{"title": "Complex-Cell Responses Derived from Center-Surround Inputs: The Surprising Power of Intradendritic Computation", "book": "Advances in Neural Information Processing Systems", "page_first": 83, "page_last": 89, "abstract": null, "full_text": "Complex-Cell Responses Derived from \nCenter-Surround Inputs:  The Surprising \n\nPower of Intradendritic Computation \n\nBartlett W. Mel and Daniel L.  Ruderman \n\nDepartment of Biomedical Engineering \n\nUniversity of Southern California \n\nLos  Angeles,  CA 90089 \n\nKevin A.  Archie \n\nNeuroscience  Program \n\nUniversity of Southern California \n\nLos  Angeles,  CA 90089 \n\nAbstract \n\nBiophysical  modeling  studies  have  previously  shown  that  cortical \npyramidal  cells  driven  by  strong  NMDA-type  synaptic  currents \nand/or containing dendritic voltage-dependent Ca++ or Na+  chan(cid:173)\nnels, respond more strongly when synapses are activated in several \nspatially  clustered  groups  of  optimal  size-in  comparison  to  the \nsame  number  of synapses  activated  diffusely  about  the  dendritic \narbor  [8]- The  nonlinear  intradendritic  interactions  giving  rise  to \nthis  \"cluster sensitivity\"  property are akin to a layer of virtual non(cid:173)\nlinear \"hidden units\" in the dendrites, with implications for the cel(cid:173)\nlular basis of learning and memory  [7,  6],  and for  certain classes of \nnonlinear sensory processing [8]- In the present study, we show that \na  single  neuron,  with  access  only  to excitatory inputs  from  unori(cid:173)\nented ON- and OFF-center cells in the LGN, exhibits the principal \nnonlinear response properties of a  \"complex\"  cell in primary visual \ncortex,  namely orientation tuning  coupled with  translation invari(cid:173)\nance  and  contrast  insensitivity_  We  conjecture  that  this  type  of \nintradendritic processing could explain how complex cell responses \ncan persist in the absence of oriented simple cell input  [13]-\n\n\f84 \n\nB.  W.  Mel,  D.  L.  Ruderman and K.  A. Archie \n\n1 \n\nINTRODUCTION \n\nSimple and complex cells were first  described in  visual cortex by Hubel  and Wiesel \n[4].  Simple  cell  receptive fields  could  be  subdivided into ON  and OFF subregions, \nwith  spatial  summation  within  a  subregion  and  antagonism  between  subregions; \ncells of this type have historically been modeled as linear filters followed by a thresh(cid:173)\nolding nonlinearity (see  [13]).  In contrast, complex cell receptive fields  cannot gen(cid:173)\nerally  be  subdivided into  distinct  ON  and  OFF subfields,  and  as  a  group  exhibit \na  number  of  fundamentally  nonlinear  behaviors,  including  (1)  orientation  tuning \nacross  a  receptive  field  much  wider  than  an  optimal  bar,  (2)  larger  responses  to \nthin bars than thick bars-in direct violation of the superposition principle, and (3) \nsensitivity to both light  and dark bars across the receptive field. \n\nThe traditional Hubel-Wiesel model for complex cell responses involves a hierarchy, \nconsisting  of center-surround inputs that  drive  simple  cells,  which  in  turn provide \noriented, phase-dependent input to the complex cell.  By pooling over a set of simple \ncells with different  positions and phases,  the complex cell  could respond selectively \nto stimulus  orientation,  while  generalizing over  stimulus  position  and contrast.  A \npure  hierarchy  involving  simple  cells  is  challenged,  however,  by  a  variety  of more \nrecent experimental results indicating many complex cells receive monosynaptic in(cid:173)\nput from  LGN cells  [3],  or do not depend on simple cell  input  [10,  5,  1].  It remains \nunknown how  complex cell responses might derive from  intracortical network com(cid:173)\nputations that do no depend on simple cells, or whether they could originate directly \nfrom  intracellular computations. \n\nPrevious biophysical modeling studies have indicated that the input-output function \nof a dendritic tree containing excitatory voltage-dependent membrane mechanisms \ncan be abstracted as low-order polynomial function,  i.e.  a big sum of little products \n(see [9]  for review).  The close match between this type of computation and \"energy\" \nmodels  for  complex  cells  [12,  11,  2]  suggested  that  a  single-cell  origin  of complex \ncell  responses was  possible. \n\nIn  the  present  study,  we  tested the  hypothesis  that  local  nonlinear  processing  in \nthe dendritic tree of a single neuron,  which receives only excitatory synaptic input \nfrom  unoriented  center-surround LGN  cells,  could in and of itself generate nonlin(cid:173)\near complex cell response properties, including orientation selectivity, coupled with \nposition and contrast invariance. \n\n2  METHODS \n\n2.1  BIOPHYSICAL MODELING \n\nSimulations  of a  layer  5 pyramidal cell  from  cat  visual  cortex  (fig.  1)  were  carried \nout in  NEURON 1 .  Biophysical  parameters and other implementation  details  were \nas in  [8]  andj or shown  in Table  2,  except  dendritic spines were  not modeled here. \nThe soma contained modified Hodgkin-Huxley channels with peak somatic conduc(cid:173)\ntances of UNa  and 90R 0.20 Sjcm2  and 0.12 Sjcm2,  respectively; dendritic membrane \nwas  electrically  passive.  Each  synapse  included  both an NMDA  and AMPA-type \n\nINEURON simulation environment courtesy Michael  Hines and John Moore;  synaptic \n\nchannel implementations courtesy Alan Destexhe and Zach Mainen. \n\n\fComplex-cell Responses Derived from Center-surround Inputs \n\n85 \n\n\u2022 \n\nFigure 1:  Layer 5 pyramidal neuron used in  the simulations,  showing 100 synaptic \ncontacts.  Morphology courtesy Rodney Douglas and Kevan  Martin. \n\nexcitatory  conductances  (see  Table  1).  Conductances  were  scaled  by  an  estimate \nof the local input resistance, to keep local EPSP size approximately uniform across \nthe dendritic tree.  Inhibitory synapses were not modeled. \n\n2.2  MAPPING VISUAL  STIMULI ONTO THE DENDRITIC  TREE \n\nA  stimulus  image  consisted  of  a  64  x  64  pixel  array  containing  a  light  or  dark \nbar  (pixel  value  \u00b11  against  a  background  of  0).  Bars  of length  45  and  width  7 \nwere presented at various orientations and positions within the image.  Images were \nlinearly filtered  through  difference-of-Gaussian  receptive  fields  (center  width:  0.6, \nsurround  width:  1.2,  with  no  DC  response).  Filtered  images  were  then  mapped \nonto 64  x  64  arrays of ON-center and OFF-center LGN  cells,  whose  outputs were \nthresholded at \u00b10.02 respectively.  In a crude model of gain control, only a random \nsubset  of  100  of the LGN  neurons  remained  active  to  drive  the  modeled  cortical \ncell. \n\nEach  LGN  neuron  gave  rise  to  a  single  synapse  onto  the  cortical  cell's  dendritic \ntree.  In a  given run, excitatory synapses originating from the 100 active LGN  cells \nwere  activated asynchronously at 40 Hz,  while all  other synapses  remained silent. \n\nThe  spatial  arrangement  of  connections  from  LGN  cells  onto  the  pyramidal  cell \ndendrites  was  generated automatically,  such that pairs of LGN  cells  which  are co(cid:173)\nactive  during  presentations  of optimally  oriented  bars formed  synapses  at  nearby \nsites  in  the  dendritic  tree.  The  activity  of  the  LGN  cell  array  to  an  optimally \noriented  bar is  shown  in fig.  3.  Frequently co-activated pairs of LGN  neurons  are \nhereafter referred to as  \"friend-pairs\", and lie in a geometric arrangement as shown \nin fig.  4.  Correlation-based clustering of friend-pairs  was  achieved  by  (1)  choosing \na random LGN  cell  and placing it at the next available dendritic site,  (2)  randomly \n\n\f86 \n\nB.  W.  Me~ D. L.  Ruderman and K.  A. Archie \n\nParameter \nRm \nRa \nem \nVrest \nSomatic 9Na \nSomatic !/DR \nSynapse count \nStimulus frequency \nTAMPA (on, off) \n9AMPA \n'TNMDA(on, of f) \n9NMDA \nEsyn \n\nValue \nlOkncm~ \n200ncm \n\n1.0JLF/cm~ \n\n-70 mV \n\n0.20 S/cm~ \n0.12  S/cm~ \n\n100 \n40 Hz \n\n0.5  ms,  3 ms \n\n0.27 nS  - 2.95  nS \n\n0.5 ms,  50 ms \n\n0.027 nS  - 0.295 nS \n\nOmV \n\nFigure 2:  Table 1.  Simulation Parameters. \n\nchoosing one of its friends and placing it at the next available dendritic site, and so \non, until until either all of the cell's friends had already been deployed, in which case \na new cell was chosen at random to restart the sequence, or all cells had been chosen, \nmeaning that all  of the 8192  (= 64  x 64  x  2)  LGN  synapses had been successfully \nmapped onto the dendritic tree.  In previous modeling work it was  shown that this \ntype  of  clustering  of  correlated  inputs  on  dendrites  is  the  natural  outcome  of  a \nbalance  between  activity-independent  synapse  formation,  and  activity  dependent \nsynapse stabilization [6]. \n\nThis method guaranteed that an optimally oriented bar stimulus activated a larger \nnumber of friend-pairs on  average than did bars at non-optimal orientations.  This \nled in turn to relatively clustery distributions of activated synapses in the dendrites \nin  response to optimal bar orientations, in comparison to non-optimal orientations. \nIn previous work, it was shown that synapses activated in clusters about a dendritic \narbor  could  produce  significantly  larger  cell  responses  than  the  same  number  of \nsynapses activated diffusely  about the dendritic tree  [7,  8]. \n\n3  Results \n\nResults  for  two  series  of runs  are  shown  in  fig.  5.  For  each  bar  stimulus,  average \nspike rate was measured over a 250 ms period, beginning with the first spike initiated \nafter stimulus onset (if any).  This measure de-emphasized the initial transient climb \noff  the  resting  potential,  and  provided  a  rough  steady-state  measure  of  stimulus \neffectiveness.  Spike rates for  30 runs were  averaged for  each input condition. \n\nOrientation  tuning  curves  for  a  thin  bar  (7  x  45  pixels)  are shown  in  fig.  5.  The \norientation  tuning  peaks  sharply  within  about  10\u00b0  of  vertical,  and  then  decays \nslowly  for  larger  angles.  Tuning  is  apparent  both  for  dark  and  light  bars,  and \nremains independent of location within the receptive field. \n\n\f4  Discussion \n\nThe results of fig.  5 indicate that a  pyramidal cell  driven exclusively  by  excitatory \ninputs from ON- and OFF-center LGN cells, is at a biophysical level  capable of pro(cid:173)\nducing the hallmark nonlinear response  property of visual  complex  cells.  Further(cid:173)\nmore,  the  cell's  translation-invariant preference for  light  or dark vertical  bars  was \nestablished by manipulating only the spatial arrangement of connections from LGN \ncells onto the pyramidal cell dendrites.  Since exactly 100 synapses were activated in \nevery tested condition, the significantly larger responses to optimal bar orientations \ncould not be explained by  a  simple elevation in  the total synaptic activity imping(cid:173)\ning  on  the  neuron  in  that  condition.  The origin  of the cell's  orientation-selective \nresponse resulted  from  nonlinear  pooling  of a  large number  of minimally-oriented \nsubunits, i.e.  consisting of pairs of ON  and OFF cells  that were co-consistent with \nan optimally oriented  bar.  We  have  achieved  similar  results  in  other experiments \nwith a  variety of different  friend-neighborhood structures including ones  both sim(cid:173)\npler  and  more  complex  than  were  used  here,  for  LGN  arrays  with  substantially \ndifferent  degrees  of receptive  field  overlap,  with  random  subsampling of the LGN \narray,  with  graded  LGN  activity  levels,  and for  dendritic  trees  containing  active \nsodium channels in addition to NMDA  channels. \n\nThus far  we  have not attempted to relate physiologically-measured orientation and \nwidth tuning curves,  and other detailed  aspects of complex cell  physiology,  to our \nmodel cell,  as  we  have been principally interested in establishing whether the most \nsalient  nonlinear features  of complex  cell  physiology  were  biophysically feasible  at \nthe single cell level.  Detailed comparisons between our results and empirical tuning \ncurves, etc., must be made with caution, since our model cell has been  \"explanted\" \nfrom  the  network in  which  it  normally  exists,  and is  therefore  absent  the  normal \nrecurrent excitatory and inhibitory influences  the cortical network provides. \n\n\f88 \n\nB.  W  Me~ D.  L.  Ruderman and K.  A. Archie \n\nw \n\nw \n\nI eo \n\nI eo \n\noe \n\noe \n\nw \n\nw \n\nFigure 4:  Layout  of friends  for  an  ON-center LGN  cell for  vertically  oriented thin \nbars  (top).  The linear friendship  linkage for  a  given  ideal  vertical  bar of width  w \nwas  determined as follows.  Suppose an LGN  cell is  chosen at random, e.g.  an ON(cid:173)\ncenter cell  at location  (i,j) within the cell array.  When a  vertical bar is  presented, \nLGN  cells  along  the  two  vertical  edges  of the  bar become  active.  The  ON-center \ncell at position (i,j) is active to a light bar when it is in a column of cells just inside \neither edge of the bar.  Those cells  which are co-active under this  circumstance are: \n(a)  other on-center cells  in the same vertical column,  (b)  on-center cells  in  vertical \ncolumns  a  distance  w  - 1  to  the  right  and  left  (depending  on  the  bar  position), \n(c)  off-center cells  in columns  a distance  \u00b11 away  (due to the negative-going edge \nadjacent),  and  (d)  off-center  cells  a  distance  w  to  the  right  and  left  (due  to  the \nopposite edge).  As  \"friend-pairs\"  we take only those LGN  cells a distance \u00b1(w -1) \nand \u00b1w away.  Those in  the same  and neighboring columns  are not  included.  The \nfriends  of an  off-center  cell  are shown  in  the  bottom figure.  It and  its  friends  are \noptimally  stimulated by  bars of width  w  placed  as  shown.  The width  selected for \nour friend-pairs  was w = 7,  the same width  as  all bars presented as stimuli. \n\nExperimental validation of these simulation results would imply a significant change \nin our conception of the role of the single neuron in  neocortical processing. \n\nAcknowledgments \n\nThis  work  was  funded  by  grants  from  the  National  Science  Foundation  and  the \nOffice  of Naval  Research. \n\nReferences \n\n[1]  G.M.  Ghose, R.D.  Freeman, and I. Ohzawa.  Local intracortical connections in \nthe cats visual-cortex - postnatal-development and plasticity.  J. Neurophysiol. , \n72:1290- 1303,1994. \n\n[2]  D.J.  Heeger.  Normalization  of  cell  responses  in  cat  striate  cortex.  Visual \n\nNeurosci.,  9:181-197, 1992. \n\n[3]  K.P.  Hoffman  and  J.  Stone.  Conduction  velocity  of  afferents  to  cat  visual \ncortex:  a correlation with cortical receptive field properties. Brain Res., 32:460-\n466, 1971. \n\n[4]  D.H.  Hubel and T.N.  Wiesel.  Receptive fields,  binocular interaction and func(cid:173)\ntional architecture in the cat's visual cortex.  J.  Physiol.,  160:106- 154, 1962. \n\n\fComplex-cell Responses Derived from Center-surround Inputs \n\n89 \n\n70 \n\n60 \n\n50 \n\n30 \n\n20 \n\n'0 \n\n. . . ..... .. -\u00a3. \n\n\" \n\n\u00b00~--~,0--~~--~3~0---~L---~50--~60L---mL---~60--~~ \n\nOrientation (degrees) \n\nFigure  5:  Orientation  tuning  curves  for  the  model  neurons. \ntered in the receptive field;  diamonds:  light bars displaced by 6 pixels horizontally; \nsquares:  dark  bars  centered  in  the  receptive  field;  '+':  dark  bars  displaced  by  6 \npixels.  Standard errors on the data are about 5 spikes/sec. \n\n'X':  light  bars  cen(cid:173)\n\n[5]  J.G. Malpeli,  C. Lee, H.D.  Schwark, and T.G. Weyand.  Cat area 17. I. Pattern \n\nof thalamic control of cortical layers.  J.  Neurophyiol.,  46:1102-1119, 1981. \n\n[6]  B.W.  Mel.  The  clusteron:  Toward  a  simple  abstraction  for  a  complex  neu(cid:173)\n\nron.  In J.  Moody,  S.  Hanson,  and R.  Lippmann, editors,  Advances  in  Neural \nInformation  Processing  Systems,  vol. 4,  pages 35-42. Morgan Kaufmann,  San \nMateo, CA,  1992. \n\n[7]  B.W. Mel.  NMDA-based pattern discrimination in a  modeled cortical neuron. \n\nNeural  Computation,  4:502-516, 1992. \n\n[8]  B.W. Mel.  Synaptic integration in an excitable dendritic tree.  J.  Neurophysiol., \n\n70(3):1086-1101 , 1993. \n\n[9]  B.W.  Mel.  Information  processing  in  dendritic  trees.  Neural  Computation, \n\n6:1031- 1085, 1994. \n\n[10]  J .A.  Movshon.  The  velocity  tuning  of  single  units  in  cat  striate  cortex.  J. \n\nPhysiol.  (Lond), 249:445-468, 1975. \n\n[11]  I. Ohzawa, G.C.  DeAngelis, and R.D  Freeman.  Stereoscopic depth discrimina(cid:173)\n\ntion in the visual cortex:  Neurons ideally suited as disparity detectors.  Science, \n279:1037-1041, 1990. \n\n[12]  D.  Pollen and S.  Ronner.  Visual cortical neurons as localized spatial frequency \n\nfilters.  IEEE  Trans.  Sys.  Man  Cybero.,  13:907- 916, 1983. \n\n[13]  H.R.  Wilson,  D.  Levi, L.  Maffei,  J. Rovamo,  and R.  DeValois.  The perception \nof form:  retina to striate cortex. In L.  Spillman and J.s. Werner, editors,  Visual \nperception:  the neurophysiological foundations,  pages 231-272. Academic Press, \nSan Diego,  1990. \n\n\f", "award": [], "sourceid": 1209, "authors": [{"given_name": "Bartlett", "family_name": "Mel", "institution": null}, {"given_name": "Daniel", "family_name": "Ruderman", "institution": null}, {"given_name": "Kevin", "family_name": "Archie", "institution": null}]}