{"title": "Effects of Firing Synchrony on Signal Propagation in Layered Networks", "book": "Advances in Neural Information Processing Systems", "page_first": 141, "page_last": 148, "abstract": null, "full_text": "Effects of Firing Synchrony on Signal Propagation in Layered Networks \n\n141 \n\nEffects  of Firing  Synchrony  on  Signal \n\nPropagation in  Layered Networks \n\nG. T.  Kenyon,l  E.  E.  Fetz,2  R.  D.  Puffl \n\n1 Department of Physics  FM-15,  2Department of Physiology and  Biophysics SJ-40 \n\nUniversity of Washington, Seattle,  Wa.  98195 \n\nABSTRACT \n\nSpiking  neurons  which  integrate  to  threshold  and  fire  were  used \nto  study  the  transmission  of  frequency  modulated  (FM)  signals \nthrough  layered networks.  Firing correlations  between cells  in  the \ninput  layer  were  found  to  modulate  the  transmission  of  FM  sig(cid:173)\nnals  under  certain dynamical  conditions.  A  tonic  level  of activity \nwas  maintained  by  providing  each  cell  with  a  source  of Poisson(cid:173)\ndistributed  synaptic  input.  When  the  average  membrane  depo(cid:173)\nlarization  produced  by  the  synaptic  input  was  sufficiently  below \nthreshold,  the  firing  correlations  between  cells  in  the  input  layer \ncould greatly amplify the signal present in subsequent layers.  When \nthe  depolarization was sufficiently close  to threshold,  however,  the \nfiring  synchrony  between cells  in the  initial layers could  no  longer \neffect  the propagation of FM  signals.  In this latter case,  integrate(cid:173)\nand-fire  neurons  could  be  effectively  modeled  by  simpler  analog \nelements governed by a  linear input-output relation. \n\n1 \n\nIntroduction \n\nPhysiologists have long  recognized  that  neurons  may code  information in their  in(cid:173)\nstantaneous firing  rates.  Analog neuron  models have been  proposed  which assume \nthat  a  single  function  (usually identified  with  the  firing  rate)  is  sufficient  to  char(cid:173)\nacterize  the  output state of a  cell.  We  investigate whether  biological neurons  may \nuse  firing  correlations as  an additional  method  of coding  information.  Specifically, \nwe  use  computer simulations of integrate-and-fire neurons  to examine how various \nlevels of synchronous firing activity affect  the transmission of frequency-modulated \n\n\f142 \n\nKenyon, Fetz and Puff \n\n(FM) signals through layered networks.  Our principal observation is that for certain \ndynamical modes of activity, a  sufficient  level of firing  synchrony can  considerably \namplify  the  conduction  of  FM  signals.  This  work  is  partly  motivated  by  recent \nexperimental  results  obtained  from  primary  visual  cortex  [1,  2]  which  report  the \nexistence of synchronized stimulus-evoked oscillations (SEa's)  between populations \nof cells  whose  receptive fields  share some  attribute. \n\n2  Description of Simulation \n\nFor  these  simulations  we  used  integrate-and-fire  neurons  as  a  reasonable  compro(cid:173)\nmise  between biological accuracy and mathematical convenience.  The subthreshold \nmembrane  potential of each  cell  is  governed  by  an  over-damped second-order  dif(cid:173)\nferential  equation with source  terms to account for  synaptic  input: \n\n(1) \n\nwhere  \u00a2Ic  is  the membrane potential of cell  k,  N  is  the  number of cells,  Tic;  is  the \nsynaptic weight from cell  j  to cell  k, tj  are the firing  times for  the ph  cell,  Tp  is the \nsynaptic  weight  of the  Poisson-distributed  input  source,  Pic  are  the  firing  times  of \nPoisson-distributed input, and  Tr  and  Ttl  are the rise  and decay  times of the  EPSP. \nThe Poisson-distributed input represents the synaptic drive from a large presynaptic \npopulation of neurons. \n\nEquation  1 is  augmented by a  threshold firing  condition \n\nthen \n\n(2) \n\nwhere  9(t - tAJ  is  the  threshold  of the  kth  cell,  and  T/1  is  the  absolute  refractory \nperiod.  If the  conditions  (2)  do  not  hold  then  \u00a2Ic  continues  to  be  governed  by \nequation  1. \n\nThe threshold  is  00 during the absolute refractory  period and decays exponentially \nduring the relative refractory  period: \n\n9(t - tk) =  { ~' -(t-t' )/., \n\nupe \n\nI t \"  +uo, \n\nn \n\nif t  - t~ < T /1  ; \notherwise, \n\n(3) \n\nwhere,  60  is the resting  threshold  value,  f)p  is the maximum increase of 9 during the \nrelative  refractory  period,  and  Tp  is  the  time  constant  characterizing  the  relative \nrefractory  period. \n\n2.1  Simulation Parameters \n\nTr  and  Ttl.  are  set  to  0.2  msec  and  1  msec,  respectively.  Tp  and  TAl;  are  always \n(1/100)90 \u2022  This strength  was chosen as typical of synapses  in  the  eNS. To sustain \n\n\fEffects or Firing Synchrony on Signal Propagation in Layered Networks \n\n143 \n\n..-.. \n\n> e --\n\no \no \n\n20 \n\n(mae<:) \n\n40 \n\n0 \n\n20 \n\n(msec) \n\n40 \n\nFigure  1:  Example  membrane  potential  trajectories  for  two  different  modes  of \nactivity.  EPSP's arrive at mean frequency,  LIm, that is higher for  mode I (a) than for \nmode II  (b).  Dotted line below threshold  indicates asymptotic membrane potential. \n\nactivity,  during  each  interval  Ttl,  a  cell  must  receive  ~ (Bo/Tp)  = 100  Poisson(cid:173)\n~istributed inputs.  Resting  potential  is  set  to  0.0  mV  and  Bo  to  10  mY .  4>1'  and \n4>1'  are  set  to 0.0 mV  and -1.0 mV /msec,  which simulates a small hyperpolarization \nafter firing.  Ta  and  Tp  were  each set  to  1 msec,  and  Bp  to  1.0  mY . \n\n3  Response  Properties of Single  Cells \n\nFigure  1  illustrates  membrane  potential  trajectories  for  two  modes  of activity.  In \nmode  I  (fig.  la),  synaptic  input  drives  the  membrane  potential  to  an  asymptotic \nvalue  (dotted  line)  within  one  standard  deviation of ()o.  In  mode  II  (fig.  1b),  the \nasymptotic membrane potential is  more  than one standard  deviation  below ()o' \n\nFigure  2  illustrates  the  change  in  average  firing  rate  produced  by  an  EPSP,  as \nmeasured  by a  cross-correlation  histogram  (CCH)  between  the  Poisson source  and \nthe  target  cell.  In  mode  I  (fig.  2a),  the  CCH  is  characterized  by  a  primary  peak \nfollowed  by  a  period  of reduced  activity.  The derivative of the  EPSP,  when  mea(cid:173)\nsured  in  units  of  Bo ,  approximates the  peak  magnitude  of  the  CCH.  In  mode  II \n(fig.  2b),  the  CCB  peak is  not followed by a  period of reduced  activity.  The  EPSP \nitself,  measured  in  units  of Bo  and  divided  by  Td,  predicts  the  peak  magnitude  of \nthe  CCB.  The transform between the EPSP  and the resulting change in firing rate \nhas  been  discussed  by  several  authors  [3,  4].  Figures  2c  and  2d  show  the  cumula(cid:173)\ntive  area  (CUSUM)  between  the  CCH  and  the  baseline  firing  rate.  The  CUSUM \nasymptotes to a finite  value,  ~, which can  be  interpreted  as  the average number of \nadditional firings  produced  by  the  EPSP. \n\n~ increases  with  EPSP  amplitude  in  a  manner  which  depends  on  the  mode  of \nactivity  (fig.  2e).  In  mode  II,  the  response  is  amplified  for  large  inputs  (concave \nup).  In mode I,  the response curve is concave down.  The amplified response to large \ninputs during mode II  activity is  understandable in terms of the  threshold crossing \nmechanism.  Populations of such cells  should  respond  preferentially  to synchronous \nsynaptic input  [5]. \n\n\f144 \n\nKenyon, Fetz and Puff \n\n0 \n\n6 \n\n0 \n\n6 \n\nb) \n\nmode  II \n\n-. \ni \nu \n11/ \nt/) \n\nE --\n\nmode  II \n\nd) \n\n.02 \n\n.01 \n\n.2 \n\n0 \n\no \n\n6 \n\n0 \n\n6 \n\n(msec) \n\n.2 \n0 , .1  \nEPSP  Amplitude  in  units  01  fl. \n\nFigure  2:  Response  to  EPSP  for  two  different  modes  of  activity.  a)  and  b) \nCross-correlogram  with  Poisson  input  source.  Mode  I  and  mode  II  respectively. \nc)  and  d)  CUSUM  computed  from  a)  and  b).  e)  A  vs.  EPSP  amplitude for  both \nmodes  of activity. \n\n4  Analog  Neuron  Models \n\nThe histograms shown in Figures 2a,b may be used to compute the impulse response \nkernel,  U, for a  cell in either of the two modes of activity, simply by subtracting the \nbaseline firing  rate  and  normalizing to a  unit  impulse strength.  If the  cell  behaves \nas  a  linear system  in  response  to a  small impulse,  U  may  be  used  to  compute  the \nresponse  of the  cell  to  any time-varying input.  In  terms of  U,  the  change  in firing \nrate,  6F,  produced  by an  external  source  of Poisson-distributed  impulses  arriving \nwith an  instantaneous frequency  Ft(t)  is  given by \n\nwhere,  T t  is the amplitude of the incoming EPSP's.  For the layered network used in \nour simulations, equation 4 may be  generalized  to yield  an iterative relation giving \nthe signal  in one  layer in  terms  of the  signal in  the  previous  layer. \n\n(4) \n\n(5) \n\n\fEffects of Firing Synchrony on Signal Propagation in Layered Networks \n\n145 \n\n:z: u \nu \n\ntI  \u2022 \n1/ \n\n-I \ntil a --\n~. \n\no \n\n4 \n\no \n4 \n(msec) \n\no \n\n4 \n\n-4  0  4 \n\n-4  0  4 \n(msec) \n\n-4  0  4 \n\nFigure 3:  Signal propagation in  mode  I  network.  a)  Response  in first  three  layers \ndue  to a  single impulse delivered simultaneously to all cells  in  the  first  layer.  Ratio \nof common  to  independent  input  given  by  percentages  at  top  of figure.  First  row \ncorresponds  to  input  layer.  Firing  synchrony  does  not  effect  signal  propagation \nthrough  mode  I  cells.  Prediction  of analog  neuron  model  (solid  line)  gives  a  good \ndescription  of signal  propagation  at all  synchrony  levels  tested.  b)  Synchrony be(cid:173)\ntween  cells  in  the  same layer measured  by  MGH.  Firing synchrony  within a  layer \nincreases  with  layer depth for  all  initial values of the  synchrony in  the first  layer. \n\nwhere,  6Fi  is  the change in  instantaneous firing  rate for  cells  in  the  ith  layer,1i+l,t \nis  the synaptic  weight  between  layer i  and  i + 1,  and  N  is  the  number of cells  per \nlayer.  Equation  5  follows  from  an  equivalent  analog  neuron  model  with  a  linear \ninput-output  relation.  This convolution method  has  been  proposed  previously  [6). \n\n5  Effects of Firing  Synchrony on  Signal  Propagation \nA layered network was designed such that the cells in the first  layer receive impulses \nfrom  both  common  and  independent  sources.  The  ratio  of  the  two  inputs  was \nadjusted  to control the degree  of firing  synchrony between cells  in the  initial layer. \nEach cell  in  a  given layer projects  to all the cells in  the succeeding  layer with equal \nstrength,  1~o9o.  All  simulations use  50  cells  per  layer. \n\nFigure  3a  shows  the  response  of cells  in  the  mode  I  state  to  a  single  impulse  of \nstrength  1~o9o delivered simultaneously to all the cells in the first  layer.  In  this and \nall subsequent figures,  successive layers are shown from top to bottom and synchrony \n(defined  as  the  fraction  of common  input for  cells  in  the first  layer) increases  from \n\n\f146 \n\nKenyon, Fetz and Puff \n\n.03 \n\n..-.. \ni \n\n(.) \n1/ \n\nIII e \n....... \n!I: u \nu \n\n.2 \n\n.2 \n\no \n\n4 \n\no \n4 \n(msec) \n\n-4  0  4 \n\n-4  0  4 \n(msec) \n\n-4  0  4 \n\nFigure  4:  Signal  propagation  in  mode  II  network.  Same  organization  as  fig.  3. \na)  At  initial  levels  of synchrony above::::::  30%,  signal  propagation  is  amplified  sig(cid:173)\nnificantly.  The  propagation  of relatively  asynchronous  signals  is  still  adequately \ndescribed  by  the analog neuron  model.  b)  Firing synchrony within a  layer increases \nwith  layer  depth  for  initial  synchrony  levels  above::::::  30%.  Below  this  level  syn(cid:173)\nchrony within  a  layer decreases  with  layer depth. \n\nleft  to right.  Figure  3a shows that signals propagate through  layers of interneurons \nwith  little dependence  on  firing  synchrony.  The solid  line  is  the  prediction from  an \nequivalent analog  neuron  model  with  a  linear  input-output  relation  (eq.  5).  At all \nlevels  of input  synchrony,  signal  propagation  is  reasonably  well  approximated  by \nthe simplified  model. \n\nFiring  synchrony  between cells  in  the  same  layer  may  be  measured  using  a  mass \ncorrelogram (MeH). The MeH is defined  as the auto-correlation of the population \nspike record,  which combines the individual spike records of all cells in a given layer. \nFigure  3b shows  that for  all  initial levels of synchrony produced  in  the input layer, \nthe intra-layer firing  synchrony increased  rapidly  with  layer depth. \n\nThe simulations were  repeated  using an  identical network,  but  with  the tonic level \nof input reduced  sufficiently to fix  the cells  in the mode II state  (fig.  4).  In contrast \nwith  the  mode  I  case,  the  effect  of firing  synchrony  is  substantial.  When  firing  is \nasynchronous  only  a  weak  impulse  response  is  present  in  the  third  layer  (fig.  4a, \nbottom left),  as  predicted  by  the  analog neuron  model  (eq.  5).  For  levels  of input \nsynchrony  above  ~ 30%,  however,  the  response  in  the  third  layer  is  substantially \nmore  prominent.  A  similar  effect  occurs  for  synchrony  within  a  layer.  At  input \n\n\fEffects of Firing Synchrony on Signal Propagation in Layered Networks \n\n147 \n\no \n\n4  804   8 04   8 \n\n(msee) \n\no \n\n4  804   80 4   8 \n\n(msec) \n\nFigure 5:  Propagation of sinusoidal signals .  Similar organization to figs.  3,4.  Top \nrow  shows  modulation of input sources.  a)  Mode  I  activity.  Signal propagation is \nnot  significantly  influenced  by  the  level  of firing  synchrony.  Analog neuron  model \n(solid  line)  gives  reasonable  prediction  of signal  tranmission.  b)  Mode  II  activity. \nAt  initial  levels  of firing  synchrony above::::::  30%,  signal  propagation  is  amplified. \nThe propagation of asynchronous signals is  still well described  by the analog neuron \nmodel.  Period of applied oscillation =  10  msec. \n\nsynchrony  levels  below  ::::::  30%,  firing  synchrony  between  cells  in  the  same  layer \n(fig.  4b)  falls  off  in  successive  layers.  Above  this  level,  however,  synchrony  grows \nrapidly from  layer to layer. \n\nTo confirm  that our results  are  not  limited to the  propagation of signals  generated \nby  a  single  impulse,  oscillatory signals  were  produced  by  sinusoidally  modulating \nthe firing  rates of both the common and independent input sources  to the first  layer \n(fig.  5).  In  the  mode  I  state  (fig.  5a),  we  again  find  that  firing  synchrony  does \nnot  significantly  alter  the  degree  of signal  penetration.  The  solid  line  shows  that \nsignal  transmission  is  adequately  described  by  the  simplified  model  (eqs.  4,5).  In \nthe  mode  II  case,  however,  firing  synchrony  is  seen  to  have  an  amplifying  effect \non  sinusoidal  signals  as  well  (fig.  5b).  Although  the  propagation  of asynchronous \nsignals  is  well  described  by the  analog neuron  model,  at higher  levels of synchrony \npropagation is  enhanced. \n\n\f148 \n\nKenyon, Fetz and Puff \n\n6  Discussion \n\nIt is  widely  accepted  that  biological  neurons  code  information  in  their  spike  den(cid:173)\nsity or firing  rate.  The  degree  to which  the firing  correlations  between neurons  can \ncode additional information by modulating the transmission of FM signals, depends \nstrongly  on  dynamical factors.  We  have shown  that  for  cells  whose  average  mem(cid:173)\nbrane  potential is  sufficiently  below  the  threshold  for  firing,  spike  correlations  can \nsignificantly enhance the  transmission  of FM  signals.  We have also shown that the \npropagation of asynchronous signals is  well described  by analog neuron models with \nlinear transforms.  These  results may be useful  for  understanding the role played by \nsynchronized  SEQ's in primary visual cortex [1,2].  Such signals may be propagated \nmore  effectively  to  subsequent  processing  areas  as  a  consequence  of  their  relative \nsynchronization. \n\nThese  observations may  also  pertain  to  the  neural  mechanisms  underlying the  in(cid:173)\ncreased levels of synchronous discharge of cerebral cortex cells observed in slow wave \nsleep [7J.  Another relevant phenomenon is the spread of synchronous discharge from \nan epileptic focus;  the extent  to  which  synchronous  activity is  propagated  through \nsurrounding areas  may  be  modulated  by  changing their  level  of activation through \nvoluntary effort  or  changing levels of arousal.  These  physiological phenomena may \ninvolve mechanisms similar to  those  exhibited  by our  network model. \n\n, \n\nAcknowledgements \n\nThis  work  is  supported  by  an  NIH  pre-doctoral  training  grant  in  molecular  bio(cid:173)\nphysics  (grant  #  T32-GM  08268)  and  by  the  Office  of  Naval  Research  (contract \n#  N  00018-89-J-1240). \n\nReferences \n[1J  C.  M.  Gray, P.  Konig,  A.  K.  Engel,  W.  Singer,  Nature 338:334-337 (1989) \n\n[2)  R.  Eckhorn,  R.  Bauer,  W. Jordan, M.  Brosch,  W.  Kruse,  H.  J.  Reitboeck,  Bio. \n\nCyber.  60:121-130  (1988) \n\n[3)  E.  E.  Fetz,  B.  Gustafsson,  J.  Physiol.  341:387-410 (1983) \n\n[4J  P.  A.  Kirkwood,  J.  Neurosci.  Meth.  1:107-132 (1979) \n\n[5]  M.  Abeles,  Local  Cortical  Circuits:  Studies  of Brain Function.  Springer,  New \n\nYork,  Vol.  6  (1982) \n\n[6]  E.  E.  Fetz,  Neural  Information  Processing  Systems  American  Institute  of \n\nPhysics.  (1988) \n\n[7]  H.  Noda,  W.R.Adey, J.  Neurophysiol.  23:672-684 (1970) \n\n\f", "award": [], "sourceid": 223, "authors": [{"given_name": "G.", "family_name": "Kenyon", "institution": null}, {"given_name": "Eberhard", "family_name": "Fetz", "institution": null}, {"given_name": "R.", "family_name": "Puff", "institution": null}]}