{"title": "Directional Hearing by the Mauthner System", "book": "Advances in Neural Information Processing Systems", "page_first": 574, "page_last": 581, "abstract": null, "full_text": "Directional Hearing by the Mauthner \n\nSystem \n\n.Audrey L.  Gusik \n\nDepartment of Psychology \n\nUniversity  of Colorado \n\nBoulder,  Co.  80309 \n\nRobert c. Eaton \nE.  P.  O.  Biology \n\nUniversity  of Colorado \n\nBoulder,  Co.  80309 \n\nAbstract \n\nWe provide a computational description of the function of the Mau(cid:173)\nthner  system.  This  is  the  brainstem  circuit  which  initiates  fast(cid:173)\nstart  escapes  in  teleost  fish  in  response  to  sounds.  Our  simula(cid:173)\ntions,  using  back propagation in  a  realistically  constrained  feedfor(cid:173)\nward  network,  have generated hypotheses  which  are directly inter(cid:173)\npretable  in  terms  of the  activity  of the  auditory  nerve  fibers,  the \nprinciple  cells  of the  system  and  their  associated  inhibitory  neu(cid:173)\nrons. \n\n1 \n\nINTRODUCTION \n\n1.1  THE M.AUTHNER SYSTEM \n\nMuch is known about the brainstem system that controls fast-start escapes in teleost \nfish.  The  most  prominent  feature  of this  network  is  the  pair  of large  Mauthner \ncells  whose  axons  cross  the  midline  and  descend  down  the  spinal  cord  to synapse \non primary  motoneurons.  The  Mauthner system also  includes  inhibitory  neurons, \nthe  PHP cells,  which  have  a  unique  and intense  field  effect  inhibition  at the spike(cid:173)\ninitiating zone of the Mauthner cells  (Faber and Korn, 1978).  The Mauthner system \nis  part  of the  full  brainstem  escape  network  which  also  includes  two  pairs  of cells \nhomologous  to the  Mauthner cell  and other  populations  of reticulospinal  neurons. \nWith  this  network  fish  initiate  escapes  only  from  appropriate  stimuli,  turn  away \nfrom the offending stimulus,  and do so  very  rapidly  with  a latency  around 15  msec \nin goldfish.  The Mauthner cells  play an important role in  these functions.  Only one \n\n574 \n\n\fDirectional Hearing by the Mauthner System \n\n575 \n\nfires  thus controlling  the direction  of the initial turn,  and it fires  very  quickly  (4-5 \nmsec).  They also  have  high  thresholds  due  to instrinsic  membrane  properties  and \nthe inhibitory  inlluence  of the  PHP cells.  (For reviews,  see  Eaton, et al,  1991  and \nFaber and Korn,  1978.) \n\nAcoustic stimuli are thought to be sufficient  to trigger the response  (Blader, 1981), \nboth Mauthner cells and PHP cells receive  innervation from primary auditory fibers \n(Faber and  Korn,  1978).  In addition,  the  Mauthner cells  have  been shown  physio(cid:173)\nlogically  to be very sensitive  to acoustic  pressure  (Canfield  and Eaton,  1990). \n\n1.2  LOCALIZING SOUNDS UNDERWATER \n\nIn contrast  to  terrestrial  vertebrates,  there  are  several  reasons  for  supposing  that \nfish  do not use time of arrival or intensity differences  between the two ears to localize \nsounds:  underwater  sound  travels  over  four  times  as fast  as  in  air;  the  fish  body \nprovides no acoustic shadow; and fish  use a single transducer to sense pressure which \nis  conveyed  equally  to  the  two  ears.  Sound  pressure  is  transduced  into  vibrations \nby the swim  bladder which,  in goldfish,  is  mechanically  linked  to the inner ear. \n\nFish  are  sensitive  to  an  additional  component  of the  acoustic  wave,  the  particle \nmotion.  Any particle ofthe medium taking part in the propagation of a longitudenal \nwave  will  oscillate  about an equilibrium  point  along  the axis  of propagation.  Fish \nhave roughly the same density  as water, and will  experience  these oscillations.  The \nmotion  is  detected  by  the  bending  of sensory  hairs  on  auditory  receptor  cells  by \nthe otolith,  an inertial mass suspended  above the hair cells.  This component of the \nsound will  provide the axis of propagation, but there is  a  180 degree  ambiguity. \nBoth  pressure  and  particle  motion  are  sensed  by  hair  cells  of the  inner  ear.  In \ngoldfish these signals may be nearly segregated.  The linkage with the swim bladder \nimpinges primarily on a boney chamber containing two of the endorgans of the inner \near:  the  saccule  and  the  lagena.  The  utricle  is  a  third  endorgan  also  thought  to \nmediate some acoustic function,  without such direct  input from  the 3wimbladder. \nUsing  both of these  components  fish  can  localize  sounds.  According  to  the  phase \nmodel  (Schuijf,  1981)  fish  analyze  the  phase  difference  between  the  pressure  com(cid:173)\nponent of the sound and the particle  displacement  component to calculate distance \nand  direction.  When  pressure  is  increasing,  particles  will  be  pushed  in  the  direc(cid:173)\ntion of sound propagation, and when pressure is decreasing particles  will  be pulled \nback.  There will  be a  phase lag between  pressure  and particle  motion which  varies \nwith frequency  and distance from the sound source.  This, and the separation of the \npressure from  the displacement  signals in  the ear of some species  pose the greatest \nproblems for  theories of sound localization  in fish. \n\nThe  acoustically  triggered  escape  in  goldfish  is  a  uniquely  tractable  problem  in \nunderwater sound localization.  First, there is the fairly good segregation of pressure \nfrom  particle  motion  at  the  sensory  level.  Second I  the  escape  is  very  rapid.  The \ndecision to turn left or right is equivalent to the firing of one or the other Mauthner \ncell,  and this  happens within  about 4 msec.  With transmission delay,  this  decision \nrelies  only on the initial  2 msec  or so of the stimulus.  For most salient  frequencies, \nthe phase lag will  not introduce  uncertainty:  both the first  and second  derivatives \nof particle  position and acoustic  pressure  will  be  either positive  or negative. \n\n\f576 \n\nGuzik and Eaton \n\n1.3  THE XNOR MODEL \n\nA \n\nActive \npressure \n\ninput \n\nActive \n\ndisplacement \n\ninput \n\nleft \n\nMauthner \n\noutput \n\nRight \n\nMauthner \n\noutput \n\nOl \n\nDR \n\nOL \n\nDR \n\nOn \n\nOff \n\norr \n\nOn \n\nOfr \n\nOn \n\nOn \n\nOff \n\np+ \n\np+ \n\np-\n\np-\n\nB \n\nLeft sound \nsource \n\nOR---a \np+  -------.. \np(cid:173)\nOL---a \n\n1 ) - - - - DL \n__  ..;:Jo.. ___  P+ \n\n--..,----p. \n1 ) - - - - DR \n\n.. inhibitory \n\n0- excitatory \n\nNo  response \n\nFigure 1 Truth table and minimal  network for  the  XNOR model. \n\nGiven  the  above  simplification  of the  problem,  we  can  see  that  each  Mauthner \ncell  must  perform a  logical  operation  (Guzik  and  Eaton,  1993j  Eaton et al,  1994). \nThe left  Mauthner  cell  should  fire  when  sounds  are  located  on  the  left,  and  this \noccurs  when  either  pressure  is  increasing  and  particle  motion  is  from  the  left  or \nwhen  pressure  is  decreasing  and  particle  motion  is  from  the  right.  We  can  call \ndisplacement  from  the  left  positive  for  the left  Mauthner cell,  and immediately  we \n\n\fDirectional Hearing by the Mauthner System \n\n577 \n\nhave  the logical  operator exclusive-nor  (or  XNOR).  The right  Mauthner cell  must \nsolve  the same problem with  a  redefinition  of right  displacement  as  positive.  The \nconditions for  this logic  gate are shown in figure  1A for  both Mauthner cells.  This \nanalysis  simplifies  our task  of understanding  the  computational role  of individual \nelements in  the system.  For example,  a  minimal network could  appear as  in figure \nlB. \nIn  this  model  PHP  units  perform  a  logical  sub-task of the  XNOR as  AND  gates. \nThis  model  requires  at  least  two  functional  classes  of PHP  units  on  each  side  of \nthe  brain.  These  PHP  units  will  be  activated  for  the  combinations  of pressure \nand  displacement  that indicate  a  sound  coming  from  the  wrong  direction  for  the \nMauthner cell on that side.  Both Mauthner cells are activated by sufficient changes \nin pressure in either direction,  high or low,  and will be gated by the PHP cells.  This \nminimal  model  emerged  from  explorations  of the  system  using  the  connectionist \nparadigm, and inspired  us  to extend our efforts  to a  more realistic  context. \n\n2  THE NETWORK \n\nWe  used  a  connectionist  model to explore  candidate solutions  to the left/right dis(cid:173)\ncrimination  problem  that include  the  populations  of neurons  known  to  exist  and \ninclude  a  distributed  input resembling  the sort  available from  the  hair cells  of the \ninner  ear.  We  were interested  in generating a  number of alternative solutions to be \nbetter  prepared to interpret  physiological  recordings  from live  goldfish,  and to look \nfor  variations of,  or alternatives  to,  the XNOR model. \n\n2.1  THE .ARCHITECTURE \n\nAs  shown  in figure  2,  there  are four  layers  in  the connectionist  model.  The input \nlayer  consists  of four  pools  of hair cell  units.  These  represent  the  sensory  neurons \nof the  inner  ear.  There  are  two  pools  on  each  side:  the  saccule  and  the  utricle. \nTreating only the horizontal  plane,  we  have ignored  the lagena in  this  model.  The \nsaccule  is  the  organ  of pressure  sensation  and  the  utricle  is  treated  as  the  organ \nof particle  motion.  Each  pool  contains  16  hair  cell  units  maximally  responsive  for \ndisplacements  of their sensory hairs in one particular  direction.  They are activated \nas  the  eosine  of the  difference  between  their  preferred  direction  and  the  stimulus \ndellection.  All  other units use  sigmoidal activation functions. \n\nThe next layer consists of units representing the auditory fibers  of the VIIIth nerve. \nEach pool receives  inputs from only one pool of hair cell  units, as  nerve fibers  have \nnot  been  seen  to innervate  more  than one endorgan.  There  are  10  units  per  fiber \npool. \n\nThe fiber units provide input to both the inhibitory PHP units, and to the Mauthner \nunits.  There  are  four  pools  of PHP  units,  two  on  each  side  of the  fish.  One  set \non  each  side  represents  the  collateral  PHP  eells,  and  the  other set  represents  the \ncommissural PHP cells  (Faber and Korn,  1978).  Both types receive inputs from the \nauditory fibers.  The collaterals  project only to the Mauthner cell  on the same side. \nThe  commissurals  project  to  both  Mauthner  cells.  There  are  five  units  per  PHP \npool. \n\n\f578 \n\nGuzik and Eaton \n\nThe  Mauthner cell  units  receive  inputs from  saecular  and utricular  fibers  on their \nsame side  only,  as  well  as inputs from a  single  collateral  PHP population and both \ncommissural  PHP  populations. \n\nLeft Saccule  Left Utricle  Right Utricle  Right  Saccule \n\nHair Cells \n\nAuditory  Nerve \nFiber Pools \n\nPHPs \n\nLeft Mauthner \n\nRight  Mautlll1er \n\nFigure  2 The architecture. \n\nWeights from  the PHP units are all constrained  to be negative,  while  all others are \nconstrained  to be positive.  The weights are implemented  using  the function  below, \npositive  or negative  depending  on the polarity of the weight. \nf(w)  =  1/2 (w  + In  cosh(w) + In 2) \n\nThe function asymptotes to zero for  negative values,  and to the identity function for \nvalues above 2.  This function  vastly improved learning compared with  the simpler, \nbut highly  nonlinear  exponential function  used  in earlier  versions  of the model. \n\n2.2  TRAINING \n\nWe used  a  total of 240 training examples.  We  began with  a set of 24  directions  for \nparticle  motion, evenly distributed around 360 degrees.  These each appeared twice, \nonce with increasing  pressure and once with decreasing  pressure,  making a  base set \nof 48  examples.  Pressure  was introduced  as a deflection  across saccular hair cells  of \neither 0 degrees for low  pressure,  or 180 degrees  for  high pressure.  These should be \nthought of as  reflecting  the expansion  or compression  of the swim  bladder.  Targets \nfor the Mauthner cells  were either 0 or 1 depending upon the conditions as described \nin the XNOR model,  in figure  lA. \n\n\fDirectional Hearing by the Mauthner System \n\n579 \n\nN ext by randomly perturbing the activations of the hair cells  for these 48  patterns, \nwe  generated  144  noisy  examples.  These were  randomly increased  or decreased  up \nto 10%.  An additional 48 examples were generated by dividing the hair cell  adivity \nby two to represent  sub-threshold  stimuli.  These last 48  targets were set  to zero. \n\nThe network was  trained in  batch mode with backpropagation to minimize  a cross(cid:173)\nentropy  error  measure,  using conjugate  gradient  search.  Unassisted  backpropaga(cid:173)\ntion was  unsuccessful  at finding solutions. \n\nFor the eight solutions discussed  here,  two parameters were  varied at the inputs.  In \nsome solutions the utride was stimulated with a vedor sum of the displacement and \nthe pressure components, or a \"mixed\" input.  In some solutions the hair cells in the \nutride are not distributed uniformly, but in a gaussian manner with the mean tuning \nof 45  degrees  to the  right  or left,  in  the  two  ears  respedively.  This  approximates \nthe actual distribution  of hair cells  in the goldfish  utride  (Platt,  1977). \n\n3  RESULTS \n\nAnalyzing the activation of the hidden units as a fundion of input pattern we found \nactivity consistent  with known physiology, nothing inconsistent  with our knowledge \nof the system, and some predidions to be evaluated during intracellular recordings \nfrom  PHP cells  and auditory afFerents. \n\nFirst,  many PHP cells  were found  exhibiting  a  logical fUndion,  which is  consistent \nwith  our  minimal  model  described  above.  These  tended  to  projed  only  to  one \nMauthner  cell  unit,  which  suggests  that  primarily  the  collateral  PHP  cells  will \ndemonstrate  logical  properties.  Most  logical  PHP  units  were  NAND  gates  with \nvery  large  weights  to one  Mauthner cell.  An example  is  a  unit  which  is  on for  all \nstimuli  except  those  having  displacements  anywhere  on  the  left  when  pressure  is \nhigh. \n\nSecond,  saccular fibers  tended  to be either sensitive  to high or low  pressure,  consis(cid:173)\ntent  with  recordings  of Furukawa and  Ishii  (1967).  In addition  there  were  a  dass \nwhich looked like  threshold  fibers,  highly  active for all supra-threshold stimuli,  and \ninactive  for  all  sub-threshold  stimuli.  There  were  some  fibers  with  no  obvious  se(cid:173)\nledivity, as well. \n\nThird,  utricular  fibers  often  demonstrate  sensitivity  for  displacements  exclusively \nfrom one side ofthe fish, consistent with our minimal model.  Right and left utricular \nfibers  have  not  yet  been demonstrated in the  real system. \n\nUtricular fibers  also demonstrated more coarsely tuned, less  interpretable receptive \nfields.  All  solutions  that  included  a  mixed  input  to the  utrieie,  for  example,  pro(cid:173)\nduced fibers  that seemed  to be \"not 180 degree\" ,or  \"not 0 degree\",  countering the \npressure  vedors.  We  interpret  these  fibers  as  doing  dean-up  given  the  absence  of \nnegative weights  at that layer. \n\nFourth,  sub-threshold  behavior  of units  is  not  always  consistent  with  their  supra(cid:173)\nthreshold  behavior.  At sub-threshold levels  of stimulation the adivity of units may \nnot refted  their computational role  in  the  behavior.  Thus, intracellular  recordings \nshould  explore  stimulus ranges  known to elicit  the behavior. \n\n\f580 \n\nGuzik and Eaton \n\nFifth,  Mauthner units usually receive  very strong inputs from pressure fibers.  This \nis  consistent  with  physiological  recordings  which  suggest  that  the  Mauthner  cells \nin  goldfish  are  more  sensitive  to  sound  pressure  than  displacement  (Canfield  and \nEaton,  1990). \n\nSixth,  Mauthner cells  always acquired rdatively  equal high  negative biases.  This is \nconsistent  with  the  known low input  resistance  of the  real  Mauthner  eells,  giving \nthem a  high threshold  (Faber and Korn,  1978). \n\nSeventh,  PHP cells  that maintain substantial bilateral connections  tend  to be ton(cid:173)\nically  active.  These contribute additional negative bias to the Mauthner cells.  The \nrelative sizes of the connections are often assymetric.  This suggests that the commis(cid:173)\nsural  PHP  cells  serve  primarily  to regulate  Mauthner threshold,  ensure  behavioral \nresponse only to intense stimuli, consistent with Faber and Korn (1978).  These cells \ncould  only contribute to a  partial solution of the XNOR problem. \n\nEighth,  all  solutions  consistently  used  logic  gate  PHP  units  for  only  50%  to  75% \nof the training  examples.  Probably distributed  solutions  relying on the  direct  con(cid:173)\nnections  of auditory  nerve  fibers  to  Mauthner cells  were  more  easily  learned,  and \nlogic  gate units only developed  to handle the unsolved  eases.  Cases  solved  without \nlogic  gate units  were  solved  by assymetric  projections to the  Mauthner cells  of one \npolarity of pressure  and one  class  of direction  fibers,  left  or right. \n\nCuriously,  most of these  eases involved  a  preferential projection from high pressure \nfibers  to the  Mauthner units,  along with  directional fibers  encoding  displacements \nfrom  each  Mauthner  unit's  positive  direction.  This  means  the  logic  gate  units \ntended  to  handle  the  low  pressure  eases.  This  may be  a  result  of the  presence  of \nthe assymetric  distributions  of utricular  hair cells  in 6 out of the 8 solutions. \n\n4  CONCLUSIONS \n\n\\Ve  have generated predictions for the behavior of neurons in the  Mauthner system \nunder  different  conditions  of acoustic  stimulation.  The  predictions  generated  with \nour connectionist  model are consistent  with our interpretation  of the phase model \nfor underwater sound localization in fishes as a logical operator.  The results are also \nconsistent  with  previously  described  properties  of the  Mauthner  system.  Though \nperhaps  based on the characteristics  more of the training  procedure,  our solutions \nsuggest  that  we  may find  a  mixed  solution  in  the  fish.  Direct  projections  to  the \nMauthner  cells  from  the  auditory  nerve  perhaps  handle  many  of the  commonly \nencountered  acoustic  threats.  The  results  of Blaxter  (1981)  support  the  idea that \nfish  do escape from stimuli regardless  of the polarity of the initial  pressure  change. \nWithout significant  nonlinear  processing  at the  Mauthner cell  itsdf,  or  more com(cid:173)\nplex  processing  in  the  auditory  fibers,  direct  connections  could  not  handle  all  of \nthese eases.  These possibilities  deserve  exploration. \n\nWe  propose  different  computational  roles  for  the  two  classes  of inhibitory  PHP \nneurons.  We  expect  only  unilaterally-projecting  PHP  cells  to  demonstrate  some \nlogical function  of pressure  and particle  motion.  We  believe  that some elements  of \nthe Mauthner system  must be found to demonstrate such minimal logical functions \nif the phase  modd is  an explanation for  left-right  discrimination  by  the  Mauthner \nsystem. \n\n\fDirectional Hearing by the Mauthner System \n\n581 \n\nWe  are currently preparing to deliver  controlled  acoustic  stimuli to goldfish during \nacute intracellular  recording  procedures from the  PHP  neurons,  the afferent  fibers \nand  the  Mauthner  cells.  Our  insights  from  this  model  will  greatly  assist  us  in \ndesigning the stimulus regimen, and in interpreting our experimental results.  Plans \nfor future computational work are of a dynamic model that will include the results of \nthese physiological investigations, as well as a more realistic  version of the Mauthner \ncell . \n\n.Acknowledgements \n\nWe are grateful for the technical assistance of members of the Boulder Connectionist \nResearch  Group,  especially  Don  Mathis for  help  in  debugging  and optimizing  the \noriginal  code.  We  thank  P.L.  Edds-Walton for  crucial  discussions.  This  work  was \nsupported by a grant to RCE from the National Institutes of Health (ROI NS22621). \n\nReferences \n\nBlader, J.H.S., J.A.B.  Gray,  and  E.J.  Denton  (1981)  Sound  and startle  responses \nin herring  shoals.  J.  Mar.  BioI.  Assoc.  UK,  61:  851-869 \nCanfield,  J.G. and  R.C. Eaton (1990)  Swimbladder  acoustic  pressure  transduction \nintiates  Mauthner-mediated escape.  Nature,  3~7:  760-762 \nEaton, R.C., J.G. Canfield and A.L. 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Abstr. \n\nPIaU,  C.  (1977)  Hair cell distribution  and orientation in goldfish otolith organs.  J. \nCompo  Neurol.,  172:  283-298 \nSchuijf,  A.  (1981)  Models  of acoustic localization.  In  Hearing  and Sound Commu(cid:173)\nnication in Fishes,  W.N. Tavolga, A.N. Popper and R.R. Fay (eds.), Springer,  New \nYork,.  pp.  267-310 \n\n\f", "award": [], "sourceid": 793, "authors": [{"given_name": "Audrey", "family_name": "Guzik", "institution": null}, {"given_name": "Robert", "family_name": "Eaton", "institution": null}]}