A Model of the Neural Basis of the Rat's Sense of Direction
Authors: James J. Knierim, Hemant S. Kudrimoti, Bruce L. McNaughton William E. Skaggs
Published in: Advances in Neural Information Processing Systems 7  (NIPS 1994) (Main Conference Track), 1994

Abstract: In  the last decade  the outlines  of the neural  structures  subserving  the sense of direction have begun to emerge.  Several investigations  have shed  light on  the effects  of vestibular  input  and visual  input  on  the  head  direction  representation.  In  this  paper,  a  model  is  formulated of the neural mechanisms underlying the head direction  system.  The model is  built out of simple ingredients,  depending  on  nothing  more complicated than  connectional  specificity,  attractor  dynamics,  Hebbian  learning,  and  sigmoidal  nonlinearities,  but  it  behaves  in  a  sophisticated  way  and  is  consistent  with  most of the  observed properties ofreal head direction cells.  In addition it makes  a  number  of predictions  that  ought  to  be  testable  by  reasonably  straightforward experiments. 
1  Head  Direction  Cells  in  the Rat 
There  is  quite  a  bit  of  behavioral  evidence  for  an  intrinsic  sense  of  direction  in  many species  of mammals, including  rats  and  humans  (e.g.,  Gallistel,  1990).  The  first  specific  information regarding  the  neural  basis  of this  "sense"  came with  the  discovery  by  Ranck  (1984)  of a  population  of  "head  direction"  cells  in  the  dorsal  presubiculum (also known as the  "postsubiculum") of the rat.  A head direction cell 
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William  Skaggs,  James  J.  Knierim,  Hemant  S. Kudrimoti,  Bruce L.  McNaughton 
fires  at  a  high  rate  if and  only  if the rat's  head  is  oriented  in  a  specific  direction.  Many  things  could  potentially  cause  a  cell  to  fire  in  a  head-direction  dependent  manner:  what made the postsubicular  cells  particularly interesting  was  that when  their directionality was tested with the rat at different locations, the head directions  corresponding to maximal firing  were  consistently parallel, within the experimental  resolution.  This  is  difficult  to  explain  with  a  simple sensory-based  mechanism;  it  implies something more sophisticated.1 
The  postsubicular  head  direction  cells  were  studied  in  depth  by  Taube  et  al.  (1990a,b),  and,  more  recently,  head  direction  cells  have  also  been  found  in  other  parts of the rat brain,  in  particular  the anterior nuclei  of the  thalamus (Mizumori  and  Williams,  1993)  and  the  retrosplenial  (posterior  cingulate)  cortex  (Chen  et  al.,  1994a,b).  Interestingly,  all  of these  areas  are  intimately  associated  with  the  hippocampal  formation,  which  in  the  rat  contains  large numbers  of  "place"  cells.  Thus,  the  brain  contains  separate  but  neighboring  populations  of cells  coding  for  location and  cells  coding for  direction,  which taken together  represent  much of the  information needed  for  navigation. 
Figure  1 shows  directional  tuning curves  for  three  typical head  direction cells from  the  anterior  thalamus.  In each  of them the  breadth  of tuning is  on the order of 90  degrees.  This value is  also typical for  head direction cells in the postsubiculum and  retrosplenial  cortex,  though  in  each  of the  three  areas  individual  cells  may  show  considerable variability. 
Figure  1:  Polar plots  of directional  tuning  (mean firing  rate  as  a  function  of head  direction)  for  three  typical head  direction  cells from the anterior thalamus of a  rat. 
Every study  to date has indicated that the head  direction cells  constitute a unitary  system,  together  with  the  place  cells  of  the  hippocampus.  Whenever  two  head  direction  cells  have  been  recorded  simultaneously,  any  manipulation  that  caused  one of them to shift its directional  alignment caused the other to shift by  the same  amount;  and  when  head  direction  cells  have  been  recorded  simultaneously  with  place  cells,  any  manipulation that caused  the head  direction  cells  to  realign either  caused  the hippocampal place fields  to rotate correspondingly or  to  "remap" into a  different  pattern  (Knierim  et  al.,  1995). 
Head direction cells  maintain their directional tuning for  some time when  the lights  in  the recording  room are  turned  off,  leaving  an  animal in  complete  darkness;  the  directionality tends to gradually drift, though, especially if the animal moves around  (Mizumori and Williams, 1993).  Directional tuning is preserved to some degree even 
1 Sensitivity  to  the  Earth's  geomagnetic  field  has  been  ruled  out  as  an  explanation  of 
head-directional  firing . 
A Model of the  Neural Basis of the Rat's Sense of Direction 
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if an animal is  passively rotated in the dark, which indicates strongly that the head  direction system receives information (possibly indirect) from the vestibular system. 
Visual  input  influences  but  does  not  dictate  the  behavior  of head  direction  cells.  The  nature  of this  influence is  quite  interesting.  In  a  recent  series  of experiments  (Knierim  et  al.,  1995), rats were trained to forage for  food pellets in a gray cylinder  with  a  single salient  directional  cue,  a  white card  covering  90  degrees  of the  wall.  During  training,  half of the  rats were  disoriented  before  being  placed  in the  cylin(cid:173) der,  in  order  to  disrupt  the  relation  between  their  internal  sense  of direction  and  the  location  of the  cue  card;  the  other  half of the rats  were  not  disoriented.  Pre(cid:173) sumably,  the  rats  that were  not  disoriented  during  training  experienced  the same  initial relationship between their internal direction sense and the CUe card each time  they  were  placed  in  the  cylinder;  this  would  not have  been  true of the disoriented  rats.  Head  direction  cells  in  the  thalamus were  subsequently  recorded  from  both  groups of rats  as  they  moved  in  the cylinder.  All rats  were  disoriented  before  each  recording  session.  Under  these  conditions,  the  cue  card  had  much  weaker  control  over  the  head  direction  cells  in  the  rats  that had  been  disoriented  during training  than in  the  rats  that had not been  disoriented.  For  all rats the influence of the cue  card upon the head direction system weakened gradually over the course of multiple  recording  sessions,  and eventually they  broke free,  but this happened  much sooner  in  the rats  that had been  disoriented  during training.  The authors  concluded  that  a  visual  cue  could  only  develop  a  strong  influence  upon  the  head  direction  system  if  the  rat  experienced  it  as  stable. 
Figure 2 illustrates the shifts in  alignment during a typical recording session.  When  the  rat  is  initially placed  in  the  cylinder,  the  cell's  tuning  curve  is  aligned  to  the  west.  Over the first few  minutes of recording it gradually rotates to SSW, and there  it stays.  Note  the  "tail" of the curve.  This comes from spikes belonging to another,  neighboring head  direction cell, which could  not be perfectly isolated from the first.  Note that, even though they come from different cells,  both portions shift alignment  synchronously. 
Figure  2:  Shifts  in  alignment  of  a  head  direction  cell  over  the  course  of a  single  recording session  (one  minute intervals).