CA1 pyramidal neuron: as a 2-layer NN and subthreshold synaptic summation (Poirazi et al 2003)

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We developed a CA1 pyramidal cell model calibrated with a broad spectrum of in vitro data. Using simultaneous dendritic and somatic recordings, and combining results for two different response measures (peak vs. mean EPSP), two different stimulus formats (single shock vs. 50 Hz trains), and two different spatial integration conditions (within vs. between-branch summation), we found the cell's subthreshold responses to paired inputs are best described as a sum of nonlinear subunit responses, where the subunits correspond to different dendritic branches. In addition to suggesting a new type of experiment and providing testable predictions, our model shows how conclusions regarding synaptic arithmetic can be influenced by an array of seemingly innocuous experimental design choices.
1 . Poirazi P, Brannon T, Mel BW (2003) Arithmetic of subthreshold synaptic summation in a model CA1 pyramidal cell. Neuron 37:977-87 [PubMed]
2 . Poirazi P, Brannon T, Mel BW (2003) Pyramidal neuron as two-layer neural network. Neuron 37:989-99 [PubMed]
3 . Poirazi P, Brannon T, Mel BW (2003ab-sup) Online Supplement: About the Model Neuron 37 Online:1-20
4 . Polsky A, Mel BW, Schiller J (2004) Computational subunits in thin dendrites of pyramidal cells. Nat Neurosci 7:621-7 [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): Hippocampus CA1 pyramidal GLU cell;
Channel(s): I Na,p; I Na,t; I L high threshold; I T low threshold; I A; I K; I M; I h; I K,Ca; I Calcium;
Gap Junctions:
Receptor(s): GabaA; GabaB; NMDA; Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Action Potential Initiation; Activity Patterns; Dendritic Action Potentials; Active Dendrites; Influence of Dendritic Geometry; Detailed Neuronal Models; Action Potentials; Depression; Delay;
Implementer(s): Poirazi, Panayiota [poirazi at];
Search NeuronDB for information about:  Hippocampus CA1 pyramidal GLU cell; GabaA; GabaB; NMDA; Glutamate; I Na,p; I Na,t; I L high threshold; I T low threshold; I A; I K; I M; I h; I K,Ca; I Calcium;
// This experiment is used to study the effect of synapse clustering
// on the firing rate of our model cell. To this end, we perform a gradual
// dispersion of synaptic 32, 35, 36 or 40 contacts onto the thin oblique dendrites.  
// We start with the optimal number of clusters each consisting of the optimal 
// number of synapses and in each step we destroy one cluster and disperse
// it's synapses until we end up with no intact clusters.
// Type of inhibition included: 11 gabaa/gabab synapses, 5 in soma sections and 6 
// every 60um along the apical trunk 

// Cluster_size x Cluster_number cases tested with this file: 8x4, 4x8, 5x7, 7x5, 6x6, 8x5, 4x10
// Synchronous (synch=1) or asynchronous (synch=0) cases can also be tested

// In this experiment we can also include background synapses (50 excitatory and 50 inhibitory)
// firing in 5Hz for the entire duration of the experiments to account for background activity

BACK_GROUND = 0 // set to 1 when using background synapses
synch = 0        // synapses are stimulated randomly (NOT synchronously), set to 1 for synchronous stimulation

//load_template("ExperimentControl")         // load needed templates

objref econ                               // initialize template parameters
econ=new ExperimentControl(show_errs,debug_lev)
econ.morphology_dir = "../../morphology/n123"                                 // set location for morphology files
econ.add_lib_dir("Terrence","../../lib")                                      // set location for library files
econ.generic_dir    = "../../experiment/"                                     // set location for cell-setup file
econ.data_dir       = "data"                                                  // set directory to store data
strdef tips_dir
tips_dir = "../single-branch-potency/data/Apical_Tips" // set directory with single branch
sprint(econ.syscmd, "mkdir -p %s", econ.data_dir)                             // 50 Hz stimulation results

actual_resolution=75                                                          // maximum nseg number 

econ.xopen_geometry_dependent("cell")                                         // load raw cell morphology	
econ.xopen_geometry_dependent("cell-analysis")                                // load user-defined semantics on morphology 

printf("Opening cell setup\n")                                   
econ.xopen_generic("cell-setup")                                              // load cell-setup to
printf("Opened. Setting up cell\n")                                           // specify all mechanisms,
maximum_segment_length=actual_resolution                                      // membrane properties etc	 

// Set simulation parameters for the experiment

econ.defvar("Simulation Control", "tstop", "600", "Defines when the simulation stops.")
econ.defvar("Simulation Control", "dt", "0.1", "Timestep")
econ.defvar("Simulation Control", "steps_per_ms", "10", "How many points are plotted per ms")

// open files with NMDA/AMPA, GABA_A/AMPA and GABA_B/GABA_A ratios
econ.xopen_geometry_dependent("gabab-gabaa-uniform-ratio")  // use to estimate GABA_A, GABA_B conductances

// Open file with tuned AMPA conductance values for all sections
objref tune_epsp_list
tune_epsp_list=new List()
strdef tunings_file
sprint(tunings_file, "%s", "tunings")

// Open library functions that will be needed
econ.xopen_library("Terrence","choose-secs")    // used to randomly select sections from a list
econ.xopen_library("Terrence","salloc")         // used to allocate synapses on sections
econ.xopen_library("Terrence","deduce-ratio")   // used to extract NMDA/AMPA, GABA_A/AMPA and GABA_B/GABA_B ratios
econ.xopen_library("Terrence","basic-graphics") // used to plot graphics 
econ.xopen_library("Terrence","spikecount")     // used to count spikes
load_template("SynapseBand")                    // template for making bands of synapses

// use 8x4, 6x6, 7x5, 8x5 
// for cluster_size x cluster_number = 8x4 case
//init_cluster_number = 4                        // number of full-sized clusters of synapses
//init_cluster_size = 8                          // number of synapses per cluster
//disp_size = 1 			         // dispersion step size, one cluster at a time 

// use 4x8, 4x10
// Cut the cluster size in two
//for cluster_size x cluster_number = 4x8 case
//init_cluster_number = 8                         // number of full-sized clusters of synapses
//init_cluster_size = 4                           // number of synapses per cluster
//disp_size = 2                                   // dispersion step size, two clusters at a time
                               			  // dispersion step size, two clusters at a time

gmax_default = 0.0005                           // GABA_A explicit conductance value (S/cm^2)
gmaxb_default = gmax_default/3                  // GABA_B explicit conductance value (S/cm^2)
all_synapses=init_cluster_size*init_cluster_number     // total number of AMPA/NMDA synapses used 
gaba_synapses = 100                                    // maximum number of GABA synapses used  

// used with background synapses
back_syne = 50
back_syni = 50
objref input, co
input = new Vector()
co = new Vector()

experiments = init_cluster_number/disp_size + 1                 // number of experiments to run
print "Number of experiments ", experiments
double exp_ta[experiments]

for i=0, experiments-1  {
  exp_ta[i]=   init_cluster_number - i*disp_size      // number of intact clusters
  printf("Experiment %d\n", i)
  printf("Number of Intact Clusters: %d\n", exp_ta[i] )   

// define variables
objref  vf, vf2, tmpo, vrec, spikevec, band, vrec, splot, rpid, i_nmda[40], g
objref ampa[all_synapses], nmda[all_synapses], gabaa[gaba_synapses], gabab[gaba_synapses]
objref ampa_bg[back_syne], nmda_bg[back_syne], gabaa_bg[back_syni], gabab_bg[back_syni]
objref apical_tipl, cluster_list, random_list, inh_list
strdef tmpstr, tmpstr2, Fc

//                                   Cluster allocation proceedure

proc cluster_salloc() { local cluster_size, cluster_amount, b, b2
   cluster_size=$2                  // number of synapses per cluster
   cluster_amount=$3                // number of clusters

   sprint(tmpstr, "%s/cluster-sections", econ.data_dir)   // open file to store the name of branches containing a cluster
   vf = new File()

// For cluster_amount clusters, pick a different branch and put synapses on it

   cluster_list = new SectionList()
   for b=0,cluster_amount-1 {
       $o1.pick_and_remove()           // select a branch to put a cluster of synapses on
//       $o1.pick()                    // to allow branches with multiple clusters
       cluster_list.append()           // store selected branches in a list
       nseg = cluster_size             // set number of segments = number of synapses in cluster
       vf.printf("%s\n", secname())    // print branch name in file with cluster-section names

//     sprint(tmpstr,"%s.v(0.5)", secname())       
//     if (b < 4) {
//         addgraph(tmpstr,-70,0)      // use to plot trace in current branch 
//     }

// distribute synapses uniformly along each branch in the cluster

       for b2=1,cluster_size {

          posn=(2*b2 -1)/(2*cluster_size)             // define location for a new synapse  
//          rpid = new Random (b2*b) 
//          posn=rpid.uniform(0.1,0.9)
          ampa[synapses_alloced]=new GLU(posn)        // insert an AMPA mechanism at the above location 
          nmda[synapses_alloced]=new NMDA(posn)       // insert an NMDA mechanism at the above location
                                                      // allocate mechanisms and plot on shape graph 
          synapses_alloced = synapses_alloced + 1     // update the counter of AMPA/NMDA synapses allocated


//  Randomly distribute remaining synapses on the remaining obliques
     sprint(tmpstr2, "%s/random-sections", econ.data_dir)
     vf2 = new File()                                 // open file to store the name of branches with random   
     vf2.wopen(tmpstr2)                               // number of synapses on 
     for b=0, (all_synapses - cluster_size*cluster_amount)-1 {
       $o1.pick()                                     // pick a branch
       nseg = cluster_size                            // set number of segments = number of synapses in cluster
       vf2.printf("%s random_list.append()\n", secname()) // print branch name in file with random-sections names
       ampa[synapses_alloced]=new GLU(0.5)            // insert an AMPA mechanism in the middle of the branch
       nmda[synapses_alloced]=new NMDA(0.5)           // insert an NMDA mechanism in the middle of the branch
                                                      // allocate mechanisms and plot on shape graph 
       synapses_alloced=synapses_alloced+1            // update the counter of AMPA/NMDA synapses allocated

// add a small fixed amount of inhibition on soma and trunk (one gabaa/gabab) per section in list
   forsec inh_list {
       posa = 0.5
       posb = 0.5
       gabaa[gaba_synapses] = new GABAa(posa)       
       gabab[gaba_synapses] = new GABAb(posb)
       gmaxb = 3*gmaxb_default                     // explicitly define GABA_A and GABA_B conductances
       gmaxa = 4.8*gmax_default                    // for these sections (don't use GABA/AMPA ratios)
       ifsec soma_list {                      
           gmaxb = 0.03*gmaxb_default              // very little GABA_B at the soma
           gmaxa = 6*gmax_default                  // more GABA_A at the soma
       SALLOC_GABAa(gabaa[gaba_synapses],posa,0,gmaxa)   // allocate synapses using the above conductances
       gaba_synapses = gaba_synapses + 1           // update GABA synapse counter

}                                                 // End of cluster allocation proceedure


hertz=50                                          // frequency of stimulation for AMPA/NMDA synapses
gaba_hertz=50                                     // frequency of stimulation for GABA synapses
perio=0                                           // spike trains for each synapse are NOT periodic

econ.xopen_library("Terrence","basic-graphics")   // open library file for graphics
addgraph_2("soma.v(0.5)",0,tstop,-72,20)                    // make a graph of somatic voltage trace
//addgraph_2("apical_dendrite[60].v(0.5)",0,tstop,-72,20)     // make a graph of dendrite 60 voltage trace
//addgraph_2("apical_dendrite[95].v(0.5)",0,tstop,-72,20)     // make a graph of dendrite 95 voltage trace

apical_tipl=new SectionList()                     // make a list of all apical oblique dendrites
forsec apical_tip_list {
forsec apical_tip_list_addendum {

// make a list of soma/trunk sections where a fixed amount of inhibition will be inserted

inh_list=new SectionList()
forsec "soma" {

apical_dendrite[6]  inh_list.append()
apical_dendrite[26] inh_list.append()
apical_dendrite[48] inh_list.append()
apical_dendrite[64] inh_list.append()
apical_dendrite[81] inh_list.append()
apical_dendrite[104] inh_list.append()

for eiter=0,experiments-1 {                  // for all different cluster sizes
                                             // define data directory 
   sprint(econ.data_dir, "data/Syns=%d-Synch=%d-BACK_GROUND=%d/T600N=%d-NoCL=%d-SiCl=%d",all_synapses, synch, BACK_GROUND, all_synapses, init_cluster_number, init_cluster_size)
   //econ.data_dir  = "data/MSEPredictions/T600N=50-NoCL=5-SiCL=10"  

   print " ------------------------ Experiment ", eiter
   cluster_n = exp_ta[eiter]                 // get the cluster number
   // set directory name
   sprint(econ.data_dir,"%s/N=%d-CLn=%d-hertz=%d-experiment-%d",econ.data_dir, all_synapses,cluster_n,hertz,eiter)
   sprint(econ.syscmd,  "mkdir -p %s", econ.data_dir) 
   system(econ.syscmd)                       // make a directory for this experiment

   for runs=0, 9 {  // do this experiment 10 times (10 different synapse distributions for the same number of clusters)

      splot=new Shape()   
      rpid=new Random(runs+eiter)
      PID=int(rpid.uniform(1,10000))  // random seed for AMPA/NMDA synapses
      PID=-PID // choose branchwise  
      rpid=new Random(runs+eiter+1)
      PIDh=int(rpid.uniform(1,10000)) // random seed for GABA synapses
      lo=0                           // smallest distance of selected obliques from soma
      hi=10000                       // maximum  distance of selected obliques from soma

      // make a band (list) of randomly selected obliques within lo and hi microns from soma
      band=new SynapseBand(apical_tipl,lo,hi,actual_resolution,desired_resolution,PID)
      synapses_alloced=0              // initialize AMPA/NMDA synapse counter 
      gaba_synapses=0                 // initialize GABA synapse counter 

     //BACKGROUND stimulation
     // randomly distribute exitatory and inhibitory background synapses
     if (BACK_GROUND) {
            for i=0, back_syne -1 { 
              band.pick()                                     // pick a branch
              nseg = 10
              rpid=new Random(i+runs)
              pos1=int(rpid.uniform(0,10))/10                   // random selection of synapse location        
              ampa_bg[i]=new GLU(pos1)                       // insert an AMPA mechanism in the middle of the branch
              nmda_bg[i]=new NMDA(pos1)                      // insert an NMDA mechanism in the middle of the branch
            for i=0, back_syni -1 {
              band.pick()                                     // pick a branch
              nseg = 10
              rpid=new Random(2*i+3+runs)     
              pos2=int(rpid.uniform(0,10))/10                    // random selection of synapse location
              gabaa_bg[i] = new GABAa(pos2) 
              SALLOC_GABAa(gabaa_bg[i],pos2,1,gmax_default)  // allocate mechanism using the AMPA-deduced conductance 
              splot.point_mark(gabaa_bg[i],COLOR+1)         // plot on shape graph
              gabab_bg[i] = new GABAb(pos2)                  // insert a GABA_B mechanism at the above location

      printf("cluster_salloc(band, cluster_size, cluster_number)\n") // display cluster allocation proceedure start

      cluster_salloc(band,init_cluster_size,exp_ta[eiter])           // run cluster allocation proceedure
      GABA_flag = 0                                     // don't make both AMPA/NMDA and GABA trains in shiftsyn_init
      temporal_offset=0                                 // no temporal offset for spike train initiation 

      // create the stimulation trains for AMPA & NMDA synapses
      // Create the stimulation trains for GABA synapses
      //BACKGROUND stimulation
      if (BACK_GROUND) {
      // create the stimulation trains for AMPA & NMDA background synapses
      // Create the stimulation trains for GABA background synapses
      vrec=new Vector(tstop/dt)                                // prepare to record somatic voltage 
      finitialize(v_init)                                      // initialize and run

// print the synapse distribution on the cell and the respective branch names to be used later 
// to estimate the cell firing rate using various mathematical models (linear, sigmoidal, quadratic etc).
// Model predictions are calculated (with matlab scripts) using the alpha branch coefficients estimated from 
// single-branch-stimulation experiments. The alpha coefficent for each branch is just the mean somatic
// depolarization in response to 50 Hz stimulation of increasing numbers of synapses (1-10) within
// each side branch

// sort the randomly selected sections and count the number of synapses in each one.
// Save the numbers (of synapses) in random_syn using the sorted order

     sprint(Fc, "%s/random_syn", econ.data_dir )  
     sprint(econ.syscmd,  "sort < %s | uniq -c | awk '{print $1}' > %s", tmpstr2, Fc )

// sort and save the list of randomly selected sections in random-sections
     strdef tmpstr3
     sprint(tmpstr2, "%s/random-sections", econ.data_dir)
     sprint(tmpstr3, "%s/random-sections-sorted", econ.data_dir)
     sprint(econ.syscmd,  "sort < %s | uniq > %s", tmpstr2, tmpstr3)

// read the sorted list of randomly selected sections
     random_list = new SectionList()

// read the number of synapses per randomly selected section
     vf=new File()

// store the input configuration in a file, to be read from matlab scripts
     vf=new File()
     sprint(tmpstr, "%s/input_profile", econ.data_dir)    

     forsec apical_tipl {
        sprint(tmpstr, "%s", secname())    
        flag = 0
        forsec cluster_list {
            ifsec tmpstr {
                x = init_cluster_size
                vf.printf("%d\t", x)
                flag = 1
        if (flag==0) {
           i = 0  
           forsec random_list {
               ifsec tmpstr {
                   x = input.x[i] 
                   vf.printf("%d\t", x)
                   flag = 1
               i = i + 1
      if (flag==0)  {vf.printf("%d\t", 0)}

     vf=new File()
     sprint(tmpstr, "%s/%d_synapses", econ.data_dir, all_synapses)    // define file to save actual cell firing rate 
     spikevec=new Vector()
     // open file and print: spikes, time, 
     vf.printf("%d %5d\n", spikevec.sum(), tstop)

     //sprint(tmpstr, "%s/syn_distribution-CL=%d.eps", econ.data_dir, cluster_n)  // print the shape graph
     //splot.printfile(tmpstr)                                                    // with current synapse distribution

    // econ.xopen_library("Terrence","verbose-system")
    // for i=0,windex {
    //   sprint(econ.tmp_str, "%s/graph-%d.eps",econ.data_dir, i)      
    //   win[i].printfile(econ.tmp_str)
    // }
    }  // end of runs

}    // end of experiments to run

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