{"title": "An Analog VLSI Model of Central Pattern Generation in the Leech", "book": "Advances in Neural Information Processing Systems", "page_first": 622, "page_last": 628, "abstract": null, "full_text": "An Analog VLSI Model of Central Pattern \n\nGeneration in the Leech \n\nMicah  S.  Siegel* \n\nDepartment of Electrical Engineering \n\nYale University \n\nNew Haven, CT  06520 \n\nAbstract \n\nI  detail  the  design  and construction  of an  analog  VLSI  model  of the \nneural system responsible for swimming behaviors of the leech.  Why \nthe  leech?  The  biological  network  is  small  and  relatively  well \nunderstood,  and  the  silicon  model  can  therefore  span  three  levels  of \norganization in  the leech nervous system (neuron, ganglion, system); it \nrepresents  one of the first comprehensive models of leech  swimming \noperating in  real-time.  The circuit employs  biophysically  motivated \nanalog neurons networked to form  multiple biologically inspired silicon \nganglia.  These  ganglia  are  coupled  using  known  interganglionic \nconnections.  Thus  the  model  retains  the  flavor  of  its  biological \ncounterpart, and  though  simplified,  the output of the  silicon circuit is \nsimilar to  the output of the leech swim central pattern generator.  The \nmodel operates on the same time- and spatial-scale as the leech nervous \nsystem  and  will  provide an  excellent platform  with  which  to  explore \nreal-time  adaptive  locomotion  in  the  leech  and  other  \"simple\" \ninvertebrate nervous systems. \n\n1.  INTRODUCTION \nA  Central  Pattern  Generator  (CPG)  is  a  network  of neurons  that  generates  rhythmic \noutput  in  the  absence  of sensory  input  (Rowat  and  Selverston,  1991).  It  has  been \n\n* Present address:  Micah Siegel, Computation and Neural Systems, Mail Stop 139-74 \nCalifornia Institute of Technology, Pasadena, CA 91125. \n\n622 \n\n\fAn Analog VLSI Model of Central Pattern Generation in the Leech \n\n623 \n\nI 'oult \n\n~v \n\nI \n\nlre=ov \n\n~ \"iuhib \n\nI \n\nFigure  l.  Silicon neuromime.  The circuit includes tonic excitation, inhibitory synapses \nand an  inhibitory recovery time.  Note  that there are two inhibitory synapses per device. \nIionic  sets  the  level  of tonic  excitatory  input;  V inhib  sets  the  synaptic  strength;  Irecov \ndetermines the inhibitor  recover  time. \n\nsuggested that invertebrate central pattern  generation may represent an excellent theatre \nwithin which to explore silicon implementations of adaptive neural systems: invertebrate \nCPG networks are orders of magnitude smaller than  their vertebrate counterparts, much \ndetailed information is available about them,  and  they  guide behaviors  that  may  be  of \ntechnological  interest  (Ryckebusch  et  al.,  1989).  Furthermore,  CPG  networks  are \ntypically  embedded  in  larger  neural  circuits and are integral  to the  neural correlates of \nadaptive behavior in many natural organisms (Friesen, 1989). \n\nOn  strategy for  modeling \"simple\" adaptive behaviors  is  first  to  evolve a  biologically \nplausible  framework  within  which  to  include  increasingly  more  sophisticated  and \nverisimilar adaptive mechanisms; because the model of leech swimming presented in this \npaper encompasses  three  levels of organization  in  the  leech  central  nervous  system,  it \nmay  provide an  ideal  such  structure  with  which  to  explore potentially  useful  adaptive \nmechanisms in the leech behavioral repertoire. Among others, these mechanisms include: \nhabituation of the  swim response  (Debski  and  Friesen,  1985), the  local  bending reflex \n(Lockery  and  Kristan,  1990),  and  conditioned  learning  of the  stepping and shortening \nbehaviors (Sahley and Ready, 1988). \n\n\f624 \n\nSiegel \n\nA  Co. \n\n113 \n11& \na\", \n\n01-1(12 \n\n0;-, \n\n.1 \n\n.0 \n\nIJ \nn \n\nCel \n\n\"0' \n11:1' \n\n,ao\u00b7  e \n\n-1O\u00b7 \n\n10' \n1O' \n\n-..\u2022. ~ .. \n\n, \n. ........ -\n\n~l  ~- phase \nl= -\n1= \n\n'10'  )I.IY' /0'  ,..,.  Je(l\"1C\" \n\n120' \n150\u00b7 \nleo' \n\nI \n\nC~;;Ip.  f1' \np::66e \n\nB \n\n~~U, \n\n~~I} \n\n~,II \n~JllU\\ \n123  L--J  ___ I \n2S J  L_-' \n27-..J  ~ I \n\nl. \n'IIL~' \n\n,i~ \n\nI \n\nFigure 2.  The  individual  ganglion.  (A)  Cycle  phases  of the \noscillator  neurons  in  the  biological  ganglion  (from  Friesen, \n1989).  (B)  Somatic  potential  of  the  simplified  silicon \nganglion.  (C)  Circuit diagram  of silicon  ganglion  using  cells \nand s  na  tic connections identified in the leech  an  lion. \n\n2.  LOCOMOTORY  CPG  IN  THE  LEECH \nAs  a first  step  toward  modeling  a full  repertoire of adaptive behavior in  the  medicinal \nleech (Hirundo medicinalis), I have designed, fabricated, and successfully tested an analog \nsilicon model of one critical neural subsystem -\nthe coupled oscillatory central pattern \ngeneration  network  responsible  for  swimming.  A  leech  swims  by  undulating  its \nsegmented body  to form  a rearward-progressing body  wave.  This wave is analogous to \nthe  locomotory  undulations  of most  elongated  aquatic  animals  (e.g.  fish),  and  some \nterrestrial  amphibians and reptiles  (including  salamanders and  snakes)  (Friesen,  1989). \nThe moving crests and troughs in the body wave are produced by phase-delayed contractile \nrhythms of the dorsal and ventral body wall along successive segments (Stent and Kristan, \n1981).  The  interganglionic neural subsystem that subserves this behavior constitutes an \nimportant modeling platform because it guides locomotion in the leech over a wide range \nof frequencies and adapts to varying intrinsic and extrinsic conditions (Debski and Friesen, \n1985). \nIn  the medicinal leech, interneurons that coordinate the rearward-progressing swimming \ncontractions  undergo oscillations in  membrane potential and fire  impulses  in  bursts.  It \nappears  that the oscillatory activity of these intemeurons arises  from  a network rhythm \nthat depends  on  synaptic  interaction  between  neurons rather than  from  an  endogenous \npolarization rhythm arising from inherently oscillatory membrane potentials in individual \n\n\fAn Analog VLSI Model of Central Pattern Generation in the Leech \n\n625 \n\nganglion: \n\n9 \n\n10 \n\n11 \n\n.... ~II----- head \n\ntail ----i~~ \n\nA \n\n8 \n\n9  { \n\n{ \n\n10 \n\n28  __ ----' \n27  -------+---\n123 \n\n28  __  ---I \n\n27  -,...-___ _  +-__ \n123~ \n28  ____ __' \n\n~---r---------~ \n\n~-------------~~~~-----\n\n{ \n\n11 \n\n27  ______  +-.--I \n\nlOOms \n\nFigure 3.  The complete silicon model. (A) Coupled oscillatory ganglia.  As in  the leech \nnervous  system,  interganglionic  connections  employ  conduction  delays.  (B)  Somatic \nrecording  of cells  (28,  27,  123)  from  three  midbody  ganglia  (9,10,11)  in  the  silicon \nmodel.  Notice the phase-delay in  homologous cells of successive ganglia. (The apparent \n\"beat\"  frequencies  riding  on  the  spike  bursts  are  an  aliasing  artifact  of the  digital \noscilloscope  measurement  and  the  time-scale;  all  spikes  are  approximately  the  same \nhei  ht. \n\nneurons (Friesen, 1989).  The phases of the oscillatory intemeurons fonn groups clustered \nabout  three  phase  points  spaced  equally  around  the  activity  cycle.  To  first \napproximation, all midbody  ganglia of the leech nerve cord express an  identical activity \nrhythm.  However,  activity  in  each  ganglion  is  phase-delayed  with  respect  to  more \nanterior ganglia (Friesen,  1989); presumably this is responsible for the undulatory body \nwave characteristic of leech swimming. \n\n\f626 \n\nSiegel \n\n3.  THE  SILICON  MODEL \nThe silicon analog model employs biophysically realistic neural elements (neuromimes), \nconnected  into  biologically  realistic  ganglion  circuits.  These  ganglion  circuits  are \ncoupled  together  using  known  interganglionic  connections.  This  silicon  model  thus \nspans  three  levels  of  organization  in  the  nervous  system  of  the  leech  (neuron, \nganglion,  system),  and  represents  one  of the  first  comprehensive  models  of leech \nswimming (see also Friesen and Stent,  1977).  The hope is that this model will provide a \nframework  for  the  implementation  of  adaptive  mechanisms  related  to  undulatory \nlocomotion in  the leech and other invertebrates. \n\nThe building block of the model CPO is the analog neuromime (see figure  I); it exhibits \nmany  essential similarities to  its biological counterpart.  Like CPO  interneurons  in  the \nleech  swim  system,  the  silicon  neuromime  integrates  current  across  a  somatic \n\"capacitance\" and uses positive feedback to generate action potentials whose frequency is \ndetermined by the magnitude of excitatory current input (Mead,  1989).  In  the leech swim \nsystem. nearly tonic excitatory input is  transformed by a system of inhibition to produce \nthe  swim  pattern  (Friesen.  1989);  adjustable  tonic  excitation  is  therefore  included in \nthe individual silicon neuromime. \n\nInhibitory  synapses  with  adjustable  weights  are  also  implemented.  Like  its \nbiological counterpart, the silicon neuromime includes a characteristic recovery time from \ninhibition.  From  theoretical  and experimental  studies. such  inhibition  recovery  time is \nthought to play an important functional role in  the interneurons that constitute the leech \nswim  system  (Friesen and Stent,  1977).  Axonal  delays  have been  demonstrated in  the \nintersegmental interaction between ganglia in  the leech.  Similar axonal delays have been \nimplemented in the silicon model using Shifting delay lines. \n\nThe building  block of the  distributed  model for the leech  swim  system  is  the ganglion. \nThese biologically motivated silicon ganglia are constructed using only (though not all) \nidentified cells and synaptic connections  between  cells in  the biological system.  Cells \n27,  28,  and  123  constitute  a  central  inhibitory  loop  within  each  ganglion.  Figure  2 \nexhibits  the simplified diagram  and the cycle phases of oscillatory interneurons in  both \nthe biological and the silicon ganglion.  As  in  the leech ganglion, the phase relationships \nin the model ganglion fall  into three groups, with cells 27. 28. and  123 participating each \nin  the appropriate group of the oscillatory cycle.  It is interesting that, though the silicon \nmodel captures  the spirit of the  tri-phasic output,  the model is imprecise with respect to \nthe  exact phase locations of cells 27.  28. and  123  within  their respective  groups.  This \ndiscrepancy  between  the  silicon  model  and  the  biological  system  may  point  to  the \nsignificance  of other  swim  interneurons  for  swim  pattern  generation  in  the  leech. \nUndoubtedly.  the  additional  oscillatory  interneurons  sculpt  this  tri-phasic  output \nsignificantly. \n\nThe  silicon  model  of coupled  successive segments  in  the  leech  is  implemented  using \nthese  silicon  neurons  and  biologically  motivated  ganglia.  The  model  employs \ninterganglionic  connections  known  to  exist  in  the  biological  system  and  generates \nqualitatively  similar output at the same time-scale as  the leech system.  It appears in the \nleech  that synchronization  between ganglia  is governed by the interganglionic synaptic \ninteraction of interneurons involved in  the oscillatory pattern rather than by autonomous \n\n\fAn Analog VLSI Model of Central Pattern Generation in the Leech \n\n627 \n\ncoordinating neurons (Friesen. 1989).  In  the silicon model. interganglionic interaction is \nrepresented by a projection from  more anterior cell 123 to more posterior cell 28; this \n\nA \n\nB \n\n----.1UJV'lJNil \n\nWf;tU12i'l .. \n\nlOOms \n\nFigure 4.  Phase lag between more anterior and more posterior \nsegments  in  both  systems.  (A)  Intersegmental  phase  lag  in \nthe  leech  swim  system  (from  Friesen.  1989). \n(B) \nIntersegmental  phase  lag  in  the  silicon  model.  Though  not \nshown in the figure, this cycle repeats at the same frequency as \nthe c  cle in A. \n\note chan  e of time scale. \n\nprojection  is  also observed between  cells  123  and  28 of successive ganglia in  the leech \n(Friesen,  1989). however it is by  no means the only such interganglionic connection.  In \naddition,  the  biological  system  utilizes  conduction  delays  in  its  interganglionic \nprojections;  each of these  is  modeled in  the  silicon system  by  a delay line (Friesen  and \nStent.  1977) analogous  to  an  active cable with  adjustable propagation  speed.  Figure 3 \ndemonstrates the silicon model of three coupled ganglia with transmission delays.  Notice \nthat  neuromimes  in  each  successive  ganglion  are  phase-delayed  from  homologous \nneuromimes in  more anterior ganglia.  Figure 4 shows this phase delay more explicitly. \n\n4.  DISCUSSION \nThe analog silicon model of central pauern generation in  the leech successfully captures \ndesign  principles from  three levels of organization in  the leech  nervous  system  and has \nbeen tested over a wide range of network parameter values.  It operates on the same time(cid:173)\nscale as its biological counterpart and gives rise to ganglionic activity that is qualitatively \nsimilar  to  activity  in  the  leech  ganglion.  Furthermore.  it  maintains  biologically \nplausible phase relationship between  homologous elements of successive ganglia.  The \ndesign  of the  silicon  model  is  intentionally compatible  with  analog  Very  Large  Scale \nIntegration  (VLSI)  technology.  making  its  integrated  spatial-scale  close  to  that of the \nIt is  interesting  that  this  highly  simplified  model  captures \nleech  nervous  system. \nqualitatively  the  output  both  within  and  between  ganglia  of  the  leech;  it  may  be \nilluminating to  explore  the  functional  significance of other swim  interneurons  by  their \ninclusion in  similar silicon networks.  The current model provides an  important platform \nfor future implementations of invertebrate adaptive behaviors, especially those behaviors \nrelated to swim and other locomotory pattern generation.  The hope is that such behaviors \n\n\f628 \n\nSiegel \n\ncan be evolved incrementally using neuromime models of identified adaptive interneurons \nto modulate the swim central pattern generating network. \n\nAcknowledgments \n\nI  would  like  to  thank  the  department of Electrical Engineering at  Yale  University  for \nencouraging and generously supporting independent undergraduate research. \n\nReferences \n\nRowat, P.P. and Selverston, A.I.  (1991). Network, 2,  17-41. \n\nRyckebusch,  S.,  Bower,  J.M.,  Mead,  C.,  (1989).  In  D.Touretzky  (ed.),  Advances  in \nNeural Information Processing Systems, 384-393. San Mateo, CA:  Morgan Kaufmann. \n\nFriesen, W.O.  (1989).  In  J.  Jacklet  (ed), Neuronal  and Cellular  Oscillators,  269-316. \nNew York: Marcel Dekker. \n\nDebski,  E.A.  and  Friesen,  W.O.  (1985).  Journal  of Experimental Biology,  116,  169-\n188. \n\nLockery, S.R. and Kristan, W.B. (1990).  Journal of Neuroscience,  10(6), 1811-1815. \n\nSahley, C.L. and Ready, D.P.  (1988). Journal of Neuroscience, 8(12), 4612-4620. \n\nStent,  G.S.  and  Kristan,  W.B.  (1981).  In  K.Muller,  J  Nicholls,  and  G.  Stent  (eds) , \nNeurobiology  of the  Leech,  113-146.  Cold  Spring  Harbor:  Cold  Spring  Harbor \nLaboratory . \n\nMead, C.A. (1989). Analog VLSl and Neural Systems, Reading, MA:  Addison-Wesley. \n\nFriesen, W.O. and Stent, G.S. (1977).  Biological Cybernetics, 28,27-40. \n\n\f", "award": [], "sourceid": 743, "authors": [{"given_name": "Micah", "family_name": "Siegel", "institution": null}]}