{"title": "3 state neurons for contextual processing", "book": "Advances in Neural Information Processing Systems", "page_first": 229, "page_last": 236, "abstract": null, "full_text": "3  state neurons for  contextual processing \n\nAdam Kepecs* and  Sridhar Raghavachari \n\nVolen  Center for  Complex Systems \n\nBrandeis University \nWaltham MA  02454 \n\n{kepecs,sraghava}@brandeis.edu \n\nAbstract \n\nNeurons  receive  excitatory  inputs  via  both  fast  AMPA  and  slow \nNMDA  type  receptors.  We  find  that  neurons  receiving  input  via \nNMDA  receptors  can have  two  stable  membrane states  which  are \ninput  dependent.  Action potentials can only be initiated from  the \nhigher voltage state.  Similar observations have been  made in sev(cid:173)\neral  brain areas  which  might  be  explained  by our model.  The  in(cid:173)\nteractions  between the two  kinds  of inputs lead us  to suggest that \nsome  neurons  may  operate in  3  states:  disabled,  enabled  and  fir(cid:173)\ning.  Such  enabled,  but non-firing modes  can be used to introduce \ncontext-dependent  processing  in  neural  networks.  We  provide  a \nsimple example and discuss possible implications for  neuronal pro(cid:173)\ncessing and response variability. \n\n1 \n\nIntroduction \n\nExcitatory interactions  between  neurons  are  mediated  by  two  classes  of synapses: \nAMPA  and NMDA.  AMPA synapses act on a  fast  time scale  (TAMPA'\" 5ms) , and \ntheir role in shaping network dynamics  has  been extensively studied.  The NMDA \ntype receptors  are slow  ((TNMDA  '\" 150ms)  and have been mostly  investigated for \ntheir critical role in the induction of long term potentiation, which is thought to be \nthe mechanism for  storing long term memories.  Crucial to this is the unique voltage \ndependence  of NMDA  receptors  [6]  that  requires  both  the  presynaptic  neuron  to \nbe  active  and the post-synaptic neuron  to  be  depolarized for  the channel  to  open. \nHowever, pharamacological studies which block the NMDA receptors impair a  vari(cid:173)\nety of brain processes, suggesting that NMDA  receptors also playa role in shaping \nthe dynamic activity of neural networks  [10,  3,  8,  11,  2]. \n\nTherefore,  we  wanted  to  examine  the  role  of  NMDA  receptors  in  post-synaptic \nintegration.  Harsch and  Robinson  [4]  have observed  that injection  of NMDA  con(cid:173)\nductance  that  simulates  synchronous  synaptic  input  regularized  firing  while  low(cid:173)\nering  response  reliability.  Our  initial  observations  using  a  minimal  model  with \n\n'The authors contributed equally to this work. \n\n\flarge  NMDA  inputs  in  a  leaky  dendrite  showed  a  large  regenerative  depolariza(cid:173)\ntion.  Neurons  however,  also  possess  a  variety  of potassium  currents  that  are able \nto  limit  these  large  excursions  in  voltage.  In  particular,  recent  observations  show \nthat  A-type  potassium  currents  are abundant  in  dendrites  of a  variety  of neurons \n[7] .  Combining  these  potassium currents with  random  NMDA  inputs  showed  that \nthe membrane voltage alternated between two distinct  subthreshold states.  Similar \nobservations  of  two-state  fluctuations  have  been  made  in  vivo  in  several  cortical \nareas  and  the  striatum  [17,  9,  1].  The origin  and  possible  functional  relevance  of \nthese fluctuations  have remained a  puzzle.  We suggest that the NMDA  type inputs \ncombined with potassium currents are sufficient to produce such membrane dynam(cid:173)\nics.  Our results  lead us  to suggest that the fluctuations  could be used to represent \ncontextual modulation of neuronal firing. \n\n2  NMDA-type input  causes  2  state membrane fluctuations \n\n2 .1  Model \n\nTo  examine  the  role  of NMDA  type  inputs,  we  built  a  simple  model  of a  cortical \nneuron  receiving  AMPA  and  NMDA  type  inputs.  To  capture  the  spatial  extent \nof  neuronal  morphology  we  use  a  two-compartment  model  of  pyramidal  neurons \n[15].  We  represent  the  soma,  proximal  dendrites  and  the  axon  lumped  into  one \ncompartment containing the channels necessary for  spike generation  (INa  and IK). \nThe dendritic compartment includes two potassium currents, a fast  activating IKA \nand the slower  IKS  along with a  persistent sodium current INaP.  The dendrite also \nreceives  synaptic input as  INMDA  and  IAMPA . \n\nThe membrane voltage of the neuron obeys the current balance equations: \n\nwhile  the dendritic voltage, \"\\lid  obeys: \n\nwhere em  is  the specific  membrane capacitance which is  taken to be  1 I1F / cm2  for \nboth the  dendrite  and the soma for  all  cells  and p  =0.2, gc  =0.05  determining  the \nelectrotonic structure of the neuron. \n\nThe passive leak current in  both the soma and dendrites  were  modeled  as  h eak  = \ngl eak(V  - El eak ),  where  gl eak  was  the  leak  conductance  which  was  taken  to  be \n0.3  mS/cm2  for  the  soma  and  dendrite.  El eak  =  -80mV  was  the  leak  reversal \npotential for both the compartments.  The voltage-dependent currents were modeled \naccording to the Hodgkin-Huxley formalism,  with the gating variables  obeying the \nequation: \n\ndx \ndt  =  \u00a2x(ax(V)(1  - x)  - ,sx(V)x) =  \u00a2x \n\n(xoo(V)  - x) \n, \n\nTx(V) \n\n(3) \n\n\fwhere x  represents the activation/inactivation gates for  the voltage-dependent cur(cid:173)\nrents. \n\nThe  sodium  current,  INa  =  gNam~ h(VS - E Na ),  where  gNa  =  45  mS/cm2  and \nsodium  reversal  potential,  ENa  =  55  mV  with  m oo(V)  =  a=(~)~~~(V).  The \nactivation  variables,  O::m(V)  =  -O.l(V +  32)/[exp( -(V +  32)/10)  - 1],  'sm(V)  = \n4exp( -[V +  57]/18); O::h(V)  =  0.07 exp( -[V +  48]/20)  and 'sh (V)  =  l/[exp( -{V + \n18}/10) +  1],  with \u00a2m  =  \u00a2h  =  2.5. \n\nThe  delayed  rectifier  potassium  current,  IKDr  =  gKn4(VS  - EK),  where  gK  =  9 \nmS/cm2  and potassium reversal potential, EK  =  -80 mV with O::n(V)  =  -O.Ol(V + \n34)/[exp( -(V +  34)/10) - 1], 'sn(V)  =  0.125 exp( -[V +  44]/80), with \u00a2n  =  2.5. \n\nIn the dendrite, the persistent sodium current, INaP  =  gNapr~(V)(V - VNa ),  with \nroo(V)  =  1/(1 +  exp( -(V +  57)/5))  and gNaP  =0.25 mS/cm2 \u2022  The two  potassium \ncurrents were  hs =  gKsq(V - VK),  with qoo (V)  =  1/(1 +  exp( -(V +  50)/2))  and \nTq(V)  =  200/(exp( -(V + 60)/10) + exp((V + 60)/10)) and gKS  =  0.1  mS/cm2 ;  and \nhA =  gKAa~ (V)b(V - VK),  with  aoo(V)  =  1/(1 +  exp(-(V +  45)/6)),  boo (V)  = \n1/(1 +  exp(-(V +  56)/15))  and Tb(V)  =  2.5(1  +  exp((V +  60)/30))  and gKA  =  10 \nmS/cm2 . \n\nThe NMDA  current,  INMDA  =  fgNMDAS(V  - ENMDA)/(l + 0.3[Mg] exp( -0.08V)), \nwhere  S  was the activation variable and f  denoted the inactivation of NMDA  chan(cid:173)\nnels due to calcium entry.  AMPA and NMDA  inputs were modeled as  conductance \nkicks  that  decayed  with  TAMPA  =  5  ms  and  TNMDA  =  150  ms.  Calcium  depen(cid:173)\ndent  inactivation  of the  NMDA  conductance  was  modeled  as  a  negative  feedback \ndf /dt =  (foo  -\nf)/2 , where  f oo  was  a  shallow sigmoid function  that was  1 below a \nconductance threshold of 2 ms/cm2  and was  inversely  proportional to the  NMDA \nconductance above  threshold.  The coupling conductance is  gc  =0.1  mS/cm  2.  The \nasymmetry between the areas of the two compartments is  taken into account in the \nparameter p  =  somatic area/total area  =  0.2.  The temperature scaling factors \nare  \u00a2h  =  \u00a2n  =  3.33.  Other  parameter  values  are:  gLeak  =0.3,  gNa  =36,  gK  =6, \ngNaP  =0.15,  gKS  =1,  gKA  =50  in  mS/cm2  unless  otherwise  noted;  ELeak  =  -75, \nENa  =  +55,  EK  =  -90, EKA  =  -80 in  m V.  Synchronous inputs  were  modeled  as \na  compound Poisson process representing 100 inputs firing  at a rate  A each spiking \nwith a probability of 0.1.  Numerical integration was  performed with a fourth-order \nRunge-Kutta method using a  0.01  ms  time step. \n\n2.2  NMDA induced two-state fluctuations \n\nFigure  1A  shows  the  firing  produced  by  inputs  with  high  AMPA/NMDA  ratio. \nFigure 1B shows that the same spike train input delivered via synapses with a high \nNMDA  content results in robust two-state membrane behavior.  We  term the lower \nand higher  voltage states as  UP and  DOWN states respectively.  Spikes  caused  by \nAMPA-type  inputs  only  occur  during  the  up-state.  In  general,  the  same  AMPA \ninput  can  only  elicit  spikes  in  the  postsynaptic  neuron  when  the  NMDA  input \nswitches that neuron into the up-state. \n\nTransitions  from  down  to  up-state  occur  when  synchronous  NMDA  inputs  depo(cid:173)\nlarize  the  membrane  enough  to  cause  the  opening  of additional  NMDA  receptor \nchannels  (due  to  the  voltage-dependence  of  their  opening).  This  results  in  a  re(cid:173)\ngeneretive  depolarization event,  which  is  limited  by  the  fast  opening  of IKA-type \n\n\fTime [s] \n\nFigure  1: \nInputs  with  high  AMPA-NMDA  ratio  cause  the  cell  to  spike  (top  trace, \ngAM PA  =0.05,  g N MDA  =0.01).  Strong  NMDA  inputs  combined with  potassium  currents \n(for  the  same  AMPA  input)  result  in  fluctuations  of  the  membrane  potential  between \ntwo  subthreshold  states,  with  occasional  firing  due  to  the  AMPA  inputs  (bottom trace, \ngAMPA  =0.01,  gNMDA  =0.1) \n\npotassium  channels.  This  up-state  is  stable  because  the  regenerative  nature  and \nlong  lifetime  of  NMDA  receptor  opening  keeps  the  membrane  depolarized,  while \nthe  slower  I Ks  potassium  current  prevents  further  depolarization.  When  input \nceases,  NMDA  channels  eventually  (TNMDA  ~ 150ms)  close  and  the  membrane \njumps  to  the  down-state.  Note  that  while  this  bistable  mechanism  is  intrinsic  to \nthe  membrane,  it  is  also  conditional  upon  input.  Since  the  voltage  threshold  for \nspike generation in the somal axon compartment is  above the up-state,  it acts as a \nbarrier.  Thus, synchronous AMPA input in the down-state has a  low probability of \neliciting a  spike. \n\nA  number  of  previous  experimental  studies  have  reported  similar  phenomena  in \nvarious  brain regions  [16,  9,  1]  where  the  two  states persist  even  with  all  intrinsic \ninward  currents  blocked  but  the  inputs  left  intact  [17] .  Pharmacological  block  of \nthe  potassium  currents  resulted  in  prolonged  up-states  [17] .  These  experimental \nresults suggested  a  conceptual  model  in  which  two-state fluctuations  are  (i)  input \ndriven,  (ii)  the membrane states are stabilized by potassium currents.  Nevertheless, \nthere remained a  puzzle  that  (iii)  up-state transitions  are  abrupt  and  (iv)  the the \nup-state is  prolonged  and  restricted  to  a  relatively narrow  range of voltages.  Our \nmodel  suggests  a  plausible  mechanism for  this  phenomenon consistent  with all  ex(cid:173)\nperimental constraints.  Below,  we  examine the origins of the two-state fluctuations \nin light of these findings. \n\n2.3  Analysis  of two  state fluctuations \n\nFigure 2A  shows the histogram of membrane potential for  a  neuron driven by com(cid:173)\nbined AMPA and NMDA input at 30 Hz.  There are two clear modes corresponding \nto the up and down-states.  The variability of the up-state and down-state voltages \nis  very  low  (u  =  1.4  mV  and  2.4  mV  respectively)  as  observed.  Figure  2B  shows \nthe  distribution  of the  up-state  duration.  The  distribution  of the  up-state  dura(cid:173)\ntions  depend  on  the  maximal  NMDA  conductance  and  the  decay  time  constant \nof  NMDA  (not  shown),  as  well  as  the  mean  rate  of  NMDA  inputs  (Figure  2C). \n\n\fA \n\nO. \n\n>-\n~O. \n:c \nCQ \n.c \n\u00a30. \n\nB \n\n40 \n\n30 \n\nC \n\n400 \n\n300 \n\n200 \n\nU) \nE \n'\"\" \nQ) \nE \ni= \n\n100 \n\n1000 \n\n500 \n\nTime (ms) \n\n20  30  40  50 \nNMDA Rate (Hz) \n\nFigure  2:  A.  Histogram  of the  up  and  down  states.  B.  Dwell  times  of the up  states  C. \nMean  duration of the up states increases with rate of NMDA  inputs.  Each histogram was \ncalculated over  a run of 120  seconds. \n\nAdditionally,  larger  maximal  potassium  conductances  shorten the  duration  of the \nup  states.  Thus,  we  predict  that  the  NMDA  receptors  are  intimately  involved  in \nshaping  the  firing  characteristics  of these  neurons.  Furthermore,  our  mechanistic \nexplanation leads a strong prediction about the functional role for  these fluctuations \nin neuronal processing. \n\n3  Contextual processing with  NMDA and  AMPA pathways \n\nSince NMDA and AMPA pathways have distinct roles in respectively switching and \nfiring  our model  neuron, we  suggest  the  following  conceptual  model  shown on  Fig \n3A. Without any input the neuron is at the rest or  disabled  state.  Contextual input \n(via  NMDA  receptors)  can  bring the  neuron  into  an  enabled  state.  Informational \n(for instance, cue or positional)  input  (via  AMPA receptors)  can fire  a  neuron only \nfrom  this enabled state. \n\nWhere  might  such  an  architecture  be  used?  In  the  CAl  region  of the  hippocam(cid:173)\npus,  pyramidal  cells receive  two distinct,  spatially  segregated input  pathways:  the \nperforant path from  cortex and the Schaffer  collaterals from  the  CA3  region.  The \nperforant  path  has  a  very  large  NMDA  receptor  content  [14]  which  is,  interest(cid:173)\ningly,  co-localized  with high  densities  of I KA  conductances  [5].  Experimental  [13] \nand  theoretical  [12]  observations  suggest  that  these  two  pathways  carry  distinct \ninformation.  Lisman has suggested that the perforant path carries contextual infor(cid:173)\nmation and the Schaffer collaterals bring sequence information [12].  Thus our model \nseems  to apply  biophysically  as  well  as  suggest a  possible way for  CAl neurons  to \ncarry out  contextual computations.  It is  known  that these  cell  can  fire  at  specific \nplaces in specific contexts.  How might these different signals interact?  As shown on \nFig3B , our model neuron can only fire  spikes due to positional input when the right \ncontext enables it.  We  note that a requirement for  contextual processing is  that the \ntwo  inputs  be  anatomically  segregated,  as  they  are  in  the  CAl  region.  However, \nwe  stress  that  the  phenomenon  of 2-state  fluctuations  itself is  independent  of the \nlocation of the two  kinds  of inputs. \n\nFigure  4A  shows  a  similar  processing  scheme  adapted  for  higher-order  language \n\n\fFiring state \n\na .... ;.~, ... , <;; \n\nB'5 \n.~ \n\n~ \n\n0 \n\n~~'-) \n\nContextual input \n\n\u2022 \n\nDown-state / Disabled \n\nA \n\nContext off \n\nContext on \n\nQ. \n\n~ 0 \n\"\" \n~~ \n\n'5 \n.~ \n<;; \n~ \n\nQ. \n\n~ 0 \ng> \n~~ \n\n~A/ \nJll \n\nFigure  3:  A.  Contextual  input  (high  NMDA)  switches  the  neuron  from  a  rest  state  to \nan  up  state.  Informational  input  (high  AMPA)  cause  the neuron  to  spike  only  from  the \nup  state.  B.  Weak  informational  input  can  cause  the  cell  to  fire  in  conjunction  with \nthe  contextual  input,  (left  traces)  while  strong  informational  input  will  not  fire  the  cell \nin  the  absence  of contextual  input  (right  traces).  In  this  simulation, the soma/proximal \ndendrite compartment receives  AMPA input, while  the NMDA input targets the dendritic \ncompartment. \n\nprocessing.  We  simulated 3 neurons each receiving the same AMPA,  informational \ninput.  This might represent the word  \"green\".  Each of these neurons  also  receives \ndistinct  contextual  input  via  NMDA  type  receptors.  These  might,  for  instance, \nrepresent  specific  noun  groups:  objects,  people  and  fruit.  The  word  \"green\"  may \nhave  very  different  meanings  in these  different  contexts  such  as  the  color  green,  a \nperson who is a  novice or an unripe fruit.  We simulated this simple scenario shown \nin Figure 4C.  Even though each neuron receives the same strong AMPA input, their \nfiring seems uncorrelated.  To evaluate the performance of the network in processing \ncontextual conjunctions, we measured the correlations between the information and \neach contextual input.  The most  correlated at each moment was  designated to be \nthe  correct  meaning.  We  then  measured  the  number  of spikes  emitted  by  each \nneuron during each  \"meaning\" .  Figure 4B  shows that the neurons performed well, \neach tuned to fire  preferentially in its appropriate context. \n\nThis  simple  example  illustrates  the  use  of a  plausible  biophysical  mechanism  for \ncomputing conjuctions or multiplying with neurons. \n\n4  Discussion \n\nVoltage fluctuations  between two subthresold levels  with similar properties are ob(cid:173)\nserved  in  vivo  in  a  variety of brain regions.  Our model is  in accordance with these \ndata and lead us to a new picture of how might these neuron operate in a functional \nmanner.  Figure 3A shows  our model  operating as  a  3-state device.  It has a  stable \nlow  membrane state from  which  it cannot fire  spikes,  which  we  called  disabled.  It \nalso  has  a  stable  depolarized  state  from  which  action  potentials  can  be  elicited, \nwhich  this  we  call  enabled  state.  Additionally,  it  has  a  firing  state  which  is  only \nreachable from  the enabled state. \n\nWhat  might  be the role  of the  two  non-firing  states?  We  suggest  that if high  and \nlow NMDA-content pathways carry separate information these neurons can compute \n\n\fA  Contextual input: \n\"objects\" \n\n\"people\" \n\n\"fruit\" \n\n111 \n0)(2)(3) \n\nB \n\nC 90 \n\n0 \n\n0 \n\nobjects \n\npeople \n\nfrun \n\n0 \n\n0 \n\nJ \n\n!6 o \n~5 \n\u2022 \u00b7 o  4 o \n0 \n~ \u2022 \u00a3 3 \n\n0 \n\nSensory input: \n\n\"green\" \n\no \n\n2 \n\nTime(s) \n\n0 \n\n0 \n\n0 \n\n4 \n\n1  2  3 \n\nI \n\n1  2  3 \n\n1  2  3 \n\nFigure 4:  A.  Illustrative task  for  contextual processing  in  semantic inference.  3 neurons \neach receive independent contextual  (NMDA)  and common informational  (AMPA)  input. \nB.  Voltage traces  showing  differences in  firing  patterns depending  upon context.  C.  Each \nneuron is tuned to its defined context.  Correlation was measured between the informational \nspike  train  and each  contextual  spike train  smoothed with  a  gaussian  filter  (a  = 60ms). \nThe most correlated context was  defined to be the right  one  and the spikes  of all neurons \nwere  counted. \n\nconjuctions,  a  simple  form  of multiplication.  If the  high  NMDA-content  pathway \ncarries  contextual  information then  it  would  be  in  position  to  enable  or  disable  a \nneuron.  In  the  enabled  state,  AMPA-type  informational  input  could  then  fire  a \nneuron  (Fig 3B). \n\nWe  have  presented  a  biophysical  model  for  two-state fluctuations  that  is  strongly \nsupported by data.  One concern might be that most observations of 2-state fluctu(cid:173)\nations  in  vivo  have been  when  the animal is  anesthetized,  implying  that this  kind \nof neuronal dynamics  is  an artifact of the  anesthetized state.  However,  these fluc(cid:173)\ntuations have been observed in several different  kinds of anesthesia, including local \nanesthesia [16].  Furthermore, it has been shown that the duration of the up-states \ncorrelate with orientation selectivity in visual cortical neurons suggesting that these \nfluctuations might playa role in information processing.  These observations suggest \nthat this phenomenon may be more indicative of a natural state of the cortex rather \nthan a  by-product of anesthesia. \n\nWhen the inputs with different AMPA/NMDA content are anatomically segregated, \nt he  NMDA  input  alone generates voltage fluctuations  between a  resting and depo(cid:173)\nlarized state, while the AMPA input causes the neuron to spike when in the up-state. \nThis mechanism  naturally leads to the suggestion that such  two-state fluctuations \ncould  have  a  function  in  computing  context/input  conjuctions.  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Neurosci.,  16:2397- 2410,  1996. \n\n\f", "award": [], "sourceid": 2115, "authors": [{"given_name": "\u00c1d\u00e1m", "family_name": "Kepecs", "institution": null}, {"given_name": "S.", "family_name": "Raghavachari", "institution": null}]}