{"title": "Correlated Neuronal Response: Time Scales and Mechanisms", "book": "Advances in Neural Information Processing Systems", "page_first": 68, "page_last": 74, "abstract": null, "full_text": "Correlated Neuronal  Response: \nTime Scales and  Mechanisms \n\nWyeth Bair \n\nHoward Hughes  Medical Inst. \nNYU  Center for  Neural Science \n\n4 Washington PI., Room 809 \n\nNew  York,  NY  10003 \n\nEhud  Zohary \n\nDept.  of Neurobiology \nInstitute of Life  Sciences \n\nThe Hebrew  University,  Givat Ram \n\nJerusalem, 91904 ISRAEL \n\nChristof Koch \n\nComputation and  Neural Systems \n\nCaltech,  139-74 \n\nPasadena, CA  91125 \n\nAbstract \n\nWe  have  analyzed the relationship between  correlated spike  count \nand the peak in the cross-correlation of spike trains for  pairs of si(cid:173)\nmultaneously recorded neurons  from  a  previous  study of area MT \nin  the  macaque  monkey  (Zohary  et  al.,  1994).  We  conclude  that \ncommon  input,  responsible  for  creating peaks  on  the order of ten \nmilliseconds  wide  in  the  spike  train  cross-correlograms  (CCGs), \nis  also  responsible  for  creating  the  correlation  in  spike  count  ob(cid:173)\nserved  at  the  two  second  time  scale  of  the  trial.  We  argue  that \nboth common excitation and  inhibition  may  play significant  roles \nin establishing this  correlation. \n\n1 \n\nINTRODUCTION \n\nIn  a  previous  study  of  pairs  of  MT  neurons  recorded  using  a  single  extracellular \nelectrode,  it  was  found  that  the  spike  count  during  two  seconds  of  visual  motion \nstimulation  had  an  average  correlation  coefficient  of r  =  0.12  and  that  this  cor(cid:173)\nrelation  could significantly limit  the usefulness  of pooling across increasingly large \npopulations  of neurons  (Zohary  et aI.,  1994).  However,  correlated spike  count  be(cid:173)\ntween two neurons  could in  principle occur at several time-scales.  Correlated drifts \n\n\fCorrelated Neuronal  Response:  Time Scales and Mechanisms \n\n69 \n\nin  the  excitability  of  the  cells,  for  example  due  to  normal  biological  changes  or \nelectrode  induced  changes,  could  cause  correlation  at  a  time  scale  of many  min(cid:173)\nutes.  Alternatively,  attentional  or  priming effects  from  higher  areas  could  change \nthe responsivity of the cells  at the time scale of an experimental trial.  Or,  as  sug(cid:173)\ngested  here,  common  input  that  changes  on the  order of milliseconds  could  cause \ncorrelation in spike count.  The first  section determines the time scale at which  the \nneurons are correlated by analyzing the relationship between the peak in the spike \ntrain cross-correlograms (CCGs) and the correlation between the spike counts using \na  construct we  call the  trial CCG.  The second section examines temporal structure \nthat is indicative of correlated suppression of firing, perhaps due to inhibition, which \nmay also contribute to the spike count correlation. \n\n2  THE TIME SCALE OF  CORRELATION \n\nAt the time scale of the single trial, the correlation, r se, of spike counts x  and y from \ntwo neurons recorded during nominally identical two second stimuli was  computed \nusing Pearson's correlation coefficient, \n\nrse  = \n\nE[xy] - ExEy \n, \n\nuxuy \n\n(1) \n\nwhere  E  is  expected  value  and  u2  is  variance.  If spike  counts  are  converted  to \nz-scores,  i.e.,  zero  mean  and  unity  variance,  then  rse  =  E[xy],  and  rse  may  be \ninterpreted as the zero-lag value of the cross-correlation of the z-scored spike counts. \nThe trial CCGs resulting from  this procedure are shown for two pairs of neurons in \nFig.  l. \n\nTo distinguish between cases like the two shown in Fig. 1, the correlation was broken \ninto  a  long-term  component,  rlt,  the  average  value  (computed  using  a  Gaussian \nwindow of standard deviation 4 trials) surrounding the zero-lag value, and a  short(cid:173)\nterm component,  rst,  the  difference  between the zero-lag  value  and  rlt.  Across  92 \npairs of neurons from  three monkeys,  the average rst  was  0.10  (s.d.  0.17)  while  rlt \nwas  not  significantly  different  from  zero  (mean  0.01,  s.d.  0.11).  The mean  of  rst \nwas  similar to the overall correlation of 0.12  reported by  Zohary et al.  (1994). \n\nUnder certain assumptions, including that the time scale of correlation is  less  than \nthe  trial  duration,  rst  can  be  estimated  from  the area under  the  spike  train  CCG \nand the areas under the autocorrelations (derivation omitted).  Under the additional \nassumption that the spike  trains  are  individually  Poisson and have  no  peak in the \nautocorrelation except  that which  occurs  by  definition  at lag zero,  the correlation \ncoefficient for  spike count can be estimated by \n\nrpeak  ~ j.AA.ABArea, \n\n(2) \n\nwhere .AA  and .AB  are the mean firing rates of neurons A and B, and Area is the area \nunder the spike train CCG peak, like  that shown in Fig.  2 for  one  pair of neurons. \nTaking Area to be the area under the CCG between \u00b132 msec gives a good estimate \nof short-term rst, as shown in Fig. 3.  In addition to the strong correlation (r =  0.71) \nbetween rpeak  and rst, rpeak  is  a less  noisy measure, having standard deviation (not \nshown)  on average one fourth as large as  those of rst. \n\nWe conclude that the common input that causes the peaks in the spike train CCGs is \nalso responsible for the correlation in spike count that has been previously reported. \n\n\f70 \n\nW.  BAIR. E. ZOHARY. C. KOCH \n\no \n\n0.3 \n\n160 \n\n80 \n240 \nTrial Number \n\n320  0 \n\n800 \n\n400 \nTrial Number \n\n1200 \n\n0.2 \nd \nU U  0.1 \n\";3 \n0 \n.~ \n~  ~~------------------~~ \n\n-0.1  +'-r-~..:...-,:......-~-.-,-~~---,-,~,.--,--, \n\n-100 \n\n-50 \n\n0 \n\n50 \n\nLag (Trials) \n\nernu090 \n-25 \n\n100 -50 \n\n0 \n\n25 \n\n50 \n\nLag (Trials) \n\nFigure  1:  Normalized  responses  for  two  pairs  of  neurons  and  their  trial  cross(cid:173)\ncorrelograms  (CCGs).  The  upper  traces  show  the  z-scored  spike  counts  for  all \ntrials  in  the  order they  occurred.  Spikes  were  counted  during  the  2  sec  stimulus, \nbut trials  occurred on average 5 sec  apart, so 100  trials  represents  about  2.5  min(cid:173)\nutes.  The lower traces show the trial CCGs.  For the pair of cells  in  the left  panel, \nresponsivity drifts during the experiment.  The CCG (lower left) shows that the drift \nis  correlated  between  the two  neurons  over  nearly  100  trials.  For  the  pair of cells \nin  the right  panel,  the trial CCG  shows  a  strong correlation only  for  simultaneous \ntrials.  Thus, the measured  correlation coefficient  (trial  CCG at zero lag)  seems  to \noccur at a long time scale on the left but a short time scale (less than or equal to one \ntrial)  on the right.  The zero-lag value  can be broken into two components, T st  and \nTlt  (short term and long  term,  respectively,  see  text).  The short-term component, \nT st,  is  the  value  at  zero  lag  minus  the  weighted  average value  at  surrounding lag \ntimes.  On the left,  Tst  ~ 0, while  on the right, Tlt  ~ O. \n\n\fCorrelated  Neuronal  Response: Time Scales and Mechanisms \n\n71 \n\n5 \n\n1 \n\n8 \n\n16 \n\no \nWidth at HH (msec) \n\n24 \n\n32 \n\no  emu064P \n-100 \n\n-50 \n\no \n\nTime Lag (msec) \n\n50 \n\n100 \n\nFigure 2:  A spike train CCG with central peak.  The frequency histogram of widths \nat half-height is  shown (inset)  for  92  cell pairs from  three monkeys.  The area of the \ncentral peak measured between  \u00b132 msec  is  used  to predict  the  correlation coeffi(cid:173)\ncients, rp eak. plotted in Fig.  3.  The y-axis indicates the probability of a  coincidence \nrelative to that expected for  Poisson processes at the measured firing  rates. \n\n0.8 \n\n0.6 \n\n~ 0.4 \n~ (1) \n~ 0.2  \u2022 \n'-\" \n~ \n\n\u2022 0 \n\u2022 \u2022 \n\n-0.2 \n\n-0.2 \n\n\u2022 \n\n\u2022  \u2022 \n\u2022  \u2022 \n\u2022 \n\n\u2022 \n\n\u2022 \n.....  \u2022 \n\u2022 \n\u2022  \u2022 \n\u2022 \u2022 \n\n\u2022 \n\n\u2022 \n\n\u2022 \n\n\u2022 \n\no \n\n0.2 \n\n0.4 \n\n0.6 \n\n0.8 \n\nr (Short Term) \n\nFigure 3:  The area of the peak of the spike train CCG yields a prediction, rpeak  (see \nEqn.  2) ,  that is  strongly  correlated  (r  =  0.71,  p  < 0.00001),  with  the  short-term \nspike  count  correlation  coefficient ,  rst .  The  absence  of  points  in  the  lower  right \ncorner of the plot indicates that there are no cases of a  pair of cells  being strongly \ncorrelated without having a  peak in the spike train CCG. \n\n\f72 \n\nw. BAIR, E. ZOHARY, C.  KOCH \n\nIn Fig.  3,  there  are no pairs of neurons that have a  short-term correlation and yet \ndo not have a  peak in  the \u00b132 msec  range of the spike train CCG. \n\n3  CORRELATED SUPPRESSION \n\nThere is  little doubt that common excitatory input causes peaks like the one shown \nin  Fig.  2 and therefore results in the correlated spike count at the time scale of the \ntrial.  However,  we  have also observed correlated  periods of suppressed firing  that \nmay point to inhibition as another contribution to the CCG peaks and consequently \nto the correlated spike count. \n\nFig.  4  A  and  B  show  the  response  of one  neuron  to  coherent  preferred  and  null \ndirection motion, respectively.  Excessively long inter-spike intervals (ISIs),  or gaps, \nappear  in  the  response  to  preferred  motion,  while  bursts  appear  in  the  response \nto  null  motion.  Across  a  database  of  84  single  neurons  from  a  previous  study \n(Britten  et  aI.,  1992),  the  occurrence  of  the  gaps  and  bursts  has  a  symmetrical \ntime course-both are most prominent on average from  600-900 msec post-stimulus \nonset,  although there are substantial variations  from  cell  to cell  (Bair,  1995).  The \ngaps,  roughly  100  msec  long,  are not  consistent  with  the  slow,  steady  adaptation \n(presumably due to potassium currents)  which  is  observed under current injection \nin  neocortical  pyramidal  neurons,  e.g.,  the  RS 1  and  RS2  neurons  of Agmon  and \nConnors  (1992). \n\nFig.  4  C  shows  spike  trains  from  two  simultaneously  recorded  neurons  stimulated \nwith  preferred  direction  motion.  The  longest  gaps  appear to  occur  at  about  the \nsame  time.  To  assess  the  correlation  with  a  cross-correlogram,  we  first  transform \nthe  spike  trains  to  interval  trains,  shown  in  Fig.  4  D  for  the  spike  trains  in  C. \nThis  emphasizes  the  presence  of long  ISIs  and  removes  some  of  the  information \nregarding  the  precise  occurrence  times  of  action  potentials.  The  interval  cross(cid:173)\ncorrelation  (ICC)  between  each  pair  of  interval  trains  is  computed  and  averaged \nover all  trials,  and the average shift  predictor is  subtracted.  Fig.  4  E  and F  show \nICCs  (thick lines)  for  two  different  pairs of neurons.  In 17 of 31  pairs  (55%),  there \nwere peaks in the raw ICC that were at least 4 standard errors above the level of the \nshift  predictor.  The peaks were on  average centered  (mean 4.3  msec,  SD  54  msec) \nand had mean width at half-height of 139 msec  (SD  59 msec). \n\nTo  isolate  the  cause  of the  peaks,  the  long  intervals  in  the  trains  were  set to the \nmean  of the  short intervals.  Long  intervals  were  defined  as  those  that  accounted \nfor  30%  of the duration of the data and  were  longer than all  short intervals.  Note \nthat this  is  only a  small fraction of the number of ISIs  in  the spike train (typically \nless  than about 10%), since a  few  long intervals consume the same amount of time \nas  many  short  intervals.  Data from  300-1950  msec  was  processed,  avoiding  the \non-transient  and  the  lack  of final  interval.  With  the  longest  intervals  neutralized, \nthe peaks  were  pushed down to the level  of the  noise in the ICC  (thin lines,  Fig.  4 \nE, F). Thus, 90%  of the action potentials may serve to set a mean rate, while a few \nperiods of long ISIs  dominate the ICC peaks. \n\nThe  correlated  gaps  are  consistent  with  common  inhibition  to neurons  in  a  local \nregion  of  cortex,  and  this  inhibition  adds  area to  the  spike  train  CCG  peaks  in \nthe  form  of a  broader  base  (not  shown).  The  data analyzed  here  is  from  behav(cid:173)\ning  animals,  so  the  gaps  may  be  related  to small  saccades  (within  the  0.5  degree \n\n\fCorrelated Neuronal  Response:  Time  Scales and Mechanisms \n\n1111  \"\"\"111111111111\"'\"\" \n\"\"II.!IIIIIIIIIIII \n\n11111'\"\"111111111\"11  \"\"11\"1'\"''''''\"'  III  \"\"'11111\"'\"''  1111111  '\"' \n\n\"11\"\"\"1111111110111111111111111111111\"\"111'1 \n\nII \n\n111\"'.\"111111111111  11111111'\"11111111111111111111 \n\n'\"IIIIIII!!I1I11'\"1I1I  1I1\"'\"tll  \"\"UIU \n\n'\"\"\"\"\"'\"11'\"111111'  11111111'\"1111111111'\"'\"\"\"'\"'  11\"\"'\"1111111 \n\nIIIIIU\"'\"IIIIIIIIIII.II' \n\n111111111111111' \n\n111111111'\"'\"111  IIItIlI! \n\n\" \" ' \" ' \"   ' \" \" \" \"  111'\"\"\"\"\"1111 \n\n1111111111111111111'\"'\"11111\"11111111'11\"11\"11111111111\"1  ' \" ' ' ' ' ' \"   I \n1111111111111\"'\"\"1111111  \"'\"111 \n\n'\"'\"1111111'\"111111111111111' \n\nI \n\n\"11'\"\" \n\n1111  \"11\"11  \"\"\"'\"111 \n\n\"'''''1111111111  11,.\"\"\"\"'\" \n\"\" II  111111\"\"\"  1111' \n\n'''.1'111111111111111,,11111111111111111111111111111111111111111111''\"1111\" \n1111111  II! I  1111  III  II! I!!\"  I \n.11111111111111 \n1111.1.11111111  '\"'1 II!!' I \n1111111.111111111111111111111' \n,\"\"'',''1''','' ,,'.',  '11I'1~I'M'i\"IlI'III\"'I,IIII\"II'\"III,III' \n\n11111111\"\"'\"1111111111111'1111111111 \n\nI!  \" ' \"   '\" III  III.  II 11.11  III  II \n\nI  ,,'''''HIII'''!I1''! \n\n11111111111111'\", \n\n1111  111'11'111111111 \n\n\" \"  11\"\" 11111111111\"1  \"'\"111'\"'\"  I I I ' \" ! I I   \" \n\n\"I  111M\"\" tI  III.  \" \n\nI  III  1M  II  ,  ' ' ' '   I \"   !  III \nI  l \" l I l l !   III \n11111 \n1111 \nI \nII! \n'1IIIII'\"IIIIIIII\"\"\"\"\"\"YlI.\"\"111I \n\"II'\"'~IIIIII,II!'\"'''',,\\ \n\n\"\"\"\"\"\"\"'\"111'\"1111111111\"1\"1 \n\nt\"\"'IIIIII \n\n111\"111  I  \u2022  \" I   \"\"I  I  I \n\n\"11'11111'1111111111 \n\nI  11111 \n\nII \n\nIlIg\"  \" '   111111111111111\"11111 \n111111  1111111111'\"1111111  1111111111 \n1111\"111'\"'\"1111111 \n\n\"\"1111111111.11.  IIUII \n111'''.,11111111111111111 \n1111 \n\nII' \n11111111\"1111'\"111  111\"\" \n\nI  1111111'111111\"\"\"11 \n\n73 \n\nA \n\nB \n\nD \n\n2000 \n\nI \nI \nII \n'I \nta' \n\u2022 \n\" \n\u2022 \nI! \n11 \nII. \nIII \nI I  \n\nIII \nN  1 \n\ni \n\nII \nI \n\nI \n\nI \n\nI \n\n0 \n\n1 \n2 \n\nII \n\nII  1111 \n\nI \n\n.111 \n\n1111 \n\nII \n\nII \n\nI' \n\n\"' \n\nI  I \n\nI \n\n\" \nII! \n\n\"11 \nII \nI \nI \n\nI\" I \nIII \n\nII \nI \n\n500 \n\nII \n\nI \n.1 \n\n11111 \n\n1000 \nmsec \n\n,. \nI'\" \n\nIII \n\nIII \n\n\"' \n\nI  I \n\n\"\" \nI' \n'111' \n\nII \n\n'\"~ \n\n'I! \n\n\"\" \n\"' \n\n\"' \n\n,  I \n\nIII \n\n\u2022 \n\n1500 \n\n2000 \n\n1111111111111111 \n1111  1 11111111  111111 \n\n11111111 \n\n11111111111111 \n11.1111  1111 \n1 \n\nII  01 n 11111111 \nI  1I11  III \n\n11111111111111111111111111111111111111111111111111118  11111  c \n\nI  11I1111I111I111I111I111111I11Im1l11111 \n\nII \n\n1000 \n\nTime (msec) \n\nE \n\nF \n\n-1000 \n\n-500 \n\no \n\n500 \n\n1000  -1000  -500 \nTime Lag (msec) \n\no \n\n500 \n\n1000 \n\nFigure  4:  (A)  The  brisk  response  to  coherent  preferred  direction  motion  is  in(cid:173)\nterrupted  by  occasional excessively  long inter-spike  intervals,  i.e.,  gaps.  (B)  The \nsuppressed response to null direction motion is  interrupted by bursts of spikes.  (C) \nSimultaneous  spike  trains from  two neurons  show  correlated gaps  in the preferred \ndirection response.  (D) The interval representation for  the spike trains in C. (E,F) \nInterval cross-correlograms have  peaks indicating that the gaps are  correlated  (see \ntext). \n\n\f74 \n\nw. BAIR. E. ZOHARY. C. KOCH \n\nfixation  window)  or eyelid  blink.  It has  been  hypothesized  that  blink suppression \nand  saccadic  visual  suppression  may  operate  through the same pathways  and  are \nof neuronal origin  (Ridder and Tomlinson, 1993).  An alternative hypothesis is  that \nthe gaps and bursts arise in cortex from  intrinsic circuitry arranged in an opponent \nfashion. \n\n4  CONCLUSION \n\nCommon input that causes central peaks on the order of tens of milliseconds wide in \nspike train CCGs is  also responsible for causing the correlation in spike count at the \ntime scale of two second long trials.  Long-term correlation due to drifts  in respon(cid:173)\nsivity exists but is zero on average across all cell pairs and may represent a source of \nnoise  which  complicates  the  accurate  measurement  of cell-to-cell  correlation.  The \narea of the peak of the spike train CCG within a window of \u00b132 msec is  the basis of \na good prediction of the spike count correlation coefficient and provides a less noisy \nmeasure of correlation between neurons.  Correlated gaps  observed in the response \nto  coherent  preferred  direction  motion  is  consistent  with  common  inhibition  and \ncontributes  to the  area of the  spike  train  CCG  peak,  and  thus  to the  correlation \nbetween  spike  count.  Correlation  in  spike  count  is  an important  factor  that  can \nlimit  the  useful  pool-size  of neuronal  ensembles  (Zohary  et  al.,  1994;  Gawne  and \nRichmond,  1993). \n\nAcknowledgements \n\nWe  thank  William  T.  Newsome,  Kenneth  H.  Britten,  Michael  N.  Shadlen,  and  J. \nAnthony Movshon for  kindly  providing data that was  recorded in  previous  studies \nand for  helpful  discussion.  This  work was  funded  by  the  Office  of Naval  Research \nand the  Air  Force  Office  of Scientific  Research.  W.  B.  was  supported by  the L.  A. \nHanson Foundation and the Howard  Hughes  Medical Institute. \n\nReferences \n\nAgmon  A,  Connors  BW  (1992)  Correlation  between  intrinsic  firing  patterns  and \n\nthalamocortical synaptic responses  of neurons  in  mouse  barrel cortex.  J  N eu(cid:173)\nrosci  12:319-329. \n\nBair  W  (1995)  Analysis  of Temporal  Structure  in  Spike  Trains  of  Visual  Cortical \n\nArea  MT.  Ph.D.  thesis,  California Institute of Technology. \n\nBritten KH, Shadlen MN, Newsome WT, Movshon JA (1992)  The analysis of visual \nmotion:  a comparison of neuronal and psychophysical performance.  J Neurosci \n12:4745-4765. \n\nGawne  T J,  Richmond  BJ  (1993)  How  independent  are  the  messages  carried  by \n\nadjacent inferior  temporal cortical neurons?  J Neurosci  13:2758-2771. \n\nRidder  WH,  Tomlinson  A  (1993)  Suppression of contrasts sensitivity during eyelid \n\nblinks.  Vision  Res 33: 1795- 1802. \n\nZohary  E,  Shadlen  MN,  Newsome  WT  (1994)  Correlated  neuronal  discharge  rate \n\nand its  implications for  psychophysical performance.  Nature 370:140-143. \n\n\f", "award": [], "sourceid": 1023, "authors": [{"given_name": "Wyeth", "family_name": "Bair", "institution": null}, {"given_name": "Ehud", "family_name": "Zohary", "institution": null}, {"given_name": "Christof", "family_name": "Koch", "institution": null}]}