{"title": "Contrast Adaptation in Simple Cells by Changing the Transmitter Release Probability", "book": "Advances in Neural Information Processing Systems", "page_first": 76, "page_last": 82, "abstract": null, "full_text": "Contrast adaptation in simple cells by changing \n\nthe transmitter release probability \n\nPeter Adorjan \n\nKlaus Obennayer \n\nDept. of Computer Science, FR2-1, Technical  University Berlin \n\nFranklinstrasse 28/2910587 Berlin, Germany \n\n{adp, oby} @cs.tu-berlin.de  http://www.ni.cs.tu-berlin.de \n\nAbstract \n\nThe contrast response function (CRF) of many neurons in the primary vi(cid:173)\nsual  cortex saturates and shifts towards higher contrast values following \nprolonged presentation of high contrast visual stimuli.  Using a recurrent \nneural  network of excitatory spiking neurons with adapting synapses we \nshow  that both effects could  be  explained  by  a fast  and  a slow compo(cid:173)\nnent in the synaptic adaptation.  (i) Fast synaptic depression leads to sat(cid:173)\nuration  of the CRF and  phase  advance  in  the cortical  response to  high \ncontrast stimuli.  (ii) Slow adaptation of the synaptic transmitter release \nprobability is derived such that the mutual information between the input \nand  the output of a cortical neuron  is  maximal.  This component-given \nby  infomax learning rule-explains contrast adaptation of the averaged \nmembrane  potential  (DC  component)  as  well  as  the surprising experi(cid:173)\nmental  result,  that  the  stimulus  modulated component  (Fl  component) \nof a cortical cell's membrane potential adapts only weakly. Based on our \nresults,  we propose a new  experiment to estimate the strength of the ef(cid:173)\nfective  excitatory  feedback  to  a  cortical  neuron,  and  we  also  suggest a \nrelatively  simple experimental  test to justify our hypothesized synaptic \nmechanism for contrast adaptation. \n\n1  Introduction \n\nCells in  the primary visual cortex  have to encode a wide range of contrast levels, and they \nstill  need  to  be  sensitive  to  small  changes  in  the  input intensities.  Because the  signaling \ncapacity is limited, this paradox can  be resolved only by  a dynamic adaptation to changes \nin  the input intensity distribution:  the contrast response function  (CRF) of many  neurons \nin  the primary visual cortex shifts towards higher contrast values following prolonged pre(cid:173)\nsentation of high contrast visual stimuli (Ahmed et al.  1997, Carandini &  Ferster 1997). \n\nOn  the  one  hand,  recent  experiments,  suggest  that  synaptic  plasticity  has  a  major  role \n\n\fContrast Adaptation and Infomax \n\n77 \n\nin  contrast  adaptation.  Because local  application  of GABA does  not  mediate  adaptation \n(Vidyasagar 1990) and the  membrane conductance does  not increase  significantly during \nadaptation (Ahmed et al.  1997, Carandini &  Ferster 1997), lateral  inhibition is unlikely to \naccount for contrast adaptation.  In  contrast, blocking glutamate (excitatory) autoreceptors \ndecreases the degree of adaptation (McLean  &  Palmer  1996). Furthermore, the adaptation \nis  stimulus specific  (e.g.  Carandini et al.  1998),  it is  strongest if the adapting and testing \nstimuli  are  the  same.  On  the  other  hand,  plasticity  of synaptic  weights  (e.g.  Chance  et \nal.  1998)  cannot  explain  the  weak  adaptation  of the  stimulus driven  modulations  in  the \nmembrane potential (FI  component) (Carandini &  Ferster  1997) and the retardation of the \nresponse  phase  after  high contrast  adaptation  (Saul  1995).  These  experimental  findings \nmotivated us  to explore  how  presynaptic factors,  such  as  a long term plasticity  mediated \nby  changes  in  the transmitter release probability (Finlayson &  Cynader 1995) affect  con(cid:173)\ntrast adaptation. \n\n2  The single cell and the cortical circuit model \n\nThe cortical cells are modeled as  leaky integrators with a firing threshold of -55 mY.  The \ninterspike membrane potential dynamics is described by \n\n8Vi(t) \n\n~ \n\nCm~ =  -91eak (Vi(t)  - Eresd  - L9ij(t) (Vi(t)  - Esyn)  . \n\n(I) \n\nThe  postsynaptic conductance 9ij (t)  is  the integral  over  the previous  presynaptic events \nand is described by  the alpha-function \n\nJ \n\n(2) \nwhere t;  is the arrival time of spike number s from  neuron j. Including short term synaptic \ndepressIOn,  the effective conductance is  weighted by  the portion of the synaptic resource \nPij (t)  . Rij (t)  that targets the postsynaptic side.  The model parameters  are Cm  = 0.5 nF, \n91e ak  = 31  nS,  E rest  = -65 mY,  Esyn  = -5 mY,  9'::':~x  = 7.8  nS,  and  Tpeak  = 1 ms, \nand the absolute refractory period is 2 ms,  and after a spike, the membrane potential is re(cid:173)\nset  1 m V  below  the  resting potential.  Following Tsodyks &  Markram  (1997)  a  synapse \nbetween  neurons j  and  i is  characterized  by  the relative  portion of the available  synaptic \ntransmitter or resource  Rij.  After a presynaptic event,  Rij decreases  by  Pij  Rij, and  re(cid:173)\ncovers  exponentially,  where Pij  is  the transmitter release  probability.  The time evolution \nof Rij between  two presynaptic spikes is then \n\n(-(t -i)) \n\nTree \n\nRij(t) =  1 -\n\n(1  - (Rij{t)  - pij(t)Rij{t))) exp \n\nA \n\n\u2022 \n\n, \n\n(3) \n\nwhere \u00a3 is  the last spike time,  and  the recovery  time constant  Tree  =  200  ms.  Assuming \nPoisson distributed presynaptic firing, the steady state of the expected resource is \n\n(4) \n\nThe stationary mean excitatory postsynaptic current (EPSC) Ii] (fj , Pij)  is proportional to \nthe presynaptic firing frequency  fj  and the activated transmitter Pij Ri] (fj , Pij ) \n\nIi] (fj, Pij)  ex  f  Pij  Ri] (fj, Pij)  . \n\n(5) \nThe mean  current saturates  for  high input rates  /j and  it also  depends on  the  transmitter \nrelease probability Pij:  with a high release probability the function is steeper at low presy(cid:173)\nnaptic frequencies  but saturates earlier than for a low release probability. \n\n\f78 \n\n(a) \n\n80  r====-'- -- - - ,  \n\n.... #  . . . .  - -\n\n,'. \n\n,A \n,,/\"  0  0 \n\n0 \n\n\u00a7 \n\n--- p=O.55 \n-\np=O.24 \n\n,-\n~. \n\nt-\" \n\n0 \n\n0 \n\n\" \n......... \n\n_ \n\ng 60 \n.\u00a3 \ne 40 \nOD \" J!  20 \n\nOF'='-4-~o~~-----~ \n102 \n\n10\u00b0 \n\n10' \n\nFiring rate [Hz 1 \n\nP Adorjem and K.  Obermayer \n\n-641. .. - - - --.====:::::::;-] \n\n--- p = 0.55 \n02 \np=  .4 \n-\n\n\u2022 \n;\\ \n: \\  : \\. \n\n:' \n>--64.2  '\\ \n, .  \nS -64.4  : \\ \n~ \n~ -64.6' \n(5 \n~ -64.8 \n\n... \n.. \n\u2022 \n\n(b) \n\n-{)5 0 \n\n50 \n\n100 \n\nTime [ms[ \n\n150 \n\n200 \n\nFigure  1:  Short term  synaptic dynamics  at  high  and  low  transmitter release  probability, \n(a) The estimated transfer function O(f, p)  for the cortical cells (Eq.  7) (solid and dashed \nlines) in  comparison with data obtained by  the integrate and fire  model  (Eq.  1,  circles and \nasterisks).  (b) EPSP trains for a series of presynaptic spikes at intervals of 31  ms (32 Hz). \np=O.55 (0.24) corresponds to adaptation to  1 % (50% ) contrast (see Section 4). \n\nIn  order to  study contrast adaptation. 30 leaky-integrator neurons are  connected fully  via \nexcitatory  fast  adapting  synapses.  Each  \"cortical\"  leaky  integrator  neuron  receives  its \n\"geniculate\" input through 30 synapses.  The presynaptic geniculate spike-trains are  inde(cid:173)\npendent Poisson-processes.  Modeling visual stimulation with a drifting grating, their rates \nare modulated sinusoidally with a temporal frequency of2 Hz.  The background activity for \neach  individual \"geniculate\" source is drawn  from  a Gaussian distribution with  a mean  of \n20 Hz and a standard deviation of 5 Hz.  In  the model the mean geniculate firing rate (Fig. \n2b) and the amplitude of modulation (Fig. 2a) increases  with stimulus log contrast accord(cid:173)\ning to  the experimental  data (Kaplan et al.  1987).  In  the following simulations CRFs are \ndetermined according to the protocol of Carandini &  Ferster (1997).  The CRFs are calcu(cid:173)\nlated using an  initial adaptation period of 5 s and a subsequent series of interleaved test and \nre-adaptation stimuli (1  s each). \n\n3  The learning rule \n\nWe  propose that contrast adaptation in  a visual  cortical  cell  is  a result of its goal to maxi(cid:173)\nmize the amount of information the cell's output conveys about the geniculate input l .  Fol(cid:173)\nlowing (Bell &  Sejnowski  1995) we derive a learning rule for the transmitter release proba(cid:173)\nbility p to  maximize the mutual information between a cortical cell's input and output.  Let \nO(f, p)  be the average  output firing rate,  f  the presynaptic firing  rate,  and p  the  synaptic \ntransmitter release  probability.  Maximizing the  mutual  information is  then  equivalent to \nmaximizing the entropy of a neuron's output if we assume only additive noise: \n\nH  [O(f,p)] \n\n-E[ In Prob(O(J,p))] \n\n[ \n\nProb(f)] \n-E  In  I(}O(f,p)/(}f l \nE [In 1 (}O~;,  p) I]  - E[ In Prob(f)] \n\n(6) \n\n(In the following all equations apply locally to  a synapse between neurons j and i.) \nIn  order to derive an  analytic expression for the relation between 0  and f  we use the fact \nthat the EPSP amplitude converges to  its steady state relatively fast compared to the mod(cid:173)\nulation of the geniculate input to the visual cortex,  and  that the average firing rates  of the \n\nI A different  approach of maximizing mutual  information  between input and  output of a  single \n\nspiking neuron  has been developed by Stemmler &  Koch (1999).  For non-spiking neurons this strat(cid:173)\negy has been demonstrated experimentally by. e.g. Laughlin (1994). \n\n\fContrast Adaptation and Infomax \n\n79 \n\npresynaptic neurons are  approximately similar.  Thus we  approximate the activation func(cid:173)\ntion by \n\nO(f,p) \n\nex  S(f)pRoo (f,p), \n\nwhere  S(f)  =  Ire  accounts  for  the  frequency  dependent  summation  of EPSCs.  The \nparameters  a  =  1.8  and e  =  15  Hz are determined  by  fitting  O(f, p)  to  the firing  rate \nof our  integrate  and  fire  single cell  model  (see  Fig.  1 a) .  The  objective  function  is  then \nmaximized by a stochastic gradient ascent learning rule for the release probability p \n\n(7) \n\nTadapt ot  -\n\nof \n\n. \n\n(8) \n\nop  _  oH [O(f, p)]  _  ~ 1  I oO(f, p) I \n\nOp \n\n- Op  n \n\nEvaluating the derivatives we obtain a non-Hebbian learning rule for the transmitter release \nprobability p, \n\nop \nTadapt ot \n\n2 \n\nTre e \n\nfR \n\n-\n\n+ - + \n\n1 \np \n\nTree(fa - 1) \n\na + TreeP  fa - 1) \n\n( \n\n(9) \n\nwhere a = }- I~e' and the adaptation time constant Tadapt  = 7 s (Ohzawa et al.  1985). \nThis  is  similar in  spirit to  the  anti-Hebbian learning mechanism  for  the synaptic strength \nproposed  by  Barlow &  Foldiak (1989) to  explain  adaptation  phenomena.  Here,  the first \nterm  is  proportional to the presynaptic firing  rate f  and  to the available synaptic resource \nR,  suggesting a  presynaptic  mechanism  for  the  learning.  Because  the  amplitude  of the \nEPSP is proportional to the available synaptic resource, we could interpret R as  an  output \nrelated  quantity  and  -2Tree f R  as  an  anti-Hebbian  learning  rule  for  the  \"strength  of the \nsynapse\", i.e. the probability p of the transmitter release.  The second term ensures that pis \nalways larger than O.  In the current model  setup for the operating range of the presynaptic \ngeniculate cells p  also  stays al ways  less  than  1.  The third term  modulates the adaptation \nslightly and increases the release probability p most if the input firing rate is close to 20 Hz, \ni.e.  the stimulus contrast is low. \n\nImage contrast  is  related to the standard deviation of the luminance levels  normalized by \nthe mean.  Because ganglion cells adapt to the mean  luminance, contrast adaptation in the \nprimary visual cortex requires only the estimation of the standard deviation.  In a free view(cid:173)\ning scenario  with an  eye saccade frequency  of 2-3 Hz,  the standard deviation can  be esti(cid:173)\nmated based on  10-20 image samples.  Thus the adaptation rate can  be fast  (Tadapt  = 7 s), \nand  it should also be fast in  order to  maintain good a representation whenever visual  con(cid:173)\ntrast changes, e.g.  by changing light conditions.  Higher order moments (than the standard \ndeviation) of the statistics of the visual world express  image structure and are represented \nby  the  receptive  fields'  profiles.  The  statistics  of the  visual  environment  are  relatively \nstatic,  thus  the  receptive  field  profiles  should  be  determined  and  constrained  by  another \nless plastic synaptic parameter.  such as  the maximal synaptic conductance 9max. \n\n4  Results \n\nFigure 2 shows the average geniculate input, the membrane potential, the firing rate and the \nresponse phase of the modeled cortical cells as  a function  of stimulus contrast.  The CRFs \nwere  calculated  for  two  adapting  contrasts  1 %  (dashed  line)  and  50%  (solid  line).  The \ncortical CRF saturates for high contrast stimuli (Fig. 2e).  This is due to the saturation ofthe \npostsynaptic current (cf. Fig.  I a) and thus induced by the short term synaptic depression.  In \naccordance with the experimental data (e.g.  Carandini et al.  1997) the delay of the cortical \nresponse (Fig.  2f) decreases  towards high contrast stimuli.  This is a consequence of fast \nsynaptic  depression  (c.f.  Chance et  al.  1998).  High  modulation  in  the  input  firing  rate \nleads to a fast transient rise in the EPSC followed by a rapid depression. \n\n\f80 \n\nLGN \n\nU'40 \n\n<L) \n\nfJj --a \n\n:-20 \n~ \n0.0 \n.S \n~ u::  0 \n102 \n(a) \nU' 40  .----~---, \n\n101 \n\n100 \n\n<L) \nfJj \n\n~30 \n~20 \n.S <c1o \nu o  0 l...-_~~_~ \n102 \n(b) \n\nContrast [%] \n\n101 \n\n100 \n\nP.  Ador}an and K.  Obermayer \n\n, \n, \n~(f \n\n.......  10 \n> \nE \n-\n....... \n~  5 \n.... \n~ \nC \n.... \n<L) \n0 \nt:l.. \n\n101 \n\n102 \n\n(c) \n....... \n>-54 \n.s \n~ \n~-58 \n'0 \n0.. \nU \n0-62  L--_~ __  --' \n102 \n\n,P.-El~-~ \n\n100 \n\n101 \n\n~..o--_ \n\n-0 \n\n(d) \n\nContrast [%] \n\n(,) \n<L) \n\n,......,  30 \n\nfJj --\n~ 20 \n\n~ \n\n10 \n\n~ \n0.0 \n.S \n...... \n~  o a \n(e)  10 \no \n~-20 \n~ \n~ -40 \nro \n~ -60 \n\n,,- -\n, , \n\n, , \n\np--e' \n, \n, \n\n101 \n\n102 \n\n, \n\nI \n\nI o \n\n-80 l...-_~~_---' \n102 \n\n101 \n\n100 \n\n(0 \n\nContrast [%] \n\nFigure 2:  The DC (a) and the FI  (b) component of the geniculate input, and the response of \nthe cortical units in the model with strong recurrent lateral connections and slow adaptation \nof the release  probability on  both  the  geniculocortical  and  lateral  synapses.  The  Fl  (c) \nand  the  DC (d)  component  of the  subthreshold  membrane  potential  of a  single  cortical \nunit,  the Fl  component of the firing  rate  (e).  and  the  response  phase (0 are  plotted as  a \nfunction of stimulus contrast after adaptation to 1 % (solid lines) and to 50% (dashed lines) \ncontrast stimuli.  The CRF for  the membrane  potential  (c,  d)  is  calculated  by  integrating \nEg.  I  without spikes and  without reset  after spikes.  The cortical  circuitry involves strong \nrecurrent lateral connections. \n\nThe model predicts a shift of 3-5 mV  in  the DC component of the subthreshold membrane \npotential (Fig. 2d)- a smaller amount than measured by Carandini &  Ferster (1997).  Nev(cid:173)\nertheless,  in  accordance  with the data  the shift caused  by  the adaptation  is larger than the \nchange  in  the DC component of the  membrane potential  from  I % contrast to  100% con(cid:173)\ntrast.  The  largest  shift in  the DC  membrane  potential during adaptation occurs for  small \ncontrast stimuli  because  an  alteration in  the transmitter release probability has  the largest \neffect  on  the  postsynaptic  current  if the presynaptic  firing  rate is  close to  the  geniculate \nbackground  activity  of 20 Hz.  The  maximal  change  in  the  Fl  component  (Fig.  2c)  is \naround 5m V  and  it  is  half of the  increase  in  the  FI  component of the  membrane  poten(cid:173)\ntial  from  1 % contrast to  100% contrast.  The CRF for the cortical firing rate (Fig. 2e) shifts \nto  the right and  the slope decreases  after adaptation to  high contrast.  The model  predicts \nthat the probability p for the transmitter release decreases by approximately a factor of two. \n\nThe Fl  component of the cortical firing rate decreases after adaptation because after tonic \ndecrease in the input modulated membrane potential, the over-threshold area of its FI com(cid:173)\nponent decreases.  The  adaptation  in  the  Fl  firing  rate  is  fed  back  via  the  recurrent  ex(cid:173)\ncitatory connections resulting in  the observable adaptation in  the FI  membrane potential. \nWithout lateral feedback  (Fig. 3) the Fl  component of the membrane potential is basically \nindependent of the contrast adaptation.  At high release probability a steep rise of the EPSC \nto a high amplitude peak is followed by rapid depression if the input is  increasing. At low \nrelease probability the current increases slower to a lower amplitude, but the depression is \n\n\fContrast Adaptation and lnfomax \n\n81 \n\n,......,  30 \nu \ntU \n<Jl -. \n.\u00a7  20 \n......... -~ 10 \n\nbtl \nt: \u00b7c \n1Z  0 \n\n(c)  10\u00b0 \n\n102 \n\n,......,  25 \nu \n\ntU -a  20 \nE ~ 15 - 10 \n.-~ \n\n~ \nbtl \nt:  5 \n1Z  0 \n(a)  10\u00b0 \n\n10 1 \n\n102 \n\n0 \n\n0 \n\n101 \n\nContrast [%] \n\n102 \n\ni-20 \n....... \n'\"0 \ntU  -40 \n~ \n...... \nr..-...---..-__ -.l ~ -60 \n-o--a-o ___ .(). __  ~ \n-80 \n\n,......, \n>-54 \nE \n......... \n~ .-..... \n5-58 \no 0.. \nU \n0-62 \n\n10\u00b0 \n\n(b) \nFigure 3 \n\n101 \n\n102 \n\nContrast [%] \n\n10\u00b0 \n\n101 \n\nContrast [%] \n\n102 \n\n(d) \n\n-60 L--~~_~...-l \n102 \n\n10 1 \n\n10\u00b0 \n\nContrast [%] \n\n(b) \nFigure 4 \n\nFigure 3:  The membrane potential (a,  b),  the phase (d) of the Fl  component of the firing \nrate,  and the Fl  component (c)  averaged  for the modeled cortical  cells after adaptation to \n1 %  (dashed  lines)  and  50% (solid  lines) contrast.  The  weight of cortical  connections is \nset to  zero.  The CRF for the membrane potential  (a,  b)  is calculated by  integrating Eq.  1 \nwithout spikes and without reset after spikes. \n\nFigure 4:  Hysteresis curve revealed  by  following the ramp  method protocol (Carandini  & \nFerster 1997).  After adaption to  I % contrast, test stimuli of 2 s duration were applied with \na contrast successively  increasing from  1 % to  100% (asterisks). and then decreasing back \nto  1 % (circles). \n\nless pronounced too.  As  a consequence,  the power at the first  harmonic  (Fl  component) \nof the subthreshold membrane potential does not change if the release probability is modu(cid:173)\nlated.  It is modulated to a large extent by the recurrent excitatory feedback . The adaptation \nof the  Fl  component of the  firing  rate  could  therefore  be  used  to  measure  the effective \nstrength of the recurrent excitatory input to a simple ceIl  in the primary visual cortex. \n\nAdditional  simulations  (data  not  shown)  revealed  that  changing  the  transmitter  release \nprobability of the geniculocortical synapses is  responsible for the adaptation in our model \nnetwork.  Fixing the value of p for the geniculocortical synapses abolishes contrast adapta(cid:173)\ntion,  while fixing the release probability p  for the lateral  synapses  has  no  effect.  Simula(cid:173)\ntions show that increasing the release probability of the recurrent excitatory synapses leads \nto oscillatory activity (e.g.  Senn et  al.  1996) without altering the mean  activity of simple \ncells.  These results suggest an  efficient functional  segregation  of feedforward  and  recur(cid:173)\nrent excitatory connections.  Plasticity of the geniculocortical connections may  playa key \nrole in  contrast adaptation, while-without affecting the CRF-plasticity of the recurrent \nexcitatory synapses could could playa key role in dynamic feature binding and segregation \nin the visual cortex  (e.g. Engel et al.  1997). \n\nFigure  4  shows  the  averaged  CRF of the  cortical  model  neurons  revealed  by  the  ramp \nmethod  (see  figure  caption)  for  strong recurrent  feedback  and  adapting feedforward  and \nrecurrent synapses.  We find  hysteresis curves for the Fl  component of the firing rate simi-\n\n\f82 \n\nP.  Adorjan and K.  Obermayer \n\nlar to the results reported by Carandini & Ferster (1997), and for the response phase. \n\nIn  summary,  by  assuming two different dynamics for a single synapse we explain  the sat(cid:173)\nuration of the CRFs,  the contrast adaptation,  and  the increase  in  the delay  of the cortical \nresponse to low contrast stimuli.  For the  visual  cortex  of higher mammals,  adaptation of \nrelease probability p as  a substrate for contrast adaptation is so far only a hypothesis.  This \nhypothesis, however,  is in  agreement with the currently available data, and could addition(cid:173)\nally  be justified experimentally by intracellular measurements of EPSPs evoked by  stimu(cid:173)\nlating the geniculocortical axons. The model predicts that after adaptation to a low contrast \nstimulus the amplitude of the EPSPs decreases  steeply  from  a  high value,  while it  shows \nonly small changes after adaptation to a high contrast stimulus (cf. Fig.  1 b). \n\nAcknowledgments The authors are  grateful  to Christian  Piepenbrock for fruitful  discus(cid:173)\nsions.  Funded by the German  Science Foundation (Ob  102/2-1, GK 120-2). \n\nReferences \n\nAhmed,  B.,  Allison,  J.  D.,  Douglas,  R. 1.  &  Martin,  K  A.  C.  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