{"title": "The Role of Activity in Synaptic Competition at the Neuromuscular Junction", "book": "Advances in Neural Information Processing Systems", "page_first": 96, "page_last": 102, "abstract": null, "full_text": "The Role of Activity in  Synaptic \nCompetition at the Neuromuscular \n\nJunction \n\nSamuel R.  H. Joseph \n\nCentre for  Cognitive Science \n\nEdinburgh University \n\nEdinburgh,  U.K. \n\nemail:  sam@cns.ed.ac.uk \n\nDavid J. Willshaw \n\nCentre for  Cognitive Science \n\nEdinburgh University \n\nEdinburgh,  U.K. \n\nemail:  david@cns.ed.ac.uk \n\nAbstract \n\nAn  extended  version  of the  dual  constraint  model  of motor  end(cid:173)\nplate morphogenesis is  presented that includes activity dependent \nand  independent  competition.  It is  supported by  a  wide  range  of \nrecent neurophysiological evidence that indicates a strong relation(cid:173)\nship  between  synaptic  efficacy  and  survival.  The  computational \nmodel is  justified  at the molecular level  and its predictions match \nthe developmental and regenerative behaviour of real synapses. \n\n1 \n\nINTRODUCTION \n\nThe  neuromuscular  junction  (NMJ)  of mammalian  skeletal  muscle  is  one  of the \nmost  extensively  studied  areas of the  nervous  system.  One aspect  of its develop(cid:173)\nment that it shares with many other parts of the nervous system is its achievement \nof single  innervation,  one  axon  terminal  connecting  to  one  muscle  fibre,  after  an \ninitial  state  of  polyinnervation.  The  presence  of  electrical  activity  is  associated \nwith  this  transition,  but  the  exact  relationship  is  far  from  clear.  Understanding \nhow  activity  interacts with the morphogenesis of neural  systems  could  provide us \nwith insights into methods for constructing artificial neural networks.  With that in \nmind, this paper examines how some of the conflicting ideas about the development \nof neuromuscular connections can be resolved. \n\n\fThe  Role of Activity in  Synaptic Competition at  the  Neuromuscular Junction \n\n97 \n\n2  EXPERIMENTAL FINDINGS \n\nThe extent to which a muscle is  innervated can be expressed in  terms of the motor \nunit size - the number of fibres  contacted by a given motor axon.  Following removal \nof some  motor axons  at birth,  the average size  of the remaining motor units  after \nwithdrawal of poly innervation is larger than normal (Fladby & Jansen, 1987).  This \nstrongly  suggests  that  individual  motor  axons  successfully  innervate  more  fibres \nas a  result  of the absence  of their neighbours.  It is  appealing to interpret this  as \na  competitive  process  where  terminals  from  different  axons  compete  for  the same \nmuscle  endplate.  Since  each  terminal  is  made  up  of  a  number  of  synapses  the \nprocess  can be viewed  as the co-existence of synapses from  the same terminal and \nthe elimination of synapses from  different terminals on the same end plate. \n\n2.1  THE EFFECTS  OF ELECTRICAL  ACTIVITY \n\nThere is  a  strong activity dependent component to synapse elimination.  Paralysis \nor  stimulation  of  selected  motor  units  appears  to  favour  the  more  active  motor \nterminals (Colman & Lichtman, 1992), while inactive axon terminals tend to coexist. \nRecent  work also shows that active synaptic sites can destabilise inactive synapses \nin  their  vicinity  (Balice-Gordon  &  Lichtman,  1994).  These  findings  support  the \nidea that  more  active  terminals  have  a  competitive  advantage over  their  inactive \nfellows , and that this competition takes  place at a  synaptic level. \n\nActivity independent competition has been demonstrated in the rat lumbrical mus(cid:173)\ncle (Ribchester, 1993).  This muscle is innervated by the sural and the lateral plantar \nnerves.  If the sural nerve is  damaged the lateral plantar nerve will expand its terri(cid:173)\ntory to the extent that it innervates the entire muscle.  On subsequent reinnervation \nthe regenerating sural nerve may displace some of the lateral plantar nerve termi(cid:173)\nnals.  If the  muscle  is  paralysed  during  reinnervation  more  lateral  plantar  nerve \nterminals  are  displaced  than  in  the  normal  case,  indicating that  competition  be(cid:173)\ntween inactive terminals does take place,  and that paralysis can give an advantage \nto some terminals. \n\n3  MODELS  AND MECHANISMS \n\nIf the nerve terminals are competing with each other for  dominance of motor end(cid:173)\nplates,  what is  the mechanism behind it?  As  mentioned above,  activity is  thought \nto  play  an  important  role  in  affecting  the  competitive  chances  of a  terminal,  but \nin  most models  the terminals compete for  some kind of trophic resource  (Gouze et \naI.,  1983;  Willshaw,  1981).  It is  possible to create models that use competition for \neither a  postsynaptic  (endplate)  resource or a  presynaptic  (motor  axon)  resource. \nBoth types of model have  advantages and disadvantages,  which  leads  naturally to \nthe possibility of combining the two into a  single model. \n\n3.1  BENNET AND ROBINSON'S DUAL  CONSTRAINT MODEL \n\nThe  dual  constraint  model  (DCM)  (Bennet  &  Robinson,  1989),  as  extended  by \nRasmussen &  Willshaw  (1993), is  based on a  reversible reaction between molecules \nfrom  a  presynaptic resource  A  and a  postsynaptic resource  B.  This  reaction takes \nplace in the synaptic cleft  and produces a  binding complex  C which  is essential for \n\n\f98 \n\nS. R.  H. JOSEPH, D. J.  Wll...LSHAW \n\nthe terminal's survival.  Each motor axon and muscle fibre  has a  limited amount of \ntheir particular resource and the size of each terminal is proportional to the amount \nof the binding complex at that terminaL  The model achieves single innervation and \na  perturbation  analysis  performed  by  Rasmussen  & Willshaw  (1993)  showed  that \nthis single innervation state is stable.  However, for the DCM to function the forward \nrate of the reaction had to be made proportional to the size of the terminal,  which \nwas  difficult  to justify  other than suggesting it was  related to electrical activity. \n\n3.2  SELECTIVE MECHANISMS \n\nWhile  the  synapses  in  the  surviving  presynaptic  terminal  are  allowed  to  coexist, \nsynapses  from  other  axons  are  eliminated.  How  do  synapses  make  a  distinction \nbetween  synapses in  their  own  terminal  and  those  in  others?  There are  two  pos(cid:173)\nsibilities:  (i)  Synchronous  transmitter  release  in  the  synaptic  boutons  of a  motor \nneuron could distinguish synapses, allowing them to compete as cartels rather than \nindividuals  (Colman &  Lichtman,  1992).  (ii)  The synapses could be employing se(cid:173)\nlective  recognition  mechanisms,  e.g  the  'induced-fit'  model  (Rib chester  &  Barry, \n1994). \n\nA  selective  mechanism  implies  that  all  the synapses  of a  given  motor neuron  can \nbe identified  by  a  molecular  substrate.  In the induced-fit  model  each  motor  neu(cid:173)\nron  is  associated  with  a  specific  isoform  of a  cellular  adhesion  molecule  (CAM); \nthe synapses compete by attempting to induce all the CAMs on the end plate into \nthe conformation associated with their neuron.  This kind of model  can be used  to \naccount for much of the developmental and regenerative processes of the NMJ. How(cid:173)\never, it has difficulty explaining Balice-Gordon &  Lichtman's (1994)  focal  blockade \nexperiments  which  show  competition  between  synapses  distinguished  only  by  the \npresence of activity.  If,  instead, activity is  responsible for  the distinction of friend \nfrom foe,  how  can competition take place at the terminal level  when  activity is not \npresent?  Could we  resolve this  dilemma by extending the dual constraint model? \n\n4  EXTENDING THE DUAL  CONSTRAINT MODEL \n\nTentative  suggestions  can  be  made  for  the  identity  of the  'mystery  molecules'  in \nthe  DCM.  According  to  McMahan  (1990)  a  protein  called  agrin  is  synthesised  in \nthe cell  bodies  of motor neurons and transported down  their axons to the muscle. \nWhen  this protein binds  to the surface of the  developing muscle,  it  causes  acetyl(cid:173)\ncholine receptors  (AChRs),  and  other components of the  postsynaptic  apparatus, \nto aggregate on  the myotube surface in  the vicinity of the activated agrin. \n\nOther work (Wallace, 1988) has provided insights into the mechanism used by agrin \nto cause the aggregation of the postsynaptic apparatus.  Initially, AChR aggregates, \nor 'speckles', are free to diffuse laterally in the myotube plasma membrane (Axelrod \net aI.,  1976).  When agrin binds to an agrin-specific receptor, AChR speckles in  the \nimmediate vicinity of the agrin-receptor complex are immobilised.  As more speckles \nare trapped larger patches are formed,  until a steady state is reached.  Such a patch \nwill remain so long as agrin is  bound to its receptor and Ca++  and energy supplies \nare available. \n\nFollowing  AChR  activation  by  acetylcholine,  Ca++  enters  the  postsynaptic  cell. \nSince Ca++  is required for both the formation and maintenance of AChR aggregates, \n\n\fThe  Role of Activity in  Synaptic Competition  at  the  Neuromuscular Junction \n\n99 \n\na  feedback  loop  is  possible  whereby  the  bigger  a  patch  is  the  more  Ca++  it  will \nhave  available  when  the  receptors are activated.  Crucially,  depolarisation  of non(cid:173)\njunctional regions blocks  AChR expression  (Andreose et al.,  1995)  and  it  is  AChR \nactivation  at  the  NMJ  that  causes  depolarisation  of the  postsynaptic  cell.  So  it \nseems  that  agrin  is  a  candidate  for  molecule  A,  but  what  about  B  or  C?  It is \ntempting to posit AChR as molecule B since it is the critical postsynaptic resource. \nHowever, since agrin does not bind directly to the acetylcholine receptor, a different \nsort of reaction is  required. \n\n4.1  A  DIFFERENT SORT OF REACTION \n\nIf AChR  is  molecule  B,  and  one  agrin  molecule  can  attract  at  least  160  AChRs \n(Nitkin et al.,  1987)  the simple reversible reaction of the DCM  is  ruled out.  Alter(cid:173)\nnatively,  AChR could exist in either free,  B f' or bound, Bb  states, being converted \nthrough  the  mediation  of  A.  Bb  would  now  play  the  role  of  C in  the  DCM.  It is \npossible  to devise  a  rate equation for  the change  in  the  number  of receptors  at  a \nnerve terminal over time: \n\ndBb \n-\ndt \n\n= nABf - (3Bb \n\n(1) \n\nwhere  n  and  (3  are  rate  constants.  The  increase  in  bound  AChR  over  time  is \nproportional to the amount of agrin at a junction and the number of free  receptors \nin  the  endplate  area,  while  the  decrease  is  proportional  to  the  amount  of  bound \nAChRs.  The rate equation (1)  can be used as the basis of an extended DCM if four \nother factors are considered:  (i)  Agrin stays active as receptors accumulate, so  the \nconservation equations for  A  and  Bare: \n\nM \n\nAo  = An + LAnj \n\nN \n\nBo  = Bmf + LBimb \n\nj=1 \n\ni=1 \n\n(2) \n\nwhere the subscript 0 indicates the fixed resource available to each muscle or neuron, \nthe lettered subscripts indicate the amount of that substance that is  present in  the \nneuron  n,  muscle fibre  m and terminal  nm,  and there are  N motor neurons and M \nmuscle  fibres.  (ii)  The size  of a  terminal  is  proportional to the  number  of bound \nAChRs,  so  if  we  assume  the  anterograde  flow  is  evenly  divided  between  the  lin \nterminals of neuron  n, the transport equation for  agrin is: \n\n(3) \n\nwhere>.  and  IS  are  transport  rate  constants  and  the  retrograde  flow  is  assumed \nproportional to the amount  of agrin  at the terminal and inversely  proportional to \nthe size  of the terminal.  (iii)  AChRs  are free  to diffuse laterally across  the surface \nof the muscle,  so  the forward  reaction rate will  be related to the probability of an \nAChR speckle  intersecting a  terminal,  which  is  itself proportional to  the terminal \ndiameter.  (iv)  The influx of Ca++  through  AChRs  on the surface of the endplate \nwill  also affect  the forward  reaction rate in  proportion to the area of the terminal. \nTaking Bb  to be  proportional to the volume  of the postsynaptic  apparatus,  these \nlast two terms are proportional to B~/3 and B;/3  respectively.  This gives the final \nrate equation: \n\n(4) \n\n\f100 \n\nS. R.  H. JOSEPH, D. J. WILLSHA W \n\nEquations  (3)  and (4)  are similar to those in  the original DCM,  only now  we  have \nbeen able to justify the dependence of the forward  reaction rate on the size of the \nterminal,  B nmb .  We  can also resolve the distinction paradox, as follows. \n\n4.2  RESOLVING  THE DISTINCTION  PARADOX \n\nIn  terms  of distinguishing  between  synapses  it  seems  plausible  that  concurrently \nactive synapses  (Le.  those  belonging to the same neuron)  will  protect  themselves \nfrom the negative effects of depolarisation.  In paralysed systems, synapses will ben(cid:173)\nefit  from  the  AChR accumulating affects  of the  agrin  molecules  in  those synapses \nnearby  (i.e.  those  in  the same terminal).  It was  suggested  (Jennings,  1994)  that \ncompetition  between  synapses  of the same terminal  was  seen  after focal  blockade \nbecause active AChRs help stabilise the receptors around them and suppress those \nfurther  away.  This  fits  in  with  the  stabilisation  role  of Ca++  in  this  model  and \nthe suppressive effects  of depolarisation,  as  well  as  the physical  range of these ef(cid:173)\nfects  during 'heterosynaptic suppression' (Lo & Poo, 1991).  It seems that Jenning's \nmechanism,  although originally  speculative,  is  actually  quite  a  plausible  explana(cid:173)\ntion  and  one  that  fits  in  well  with  the  extended  DCM.  The  critical  effect  in  the \nXDCM  is  that if the system is  paralysed during development  there is  a  change in \nthe dependency  of the forward  reaction rate on the size of an individual terminal. \nThis gives  the reinnervating terminals  a  small  initial  advantage due  to their  more \ncompetitive diameter/volume ratios.  As we shall see in the next section, this allows \nus to demonstrate activity independent competition. \n\n5  SIMULATING THE EXTENDED DCM \n\nIn  terms of achieving  single  innervation the extended  DCM  performs just  as  well \nas  the original,  and  when  subjected to the same perturbation analysis it has  been \ndemonstrated to be stable.  Simulating a  number of systems  with  as many  muscle \nfibres  and  motor neurons  as found  in  real muscles  allowed  a  direct  comparison of \nmodel findings  with experimental data (figure  1) . \n\n..... -~ ... \n'; ,-\n\\-. \n\n\u2022  E\"\"pcrimental \n+  Simulation \n\n. t\\_ \n'.  -\n\n.~\\\\ \n\" \n\n\" .... \n\n~,~ \n\n. ~.----~----+. .. ----~--~~ \n\n\u2022\u2022  1  ............. __ ..... \n\nDays after birth \n\nFigure 1:  Elimination of Polyinnervation in  Rat soleus muscle and Simulation \n\nFigure 2 shows nerve dominance histograms of reinnervation in both the rat lumbri(cid:173)\ncal  muscle and its extended DCM  simulation.  Both compare the results  produced \nwhen  the  system  is  paralysed from  the outset  of reinnervation  (removal  of B~~b \n\n\fThe  Role  of Activity in  Synaptic Competition  at  the  Neuromuscular Junction \n\n101 \n\nterm from  equation  (4))  with the normal situation.  Note that in  both the simula(cid:173)\ntion  and the experiment the percentage of fibres  singly  innervated  by  the reinner(cid:173)\nvating sural nerve is  increased in  the paralysis case.  Inactive sural nerve terminals \nare  displacing  more  inactive lateral plantar  nerve terminals  (activity  independent \ncompetition).  They  can  achieve  this  because  during  paralysis  the  terminals  with \nthe largest diameters capture more receptors,  while  the terminals with the largest \nvolumes  lose more  agrin;  so small reinnervating terminals do  a  little better.  How(cid:173)\never,  if activity  is  present the receptors are captured in  proportion to a  terminal's \nvolume, so there's no advantage to a small terminal's larger diameter/volume ratio. \n\nI Nerve Dominance Histogram (Experimental) I \n\nI I, \n,  I \n\n1:::11 \n\nI Nerve Dominance Histogram (Simulation) I \n\nSingieLPN \n\nMull! \n\nSmglcSN \n\nI \n\nI \n\nI \n\nSingleLPN \n\nMulti \n\nSingleSN \n\n________________________  ~ ~I  ____________  __  \n\nFigure 2:  Types of Innervation by  Lateral Plantar and Sural Nerves \n\n6  DISCUSSION \n\nThe  extensions  to  the  DCM  outlined  here  demonstrate  both  activity  dependent \nand  independent  competition  and  provide  greater biochemical  plausibility.  How(cid:173)\never this  is  still  only  a  phenomenological demonstration and further  experimental \nwork  is  required  to  ascertain  its  validity.  There  is  a  need  for  illumination  con(cid:173)\ncerning the specific chemical mechanisms that underlie agrin's aggregational effects \nand the roles that both Ca++  and depolarisation play in junctional dynamics.  An \nimportant connection made here is  one between synaptic efficiency  and junctional \nsurvival.  Ca++  and NO  have both been implicated in  Hebbian  mechanisms  (Bliss \n&  Collingridge,  1993)  and  perhaps  some  of the  principles  uncovered  here  may  be \napplicable to neuroneuronic synapses.  This work should be followed up with a direct \nmodel  of synaptic  interaction at the  NMJ  that  includes  the presynaptic  effects  of \ndepolarisation, allowing the efficacy of the synapse to be related to its biochemistry; \nan important step forward  in  our understanding of nervous system plasticity.  Re(cid:173)\nlating changes in synaptic efficiency to neural morphogenesis may also give insights \ninto the construction of artificial neural networks. \n\nAcknowledgements \n\nWe  are  grateful  to  Michael  Joseph  and  Bruce  Graham  for  critical  reading  of the \nmanuscript and to the M.R.C.  for  funding this  work. \n\n\f102 \n\nReferences \n\nS.  R.  H. JOSEPH, D. J.  WILLS HAW \n\nAndreose J. S.,  Fumagalli G.  &  L0mo T.  (1995)  Number of junctional acetylcholine \nreceptors:  control  by  neural and muscular influences  in  the rat.  Journal  of Physi(cid:173)\nology  483.2:397-406. \n\nAxelrod  D.,  Ravdin P.,  Koppel  D.  E., Schlessinger J.,  Webb  W.  W.,  Elson E.  L.  & \nPodleski T. R.  (1976) Lateral motion offluorescently labelled acetylcholine receptors \nin  membranes of developing muscle  fibers.  Proc.  Natl.  Acad.  Sci.  USA  73:4594-\n4598. \n\nBalice-Gordon R.  J. & Lichtman J.  W.  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(1994)  Spatial Versus Consumptive Competition at \nPolyneuronally Innervated Neuromuscular Junctions.  Exp.  Physiology  79:465-494. \n\nWallace B. G.  (1988) Regulation of agrin-induced acetylcholine receptor aggregation \nby  Ca++  and phorbol ester.  Journal  of Cell  Biol.  107:267-278. \n\nWillshaw D.  J.  (1981) The establishment and the subsequent elimination of polyneu(cid:173)\nronal innervation of developing muscle:  theoretical considerations.  Proc.  Royal Soc. \nLond.  B212:  233-252. \n\n\f", "award": [], "sourceid": 1146, "authors": [{"given_name": "Samuel", "family_name": "Joseph", "institution": null}, {"given_name": "David", "family_name": "Willshaw", "institution": null}]}