{"title": "Locomotion in a Lower Vertebrate: Studies of the Cellular Basis of Rhythmogenesis and Oscillator Coupling", "book": "Advances in Neural Information Processing Systems", "page_first": 101, "page_last": 108, "abstract": null, "full_text": "Locomotion  in a  Lower Vertebrate: \n\nStudies of the Cellular Basis  of Rhythmogenesis \n\nand  Oscillator Coupling \n\nJames  T.  Buchanan \nDepartment  of Biology \nMarquette  University \nMilwaukee,  WI 53233 \n\nAbstract \n\nTo test  whether  the  known  connectivies  of neurons  in  the lamprey spinal \ncord are sufficient to account for locomotor rhythmogenesis, a  CCconnection(cid:173)\nist\"  neural network simulation was done using identical cells connected ac(cid:173)\ncording to experimentally established  patterns.  It was  demonstrated  that \nthe  network  oscillates  in  a  stable  manner  with  the  same  phase  relation(cid:173)\nships among the neurons as observed  in the lamprey.  The model was  then \nused  to  explore  coupling  between  identical  <?scillators.  It was  concluded \nthat the neurons can have a  dual role as  rhythm generators and as coordi(cid:173)\nnators  between  oscillators to produce  the  phase relations observed  among \nsegmental oscillators during swimming. \n\n1 \n\nINTRODUCTION \n\nOne  approach  to  analyzing  neurobiological  systems  is  to  use  simpler  preparations \nthat  are  amenable  to  techniques  which  can  investigate  the  cellular,  synaptic,  and \nnetwork  levels  of organization  involved  in  the  generation  of  behavior.  This  ap(cid:173)\nproach  has yielded significant progress  in  the analysis of rhythm  pattern generat.ors \nin  several  invertebrate  preparations  (e .g.,  the  stomatogastric  ganglion  of lobster, \nSelverston  et  al.,  1983).  We  have  been  carrying  out  similar  types  of studies  of lo(cid:173)\ncomotor  rhythm  generation  in  a  vertebrate  preparation,  the  lamprey  spinal  cord, \nwhich offers many of the same technical advantages of invertebrate nervous systems. \nTo aid our understanding of how  identified lamprey interneurons  might participate \n101 \n\n\f102 \n\nBuchanan \n\nin  rhythmogenesis  and  in  the  coupling of oscillators,  we  have  used  neural  network \nmodels. \n\n2  FICTIVE  SWIMMING \n\nThe  neuronal  correlate of swimming can  be induced  in  the isolated lamprey spinal \ncord by exposure to glutamate, which  is  considered  to be the principal endogenous \nexcitatory  neurotransmitter.  As  in  the  intact  swimming  lamprey,  this  \"fictive\" \nswimming  is  characterized  by  periodic  bursts  of motoneuron  action  potentials  in \n\nA \n\nmidline -----\n\nEIN \n\naxon \n\nlateral edge \n\nB \n\nEIN-UN \n\n~\\~lltnV \n-,,\",,pot! -~ \n\n\u2022 \n\n20 tn, \n\nLIN-inhibitory  CC  IN \n&~ alrychnine \n\nI \n\n~re7.r \n\n20m. \n\nC \n\n.-.. \nN \n::t: \n'-' \n~ u \nI:l \nII) \n::s \nC1' \nII) '\" r... \n.lIII .... \n\nII) \n\nCJ. \n!'Il \n\n80 \n\n100  -- EIN \n\n...r----L-I \n\n110 \n\n40 \n\n1st \n\u2022  2nd \n\nlast \n\n20 \n\n0 \n0.0  0.&  1.0  1.5  2.0  2.&  3.0  3.&  4.0  4.&  &.0 \n\nInput  Current  (nA) \n\nFigure  1:  Lamprey spinal interneurons.  A, drawings of three types  of interneurons \nafter intracellular dye injections.  B,  inhibitory and excitatory  postsynaptic  poten(cid:173)\ntials and the effects  of selective antagonists.  C, firing frequency  of the first,  second, \nand last spike intervals during a  400ms current  injection. \n\n\fthe  ventral  roots,  and  these  bmsts  alternate  between  sides  of the  spinal  cord  and \npropagate in a  head-to-tail direction during forward swimming (Cohen and Wallen, \n1980;  Wallen  and  Williams,  1984).  Thus,  the  cellular  mechanisms  for  generating \nthe basic swimming pattern reside within the spinal cord as has been demonstrated \nfor  many other vertebrates  (Grillner,  1981). \n\nLocomotion Network \n\n103 \n\n-0.2  -0.1  0.0 \n\n0.1 \n\n0.2 \n\n0.3 \n\n0 .4 \n\n0.5 \n\n0.11 \n\n0 .7 \n\n0 .8 \n\n0.9 \n\n1.0 \n\nVR \n\nMN \n\nLIN \n\nCC \n\nII,rulJlllllfll' \n\n1Jf1tlB 111111  = \n\nEIN \n\n!!XI!  ~  !!XI! \n\np;x 2*99+&'SM \n\nPeak \n\nPeak \n\nDepolarization \n\nRepolarizalion \n\n-0.2  -0. 1  0.0 \n\n0.1 \n\n0.2 \n\n0 .3 \n\n0.4 \n\n0.5 \n\n0.8 \n\n0.7 \n\n0 .8 \n\n0.9 \n\n1.0 \n\nSWIM  CYCLE \n\nFigure  2:  Connectivity  and  activity  patterns.  Top:  synaptic  connectivity  among \nthe  interneurons  and  motoneurons  (MN).  Bottom:  histograms  summarizing  the \nactivity of cells  recorded  intracelllllar1y during fict.ive  swimming.  Timing of activit.y \nof neurons  with  the onset of the ipsilateral ventral  root  burst. \n\n\f104 \n\nBuchanan \n\nThe  swimming  rhythm  generator  is  thought  to  consist  of a  chain  of coupled  os(cid:173)\ncillators  distributed  throughout  the length  of the  spinal  cord.  The isolated  spinal \ncord  can  be  cut  into  pieces  as  small  as  two  or  three  segments  in  length  from  any \nhead-to-taillevel and still exhibit alternating ventral root bursting upon application \nof glutamate.  The  intrinsic  swimming frequency  in  each  of these  pieces  of spinal \ncord  is  different  by  as  much  as  two-fold,  and  no  consistent  relationship  between \nintrinsic  frequency  and  the  head-to-tail level  from  which  the  piece  originated  has \nbeen  observed  (Cohen,  1986).  Thus,  coupling  among  the  oscillators  must  provide \nsome  \"buffering  capacity\"  to  cope  with  these  intrinsic frequency  differences.  An(cid:173)\nother  feature  of the  coupling is  the  constancy  of phase  lag,  such  that  over  a  wide \nrange  of swimming  cycle  periods,  the  delay  of ventral  root  burst  onsets  between \nsegments  is  a  constant  fraction  of the  cycle  period  (Wallen  and  Williams,  1984). \nSince  the cycle  period  in  swimming lamprey can vary  over  a  ten-fold  range,  axonal \nconduction  time  probably is  not a  factor  in  the delay  between  segments. \n\n3  SPINAL INTERNEURONS \n\nIn  recent  years,  many  c1asses  of spinal  neurons  have  been  characterized  using  a \nvariety  of neurobiological  techniques,  particularly  intracellular  recording  of mem(cid:173)\nbrane  potential  (Rovainen,  1974;  Buchanan,  1982;  Buchanan  et  a,l.,  1989) .  Several \nof these  classes  of neurons  are  active  during  fictive  swimming.  These  include  the \nlateral int.erneurons  (LIN),  cens  with axons projecting contralaterally and caudally \n(CC),  and  the  excitatory interneurons  (EIN).  The LINs  are large  neurons  with  an \nipsilaterally and caudally projecting inhibitory axon (Fig.  lA,B) . The CC interneu(cid:173)\nrons  are medium-sized  inhibitory cells  (Fig.  lA).  The  EINs  are small interneurons \nwith  ipsilaterally and either  caudally or  rostrally  projecting  axons  (Fig.  lA,B,C). \nThe  axons  of all  these  cell  types  project  at  least  five  segments  and  interact  with \nneurons  in  multiple  segments.  The  neurons  have  similar  resting  and  firing  prop(cid:173)\nerties.  They  are  indistinguishable in  their  resting  potentials,  their  thresholds,  and \ntheir action  potential amplitudes, durat.ions,  and after-spike potentials.  Their main \ndifferences  are size-related  parameters such as input  resistance and membrane time \nconstant.  They fire  action  potentials throughout  the duration of long,  depolarizing \ncurrent  pulses,  showing some adaptation (a declining frequency  with successive  ac(cid:173)\ntion  potentials).  The  plots  of spike  frequency  vs.  input  current  for  these  various \ncell  types  are generally  monotonic,  with  a  tendency  to  saturate  at  higher  levels  of \ninput current  (Fig.  lC)(Buchanan,  1991). \n\nThe  synaptic  connectivites  of these  cells  have  been  established  with  simultaneous \nintracellular recording of pre- and post-synaptic neurons, and the results are summa(cid:173)\nrized in Fig.  2 along with their activity patterns during fictive  swimming.  All  of the \ncells exhibit oscillating membrane potentials with depolarizing peaks  which  tend  to \noccur during the ventral root  burst and with repolarizing troughs which occur about \none-half cycle  later  (Buchanan  and  Cohen  1982).  These  oscillations  appear  to  be \ndue in large part  to two  phases  of synaptic input:  an excitatory  depolarizing phase \nand an inhibitory repolarizing  phase  (Kahn,  1982;  Russell  and  Wallen,  1983).  The \nexcitatory  phase  of motoneurons  comes  from  EINs  and  the  inhibitory  phase  from \nCCs.  However,  these  interneurons  not  only  interact  with  motoneurons  but  with \nother interneurons as  well.  So  the possibility exists  that  these interneurons  provide \nthe synaptic drive for  all  neurons  of the network,  not just motoneurons.  Addition-\n\n\fLocomotion Network \n\n105 \n\nally,  it  is  possible  that  rhythmicity  itself originates  from  the  pattern  of synaptic \nconnectivity  because  the circuit  has  a  basic  alternating network  of reciprocal  inhi(cid:173)\nbition  between  ce interneurons  on  opposite  sides  of the  spinal  cord.  Reciprocal \ninhibition as an oscillatory network  needs  some form  of burst-termination, and  this \ncould  be  provided  by  the  feedforward  inhibition  of ipsilateral  ee interneurons  by \nthe  LINs.  This inhibition could  also  account  for  the  early  peak  observed  in  many \nec interneurons  during fictive  swimming (Fig.  2) . \n\n4  NEURAL  NETWORK  MODEL \n\nThe ability of the network of Fig.  2 to generate the basic oscillatory pattern of fictive \nswimming was tested using a  \"connectionist\"  neural network simulation (Buchanan, \n1992).  All  of the  cells  of the  neural  network  had  identical  S-shaped  input-output \ncurves  and  differed  only  in  their  excitatory  levels  and  their  synaptic  connectivity, \nwhich  was  set according to the scheme of Fig.  2.  If the excitation of ees was made \nlarger  than  LINs,  the  network  would  oscillate  (Fig.  3).  These  oscillations  began \nfairly  promptly  and  could  continued  for  at  least  thousands  of cycles.  The  phase \nrelations  among  the  units  were  similar  to  those  in  the  lamprey:  cells  on  opposite \nsides  of the  spinal  cord  were  anti-phasic  while  most  cells  on  the  same  side  of the \ncord  were  co-active.  Significantly,  both  in  the  model  and  in  the  lamprey,  the  CCs \nwere  phase advanced,  presumably due  to  their  inhibition by  LINs . \n\nI.UNUV iV V \nn  n:  n  (\\ \nI.CCJVU  \\j\\ \nI.  EINJV1JV~ \n\nI \n\nI \n\nFigure  3:  Activity of the  neural  network  model for  the  lamprey locomotor circuit.. \n\n\f106 \n\nBuchanan \n\n4.1  COUPLING \n\nThe  neural  network  model  of the  lamprey  swimming  oscillator  was  further  used \nto explore  how  the  coupling  among locomotor oscillators  might  be  achieved.  Two \nidentical  oscillator  networks  were  coupled  using  the  various  pairs  of cells  in  one \nnetwork connected  to pairs of cells  in the second  network.  All  nine  pairs of possible \nconnections were  tested since all of the interneurons interact with neurons in multi(cid:173)\nple segments.  The coupling was  evaluated by several criteria based on  observations \nof lamprey  swimming:  1)  the  stability  of the  phase  difference  between  oscillators \nand the rate of achieving the steady-state,  2)  the ability of the coupling t.o  tolerate \nintrinsic frequency differences  hetween oscillators, and 3)  the constancy of the phase \nlag over  a  wide range of oscillator frequencies . \n\nA \n\nC \n\n0 .8 \n\n0.6 \n\n..0 \n\n.... \n\n0 \n\nbD \nct1 \n.....:l \n(U \nfIl \nct1 \n..c: \n0... \n\n0 .4 \n\n0.2 \n\n0 .0 \n\n-0.2 \n\n-0.4 \n\n0 .0 \n\n.... \n\n\u2022  \u2022  \u2022  \u2022 \n\n0.2 \n\n0.4 \n\n0 .6 \n\n0.8 \n\n1.0 \n\n1.2 \n\nCycle  Period \n\nMNa  &  MNb \n\nB \n\n1.5 \n\n1.0 \n\n..... \n(U > (U \n\n0 .5 \n\n0 .0 \n\n....J \nQ \n..... ., \n0 \nct1 >  -0.5 \n..... ., \nu \n<: \n\n-1 .0 \n\n-1 .5 \n\n0 \n\n50 \n\n150 \n\n200 \n\n100 \nTime \n\nD \n\n1.5 \n\n(U \n\n..... \n> \n(U \n....:I \nI:l \n.., \n..... \n0 \nct1 \n.., \n> \n..... \n<: \n\nC) \n\n1.0 \n\n0 .5 \n\n0 .0 \n\n-0.5 \n\n-1.0 \n\n-1.5 \n\n50 \n\n100 \n\n150 \n\n200 \n\n250 \n\n300 \n\n350 \n\nTime \n\nFigure  4:  Coupling  between  two  identical  oscillators.  A,  the  connectivity.  H, \nsteady-state coupling within a  single cycle.  C,  constancy  of phase  lag over  a  range \nof oscillator periods.  D, adding  LIN -CC from  oscillator a-b, reverses  the  phase, \nsimulating backward  swimming. \n\n\fLocomotion Network \n\n107 \n\nEach  of the  nine  pairs  of coupled  interneurons  between  oscillat.ors  were  capable of \nproducing stable  phase locking,  although some coupling connections operated over \na  much  wider  range  of synaptic  weights  than  others.  The  steady-state  phase  dif(cid:173)\nference  between  the  oscillators  and  the  rate  of reaching it were  also  dependent  on \nthe  synaptic  weight  of the coupling connections.  The direction  of the  phase  differ(cid:173)\nence,  that is,  whether  the  postsynaptic oscillator  was  lagging or  leading,  depended \nboth  on  the  type  of postsynaptic  cell  and  the  sign  of the  coupling input  t.o  it.  If \nthe  postsynaptic  cell  was  one  which  speeds  the  network  (LIN  or  EIN)  then  their \nexcitation by  the  coupling connection  produced  a  lead  of the  postsynaptic  network \nand their inhibition produced a  lag.  The opposite pattern held  for  CCs,  which slow \nthe network. \n\nAn example of a  coupling scheme that satisfied several criteria for lamprey-like cou(cid:173)\npling is  shown in  Fig.  4.  In  this  case  (Fig.  4A),  there  was  bidirectional, symmetric \ncoupling of EINs  in  the  two  oscillators.  This gave  the  network  the  ability  to  toler(cid:173)\nate  intrinsic frequency  differences  between  the  oscillators  (buffering  capacity).  To \nprovide a  phase lag of oscillator b,  EINs were connected  to LINs  bidirectionally but \nwith  greater  weight  in  one  direction  (b---ta).  Such  coupling  reached  a  steady-state \nwithin  a  single  cycle  (Fig.  4B),  and  the  phase  difference  was  maintained  at  the \nsame value over a  range of cycle  periods  (Fig.  4C). \n\n4.2  BACKWARD  SWIMMING \n\nIt  has  been  shown  recently  that  there  is  rhythmic  presynaptic  inhibition  of in(cid:173)\nterneuronal  axons  in  the  lamprey  spinal  cord  (Alford  et  al.,  1990).  This  type  of \ncyc1e-by-cycle  modulation  of synaptic  strength  could  account  for  shifts  in  phase \ncoupling  in  the  lamprey,  such  as  occurs  when  the  animal  switches  to  brief bouts \nof backward  swimming.  One  mechanism for  backward  swimming might  be  the  in(cid:173)\nhibitory  connection  of LIN ---tCCs.  The  LINs  have  axons  which  descend  up  to  50 \nsegments  (one-half body length).  In  the  neural  network  model,  this  descending  in(cid:173)\nhibition of CC interneurons promotes  backward swimming,  i.e.  a  phase lead of the \npostsynaptic  oscillators.  Thus,  presynaptic  inhibition of these  connections  in  non(cid:173)\nlocal segments  would allow forward  swimming,  while a  removal of this presynaptic \ninhibition would initiate backward swimming (Fig.  4D). \n\n5  CONCLUSIONS \n\nThe  modeling  described  here  demonstrates  that  the  identified  interneurons  in  the \nlamprey spinal cord  may  be multi-functional.  They are known  to contribute to  the \nsynaptic input  to motoneurons during fictive  swimming and  thus  to  the shaping of \nthe  final  motor  output,  but  they  may  also  function  as  components  of t.he  rhythm \ngenerating  network  itself.  Finally,  by  virtue  of their  multi-segmental connections, \nthey  may  have  the  additional  role  of providing  the  coupling  signals  among  oscil(cid:173)\nlators.  Further  experimental  work  will  be  required  to  determine  which  of  t.hese \nconnections  are actually used  in  the lamprey spinal cord  for  these  functions. \n\n\f108 \n\nBuchanan \n\nReferences \n\nS.  Alford, J.  Christenson,  &  S.  Grillner.  (1990)  Presynaptic  GABAA  and  GABAB \nreceptor-mediated  phasic  modulation  in  axons  of spinal  motor  interneurons.  Eur. \nJ.  Neurolfci.,  3:107-117. \n\nJ .T.  Buchanan. \naxons in  the lamprey spinal cord:  synaptic interactions and morphology.  J.  Neuro(cid:173)\nphYlfiol.,  47:961-975. \n\n(1982)  Identification  of interneurons  with  contralateral,  caudal \n\nJ.T.  Buchanan.  (1991)  Electrophysiological  properties  of lamprey  spinal  neurons. \nSoc.  Neurolfci.  Ablftr.,  17:1581. \n\nJ .T.  Buchanan.  (1992)  Neural network  simulations of coupled locomotor oscillators \nin the lamprey spinal cord.  Bioi.  Cybern.,  74:  in  press. \n\nJ .T.  Buchanan  &  A.H.  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