{"title": "Simulations Suggest Information Processing Roles for the Diverse Currents in Hippocampal Neurons", "book": "Neural Information Processing Systems", "page_first": 82, "page_last": 94, "abstract": null, "full_text": "82 \n\nSIMULATIONS  SUGGEST \n\nINFORMATION PROCESSING ROLES \nFOR THE DIVERSE  CURRENTS  IN \n\nHIPPOCAMPAL NEURONS \n\nLyle J.  Borg-Graham \n\nHarvard-MIT Division of Health Sciences and Technology and \n\nCenter for  Biological Information Processing, \n\nMassachusetts Institute of Technology,  Cambridge, Massachusetts 02139 \n\nABSTRACT \n\nA computer model of the hippocampal pyramidal cell (HPC) is  described \n\nwhich  integrates  data from  a  variety  of sources  in order  to  develop  a  con(cid:173)\nsistent description for  this cell  type.  The model  presently includes  descrip(cid:173)\ntions  of eleven non-linear somatic currents of the HPC, and the electrotonic \nstructure of the neuron is modelled with a soma/short-cable approximation. \nModel simulations qualitatively or quantitatively reproduce a  wide range of \nsomatic electrical behavior i~ HPCs, and demonstrate possible  roles  for the \nvarious currents in information  processing. \n\n1  The  Computational Properties of Neurons \n\nThere  are  several  substrates  for  neuronal  computation,  including  connec(cid:173)\ntivity, synapses,  morphometries of dendritic  trees,  linear parameters  of cell \nmembrane, as well as non-linear, time-varying membrane conductances, also \nreferred  to as  currents or channels.  In  the classical  description  of neuronal \nfunction,  the contribution  of membrane channels  is  constrained  to  that  of \ngenerating the action potential, setting firing  threshold, and establishing the \nrelationship  between (steady-state)  stimulus  intensity and  firing  frequency. \nHowever,  it is  becoming clear that  the role  of these channels  may  be much \nmore complex, resulting in a variety of novel \"computational operators\" that \nreflect  the information  processing occurring in  the biological neural  net. \n\n\u00a9 American Institute of Physics 1988 \n\n\f83 \n\n2  Modelling  Hippocampal Neurons \n\nOver the  past  decade  a  wide  variety of non-linear  ion channels,  have  been \ndescribed  for  many  excitable  cells,  in  particular  several  kinds  of neurons. \nOne  such  neuron  is  the  hippocampal  pyramidal  cell  (HPC).  HPC  chan(cid:173)\nnels  are  marked  by  their  wide  range  of temporal,  voltage-dependent,  and \nchemical-dependent characteristics,  which  results  in very complex  behavior \nor  responses  of these  stereotypical  cortical  integrating cells.  For example, \nsome HPC channels are activated (opened)  transiently and quickly, thus pri(cid:173)\nmarily affecting  the action  potential shape.  Other channels  have longer  ki(cid:173)\nnetics, modulating the response of HPCs over hundreds of milliseconds.  The \nmeasurement  these  channels  is  hampered  by  various  technical  constraints, \nincluding the small size and extended electrotonic structure of HPCs and the \ndiverse  preparations  used  in experiments.  Modelling the electrical  behavior \nof HPCs  with computer simulations is  one method  of integrating data from \na  variety of sources in order to develop  a  consistent description for  this  cell \ntype. \n\nIn the model referred to here putative mechanisms for  voltage-dependent \n\nand  calcium-dependent  channel gating  have  been  used  to generate  simula(cid:173)\ntions of the somatic electrical behavior of HPCs, and to suggest mechanisms \nfor  information processing at  the single cell  level.  The model  has  also  been \nused  to suggest experimental protocols  designed  to test  the validity of sim(cid:173)\nulation results.  Model simulations qualitatively or quantitatively reproduce \na  wide  range of somatic electrical behavior in HPCs, and  explicitly  demon(cid:173)\nstrate possible functional  roles  for  the various currents [1]. \n\nThe model  presently includes  descriptions  of eleven  non-linear somatic \ncurrents,  including  three  putative  N a+  currents  -\nINa-trig,  INa-rep,  and \nINa-tail;  six  K+  currents  that  have  been  reported  in  the  literature - IDR \n(Delayed  Rectifier),  lA,  Ie,  IAHP  (After-hyperpolarization),  1M,  and  IQ; \nand two Ca2+ currents, also reported  previously - lea  and  leas. \n\nThe  electrotonic  structure  of the  HPC  is  modelled  with  a  soma/short(cid:173)\n\ncable approximation, and  the dendrites are assumed to be linear.  While the \nconditions  for  reducing  the dendritic  tree  to a  single  cable are  not  met  for \nHPC  (the so-called Rall conditions  [3]),  the  Zin  of the cable is  close  to that \nof the tree.  In addition, although HPC dendrites have non-linear membrane, \nit  assumed  that  as  a  first  approximation  the contribution of currents  from \nthis membrane may be ignored in the somatic response  to somatic stimulus. \nLikewise,  the  model structure assumes  that axon-soma current  under these \nconditions can be lumped into the soma circuit. \n\n\f84 \n\nIn  part  this  paper  will  address  the  following  question:  if  neural  nets \n\nare realizable using elements that  have simple integrative all-or-nothing re(cid:173)\nsponses,  connected  to each other  with  regenerative  conductors,  then  what \nis  the function  for all  the channels observed experimentally in real neurons? \nThe results  of this  HPC  model study suggest  some  purpose for  these com(cid:173)\nplexities, and in this  paper we  shall investigate some of the possible roles  of \nnon-linear channels in neuronal information processing.  However, given the \nspeculative  nature  of many of the  currents  that  we  have  presented  in  the \nmodel, it is  important to view  results  based  on  the interaction of the many \nmodel  elements as  preliminary. \n\n3  Defining Neural Information Coding is the First \n\nStep  in  Describing  Biological Computations \n\nDetermination of computational properties  of neurons  requires  a  priori as(cid:173)\nsumptions  as  to how information is  encoded in  neuronal  output.  The clas(cid:173)\nsical  description  assumes  that  information  is  encoded  as  spike  frequency. \nHowever,  a  single  output variable,  proportional to firing  frequency,  ignores \nother potentially information-rich degrees  of freedom,  including: \n\n\u2022  Relative phase of concurrent inputs. \n\n\u2022  Frequency modulation during single  bursts. \n\n\u2022  Cessation of firing  due to intrinsic mechanisms. \n\n\u2022  Spike shape. \n\nNote  that  these  variables  apply  to  patterns  of  repetitive  firingl.  The \nrelative  phase  of different  inputs  to  a  single  cell  is  very  important  at  low \nfiring  rates,  but  becomes  less  so  as  firing  frequency  approaches  the  time \nconstant of the postsynaptic membrane or some other rate-limiting  process \nin  the synaptic  transduction  (e.g.  neurotransmitter release  or  post synap(cid:173)\ntic  channel activation/deactivation kinetics).  Frequency modulation during \nbursts/spike  trains  may  be important in  the  interaction  of a  given  axon's \noutput  with  other inputs  at  the  target  neuron.  Cessation  of firing  due  to \nmechanisms  intrinsic  to  the  cell  (as  opposed  to  the  end  of input)  may  be \n\nlSingle spikes may be considered as degenerate cases of repetitive firing  responses. \n\n\f85 \n\nimportant, for  example, in  that cell's  transmission function.  Finally, modu(cid:173)\nlation of spike shape may have several consequences, which will be discussed \nlater. \n\n4 \n\nPhysiological Modulation of HPC  Currents \n\nIn  order for  modulation  of HPC  currents  to  be  considered  as  potential in(cid:173)\nformation  processing mechanisms  in vivo,  it is  necessary to identify physio(cid:173)\nlogical  modulators.  For several of the currents  described  here  such factors \nhave  been  identified.  For example,  there  is  evidence  that  1M  is  inhibited \nby  muscarinic  (physiologically,  cholinergic)  agonists  [2],  that  1A  is  inhib(cid:173)\nited  by acetylcholine  [6],  and  that  1AHP  is  inhibited  by noradrenaline  [5]. \nIn  fact,  the  list  of neurotransmitters  which  are  active  non-synaptically  is \ngrowing  rapidly.  It remains  to  be seen  whether  there  are  as  yet  undiscov(cid:173)\nered  mechanisms for  modulating other HPC currents, for  example the three \nN a+  currents  proposed  in  the present  model.  Some  possible consequences \nof such mechanisms  will  be discussed later. \n\n5  HPC  Currents and Information  Processing \n\nThe role  of a  given channel on  the  HPC  electrical  response  depends  on  its \ntemporal  characteristics  as  a  function  of voltage,  intracellular messengers, \nand  other variables.  This  is  complicated  by  the fact  that  the  opening and \nclosing of channels is  equivalent to varying conductances, allowing both lin(cid:173)\near  and  non-linear  operations  (e.g. \nIn  particular,  a  current \nwhich  is  activated/deactivated  over  a  period  of hundreds  of milliseconds \nwill,  to a  first  approximation,  act  by slowly  changing  the  time constant of \nthe  membrane.  At  the  other  extreme,  currents  which  activate/deactivate \nwith  sub-millisecond  time  constants  act  by changing the  trajectory of the \nmembrane  voltage in  complicated  ways.  The classic  example  of this  is  the \nrole of N a+  currents  underlying  the action potential. \n\n[4]  and  [7]). \n\nTo  investigate  how  the  different  HPC  currents  may  contribute  to  the \ninformation  processing of this  neuron,  we  have looked  at  how  each current \nshapes  the  HPC  response  to  a  simple  repertoire  of inputs.  At  this  stage \nin  our  research  the  inputs  have  been  very  basic  - short  somatic  current \nsteps  that evoke single spikes, long lasting somatic current steps  that evoke \nspike  trains,  and  current steps  at  the distal end  of the dendritic  cable.  By \nexamining  the  response  to  these  inputs  the  functional  roles  of  the  HPC \n\n\f86 \n\nI Current\" Spike Shape I Spike Threshold  I Tm/Frequency-Intensity I \n\nINa-trig \nINa-rep \n\nICa \nIDR \nIA \nIc \n\nIAHP \n1M \n\n- (++) \n\n+ \n+ \n\n++ \n+ \n+ \n-\n-\n\n+++ \n++ \n-(+) \n\n+ \n++ \n-\n++ \n+ \n\n-\n\n+++ \n\n+ (+++) \n\n++ \n++ \n+++ \n+++ \n+ \n\nTable  1:  Putative  functional  roles  of  HPC  somatic  currents.  Entries  in \nparentheses indicate secondary role,  e.g.  Ca 2+  activation of J(+  current. \n\ncurrents can be  tentatively grouped  into three (non-exclusive)  categories: \n\n\u2022  Modulation of spike shape. \n\n\u2022  Modulation of firing  threshold,  both for  single  and repetitive spikes. \n\n\u2022  Modulation of semi-steady-state membrane time constant. \n\n\u2022  Modulation  of repetitive  firing,  specifically  the  relationship  between \nstrength of tonic input and frequency of initial burst and later \"steady \nstate\"  spike train. \n\nTable  1 summarizes  speculative roles  for  some  of the  HPC  currents  as \nsuggested  by  the  simulations.  Note  that  while  all  four  of the  listed  char(cid:173)\nacteristics  are interrelated,  the last  two are particularly so  and  are lumped \ntogether in Table  1. \n\n5.1  Possible Roles  for  Modulation of FI Characteristic \n\nAgain,  it has  been traditionally assumed  that neural information is  encoded \nby (steady-state) frequency modulation, e.g.  the number of spikes per second \nover  some  time  period  encodes  the  output  information  of a  neuron.  For \nexample, muscle fiber contraction is  approximately proportional to the spike \nfrequency  of its  motor neuron  2.  If the physiological inhibition of a  specific \n\n2In  fact,  where  action  potential  propagation  is  a  stereotyped  phenomena,  such  as in \n\nlong  axons,  then  the timing of spikes is the only  parameter that may be modulated. \n\n\f87 \n\n. ~  .. --\n--\n\n'--;-\n, \n\n......... \n\n, \n, , \n, , \n, , , , , \n\n\\ \n\n\\ \n\\ \n\\ \n\\ \n\nStimulus Intensity  (Constant Current) \n\nFigure  1:  Classical  relation  between  total  neuronal  input  (typically  tonic \ncurrent  stimulus)  and  spike  firing  frequency  [solid  line]  and  (qualitative) \nbiological  relationships  [dashed  and  dotted  lines].  The  dotted  line  applies \nwhen  INa-rep  is  blocked. \n\ncurrent changes the FI characteristic, this allows  one way  to modulate that \nneuron's  information  processing by various agents. \n\nFigure 1  contrasts  the  classical  input-output  relation  of a  neuron  and \n\nmore  biological  input-output  relations.  The relationships  have several fea(cid:173)\ntures  which  can  be  potentially  modulated  either  physiologically  or  patho(cid:173)\nlogically,  including saturation, threshold,  and shape of the curves.  Note in \nparticular  the cessation  of output  with increased  stimulation,  as  the  depo(cid:173)\nlarizing stimulus prevents  the resetting of the transient inward currents. \n\nFor the HPC, simulations show (Figure 2 and Figure 3) that blocking the \nputative INa-rep  has  the effect  of causing the cell  to \"latch-up\"  in response \nto  tonic  stimulus  that  would  otherwise  elicit  stable  spike  trains.  Both  de(cid:173)\npolarizing  currents  and  repolarizing  currents  playa role  here.  First,  spike \nupstroke is  mediated  by both  INa-rep  and  the lower  threshold  INa-trig;  at \nhigh stimuli repolarization between spikes does  not get low enough to reset \nINa-trig'  Second, spikes  due  to only one of these  N a+  currents  are  weaker \nand  as  a  result  do  not  activate  the  repolarizing  [(+  currents  as  much  as \nnormal  because a)  reduced  time at depolarized  levels  activates  the voltage(cid:173)\ndependent  [(+  currents  less  and  b)  less  Ca2+  influx  with  smaller  spikes \nreduces  the  Ca2+ -dependent activation of some  [(+  currents.  The  net  re(cid:173)\nsult is that repolarization between spikes is  weaker and, again, does not reset \nINa-trig. \n\nAlthough  the current being modulated here (INa-rep)  is  theoretical,  the \n\n\f88 \n\nVoltage  (nV) \n,~ \n\n;299.9 \n\n499.9 \n\n699.9 \n\nTine  (sec)  (x  1.ge-3) \n\n,899.9 \n\n~~VL--\n\nVo leage  (nV) \nb~ \n\n--\n\n2  nA  Stinulus,  Nornal \n\n'---\n\n,299.9 \n\n499.9 \n\n699.9 \n\nTine  (sec)  (x  1.ge-3) \n\n,899.9 \n\nI!J(~VVVVVVL.--'L.--V--V--~~N~ \n\nVoltage  (P'lV) \nh~ \n\n,299.9 \n\n499.9 \n\n699.9 \n\nTine  (se~ (x  1.ge-3) \n\n99.9 \n\nI \n\nI  ~VVl/VvI/\\/VV\\/\\/VVVVV1.,/VVVVV-~~ \n\n6  nA  StiP'lulus,  Nornal \n\nFigure  2:  Simulation  of repetitive  firing  in  response  to  constant  current \ninjection  into the soma.  In  this  series,  with  the  \"normal\"  cell,  a  stimulus \nof about 8  nA  (not shown)  will  cause  to cell  to fire  a  short  burst  and  then \ncease firing. \n\npossibility  of selective  blocking  of  INa-rep  allows  a  mechanism  for  shifting \nthe saturation  of the  neuron's  response  to  the  left  and,  as  can  be  seen  by \ncomparing  Figures 2  and 3,  making  the FI curve steeper over  the  response \nrange. \n\n5.2  Possible Roles  for  Modulation of Spike Threshold \n\nThe  somatic  firing  threshold  determines  the  minimal  input  for  eliciting  a \nspike,  and  in  effect  change  the  sensitivity  of a  cell.  As  a  simple  example, \nblocking INa-trig  in the HPe model raises  threshold by about 10  millivolts. \nThis  could  cause  the  cell  to  ignore  input  patterns  that  would  otherwise \ngenerate action potentials. \n\nThere  are  two  aspects  of the  firing  \"threshold\"  for  a  cell  - static  and \n\ndynamic.  Thus,  the  rate at which  the  soma  membrane approaches  thresh(cid:173)\nold  is  important  along  with  the  magnitude  of that  threshold.  In  general \nthe threshold level rises  with a slower depolarization for  several reasons, in(cid:173)\ncluding  partial  inactivation  of inward  currents  (e.g.  INa-trig)  and  partial \nactivation of outward currents (e.g.  IA  [8])  at subthreshold levels. \n\n\f89 \n\n499.9 \n\n99.9 \n\nTine  (sec)  (x  1.ge-3) \n\n899.9 \n\n2  nA  Stinulus,  u~o  I-Na-Rep \n\n4  nA  Stinulus,  u~o I-Na-Rep \n\n499 . 9 \n\n99.9 \n\nTine  (sec)  ex  1.ge-3} \n\n899.9 \n\n-89.9 \n\n6  nA  Stinulus,  u~o  I-Na-Rep \n\nFigure 3:  Blocking one of the  putative N a+  currents  (INa-rep)  causes  the \nHPC repetitive firing response to fail at lower stimulus than \"normal\".  This \ncorresponds  to  the  leftward  shift  in  the  saturation  of  the  response  curve \nshown in Figure 1. \n\nThus it is  possible, for  example,  that  IA  helps  to distinguish  tonic  den(cid:173)\n\ndritic distal synaptic input from  proximal input.  For input  that eventually \nwill  supply  the same depolarizing current at the soma,  dendritic  input will \nhave a  slower onset due  to the cable  properties  of the dendrites.  This  slow \nonset  could  allow  IA  to  delay  the  onset  of  the  spike  or  spikes.  A  simi(cid:173)\nlar depolarizing current applied more proximally would  have a faster onset. \nSub-threshold  activation of IA  on  the depolarizing phase would  then  be in(cid:173)\nsufficient  to delay the spike. \n\n5.3  Possible Roles for  Modulation of Somatic Spike Shape \n\nHow  important is  the  shape of an  individual  spike generated at the soma? \nFirst, we can assume that spike shape, in particular spike width, is  unimpor(cid:173)\ntant at  the soma spike-generating membrane - once  the soma fires,  it fires. \nHowever,  the  effect  of the spike beyond  the soma  mayor may not  depend \non  the  spike shape,  and  this  is  dependent  on  both  the degree  which  spike \npropagation is  linear and on  the properties of the pre-synaptic membrane. \nAxon  transmission  is  both a  linear and  non-linear  phenomena,  and  the \nshorter  the  axon's  electrotonic  length,  the  more  the  shape  of the  somatic \n\n\f90 \n\naction  potential  will  be  preserved  at  the  distal  pre-synaptic  terminal.  At \none extreme,  an  axon could  transmit  the spike  a  purely  non-linear  fashion \n- once  threshold  was  reached,  the  classic  \"all-or-nothing\"  response  would \ntransmit a  stereotyped action potential whose  shape would  be independent \nof the post-threshold soma response.  At the other extreme, i.e.  if the axonal \nmembrane were  purely linear,  the propagation  of the somatic event at  any \npoint  down  the  axon  would  be  a  linear  convolution  of the  somatic  signal \nand the axon cable properties.  It is  likely that the situation in the brain lies \nsomewhere  between  these limits,  and  will  depend on  the wavelength of the \nspike, the axon  non-linearities  and  the axon length. \n\nWhat role could  be served  by the somatic action  potential shape modu(cid:173)\n\nlating the pre-synaptic terminal signal?  There are at least three possibilities. \nFirst, it has  been demonstrated that the release of transmitter at some pre(cid:173)\nsynaptic  terminals is  not an \"all-or-nothing\" event, and in fact  is  a function \nof the pre-synaptic  membrane  voltage  waveform.  Thus,  modulation  of the \nsomatic spike width may determine how much transmitter is  released  down \nthe  line,  providing  a  mechanism for  changing  the  effective strength  of the \nspike as  seen by the target neuron.  Modulation of somatic spike width could \nbe equivalent to a modulation ofthe \"loudness\" of a given neuron's message. \nSecond, pyramidal cell axons often project collateral branches back to the \noriginating soma, forming  axo-somatic synapses  which  result  in  a  feedback \nloop.  In this case, modulation of the somatic spike could affect this feedback \nin  complicated ways, particularly since the collaterals  are  typically short. \n\nFinally, somatic spike shape may also  playa role  in  the transmission of \nspikes at axonal branch points.  For example, consider a axonal branch point \nwith an impedance mismatch and  two daughter branches, one  thin  and one \nthick.  Here  a  spike  that  is  too  narrow  may  not  be  able  to  depolarize  the \nthick branch sufficiently for transmission of the spike down that branch, with \nthe spike propagating only down  the thin branch.  Conversely, a  wider spike \nmay  be  passed  by  both  branches.  Modulation  of the somatic  spike shape \ncould  then  be  used  to  direct  how  a  cell's  output  is  broadcast,  some  times \nallowing transmission to all the destinations of an HPC , and at other times \ninhibiting transmission  to a limited set of the target  neurons. \n\nFor  HPCs  much  evidence  has  been  obtained  which  implicate  the  roles \nof various  HPC  currents  on  modulating  somatic  spike  shape,  for  example \nthe  Ca2+ -dependent  K+  current  Ie  [9].  Simulations  which  demonstrate \nthe effect  of Ie  on  the  shape  of individual  action  potentials  are  shown  in \nFigure 4. \n\n\f91 \n\nVolt\"9\"  (!'IV) \n\nVolts\"  (nU) \n\nTin\"  (~\"c)  (x  1.9,,-3) \nIl  3.1l  4 . 9  S.1l \n\nTin\"  (~\"c)  (x  1.9,,-3) \nIl  3.1l  4.1l  5.9 \n\n.9 \n\n-81l.1l \n\n-81l.9 \n\n\"  . \n. \n,:\" \n1 ' \\  \n, :  \\ \n\n.... \n\nCurr\"nt  (nA)\" \n\n1l.1l \n\n\"  \" \nI \n\n... ... \n\nI \"  \nTi~,, : (~ec)  (x.1.1l,,-3) \n\u2022 .9  3.'8- .'\\. \u2022 .il\"_\".5.1l \n\n.. \n\n.Il \n\n-11l.1l \n\nI-Na-Tris \n\n-_.  I-DR \n\"  ..  \"  I-C \n\nFigure 4:  Role of Ie  during repolarization of spike.  In the simulation on the \nleft,  Ie  is  the  largest  repolarizing  current.  In  the  simulation  on  the  right, \nblocking Ie  results in an wider spike. \n\n6  The  Assumption  of Somatic  Vs.  Non-Somatic \n\nCurrents \n\nIn  this  research  the somatic  response of the  HPC  has  been  modelled  under \nthe  assumption  that  the  data on  HPC  currents  reflect  activity of channels \nlocalized at the soma.  However, it must be considered  that all channel pro(cid:173)\nteins,  regardless  of  their  final  functional  destination,  are  manufactured  at \nthe  soma.  Some  of the  so-called  somatic  channels  may  therefore  be  ves(cid:173)\ntiges  of channels intended for  dendritic, axonal,  or pre-synaptic  membrane. \nFor example, if the spike-shaping channels are intended to be expressed for \npre-synaptic  membrane,  then  modulation  of these  channels  by endogenous \nfactors  (e.g.  ACh)  takes  place  at  target  neuron.  This  may seem  disadvan(cid:173)\ntageous  if a factor  is  to act selectively on some afferent  tract.  On  the other \nhand, in  the dendritic field  of a  given  neuron  it is  possible only  some affer(cid:173)\nents  have certain  channels,  thus  allowing selective  response  to modulating \nagents.  These  possibilities  further expand  the  potential roles  of membrane \nchannels for  computation. \n\n\f92 \n\n7  Other Possible Roles of Currents for  Modulat(cid:173)\n\ning  HPC  Response \n\nThere are many other potential ways  that HPC currents may modulate the \nHPC  response.  For example,  the  relationship  between  intracellular  Ca2+ \nand  the Ca2+-dependent K+  currents, Ic and  IAHP,  may indicate possible \ninformation processing mechanisms. \n\nIntracellular Ca2+ is an important second messenger for  several intracel(cid:173)\n\nlular processes, for  example muscular contraction, but excessive [Ca2+]in  is \nnoxious.  There are at least three negative feedback mechanisms for  limiting \nthe flow  of Ca2+  :  voltage-dependent inactivation of Ca2+  currents; reduc(cid:173)\ntion of ECa  (and thus the Ca2+  driving force)  with Ca2+  influx;  and the just \nmentioned Ca2+ -mediation of repolarizing currents.  A possible information \nprocessing mechanism could  be by modulation of IAHP,  which plays an im(cid:173)\nportant role in limiting repetitive firing;.  Simulations suggest  that blocking \nthis current causes  Ic  to step in and  eventually limit further repetitive fir(cid:173)\ning, though after many more spikes in a train.  Blocking both these currents \nmay allow other mechanisms  to control repetitive firing,  perhaps  ones  that \noperate independently of [Ca2+]in.  Conceivably,  this  could  put the  neuron \ninto quite a  differen t  operating region. \n\n8  Populations  of Neurons  V s.  Single  Cells:  Im(cid:173)\nplications for Graded Modulation of HPC Cur(cid:173)\nrents \n\nthe  entire  population  of  a  given  channel  type  is  either \n\nIn  this  paper we  have considered  the all-or-nothing contribution of the var(cid:173)\nious  channels,  Le. \nactivated  normally  or all  the  channels  are  disabled/blocked.  This  descrip(cid:173)\ntion may be oversimplified in  two ways.  First, it is  possible  that a  blocking \nmechanism for  a  given channel may have a graded effect.  For example, it is \npossible that cholinergic input is not homogeneous over the soma membrane, \nor  that  at  a  given  time  only  a  portion  of these  afferents  are  activated.  In \neither case it is possible that only a  portion of the cholinergic receptors are \nbound, thus inhibiting a  portion  of channels.  Second,  the result  of channel \ninhibition  by  neuromodulatory  projections  must  consider  both  single  cell \n\n3The  slowing  down  of the  spike  trains  in  Figure 2  and  Figure 3  is  mainly  due  to  the \n\nbuildup of [Ca 2+];n,  which  progressively activates more  IAHP. \n\n\f93 \n\nresponse  and  population response,  the size  of the population  depending on \nthe  neuro-architecture of a  cortical  region  and  the afferents.  For example, \nactivation of a cholinergic tract which terminates in a localized hippocampal \nregion  may effect  thousands  of HPCs.  Assuming that  the 1M of individual \nHPCs  in  the  region  may be  either  turned  on  or off completely  with  some \nprobability, the behavior of the  population will  be that of a graded response \nof 1M  inhibition.  This graded response will in  turn depend  on the strength \nof the cholinergic tract activity. \n\nThe key  point is  that  the  information  processing  properties  of isolated \nneurons  may  be  reflected  in  the  behavior  of a  population,  and  vica-versa. \nWhile it is  likely that removal of a single pyramidal cell from  the hippocam(cid:173)\npus  will  have  zero  functional  effect,  no  neuron  is  an  island.  Understand(cid:173)\ning the central nervous system  begins  with  the spectrum of behavior in  its \nfunctional units,  which  may range  from  single  channels,  to specific areas  of \na  dendritic  tree,  to  the  single  cell,  to  cortical  or  nuclear  subfields,  on  up \nthrough the main subsystems of CNS. \n\nReferences \n\n[1]  L.  Borg-Graham.  Modelling  the  Somatic  Electrical  Behavior  of Hip(cid:173)\n\npocampal  Pyramidal  Neurons.  Master's  thesis,  Massachusetts  Institute \nof Technology,  1987. \n\n[2]  J. Halliwell and  P.  Adams.  Voltage clamp analysis of muscarinic excita(cid:173)\n\ntion in hippocampal neurons.  Brain Research, 250:71-92, 1982. \n\n[3]  J.  J.  B.  Jack,  D.  Noble,  and  R.  W.  Tsien.  Electric  Current  Flow  In \n\nExcitable  Cells.  Clarendon Press, Oxford, 1983. \n\n[4]  C.  Koch  and  T.  Poggio.  Biophysics of computation:  neurons,  synapses \nand  membranes.  G. B.!. P.  Paper,  (008),  1984.  Center  for  Biological \nInformation Processing,  MIT. \n\n[5]  D. Madison and R.  Nicoll.  Noradrenaline blocks accommodation ofpyra(cid:173)\n\nmidal cell  discharge in the hippocampus.  Nature,  299:,  Oct 1982. \n\n[6]  Y.  Nakajuma,  S.  Nakajima,  R.  Leonard,  and  K.  Yamaguchi.  Actetyl(cid:173)\n\ncholine inhibits  a-current in dissociated  cultured  hippocampal neurons. \nBiophysical Journal,  49:575a,  1986. \n\n\f94 \n\n[7]  T.  Poggio  and  V.  Torre.  Theoretical  Approaches  to  Complex  Systems, \nLecture  Notes  in  Biomathematics,  pages  28- 38.  Volume  21,  Springer \nVerlag,  Berlin, 1978.  A New  Approach to Synaptic Interaction. \n\n[8]  J. Storm.  A-current and ca-dependent transient outward current control \nthe initial repetitive firing in hippocampal neurons.  Biophysical Journal, \n49:369a,  1986. \n\n[9]  J. Storm.  Mechanisms of action potential repolarization and a fast after(cid:173)\nhyperpolarization in rat  hippocampal pyramidal cells.  Journal of Phys(cid:173)\niology,  1986. \n\n\f", "award": [], "sourceid": 82, "authors": [{"given_name": "Lyle", "family_name": "Borg-Graham", "institution": null}]}