect hill(0), 0.5
  hill connect iseg(0), 1
  iseg connect myelin[0](0), 1
  myelin[0] connect node[0](0), 1

  for i=0,n_axon_seg-2  { 
      node[i] connect myelin[i+1](0), 1 
      myelin[i+1] connect node[i+1](0), 1
  }
}

// --------------------------------------------------------------
// Spine
// --------------------------------------------------------------

      // Based on the "Folding factor" described in
      // Jack et al (1989), Major et al (1994)
      // note, this assumes active channels are present in spines 
      // at same density as dendrites


create spine
access spine
L=0.5
diam=L
insert NMDAKIT
gmax_NMDAKIT=0.05


objectvar ampasyn,kin
ampasyn=new AMPAKIT(0.5)
kin=new KINASE(0.5)
spines_corr=1.5

access spine

create neck
access neck
L=1.0
diam=0.1

create dendrite
access dendrite
L=1000
diam=1.4
nseg=100



proc init_cell() {

  // passive
  forall {
    insert pas
    Ra = ra 
    cm = c_m
    g_pas = 1/rm
    e_pas = -70
  }

  dendrite {
    cm = c_m*spines_corr
    g_pas = 1/(rm/spines_corr)
  }


  // exceptions along the axon
  forsec "myelin" cm = cm_myelin
  forsec "node" g_pas = g_pas_node

  // na+ channels
  forall insert na
  dendrite.gbar_na = gna_dend*spines_corr
  spine.gbar_na = gna_dend
  neck.gbar_na = gna_dend 
  forsec "myelin" gbar_na = gna_soma
  hill.gbar_na = gna_iseg
  iseg.gbar_na = gna_iseg
  forsec "node" gbar_na = gna_node

  // kv delayed rectifier channels
  iseg { insert kv  gbar_kv = gkv_axon }
  hill { insert kv  gbar_kv = gkv_axon }
  soma { insert kv  gbar_kv = gkv_soma }
  dendrite { insert kv  gbar_kv = gkv_soma*spines_corr }
  spine { insert kv  gbar_kv = gkv_soma }
  neck { insert kv  gbar_kv = gkv_soma }

  // dendritic channels
  dendrite {
    insert km    gbar_km  = gkm_dend*spines_corr
    insert kca   gbar_kca = gkca*spines_corr
    insert ca    gbar_ca = gca_dend*spines_corr
    insert cad
  }
  spine {
    insert km    gbar_km  = gkm_dend
    insert kca   gbar_kca = gkca
    insert ca    gbar_ca = gca_dend
    insert cadspine
    lneck_cadspine=neck.L
    sneck_cadspine=pi*neck.diam*neck.diam/4
    vspine_cadspine=pi*spine.diam*spine.diam*spine.L/4
  }
  neck {
    insert km    gbar_km  = gkm_dend
    insert kca   gbar_kca = gkca
    insert ca    gbar_ca = gca_dend
    insert cad
  }  

  soma {
    gbar_na = gna_soma
    insert km gbar_km = gkm_soma
    insert kca gbar_kca = gkca_soma
    insert ca gbar_ca = gca_soma
    insert cad
  }

 
  forall if(ismembrane("k_ion")) ek = Ek
  forall if(ismembrane("na_ion")) {
    ena = Ena
    // seems to be necessary for 3d cells to shift Na kinetics -5 mV
    vshift_na = -5
  }
  forall if(ismembrane("ca_ion")) {
    eca = 140
    ion_style("ca_ion",0,1,0,0,0)
    vshift_ca = 0
  }
}


create_axon()

init_cell()
objectvar st
access iseg
st=new IClamp(1)
st.dur = 1
st.del = 70
st.amp = 2



connect spine(0), neck(1)
connect neck(0), dendrite(0.5)
connect dendrite(0), soma(1)






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