{"title": "Computer Modeling of Associative Learning", "book": "Advances in Neural Information Processing Systems", "page_first": 419, "page_last": 435, "abstract": null, "full_text": "COMPUTER  MODELING  OF  ASSOCIATIVE  LEARNING \n\nDANIEL  L.  ALKON' \n\nFRANCIS  QUEK2a \n\nTHOMAS  P.  VOGL2b \n\n419 \n\n1.  Laboratory  for  Cellular  and  Molecular \n\nNeurobiologYt  NINCDS t  NIH t  Bethesda t  MD  20892 \n2.  Environmental  Research  Institute  of  Michigan \n\na)  P.O.  Box  8G18 t  Ann  Arbor t  MI  48107 \nb)  1501  Wilson  Blvd. t  Suite  1105 t  Arlington t  VA  22209 \n\nINTRODUCTION \n\nlearning \n\nin \n\nThe  effort  is  des i gned \n\nMost  of  the  current  neural  networks  use  models  which  have \nonly  tenuous  connections  to  the  biological  neural  systems \non  which  they  purport  to  be  based t  and  negligible  input \nfrom  the  neuroscience/biophysics  communities.  This  paper \ndescribes  an  ongoing  effort  which  approaches  neural  net \nresearch  in  a  program  of  close  collaboration  of  neuros(cid:173)\nc i ent i sts  and  eng i neers. \nto \nelucidate  associative \nthe  marine  snail \nHermissenda  crassicornis t  in  which  Pavlovian  conditioning \nhas  been  observed.  Learning  has  been  isolated  in  the  four \nneuron  network  at  the  convergence  of  the  v i sua 1  and \nvestibular  pathways \nthis  animal t  and  biophysical \nchanges t  specific  to  learning t  have  been  observed  in  the \nmembrane  of  the  photoreceptor  B cell.  A basic  charging \ncapacitance  model  of  a  neuron  is  used  and  enhanced  with \nbiologically  plausible  mechanisms  that  are  necessary  to \nreplicate  the  effect  of  learning  at  the  cellular  level. \nThese  mechanisms  are  non-linear  and  are t  primarilYt \ninstances  of  second  order  control  systems  (e.g. t  fatigue t \nmodul at i on  of  membrane \ntime  dependent \nrebound)t  but  also  include  shunting  and  random  background \nfi ri ng. \nThe  output  of  the  model  of  the  four- neuron \nnetwork  di sp 1 ays  changes \nin  the  temporal  vari at i on  of \nmembrane  potential  similar  to  those  observed  in  electro(cid:173)\nphysiological  measurements. \n\nres i stance t \n\nin \n\n\f420 \n\nAlkon, Quek and Vogl \n\nNEUROPHYSIOLOGICAL  BACKGROUND \n\nfollowed \n\nthe \n\nto  ordered  pairs \n\nturbulence \ntime \n\nintervals, \n\nrepeated  exposures \n\nAlkon 1  showed  that  Hermissenda  crassicornis,  a  marine \nsnail,  is  capable  of  associating  two  stimuli  in  a fashion \nwhich  exhibits  all \nthe  characteristics  of  classical \nPavlovian  conditioning  (acquisition,  retention,  extinc(cid:173)\ntion,  and  savings)2. \nIn  these  experiments,  Hermissenda \nwere  trained  to  associate  a  visual  with  a  vestibular \nstimulus. \nIn  its  normal  environment,  Hermissenda  moves \ntoward  light;  in  turbulence,  the  animal  increases  the  area \nof  contact  of  its  foot  with  the  surface  on  which  it  is \nmoving,  reducing  its  forward  velocity.  Alkon  showed  that \nthe  snail  can  be  condi-tioned  to  associate  these  stimuli \nthrough \n(light \nfollowed  by  turbulence). \nWhen  the  snails  are  exposed  to  light  (the  unconditioned \nstimulus) \nby \n(the  conditioned \nstimulus)  after  varying \nsnails \ntransfer  to  the  light  their  unconditioned  response  to \nturbulence  (increased  area  of  foot  contact);  i.e.,  when \npresented  with  light  alone,  they  respond  with  an  increased \narea  of  foot  contact.  The  effect  of  such  training  lasts \nfor  several  weeks. \nIt was  further  shown  that  the  learning \nwas  maximized  when  rotation  followed  light  by  a  fixed \ni nterva 1  of  about  one  second,  and  that  such  1 earn i ng \nexhibits all  the  characteristics of classical  conditioning \nobserved  in  higher  animals. \nThe  relevant  neural  interconnections  of  Hermissenda  have \nbeen  mapped  by  Alkon,  and  learning  has  been  isolated  in \nthe  four  neuron  sub-network  (Figure  1)  at  the  con-vergence \nof  the  visual  and  vestibular  pathways  of  this  animal. \nLight  generates  signals  in  the  B cells while  turbulence  is \ntransduced  into  signals  by  the  statocyst's  hair cells,  the \nThe  optic  ganglion  cell \nanimal's  vestibular  organs. \nmedi ates  the  interconnect ions  between  the \ntwo  sensory \npathways. \nThe  effects  of  learning  also  h\\ve  been  observed  at  the \ncellular  level.  Alkon  et  al.  have  shown \nphys i ca 1  changes  assoc i ated  wi th  1 earni ng  occur  in  the \nphoto-receptor  B  cell  of  Hermissenda.  The  signals  in \nthe  neurons \nion \n\nform  of  voltage  dependent \n\nthat  bio(cid:173)\n\ntake \n\nthe \n\n\fComputer Modeling of Associative Learning \n\n421 \n\nOptic \ngon<;llion \n\n, \n\nI \nI \nI \n\\ \n\nc \n\nAll \n\nindicate \n\nfilled  endings \n\nFigure  1.  The  four  neuron  network  at  the  convergence  of \nthe  visual  and  vestibular  pathways  of  Hermissenda  cras(cid:173)\ninhibitory \nsicornis. \nsynapses;  all  open  endings  indicate  excitatory  synapses. \n(a)  Convergence  of  synaptic  inhibition  from  the  photo(cid:173)\nreceptor  B cell  and  caudal  ha i r  cell s  unto  the  opt i c \nganglion  cell. \n(b)  Pos it i ve  synapt i c  feedback  onto  the  type  B photo(cid:173)\nreceptor:  1,  direct  synaptic  excitation;  2, \nindirect \nexcitation  -- the  ganglion  excites  the  cephalic  hair  cell \nthat  inhibits  the  caudal  hair  cell,  and  thus  disinhibits \nthe  type  B cell;  3,  indirect  excitation  -- the  ganglion \ninhibits  the  caudal  hair  cell  and  thus  disinhibits  the \ntype  B cell. \n(c)  Intra- and  intersensory  inhibition.  The  cephalic  and \ncaudal  hair  cells  are  mutually  inhibitory.  The  B cell \ninhibits  mainly  the  cephalic  hair  cell. \nFrom:  Tabata,  M.,  and  Alkon,  D.  L. \nPositive  synaptic \nfeedback  in  visual  system  of nudibranch  mollusk  Hermissen(cid:173)\nJ.  of  Neurophysiology  48:  174-191 \nda  Crassicornis. \n(1982). \n\n\f422 \n\nAlkon, Quek and VogI \n\nis  to  model \n\ncurrents,  and  learning  is  reflected  in  biophysical  changes \nin  the  membrane  of  the  B  cell. \nThe  effects  of  ion \ncurrents  can  be  observed  in  the  form  of  time  variations  in \nmembrane  potential  recorded  by  means  of  microelectrodes. \nIt  is  the  variation  in  membrane  potential  resulting  from \nassociative  learning  that  is  the  focus  of  this  research. \nOur  goal \nthose  properties  of  biological \nneurons  suffi c i ent  (and  necessary)  to  demonstrate  assoc i a(cid:173)\ntive  learning  at  the  neural  network  level. \nIn  order  to \nunderstand  the  effect  and  necessity  of  each  component  of \nthe  model,  a minimalist  approach  was  adopted.  Nothing  was \nadded  to  the  model  which  was  not  necessary  to  produce  a \nrequired  effect,  and  then  only  when  neurophysiologists, \nbiophysicists,  electrical  engineers,  and  computer  scien(cid:173)\ntists  agreed  that  the  addition  was  reasonable  from  the \nperspective  of  their  disciplines. \n\nMETHOD \nthe  model  is  described \nFollowing  Kuffler  and  Nicholas4 , \nin  terms  of  circuit  elements. \nIt  must  be  emphasized \nhowever,  that  this  is  simply  a  recognition  of  the  fact \nthat  the  chemical  and  physical  processes  occurring  in  the \nneuron  can  be  described  by  (partial)  differential  equa(cid:173)\ntions,  as  can  electronic circuits.  The  equivalent  circuit \nof  the  charging  and  discharging  of  the  neuron \nmembrane  is  shown  in  Figure  2.  The  model  was  constructed \nusing  the  P3  network  simulation  shell  developed  by  Zipser \nand  Rabi n5 \u2022 \nstri p-chart  capabil i ty  was \nThe \nparticularly  useful \ninterdisciplinary \ninteractions.  Figure  3  shows  the  response  of  the  basic \nmodel  of  the  neuron  as  the  frequency  of  input  pulses  is \nvaried. \nOur  aim,  however,  is  not  to  model  an  individual  neuron. \nRather,  we  consistently  focus  on  properties  of  the  neural \nnetwork  that  are  necessary  and  sufficient  to  demonstrate \nassociative  learning.  Examination  of  the  behavior  of \nbiological  neurons  reveals  additional  common  properties \nthat  express \nthe \nfunct i on  of  the  i ndi vi dua 1  neuron. \nThese  propert i es \ninc 1 ude  background  fi ri ng,  second  order  cont ro 1 s,  and \nshunting.  Their  inclusion  in  the  model  is  necessary  for \nthe  simulation  of  associative  learning,  and  their  im(cid:173)\nplementation  is  described  below. \n\nthemselves  differently  depending  on \n\nP3 \nin  facilitating \n\n\fComputer Modeling of Associative Learning \n\n423 \n\nINPUT CIRCUITRY \n\n~ .-\n\nR, \"\"\"'.  ~ S, ~ --.---i ______ - -\n\nu--------' ...  ~ - -\n\u2022 \n\u2022  S \n\nR \n\n~ \n\nc \n\nmembrane \npotential \n\nRs, \n\nRS2  Rsk \n\n\u2022 \nS,.  Sk \n\n: closes  when  there  are  input  EPSPs  to  the \nthe  cell.  otherwise.  open. \n\n\u2022  \u2022 Sd~y  : closes  when  there  is  no  input  ESPSs  to  the \n\nthe  cell.  otherwise.  open. \n\ntime  constant  of  the  capacl tor  C  When \n\nFigure  2.  Circuit  model  of  the  basic  neuron.  The  lines \nfrom  the  1 eft  are  the  inputs  to  the  neuron  from  its \ndendritic  connections -to  presynaptic  neurons.  Rsk's  are \nthe  resistances  that determine  the  magnitude  of  t~e effect \n(voltage)  of the  pulses  from  presynaptic  neurons.  The  gap \nindicated  by  open  circles  is  a high  impedance  coupler.  R1 \nthrough  R~,  together  with  C,  determine  the  rise  time  for \nthe  kth  lnput  of  the  potential  across  the  capacitor  C, \nwh i ch  represents  the  membrane. \nRdecay  cont ro 1 s  the  dis(cid:173)\nthe \ncharge \nmembrane  potential  (across  C)  exceeds  threshold  potential, \nthe  neuron  fi res  a  pul se  into  its  axon  (to  all  output \nconnections)  and \nthe \n\"discharge  quantum\"  (see  text). \nBACKGROUND  FIRING  IN  ALL  NEURONS \nBackground  fi ri ng,  i. e.,  spontaneous  fi ri ng  by  neurons \nwi thout  any  input  pul ses  from  other  neurons,  has  been \nobserved  in  all  neurons.  The  fundamental  importance  of \nbackground  firing  is  exemplified  by  the  fact  that  in  the \nfour  neuron  network  under  study,  the  optic  ganglion  does \n\nthe  charge  on  C  is  reduced  by \n\n\f424 \n\nAlkon, Quek and Vogl \n\nThe \n\nFigure  3.  Response  of  the  basic  model  of  a  single  neuron \nto  a  variety  of  inputs.  The  four  horizontal  strips,  from \ntop  to  bottom,  show:  1)  the  input  stream;  2)  the  resulting \nmembrane  potential;  3) \nthe  resulting  stream  of  output \npulses;  and  4)  the  composite  output  of  pulses  superimposed \non  the  membrane  potent i a 1,  ernul at i ng  the  correspond i ng \nelectrophysiological  measurement. \nfour  vertical \nsections,  from  left  to  right,  indicate:  a)  an  extended \ninput,  simulating  exposure  of  the  B cell  to  light;  b)  a \npresynaptic  neuron  firing  at  maximum  frequency;  c)  a \npresynaptic  neuron  firing  at an  intermediate  frequency;  d) \na presynaptic  neuron  firing  at  a frequency  insufficient to \ncause  the  neuron  to  fire \u00b7but  sufficient  to  maintain  the \nneuron  at  a  membrane  potential \nfiring \nthreshold. \nBACKGROUND  FIRING  IN  ALL  NEURONS  (Continued) \nnot  have  any  synapses  that  excite  it  (all  its  inputs  are \ninhibitory).  However,  the  optic  ganglion  provides  the \nonly  two  excitatory synapses  in  the  entire network  (one  on \nthe  photoreceptor  B cell  and  the  other  on  the  cephalad \nstatocyst  hair  cell).  Hence,  without  back-ground  firing, \ni.e.,  when \nthere  is  no  external  stimuli  of  the  neurons, \nall  activity  in  the  network  would  cease. \nFurther,  without  background  firing,  any  stimulus  to  either \nthe  vestibular  or  the  visual  receptors  will  completely \nswamp  the  response  of  the  network. \n\njust  below \n\n\fComputer Modeling of Associative Learning \n\n425 \n\nBackground  firing  is  incorporated  in  our  model  by  applying \nrandom  pul ses  to  a  'vi rtua l'  exci tatory  synapse. \nBy \naltering  the  mean  frequency  of  the  random  pulses,  various \nlevels  of  'internal'  homeostatic  neuronal  activity  can  be \nsimulated. \nPhysiologically,  this  pulse  source  yields \nresults  similar  to  an  ion  pump  or  other  energy  source, \ne.g.,  cAMP,  in  the  biological  system. \nSECOND  ORDER  CONTROL  IN  NEURONS \nSecond  order  controls,  i.e.,  the  modulation  of  cellular \nparameters  as \nthe  resul t  of  the  past  history  of  the \nneuron,  appear  in  all  biological  neurons  and  play  an \nessential  role  in  their  behavior.  The  ability of the  cell \nto  integrate  its  internal  parameters  (membrane  potential \nin  particular)  over  time  turns  out  to  be  vital  not  only  in \nunderstanding  neural  behavior  but,  more  specifically,  in \nproviding  the  mechanisms  that  permit  temporally  specific \nIn  the  course  of  this  investiga(cid:173)\nassociative  learning. \ntion,  a  number  of  different  second  order  control \nmechanisms,  essential  to  the  proper  performance  of  the \nmodel,  were  elucidated.  These  mechanisms  share  a  depen(cid:173)\ndence  on  the  time  integral  of  the  difference  between  the \ninstantaneous  membrane  potential \nreference \npotential. \nThe  part i cul ar  second  order  cont ro 1  mechan isms \nporated  into  the  model  are:  1)  Overshoot  in  the  1 i ght \nresponse  of  the  photoreceptor  B cell;  2)  maintenance  of \na  post-stimulus  state \nto \nprolonged  stimulation;  3)  modulation  of  the  discharge \nresistance  of  the  B cell;  4)  Fatigue  in  the  statocysts \nand  the  optical  ganglion;  and  5)  time  dependent  rebound \nin  the  opt i cal  gangl ion. \nIn  addi t i on  to  these  second \norder  control  effects,  the  model  required  the  inclusion \nof  the  observed  shunting  of  competing  inputs  to  the  B cell \nduring  light exposure.  The  consequence  of the  interaction \nof these  mechanisms  with  the  basic  model  of  the  neurons  in \nthe  four  neuron  network \nis  the  natural  emergence  of \ntemporally  specific  associative  learning. \nOVERSHOOT  IN  THE  LIGHT  RESPONSE  OF  THE  PHOTORECEPTOR  B \nCELL \n\nthe  B  cell  subsequent \n\ni ncor(cid:173)\n\nand \n\nsome \n\nin \n\nUnder  strong  light  exposure,  the  membrane  potential  of  an \nisolated  photoreceptor  B  cell  experiences  an \ninitial \nthen  settles  at  a  rapidly  firing  level \n'overshoot'  and \n\n\f426 \n\nAlkon, Quek and VogI \n\nfar  above  the  usual  firing  potential  of  the  neuron  (see \nFigure  4a). \n(We  refer  to  the  elevated  membrane  potential \nof  the  B cell  during  illumination  as  the  \"active  firing \nmembrane  potential\").  The  initial  overshoot  (and  slight \nringing)  observed  in  the  potential  of  the  biological  B \ncell  (F i gure  4a)  is  the  signature  of  an  integral  second \norder  control  system  at  work.  This  control  was  realized \nin  the  model  by  altering  the  quantity  of  charge  removed \nfrom  the  cell  (the  discharge  quantum)  each  time  the  cell \nfires. \n(The  biological  cell  loses  charge  whenever  it \nfi res  and  the  quant i ty  of  charge  lost  vari es  wi th  the \nmembrane  potential.)  The  discharge  quantum  is  modulated \nby  the  definite  integral  of  the  difference  between  the \nmembrane  potential  and  the  active  firing  membrane  poten(cid:173)\ntial  as  follows: \n\nQdiseharge(t)  =  K  X h' {Potmembrane(t)  - Potaetive  ffring(t)}dt \n\no \n\nto  decrease  (i. e. , \n\nAs  the  membrane  potential  rises  above  the  active  firing \nmembrane  potential,  the  value  of the  integral  rises.  The \nmagnitude  of  the  discharge  quantum  rises  with  the  in(cid:173)\nTh is  increased  discharge  retards  the  membrane \ntegra 1 . \ndepolarization,  until  at  some  point,  the  size  of  the \ndischarge  quantum  outstrips  the  charging  effect  of  light \non  the  membrane  potential,  and  the  potential  falls.  As \nthe  membrane  potent i a 1  fall s  below  the  act i ve  fi ri ng \nmembrane  potential,  the  magnitude  of the discharge  quantum \nbegi ns \nintegral \nfalls).  This,  in  turn,  causes  the  membrane  potential  to \nrise  when  the  charging  owing  to  light  input  once  again \novercomes  the  declining  discharge  quantum. \nThis  process  repeats  with  each  subsequent  swing  in  the \nmembrane  potential  becoming  smaller  until  steady  state  is \nreached  at  the  active  fi ri ng  membrane  potent i a 1 .  The \nresponse  of the  model  to  simulated  light  exposure  is  shown \nin  Figure  4b.  Note  that  only  a  single  overshoot  is \nobvious  and  that  steady  state  is  rapidly  reached. \nMAINTAINING  THE  POST-STIMULUS  STATE  IN  THE  B CELL \n\nthe  value  of  the \n\nlight, \n\nDuring  exposure \nis  strongly \ndepolarized,  and \nis  maintained \nsubstantially  above  the  firing  threshold  potential.  When \nthe  light  stimulus  is  removed,  one  would  expect  the  cell \nto  fire  at  its  maximum  rate  so  as  to  bring  its  membrane \n\nto \nthe  B  cell \nthe  membrane  potential \n\n\fComputer Modeling of Associative Learning \n\n427 \n\neel) \n\nLig!!.!J \n\nI \n\nto  2.9  1  pixels~tick \n\nFigure  4.  Response  of  the  B cell  and  the  model  to  a  light \npulse. \n(a).  Electrophysiological  recording  of  the  response  of \nthe  photoreceptor  B cell  to  1 i ght.  Note  the  in it i a 1 \novershoot  and  one  cycle  of oscillation  before  the  membrane \npotential  settles at  the  \"active  firing  potential.\"  From: \nAlkon t  D.L.  Memory  Traces \nthe  Brain. \nCambridge \nUniversity  Press t  London  (1987)t  p.S8. \n(b)  Response  of  the  model  to  a  light  pulse. \n\nin \n\n\f428 \n\nAlkon, Quek and Vogl \n\npotential  below  the  firing  threshold  (by  releasing  a \ndischarge  quantum  w\u00b7ith  each  output  pulse).  This  does  not \nhappen  in  Herm;ssenda;  there  is,  however,  a  change  in \nthe  amount  of  charge  released  with  each  output  pulse  when \nthe  cell  is  highly  depolarized. \nNote  that the di scharge  quantum  is modul ated  post-exposure \nin  a manner  analogous  to  that occurring  during  exposure  as \ndiscussed  above:  It  is  modulated  by  the  magnitude  of  the \nmembrane  potential  above  the  firing  threshold.  The  result \nof  this modulation  is  that  the  more  positive  the  membrane \npotential,  the  smaller  the  discharge  quantum,  (subject  to \na  non-negative  minimum  value).  The  average  value  of  the \ninterval  between  pulses  is  also  modulated  by  the magnitude \nof  the  discharge  quantum.  This  modulation  persists  until \nthe  membrane  potential  returns  to  the  fi ri ng  threshold \nafter  cessation  of  light  exposure. \nThis  mechanism  is  particular  to  the  B cell.  Upon  cessa(cid:173)\ntion  of  vestibular  stimulation,  hair  cells  fire  rapidly \nunt il  thei r  membrane  potent i a 1 s  are  below \nthe  fi ri ng \nthreshold,  just  as  the  basic  model  predicts. \nMODULATION  OF  DISCHARGE  RESISTANCE  IN  THE  B CELL \nThe  duration  of  the  post-stimulus  membrane  potential  is \ndetermined  by  the  magnitude  of  the  discharge  resistance \nIn  the  model,  the  discharge  resistance \nof  the  B cell. \nchanges  exponentially \ntoward  a  predetermined  maximum \nvalue,  R~x' when  the  membrane  potential  exceeds  the  firing \nthreshola.  Roose  is  the  baseline  value.  That  is, \n\nRdisch(t-to)  =  Rmax  - {Rmax  - RdiSCh(tO)}exp{(t-to)/rrise} \nwhen  the  membrane  potential  is above  the  firing  threshold, \nand \n\nRdisch(t-to)  =  Roose- {Rbase- Rdisch(to)}exp{(t-to)/1'decay} \nwhen  the  membrane  potential  is  below  the  firing  threshold. \n\nFATIGUE  IN  STATOCYST  HAIR  CELLS \nIn  Hermissenda,  caudal  cell  activity  actually  decreases \nimmediately  after  it  has  fired  strongly,  rather  than \nreturning  to  its  normal  background  level  of  firing.  This \neffect,  which  results  from \ntendency  of  membrane \npotential \nto  \"fatigue\"  toward  its  resting  potential,  is \n\nthe \n\n\fComputer Modeling of Associative Learning \n\n429 \n\nis  above \n\nthe \n\nthe  optical  ganglion  undergoes  hyper(cid:173)\n\nincorporated  into  our  model  of  the  statocyst  hair  cells \nthe  second  order  control  mechanism  previously \nusing \ndescribed. \nI.e.,  when  the  membrane  potential  of  a  hair \ncell  is  above  the  firing  threshold  (e.g.,  during  vesti(cid:173)\nbular  stimulation),  the  shunting  resistance  of  the  cell \ndecays  exponentially  with  time  toward  zero  as  long  as  the \nhair  cell  membrane  potential \nfiring \nthreshold.  This  resistance  is allowed  to  recover  exponen(cid:173)\ntially  to  its  usual  value  when  the  membrane  potential \nfalls  below  the  firing  threshold. \nFATIGUE  OF  THE  OPTICAL  GANGLION  CELL  DURING  HYPER(cid:173)\nPOLARIZATION \nIn  Hermissenda \npolarization  at  the  beginning  of  the  light  pulse  and/or \nvestibular  stimulus.  Contrary  to  what  one  might  expect, \nit  then  recovers  and  is  close  to  the  firing  threshold  by \nthe  time  the  stimuli  cease.  This  effect  is  incorporated \ninto  the  model  by  fatigue  induced  by  hyperpolarization. \nAs  above, \nthis  fatigue  is  implemented  by  allowing  the \nshunt i ng  res i stance \nto  decrease \nexponentially  toward  a  minimum  value,  while  the  membrane \npotential  is  below  the  firing  threshold  by  a  prespecified \namount.  The  value  of  the  minimum  shunting  resistance  is \nmodulated  by  the magnitude  of hyperpolarization  (potential \ndifference  between  the  membrane  potential  and  the  firing \nthreshold). \nrecovers \nexponentially  from  its  hyperpolarized  value,  once  the \nmembrane  potential  returns  to  its  firing  threshold  as  a \nresult  of  background  firing  input. \nThe  effect  of  this decrease  is  that  the  ganglion  cell  will \ntemporarily  remain  relatively  insensitive  to  the  enhanced \npost-stimulus  firing  of  the  B cell  until  the  shunting \nresistance  recovers.  Once  the  membrane  potential  of  the \nganglion  cell  recovers,  the  pulses  from  the  ganglion  cell \nwill  excite  the  B  cell  and  maintain  its  prolongation \neffect. \nThe  modulation  of  the  minimuM  shunting  resistance  by  the \nmagnitude  Qf  hyperpolarization \nthe  first \nstimulus  pairing  dependent  component  in  the  post-stimulus \nbehavi or  of \nthe  degree  of \nstimulus \nhyperpolarization \nconditions. \n\nis  higher  under  paired \n\nthe  B  cell  because \n\nin  the  gangl ion  cell \n\nThe \n\nshunting \n\nresistance \n\n(See  Figure  1.) \n\nintroduces \n\n\f430 \n\nAlkon, Quek and YogI \n\nin \n\nto \n\nthe  cell \n\nce 11 \n(lSI). \n\nFurthermore  rebound \n\nTIME  DEPENDENT  REBOUND  IN  THE  OPTICAL  GANGLION  CELL \nExperimental  evidence  with  Hermissenda  indicates  that  the \nrebound  of  the  optical  ganglion  is  much  stronger  than  is \npossible  if  the  usual  background  activity  were  the  sole \ncause  of  this  rebound. \nthe \ngang1 ion \nis  stronger  when  t~e  1 i ght  exposure \nprecedes  vestibular stimulus  by  the optimal  inter-stimulus \ninterval \nthe  ganglion  cell  has  no \nSince \nthe  increased  rebound  must \nexc i tatory  input  synapses, \nresult \nfrom  a  mechanism \ninternal \nthat \nheightens  its  background  activity  during  pairing  at  the \noptimal  lSI.  The  mechanism  must  be  time  dependent  and \nmust  be  able  to  distinguish  between  the  inhibitory  signal \nwhich  comes  from  the  B cell  and  that  which  comes  from  the \ncaudal  hair  cell.  To  achieve  this  result,  two  mechanisms \nmust  interact. \nThe  first  mechanism  enhances  the  inhibitory  effect  of  the \ncaudal  hair  cellon  the  gangl ion  cell.  This  \"caudal \ninhibition  enhancer\",  elE,  is  triggered  by  pu1 ses  from \nthe  B  cell. \nThe  elE  has  the  property  that  it  rises \nexponentially  toward  1.0  when  a  pulse  is  seen  at  the \nsynapse  from  the  B cell  and  decays  toward  zero  when  no \nsuch  pulses  are  received. \nThe  second  mechanism  provides  an  increase  in  the  back(cid:173)\nground  act i vi ty  of  the  opt i c  gang1 i on  when  the  cell  is \nhyperpolarized;  it is  a fatigue  effect  at  the  synapse  from \nthe  caudal  hair cell.  This  synapse  specific  fatigue  (SSF) \nrises \ntoward  1.0  as  any  of  the  inhibitory  synapses  onto \nthe  ganglion  receive  a  pulse,  and  decays  toward  zero  when \nthere  is  no  incoming  inhibitory  pulse.  Note  that  this \nsecond  order  control  causes  fatigue  at  the  synapse  between \nthe  caudal  hair  cell  and \nthe  ganglion  whenever  any \ninhibitory  pulse  is  incident  on  the  ganglion. \nControl  of  the  lSI  resides  in  the  interaction  of  these \ntwo  mechanisms.  The  efficacy  of  an  inhibitory  pulse  from \nthe  caudal  cell  upon  the  gang1 ion  ce 11 \nis  determi ned  by \nthe  product  of  elE  and  (1  - SSF),  the  \"lSI  convo1ver.\" \nWith \nlight  exposure  alone  or  when  caudal  stimulation \nfollows  light,  the  elE  rises  toward  1.0  along  with  the \nSSF. \nInitially,  (1  - SSF)  is  close  to  1.0  and  the  elE \nterm  dominates  the  convo1ver  function.  As  elE  approaches \n1.0,  the  (1  - SSF)  term  brings  the  convolver  toward  o.  At \nsome  intermediate  time,  the  lSI  convo1ver  is  at  a maximum. \n\n\fComputer Modeling of Associative Learning \n\n431 \n\ninteraction \n\nis \n\nthereby  bringing  about \n\nWhen  vestibular  stimulus  precedes  light  exposure,  the  SSF \nrises  at  the  start  of  the  vestibular  stimulus  while  the \nelE  remains  at  o.  When \nlight  exposure  then  begins,  the \nelE  rises,  but  by  then  (1  - SSF)  is  approaching  zero,  and \nthe  convolver  does  not  reach  any  significant  value. \nThe  result  of  this \nthat  when  caudal \nst~mulation follows  light  by  the  optimal  lSI,  the  inhibi(cid:173)\ntion  of  the  ganglion  will  be  maximal. \nThis  causes \nhe i g htened  background  act i v i ty  in  the  gang 1 ion. \n. Upon \ncessation  of  stimulus,  the  heightened  background  activity \nwill  express  itself  by  rapidly  depolarizing  the  ganglion \nmembrane, \nthe  desired  rebound \nfiring. \nSHUNTING  OF  THE  PHOTORECEPTOR  B CELL  DURING  EXPOSURE  TO \nLIGHT \nIn  experiments  in  which  light  and  vestibular  stimulus  are \npaired,  both  the  B cell  and  the  caudal  hair  statocyst  cell \nfire  strongly.  There  is  an  inhibitory  synapse  from  the \nhair  cell  to  the  B cell  (see  Figure  1).  Without  shunting, \nthe  hair  cell  output  pulses  interfere  with  the  effect  of \n1 ight  on  the  B cell  and  prevent  it  from  arriving  at  a \nlevel  of  depolarization  necessary  for  learning.  This  is \ncontrary \nthe \nresponse  of  the  B ~ell  to  light  (during  the  light  pulse) \nis constant  whether  or  not  vestibular stimulus  is present. \nBiological  experiments  have  determlned  that while  light  is \non,  the  B cell  shunting  resistance  is  very  low  making  the \ncell  insensitive  to  incoming  pulses. \nthe  current  performance  of  the \nFigures  5-8  summari.ze \nFigures  6,  7,  and  8  present  the  response  to  a \nmodel. \nlight pulse  of  the  untrained,  sham  trained  (unpaired  light \nand  turbulence),  and  trained  (paired  light and  turbulence) \nmodel  of  the  four  neuron  network. \nDISCUSSION \n\nto  experimental  data  which \n\nshows \n\nthat \n\nis  more  complex \n\nThe  model  developed  here \nthose \ngenerally  employed  in  neural  network  research  because  the \nmechanisms  invoked  are  primarily  second  order  controls. \nFurthermore,  while  we  operated  under  a paradigm  of minimal \ncommitment  (no  new  features  unless  needed),  the  functional \nrequi rements  of  network  demanded \nthat  di fferent i at i ng \nfeatures  be  added  to  the  cells.  The  model  reproduces  the \n\nthan \n\n\f432 \n\nAlkon, Quek and Vogl \n\nin  Hermissenda  that \nelectrophysio10gica1  measure-ments \nare  indicative  of  associative  learning.  These  results \ncall  into question  the  notion  that  linear and  quasi-linear \nsumming  elements  ar~ capable  of  emulating  neural  activity \nand  the  learning  inherent  in  neural  systems. \nThis  preliminary  modeling  effort  has  already  resulted  in \na  greater  understandi.ng  of  bi 01 ogi cal  systems  by  1) \nmodeling  experiments  which  cannot  be  performed  in  vivo, \n2)  testing  theoretical  constructs  on  the  model,  and  3) \ndeveloping  hypotheses  and  proposing  neurophysiological \nexperiments.  The  effort  has  also  significantly  assisted \nin \ndeve 1 opment  of  neural  network  a 1 gori thms  by \nuncoveri ng  the  necessary  and  suffi ci ent  components  for \nlearning  at  the  neurophysiological  level. \nAcknowledgements \nThe  authors  wish  to  acknowledge  the  contribution  of  Peter \nTchoryk,  Jr.  for  assistance  in  performing  the  simulation \nexperiments  and  Kim  T.  Blackwell \nfruitful \ndiscussions  of the  work  and  the  manuscript.  This  work  was \nsupported  in  part  by  ONR  contract  NOOOI4-88-K-0659. \nReferences \n\nfor  many \n\nthe \n\nin \n\n1  A1kon,  D.L.  Memory  Traces \nthe  Brain,  Cambridge \nUniversity  Press,  London,. 1987  and  publications  referenced \ntherein. \n2  A1kon,  D.L.  Learning  in  a  Marine  Snail.  Scientific \nAmerican,  249:  70-84  (1983). \n3  A1kon,  D.L.,  Sakakibara,  M.,  Forman,  M.,  Harrigan,  R., \nLederhend1er,  J.,  and  Farley,  J. \ntwo \nretention  of \nvoltage-dependent  K+  currents  mediates \nlearning  association. \nand  Neural  Bio1. \n44:278-300  (1985). \n\nReduction  of \n\nBehavioral \n\n4  Kuff1er,  S.W.,  and  Nicholas,  J.G.  From  Neural  to  Brain: \nA  Cell u1 ar  Approach \nthe  Funct i on  of  the  Nervous \nSystem.  Seinauer  Assoc.,  Pub1.,  Sunderland,  MA  (1986). \n\nthe \n\n\fComputer Modeling of Associative Learning \n\n433 \n\nRANDOM \n\n.fRA, ......... \n\nFigure  5.  Prolongation  of  B cell  post-stimulus  membrane \ndepolarization  consequent  to  learning  (exposure  to  paired \nstimuli). \nFrom:  West,  A.  Barnes,  E.,  Alkon,  D.L.  Primary  changes \nof  voltage  responses  during  retention  of  associative \nlearning.  J.  of Neurophysiol.  48:1243-1255  (1982).  Note \nthe  increase  ins i ze  of  the  shaded  area  wh i ch  is  the \neffect  of  learning. \n\nFigure  6.  Naive  model:  response  of  untrained  (\"control\" \nin  Fig.  5)  model  to  light. \n\n\f434 \n\nAlkon, Quek and VogI \n\nFigure  7.  Sham \nfollowing  presentation  of  26  randomly  alternating  (\"(cid:173)\nunpaired\"  in  Fig.  5)  light  and  turbulence  inputs. \n\ntraining:  response  of  model \n\nto  light \n\nReferences  (Continued) \n\nP3:  A  Parallel  Network \nSZipser,  D.~  and  Rabin~  D. \nIn  Parallel  Distributed  Processing, \nSimulating  System. \nVol.  I.~  Chapter  13.  Rumelhart~  McClelland,  and  the  PDP \nGroup~  Eds.  MIT  Press  (1986). \n6Buhmann~  J.~  and  Schulten~  K. \nInfluence  of  Noise  on  the \nFunction  of  a  \"Physiological\"  Neural  Network.  Biological \nCybernetics  56:313-328  (1987). \n\n\fComputer Modeling of Associative Learning \n\n435 \n\nFigure  8.  Trained  network:  response  of  network  to  light \nfollowing  presentation  of  13  light  and  turbulence  input \nat  optimum  lSI.  The  top  trace  of  this  figure  is  the  B \nce 11  response  to  1 i ght  alone.  Note  that  an  increased \nfiring  frequency  and  active  membrane  potential  is  main(cid:173)\ntained  after  the  cessation  of  light,  compared  to  Figures \n6  and  7. \nThis  is  analogous  to  what  may  be  seen  in \nHermissenda,  Figure  5.  Note  also  that  the  optic  ganglion \nand  the  cephalad  hair  cell  (trace  2 and  3 of  this  figure) \nshow  a  decreased  post-stimulus  firing  rate  compared  with \nthat  of  Figures  6  and  7. \n\n\f", "award": [], "sourceid": 126, "authors": [{"given_name": "Daniel", "family_name": "Alkon", "institution": null}, {"given_name": "Francis", "family_name": "Quek", "institution": null}, {"given_name": "Thomas", "family_name": "Vogl", "institution": null}]}