{"title": "A Model of the Neural Basis of the Rat's Sense of Direction", "book": "Advances in Neural Information Processing Systems", "page_first": 173, "page_last": 180, "abstract": null, "full_text": "A  Model of the  Neural Basis  of the  Rat's \n\nSense of Direction \n\nWilliam E.  Skaggs \nbill@nsma.arizona. edu \n\nJames  J.  Knierim \njim@nsma.arizona. edu \n\nHemant  S.  Kudrimoti \nhemant@nsma. arizona. edu \n\nBruce L.  McNaughton \nbruce@nsma. arizona. edu \n\nARL  Division of Neural  Systems,  Memory, And  Aging \n\n344  Life  Sciences  North,  University of Arizona,  'IUcson  AZ  85724 \n\nAbstract \n\nIn  the last decade  the outlines  of the neural  structures  subserving \nthe sense of direction have begun to emerge.  Several investigations \nhave shed  light on  the effects  of vestibular  input  and visual  input \non  the  head  direction  representation. \nIn  this  paper,  a  model  is \nformulated of the neural mechanisms underlying the head direction \nsystem.  The model is  built out of simple ingredients,  depending  on \nnothing  more complicated than  connectional  specificity,  attractor \ndynamics,  Hebbian  learning,  and  sigmoidal  nonlinearities,  but  it \nbehaves  in  a  sophisticated  way  and  is  consistent  with  most of the \nobserved properties ofreal head direction cells.  In addition it makes \na  number  of predictions  that  ought  to  be  testable  by  reasonably \nstraightforward experiments. \n\n1  Head  Direction  Cells  in  the Rat \n\nThere  is  quite  a  bit  of  behavioral  evidence  for  an  intrinsic  sense  of  direction  in \nmany species  of mammals, including  rats  and  humans  (e.g.,  Gallistel,  1990).  The \nfirst  specific  information regarding  the  neural  basis  of this  \"sense\"  came with  the \ndiscovery  by  Ranck  (1984)  of a  population  of  \"head  direction\"  cells  in  the  dorsal \npresubiculum (also known as the  \"postsubiculum\") of the rat.  A head direction cell \n\n\f174 \n\nWilliam  Skaggs,  James  J.  Knierim,  Hemant  S. Kudrimoti,  Bruce L.  McNaughton \n\nfires  at  a  high  rate  if and  only  if the rat's  head  is  oriented  in  a  specific  direction. \nMany  things  could  potentially  cause  a  cell  to  fire  in  a  head-direction  dependent \nmanner:  what made the postsubicular  cells  particularly interesting  was  that when \ntheir directionality was tested with the rat at different locations, the head directions \ncorresponding to maximal firing  were  consistently parallel, within the experimental \nresolution.  This  is  difficult  to  explain  with  a  simple sensory-based  mechanism;  it \nimplies something more sophisticated.1 \n\nThe  postsubicular  head  direction  cells  were  studied  in  depth  by  Taube  et  al. \n(1990a,b),  and,  more  recently,  head  direction  cells  have  also  been  found  in  other \nparts of the rat brain,  in  particular  the anterior nuclei  of the  thalamus (Mizumori \nand  Williams,  1993)  and  the  retrosplenial  (posterior  cingulate)  cortex  (Chen  et \nal.,  1994a,b).  Interestingly,  all  of these  areas  are  intimately  associated  with  the \nhippocampal  formation,  which  in  the  rat  contains  large numbers  of  \"place\"  cells. \nThus,  the  brain  contains  separate  but  neighboring  populations  of cells  coding  for \nlocation and  cells  coding for  direction,  which taken together  represent  much of the \ninformation needed  for  navigation. \n\nFigure  1 shows  directional  tuning curves  for  three  typical head  direction cells from \nthe  anterior  thalamus.  In each  of them the  breadth  of tuning is  on the order of 90 \ndegrees.  This value is  also typical for  head direction cells in the postsubiculum and \nretrosplenial  cortex,  though  in  each  of the  three  areas  individual  cells  may  show \nconsiderable variability. \n\nFigure  1:  Polar plots  of directional  tuning  (mean firing  rate  as  a  function  of head \ndirection)  for  three  typical head  direction  cells from the anterior thalamus of a  rat. \n\nEvery study  to date has indicated that the head  direction cells  constitute a unitary \nsystem,  together  with  the  place  cells  of  the  hippocampus.  Whenever  two  head \ndirection  cells  have  been  recorded  simultaneously,  any  manipulation  that  caused \none of them to shift its directional  alignment caused the other to shift by  the same \namount;  and  when  head  direction  cells  have  been  recorded  simultaneously  with \nplace  cells,  any  manipulation that caused  the head  direction  cells  to  realign either \ncaused  the hippocampal place fields  to rotate correspondingly or  to  \"remap\" into a \ndifferent  pattern  (Knierim  et  al.,  1995). \n\nHead direction cells  maintain their directional tuning for  some time when  the lights \nin  the recording  room are  turned  off,  leaving  an  animal in  complete  darkness;  the \ndirectionality tends to gradually drift, though, especially if the animal moves around \n(Mizumori and Williams, 1993).  Directional tuning is preserved to some degree even \n\n1 Sensitivity  to  the  Earth's  geomagnetic  field  has  been  ruled  out  as  an  explanation  of \n\nhead-directional  firing . \n\n\fA Model of the  Neural Basis of the Rat's Sense of Direction \n\n175 \n\nif an animal is  passively rotated in the dark, which indicates strongly that the head \ndirection system receives information (possibly indirect) from the vestibular system. \n\nVisual  input  influences  but  does  not  dictate  the  behavior  of head  direction  cells. \nThe  nature  of this  influence is  quite  interesting.  In  a  recent  series  of experiments \n(Knierim  et  al.,  1995), rats were trained to forage for  food pellets in a gray cylinder \nwith  a  single salient  directional  cue,  a  white card  covering  90  degrees  of the  wall. \nDuring  training,  half of the  rats were  disoriented  before  being  placed  in the  cylin(cid:173)\nder,  in  order  to  disrupt  the  relation  between  their  internal  sense  of direction  and \nthe  location  of the  cue  card;  the  other  half of the rats  were  not  disoriented.  Pre(cid:173)\nsumably,  the  rats  that were  not  disoriented  during  training  experienced  the same \ninitial relationship between their internal direction sense and the CUe card each time \nthey  were  placed  in  the  cylinder;  this  would  not have  been  true of the disoriented \nrats.  Head  direction  cells  in  the  thalamus were  subsequently  recorded  from  both \ngroups of rats  as  they  moved  in  the cylinder.  All rats  were  disoriented  before  each \nrecording  session.  Under  these  conditions,  the  cue  card  had  much  weaker  control \nover  the  head  direction  cells  in  the  rats  that had  been  disoriented  during training \nthan in  the  rats  that had not been  disoriented.  For  all rats the influence of the cue \ncard upon the head direction system weakened gradually over the course of multiple \nrecording  sessions,  and eventually they  broke free,  but this happened  much sooner \nin  the rats  that had been  disoriented  during training.  The authors  concluded  that \na  visual  cue  could  only  develop  a  strong  influence  upon  the  head  direction  system  if \nthe  rat  experienced  it  as  stable. \n\nFigure 2 illustrates the shifts in  alignment during a typical recording session.  When \nthe  rat  is  initially placed  in  the  cylinder,  the  cell's  tuning  curve  is  aligned  to  the \nwest.  Over the first few  minutes of recording it gradually rotates to SSW, and there \nit stays.  Note  the  \"tail\" of the curve.  This comes from spikes belonging to another, \nneighboring head  direction cell, which could  not be perfectly isolated from the first. \nNote that, even though they come from different cells,  both portions shift alignment \nsynchronously. \n\nFigure  2:  Shifts  in  alignment  of  a  head  direction  cell  over  the  course  of a  single \nrecording session  (one  minute intervals). \n\n2  The  Model \n\nAs  reviewed  above,  the most important facts  to  be  accounted  for  by  any  model of \nthe head  direction system are  (1)  the shape of the tuning curves for  head  direction \ncells, (2) the control of head direction cells by vestibular input, and (3)  the stability(cid:173)\ndependent  influence  of  visual  cues  on  head  direction  cells.  We  introduce  here  a \n\n\f176 \n\nWilliam  Skaggs,  James  J.  Knierim,  Hemant  S.  Kudrimoti,  Bruce  L  McNaughton \n\nmodel that  accounts  for  these  facts.  It is  a  refinement of a  model proposed  earlier \nby  McNaughton  et  al.  (1991),  the main addition  being  a  more specific  account  of \nneural  connections  and dynamics.  The aim of this effort  is  to develop  the simplest \npossible  architecture  consistent  with  the  available  data.  The  reality  is  sure  to  be \nmore complicated than this model. \nFigure  3  schematically  illustrates  the  architecture  of the  model.  There  are  four \ngroups  of cells  in  the  model:  head  direction  cells,  rotation  cells  (left  and  right), \nvestibular  cells  (left  and  right),  and  visual  feature  detectors.  For  expository  pur(cid:173)\nposes  it is  helpful  to  think  of the network  as  a  set of circular  layers;  this  does  not \nreflect  the  anatomical organization of the corresponding  cells in the  brain. \n\nV.oIIbul .. col (rtght) \n\n00 \n\n\u00b0\u00b000 0 \u00b0 0 \u00b0 0 \u00b0 0 0 \n\n@ \n\n@ \n@  ~ROt.lOftC~I~etQ \n\u00ae \n\u00b700---- Rotadon cell (rtght) \n@ \n\n0\u00b00 \n\n@ \n@ \n\n00 \n00  @ \n\n66  @ \n\n\u00b0 0  @ \n\n0\u00b00  @ \n\n\u00ae \n\n0  00 \u00b0  \u00b0  \u00b0  \u00b0  \u00b0  00 0 \n\n\u00ae \n00000  \u00ae \n@  @  @  \u00ae  ~H~ eM.ocUon  coM \n\n\u00ae \n\nFigure  3:  Architecture of the head  direction  cell  model. \n\nThe head  direction  cell  group  has  intrinsic connections  that are stronger  than  any \nother connections in  the model, and dominate their  dynamics, so  that other inputs \nonly  provide  relatively  small  perturbations.  The  connections  between  them  are \nset  up  so  that  the  only  possible  stable  state  of  the  system  is  a  single  localized \ncluster  of active  cells,  with  all  other  cells  virtually silent.  This  will  occur  if there \nare  strong  excitatory  connections  between  neighboring  cells,  and  strong inhibitory \nconnections between distant cells.  It is assumed that the network of interconnections \nhas  rotation  and  reflection  symmetry.  Small  deviations  from  symmetry  will  not \nimpair the model too much; large deviations may cause it to have strong attractors \nat  a few  points on  the circle,  which  would  cause  problems. \n\nThe crucial property of this network is  the following . Suppose it is  in  a stable state, \nwith  a  single  cluster  of activated  cells  at  one  point  on  the  circle,  and  suppose  an \nexternal input is  applied  that excites  the cells  selectively  on one side  (left  or  right) \n\n\fA  Model of the Neural Basis of the Rat' s Sense of Direction \n\n177 \n\nof the peak.  Then the peak will rotate toward the side at which the input is applied, \nand the rate of rotation will  increase  with the strength  of the input. \n\nThis  feature  is  exploited  by  the  mechanisms  for  vestibular  and  visual  control  of \nthe  system.  The  vestibular  mechanism  operates  via  a  layer  of  \"rotation\"  cells, \ncorresponding  to  the  circle  of head  direction  cells  (Units  with  a  similar role  were \nreferred  to  as  \"H  x  H'\"  cells  in  the  McNaughton  et  al.  (1991)  model).  There \nare  two  groups  of  rotation  cells,  for  left  and  right  rotations.  Each  rotation  cell \nreceives  excitatory  input  from  the  head  direction  cell  at  the  same  point  on  the \ncircle,  and from  the vestibular  system.  The activation function  of the rotation  cell \nis  sigmoidal or  threshold  linear,  so  that the  cell  does  not  become  active  unless  it \nreceives  input  simultaneously  from  both  sources.  Each  right  rotation  cell  sends \nexcitatory projections to head  direction cells  neighboring it on the right, but not to \nthose  that neighbor it on the left,  and  contrariwise for  left rotation  cells. \n\nIt is  easy  to see  how  the mechanism works.  When the animal turns to the right, the \nright vestibular  cells  are  activated, and  then  the right rotation cells  at the current \npeak  of the  head  direction  system  are  activated.  These  add  to  the  excitation  of \nthe head  direction  cells  to the right of the peak,  thereby  causing  the  peak  to shift \nrightward .  This  in  turn  causes  a  new  set  of rotation  cells  to  become  active  (and \nthe old  ones inactive), and thence  a further shift of the peak,  and so  on.  The  peak \nwill  continue  to  move  around  the  circle  as  long  as  the  vestibular  input  is  active, \nand  the stronger  the vestibular  input,  the more  rapidly  the  peak  will  move.  If the \ngain  of this  mechanism is  correct  (but  weak  compared  to  the gain  of the  intrinsic \nconnections  of the head  direction  cells),  then  the peak  will  move around  the  circle \nat  the  same rate  that the  animal turns,  and the  location of the  peak  will  function \nas  an  allocentric compass.  This  can only be expected  to work  over  a limited range \nof  turning  rates,  but  the  firing  rates  of cells  in  the  vestibular  nuclei  are  linearly \nproportional  to  angular  velocity  over  a  surprisingly  broad  range,  so  there  is  no \nreason why the mechanism cannot perform adequately. \n\nOf course  the mechanism is  intrinsically error-prone,  and without some sort  of ex(cid:173)\nternal correction,  deviations are sure to build up over time.  But this is  an inevitable \nfeature  of any  plausible model,  and in  any  case  does  not  conflict  with the available \ndata, which,  while sketchy, suggests that passive rotation of animals in the dark can \ncause  quite  erratic  behavior  in  head  direction  cells  (E.  J.  Markus,  J.  J .  Knierim, \nunpublished observations). \n\nThe final  ingredient of the model is  a set of visual feature  detectors,  each  of which \nresponds  if and  only  if a  particular  visual  feature  is  located  at  a  particular  angle \nwith  respect  to  the  axis  of the  rat's  head.  Thus,  these  cells  are  feature  specific \nand  direction  specific,  but direction  specific  in  the head-centered  frame,  not  in the \nworld  frame .  It is  assumed  that each  visual  feature  detector  projects  weakly  to  all \nof the  head  direction  cells,  and  that  these  connections  are  modifiable according  to \na  Hebbian  rule,  specifically, \n\n~W =  a(Wmaxt(Aposd - W)Apre, \n\nwhere  W  is the connection weight, W max  is  its maximum possible value,  Apost  is  the \nfiring  rate of the postsynaptic cell,  Apre  is  the firing  rate of the presynaptic cell,  and \nthe  function  to  has  the  shape  shown  in  figure  4.  (Actually,  the  rule  is  modified \n\nslightly  to  prevent  any  of the  weights  from  becoming  negative.)  The  net  effect  of \n\n\f178 \n\nWilliam  Skaggs,  James  J.  Knierim,  Hemant  S.  Kudrimoti,  Bruce L.  McNaughton \n\nthis  rule is  that  the  weight  will only  change  when  the  presynaptic  cell  (the  visual \nfeature  detector)  is  active,  and  the  weight  will  increase  if the  postsynaptic  cell  is \nstrongly active, but decrease ifit is weakly active or silent.  Modification rules of this \nform  have  previously  been  proposed  in theories  of the development  of topography \nin  the neocortex  (e.g.,  Bienenstock  et  al.,  1982), and there is considerable evidence \nfor  such  an  effect  in  the control  of LTP /LTD (Singer  and Artola,  1994) . \n\n1(rate) \n\nrate \n\nFigure  4:  Dependence  of synaptic  weight  change  on  postsynaptic  firing  rate  for \nconnections from visual feature  detectors  to head  direction  cells  in  the model. \n\nTo  understand  how  this  works,  suppose  we  have  a  feature  detecting  cell  that  re(cid:173)\nsponds to  a cue  card whenever  the  cue  card is  directly in front  of the rat.  Suppose \nthe rat's motion is restricted  to  a small area, and the cue card is far  away, so that it \nis  always at approximately the same absolute bearing (say, 30  degrees),  and suppose \nthe rat's head  direction system is working correctly, i.e., functioning  as  an  absolute \ncompass.  Then  the  cell  will  only  be  active  at  moments  when  the  head  direction \ncells  corresponding  to 30  degrees  are  active,  and the Hebbian  learning process  will \ncause  the feature  detecting  cell  to be linked by  strong weights to these  cells,  but by \nvanishing  weights  to other  head  direction  cells.  If the  absolute  bearing  of the cue \ncard  were  more variable,  then  the  connection strengths  from  the feature  detecting \ncell  would  be  weaker  and  more  broadly  dispersed .  In  the  limit where  the  bearing \nof the cue  card  was  completely  random, all connections  would  be  weak  and  equal. \nThus  the influence of a visual  cue  is  determined  by  the  amount of training  and  by \nthe variability in its bearing  (with respect  to the head  direction  system). \n\nIt can  be seen  that the model implements a competition between  visual inputs and \nvestibular inputs for  control of the head direction cells.  If the visual cues  are rotated \nwhile  the  rat  is  left  stationary,  then  the  head  direction  cells  may either  rotate  to \nfollow  the  visual  cues,  or  stick  with  the  inertial  frame,  depending  on  parameter \nvalues  and,  importantly, on  the  training  regimen  imposed  on  the  network.  Both \nof  these  outcomes  have  been  observed  in  anterior  thalamic  head  direction  cells \n(McNaughton  et  al.,  1993). \n\n3  Discussion \n\nDo  the  necessary  types  of cells  exist  in  the  brain?  Cells  in  the brainstem vestibular \nnuclei  are known to have the properties  required  by the model (Precht,  1978).  The \n\"rotation\"  cells would be recognizable from the fact  that they  would fire  only when \n\n\fA Model of the Neural Basis of the Rat's Sense of Direction \n\n179 \n\nthe rat is facing in a particular direction and turning in a particular direction, with \nrate at least roughly proportional to the speed ofturning.  Cells with these properties \nhave  been  recorded  in  the  postsubiculum  (Markus  et  al.,  1990)  and  retrosplenial \ncortex  (Chen  et  ai.,  1994a).  The visual  cells  would  be recognizeable  from  the fact \nthat they  would  respond  to visual  stimuli only  when  they  come  from  a  particular \ndirection  with  respect  to  the animal's head  axis.  Cells  with  these  properties  have \nbeen  recorded  in  the inferior  parietal  cortex,  the internal medullary  lamina of the \nthalamus,  and  the superior  colliculus  (e.g.,  Sparks,  1986).  The superior  colliculus \nalso contains cells that respond in a direction-dependent manner to auditory inputs, \nthus allowing a possiblility of control of the head direction system by sound sources. \nThere do  not seem to  be any strong  direct  projections from  the superior  colli cui us \nto  the  components  of the  head  direction  system,  but there  are  numerous  indirect \npathways. \nThe  most general  prediction of the model is  that the influence of vestibular input \nupon  head  direction  cells  is  not  susceptible  to experience-dependent  modification, \nwhereas  the influence of visual input is  plastic, and is  enhanced by the duration  of \nexperience,  the richness of the visual cue array, and the distance of visual cues from \nthe rat's region  of travel. \nThe  \"rotation\"  cells  should  be  responsive  to  stimulation of the vestibular  system. \nIt is  possible  to  activate  the  vestibular  system  by  applying  hot  or  cold  water  to \nthe  ears:  if this  is  done  in  the  dark,  and  head  direction  cells  are  simultaneously \nrecorded,  the model predicts  that they will  show  periodic bursts of activity, with  a \nfrequency  related  to the intensity of the stimulus. \nFor  another  prediction, suppose we  train two  groups of rats  to forage in  a  cylinder \ncontaining  a  single  landmark.  For  one  group,  the  landmark is  placed  at  the  edge \nof the  cylinder;  for  the other group, the same landmark is  placed  halfway  between \nthe center  and  the edge.  The model predicts  that in  both  cases  the landmark will \ninfluence  the  head  direction  sytem,  but  the  influence  will  be  stronger  and  more \ntightly focused  when  the landmark is  at the edge. \nIn some respects  the model is  flexible,  and may be extended  without compromising \nits  essence.  For  example,  there  is  no  intrinsic  necessity  that the  vestibular system \nbe  the  sole  input  to  the  rotation  cells  (other  than  the  head  direction  cells).  The \nperformance of the system might be improved in some ways by sending the rotation \ncells  input  about  optokinetic  flow,  or  certain  types  of motor  efference  copy.  But \nthere  is  as  yet no  clear evidence for  these  things. \n\nOn  a  more abstract level,  the mechanism used  by  the model for  vestibular  control \nmay  be  thought  of  as  a  special  case  of a  general-purpose  method  for  integration \nwith neurons.  As  such, it has significant advantages over some previously proposed \nneural  integrators,  in  particular,  better  stability  properties.  It  might  be  worth \nconsidering whether  the method is  applicable in other situations where  integrators \nare known  to exist, for  example the control  of eye  position. \n\n\f180 \n\nWilliam  Skaggs,  James  J.  Knierim,  Hemant S.  Kudrimoti,  Bruce L.  McNaughton \n\nSupported by MH46823  and  O.N .R. \n\nReferences \nBienenstock,  E.  L.,  Cooper,  L.  N.,  and Munro,  P.  W.  (1982).  Theory for  the devel(cid:173)\n\nopment of neuron  selectivity:  orientation specificity  and  binocular interaction \nin  visual  cortex.  J.  Neurosci.,  2:32-48. \n\nChen,  L.  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Effects  of environ(cid:173)\nmental manipulations.  J.  Neurosci.,  10:436-447. \n\n\fPARTm \n\nLEARNiNGTHEORYANDDYNANUCS \n\n\f\f", "award": [], "sourceid": 890, "authors": [{"given_name": "William", "family_name": "Skaggs", "institution": null}, {"given_name": "James", "family_name": "Knierim", "institution": null}, {"given_name": "Hemant", "family_name": "Kudrimoti", "institution": null}, {"given_name": "Bruce", "family_name": "McNaughton", "institution": null}]}