Cancelling redundant input in ELL pyramidal cells (Bol et al. 2011)

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The paper investigates the property of the electrosensory lateral line lobe (ELL) of the brain of weakly electric fish to cancel predictable stimuli. Electroreceptors on the skin encode all signals in their firing activity, but superficial pyramidal (SP) cells in the ELL that receive this feedforward input do not respond to constant sinusoidal signals. This cancellation putatively occurs using a network of feedback delay lines and burst-induced synaptic plasticity between the delay lines and the SP cell that learns to cancel the redundant input. Biologically, the delay lines are parallel fibres from cerebellar-like granule cells in the eminentia granularis posterior. A model of this network (e.g. electroreceptors, SP cells, delay lines and burst-induced plasticity) was constructed to test whether the current knowledge of how the network operates is sufficient to cancel redundant stimuli.
1 . Bol K, Marsat G, Harvey-Girard E, Longtin A, Maler L (2011) Frequency-tuned cerebellar channels and burst-induced LTD lead to the cancellation of redundant sensory inputs. J Neurosci 31:11028-38 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network; Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Cerebellum;
Cell Type(s): ELL pyramidal cell;
Gap Junctions:
Simulation Environment: C or C++ program; MATLAB;
Model Concept(s): Dendritic Action Potentials; Bursting; Active Dendrites; Synaptic Plasticity; Long-term Synaptic Plasticity; Learning; Unsupervised Learning; STDP; Biofeedback; Noise Sensitivity;
Implementer(s): Bol, Kieran [kieran_bol at];
#include <math.h>
#include "mex.h"

#if !defined(MAX)
#define MAX(A, B)       ((A) > (B) ? (A) : (B))

#if !defined(MIN)
#define MIN(A, B)       ((A) < (B) ? (A) : (B))

/* Revised June 26, 2011 by Kieran Bol - */

void timeloop(double sptime[], double bursttime4[], double bursttime2[],
        double w[], double signal[], double weight[], double rec[],double f, double g, double Lambda, 
        double eta, double eta2, mwSize numw, mwSize m, double tau_m, double tau_w, double delt, double wmax)
    /*Parameters from Noonan et al. 2003*/
 double A=0.15*4, B=2, alpha=20, 
        beta=0.35, D=0.1, E=3.5, tauref=0.1,taudend=50., b=0, 
        somawidth=0.05*4, dendwidth=1.0, taudecay=1., thresh=1.0;
 double realt, avgw, Lwidth, Lwidth2, Bdef4, Bdef2, lt, nper, burstT, *pfspike, *L, v=0.025, tref=0, Dxh, Dwh, Dyh, Dsh, Dx=0, Dy=0, Ds=0, Dw=0; 
 mwSize n=1, i, k, j, reci=0, index=4, index4=0, index2=0, count4=4, count2=2,  countr=0;

  /*PF initialization */
    pfspike=mxGetPr(mxCreateDoubleMatrix(3*numw,1, mxREAL));
    L=mxGetPr(mxCreateDoubleMatrix(3*numw,1, mxREAL));
 /*Burst definition and width*/   
    Bdef2=0.015/tau_m; /*defining a 2-spike burst (time is in units of tau_m within code so 15 ms = 0.015/tau_m)*/      
    Bdef4=3.0*Bdef2; /*4-spike burst has 3 ISIs so 3 x 2-spike burst definition */
    Lwidth=0.1/tau_m; /*100 ms 4-spike burst learning rule width, from experimental data*/
    Lwidth2=0.01/tau_m; /*10 ms 2-spike STDP width*/
    nper=1/f/delt; /*number of time-steps in 1 period*/

   /*Mapping given weight distribution to dynamic weight matrix w */
   /* pfspike gives start times (i.e. firing times) of each PF over 3 periods  */
   for (i=0;i<3*numw;i++){
       pfspike[i]=ceil(nper/numw*i)*delt; /* nper/numw*delt= T/numw = time span of each segment*/
    /* Initializations*/
    sptime[0]=-100; sptime[1]=-100; sptime[2]=-100;    sptime[3]=-100; 
    /*----Time loop----*/
    for (i=0;i<m;i++){
        realt=delt*i; /*realt in units of tau_m, so not real time per say*/
        k= (int) floor(fmodf(numw*realt/nper/delt,numw));
        /*k is an integer that increases stepwise and signals the start of a new PF */
        /*so for 0-2.5ms, k=0, for 2.5-5ms, k=1, etc., and loops back to k=0 when period is over (hence fmodf of numw)*/
        /*if realt is greater than the refractory period*/     
            /*GOVERNING EQUATION*/           
            v= v+delt*(-v + signal[i] + Lambda*(w[k]-g*v));
            /*k is used to change the index of the weight that is active at a given time*/
            /*Note absence of DAP*/
            /* Do this if ISI beyond dendritic ref. period*/
                if (dendwidth*Dx-somawidth*Ds > 0){  /*DAP is rectified*/  
                    v=v+delt*alpha*(dendwidth*Dx-somawidth*Ds); /*DAP is added*/
        }/*end of if realt > tref */
        /*if V >threshold, a spike is fired and a burst might be recorded*/
        if(v>thresh) {
                v=0; /*v reset to 0*/
                tref=realt+tauref+delt/2; /*refractory period is updated*/
                sptime[index]=realt; /*spike is recorded*/
                index++; /*index now moves to vacant position*/
                count4--; /*so each 4-sp burst has 4 unique spikes: COMMENT OUT THIS LINE TO REMOVE DETECTION OF 4-SPIKE BURSTS*/
                count2--; /* so each 2-spike burst has 2 unique spikes: COMMENT OUT THIS LINE TO REMOVE DETECTION OF 2-SPIKE BURSTS */
                /*DAP parameters are updated*/
                b=b+A+ B*b*b; /*updating b*/
                taudend=D+E*b; /*updating dendritic refractory period*/
                /*if the last spike occurred within Bdef2 of this spike and count2<1, then record a 2-sp burst*/
                if((realt-sptime[index-2]<Bdef2)&& (count2<1)) { /*count2 makes sure that bursts don't share spikes */
                    bursttime2[index2]=sptime[index-2];/* tracks the 1st spike in burst (hence "index-2") */
                    index2++; /*2sp burst index moves up 1*/
                    count2=2; /* reset the count*/

                    /*learning 2sp rule*/
                    burstT= fmod(sptime[index-2],nper*delt)+nper*delt; 
                    /*burstT = time of SP burst, mod the period of AM (i.e. 760 ms = 10 ms after start of 4 Hz period) + 1 period*/
                    /*to make sure that a burst at the end of a period affects weights at the beginning of the next cycle,
                      and same with a burst at the beginning of a period affecting weights at the end of the last cycle,
                      pfspike has PF "firing" times for 3 periods and burstT adds a period (i.e. +nper*delt) to the burst time*/
                    /*Also, since I know exactly when PFs will fire in the future, 
                     I apply the learning rule both pre-post and post-pre when the SP cell fires*/
                    for (j=0;j<3*numw;j++){
                        L[j]=1-pow((pfspike[j]-burstT)/Lwidth2,2); /* Quadratic Learning rule for each PF time */
                        if(L[j]<0){L[j]=0;} /*rectification of the learning rule (so it's strictly inhibitory)*/
                    for (j=0;j<numw;j++){
                        w[j]=w[j]-eta2*w[j]*(L[j]+L[j+numw]+L[j+2*numw]); /*weights updated*/
                        if(w[j]<0){w[j]=0;} /*depression at that weight's segment from each of the 3 periods looked at is added together*/
                    } /*for 2-spike bursts, Lwidth2 is small, so L <0 --> L=0 often*/

                }/*End of if 2-spike burst occurred*/
             /*if the time between this spike and the 4th last spike is less than Bdef4, record a 4-spike burst*/   
             if((realt-sptime[index-4]<Bdef4)&& (count4<1)) { 
                    bursttime4[index4]=sptime[index-4];/* tracks the 1st spike in burst*/
                    count4=4; /*no overlapping 4 sp bursts*/
                    count2=2; /* so 2sp burst can't use last spike in 4 sp burst*/
                    /*since weights change immediately, once a 4-spike burst is identified,
                      a 2-spike burst has likely just occurred and must be removed
                    (so that a 4-spike burst is not mistakenly double counted as also having 2-spike bursts in it) */
                     /*UNLEARNING LOOP: 2sp bursts within the 4sp burst*/
                    while(bursttime4[index4-1]-bursttime2[index2-1] < delt){
                        burstT= fmod(bursttime2[index2-1],nper*delt)+nper*delt;
                        for (j=0;j<3*numw;j++){
                        for (j=0;j<numw;j++){
                        /*this finds the effect of 2-sp burst that happened and does the inverse operation
                          Technically, the weights have changed since the burst because of potentiation rule, 
                         but it is negligible (time elapsed ~45 ms compared to tau_w = 980s ) */
                        index2--; /*record of 2sp burst erased*/
                    } /* repeat unlearning loop until no 2sp burst in last 4 spikes (i.e. could be 0, 1, or 2 bursts)*/
                    /*UNLEARNING LOOP: Removing 2sp burst that used the 1st spike in 4sp burst as its last spike*/
                     if (bursttime2[index2-1]==sptime[index-5]){
                        burstT= fmod(bursttime2[index2-1],nper*delt)+nper*delt;
                        for (j=0;j<3*numw;j++){
                        for (j=0;j<numw;j++){
                    } /* 5th spike unlearning loop*/

                    /*learning 4sp rule*/
                    burstT= fmod(sptime[index-4],nper*delt)+nper*delt; /*range= [T,2T) */
                    /*with Lwidth4 being large compared to T at high AM freqs, using 3 periods means that
                     sometimes one PF will be affected multiple times by 1 burst (i.e. if a PF burst 50ms 
                     before and 50ms after a SP cell burst, then PF will be depressed by the sum of both). 
                     This effect is limited to 3 periods, so at 20 Hz and especially at 32 Hz, the effect of 4-spike 
                     bursts are clipped at the ends. This was for computational simplicity, but it is unknown 
                     how this situation is resolved in vivo anyway. */
                    for (j=0;j<3*numw;j++){
                        L[j]=1-pow((pfspike[j]-burstT)/Lwidth,2); /*Learning rule*/
                    for (j=0;j<numw;j++){
                        w[j]=w[j]-eta*w[j]*(L[j]+L[j+numw]+L[j+2*numw]); /*weight update*/
             } /*end of if 4sp burst... */
        } /*end of if fired...*/
        /*Dendritic alpha f'n: how to code it dynamically*/
        Dxh=Dx+delt*Dy; /*%D for DAP = dendritic after-polarization*/

        /*Somatic alpha f'n */
        b=b +delt*(-b/taudecay); /*b dynamically decays*/    
        /*Potentiation rule*/
        for (j=0;j<numw;j++){
    }/*----end of time loop----*/
} /*end of function*/

/*The function below allows MATLAB to compile and communicate with the upper function, including input/output arrays, etc. */

void mexFunction( int nlhs, mxArray *plhs[],
                  int nrhs, const mxArray *prhs[] )
  double g,wmax, eta, eta2, delt, numw, f, *rec, *sptime, *bursttime4, 
  Lambda, *signal, *weight, *w, *bursttime2, tau_m, tau_w;
  mwSize mrows,ncols, mrows2, ncols2, endi, spsize;
  /* Check for proper number of arguments. */
  if(nrhs!=11) {
    mexErrMsgTxt("Eleven inputs required.");
  } else if(nlhs>5) {
    mexErrMsgTxt("Too many output arguments");
  mrows = mxGetM(prhs[0]);
  ncols = mxGetN(prhs[0]);
  endi= MAX(mrows,ncols);
  mrows2 = mxGetM(prhs[2]);
  ncols2 = mxGetN(prhs[2]);
  /* Create matrix for the return argument. */

  /*I assume the avg f.r. not greater than 1/tau_m; otherwise, will get segmentation faults*/
  plhs[1] = mxCreateDoubleMatrix(spsize,1, mxREAL);
  plhs[0] = mxCreateDoubleMatrix(spsize,1, mxREAL);
  plhs[2] = mxCreateDoubleMatrix(spsize,1, mxREAL);
  plhs[3] = mxCreateDoubleMatrix(mrows2,ncols2, mxREAL);
  plhs[4] = mxCreateDoubleMatrix(spsize,1, mxREAL);
  plhs[5] = mxCreateDoubleMatrix(1,1, mxREAL);
  /* OUTPUTS*/
  /* Call the timeloop subroutine. */
  timeloop(sptime,bursttime4,bursttime2, w,signal,weight,rec,f,g,Lambda,eta,eta2, numw,endi,tau_m, tau_w, delt, wmax);

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