{"title": "A Model for Chemosensory Reception", "book": "Advances in Neural Information Processing Systems", "page_first": 61, "page_last": 68, "abstract": null, "full_text": "A Model for Chemosensory Reception \n\nRainer MalakaJ  Thomas Ragg \n\nInstitut fUr Logik, Komplexitat und Oeduktionssysteme \n\nUniversitat Karlsruhe, PO Box \n0-76128 Karlsruhe, Germany \n\ne-mail:  malaka@ira.uka.de.ragg@ira.uka.de \n\nMartin Hammer \n\nInstitut fur Neurobiologie \nFreie Universitat Berlin \n0-14195 Berlin, Germany \n\ne-mail:  mhammer@castor.zedat.fu-berlin.de \n\nAbstract \n\nA new  model for chemosensory reception is presented.  It models reacti(cid:173)\nons between odor molecules and receptor proteins and the activation of \nsecond  messenger  by receptor proteins.  The mathematical  formulation \nof the  reaction  kinetics  is  transformed  into an  artificial  neural  network \n(ANN). The resulting feed-forward network provides a powerful means \nfor parameter fitting by applying learning algorithms. The weights of the \nnetwork corresponding to chemical parameters can be trained by presen(cid:173)\nting experimental data.  We demonstrate the simulation capabilities of the \nmodel with experimental data from honey bee chemosensory neurons.  It \ncan be shown that our model is sufficient to rebuild the observed data and \nthat simpler models are not able to do this task. \n\n1 \n\nINTRODUCTION \n\nTerrestrial  animals,  vertebrates  and  invertebrates,  have  developed  very  similar  solutions \nfor  the problem of recognizing  volatile substances  [Vogt et  ai.,  1989].  Odor  molecules \nbind to  receptor proteins  (receptor  sites)  at  the  cell  membrane  of the  sensory  cell.  This \ninteraction of odor molecules and receptor proteins activates a G-protein mediated second \n\n\f62 \n\nRainer Malaka,  Thomas  Ragg,  Martin  Hammer \n\n_____  odor molecules \n\n'f! \n\n\" \n\n4! /2~ ___ \n\n. action potentials \n\n\"-----\n\nIns\" \n\nsecond messengers \n\n-----\n\nIonic Influx \n\nFigure  1:  Reaction  cascade  in  chemosensory  neurons.  Volatile  odor  molecules  reach \nreceptor proteins  at  the  surface  of the chemosensory  neuron.  The  odor bound binding \nproteins activate second messengers  (e.g.  G-proteins).  The activated second messengers \ncause a change in the conductivity of ion channels.  Through ionic influx a depolarization \ncan build an action potential. \n\nmessenger process.  The concentrations of cAMP or IP3  rise rapidly and activate cyclic(cid:173)\nnucleotide-gated ion channels  or  IP3-gated  ion channels  [Breer  et  al.,  1989,  Shepherd, \n1991].  As  a  result  of this  second  messenger  reaction  cascade  the  conductivity  of ion \nchannels is changed and the cell can be hyperpolarized or depolarized, which can cause the \ngeneration of action potentials.  It has been shown that one odor is able to activate different \nsecond messenger processes and that there is some interaction between the different second \nmessenger processes [Breer &  Boekhoff, 1992]. \n\nFigure 1 shows schematically the cascade of reactions from odor molecules over receptor \nproteins and  second messengers  up  to  the changing  of ion channel  conductance and the \ngeneration of action potentials. \n\nResponses  of sensory neurons  can be very complex.  The response  as  a  function  of the \nodor concentration is  highly non-linear.  The response  to  mixtures can  be synergistic or \ninhibitory relative to the response to the components of the compound.  A synergistic effect \noccurs, if the response of one sensory cell to a binary mixture of two odors AI  and A2 with \nconcentrations [AI]'  [A2l  is  higher than  the  sum of the responses  to the odors AI, A2  at \nconcentrations [A tl, [A2] alone.  An inhibitory effect occurs, if the response to the mixture is \nsmaller than either response to the single odors.  In bee subplacode and placode recordings \nboth effects can be observed [Akers &  Getz,  1993]. \n\nModels of chemosensory reception should be complex enough to  simulate the inhibitory \nand synergistic effects  observed in  sensory neurons,  and they  must provide a  means  for \nparameter  fitting.  We  want  to  introduce  a  computational  model  which  is  constructed \nanalogously to  the chemical reaction cascade  in the  sensory  neuron.  The model can  be \nexpressed as an ANN and all unknown parameters can be trained with a learning algorithm. \n\n\fA  Model for  Chemosensory  Reception \n\n63 \n\n2  THE RECEPTOR TRANSDUCER MODEL \n\nThe first step of odor reception is done by receptor proteins located at the cell membrane. \nThere may be many receptor protein types in sensory cells at different concentrations and \nwith different sensitivity to various odors.  There is the possibility for different odors ligands \nAi to react with a receptor protein Rj, but it is also possible for a single odor to react with \ndifferent receptor proteins. \n\nThe  second  step  is  the  activation  of second  messengers.  Ennis  proposed  a  modelling \nof these complex  reactions  by a reaction  step  of activated odor-receptor complexes  with \ntransducer mechanisms  [Ennis, 1991]. These transducers are a simplification of the second \nmessengers processes.  In Ennis' model transducers and receptor proteins are odor specific. \nWe generalize Ennis' model by introducing transducer mechanisms T\" that can be activated \nby odor-receptor  complexes,  and  as  with odors  and receptor  proteins  we  allow  receptor \nproteins and transducers  to react  in  any  combination.  Receptor proteins and transducer \nproteins are not required to be odor specific. \n\nThe kinetics of the two reactions are given by \n\nAi + Rj  ~  AiRj \n\n(1) \nIn a  first reaction  odor ligands  Ai  bind to  receptor  proteins  Rj  and build odor-receptor \ncomplexes AiRj, which can activate transducer mechanisms T\" in a second reaction. \n\nAiRj + T\"  ~  AiRjT\". \n\nAffinities lcij and Ij\" describe the possibility of reactions between odor ligands Ai and recep(cid:173)\ntor proteins Rj or between odor-receptor complexes Ai Rj and transducers T\", respectively. \nThe mass action equations are \n\n[AiRj]  = \n[Ai RjT,,]  = \n\nlcij[Ad[Rj] \nIj,,[AiRj][T,,]. \n\n(2) \nThe binding of odor-receptor complexes with transducer mechanisms is not dependent on \nthe specific odor which is bound to the receptor protein, i.e.  Ij\" does not depend on i.  It is \nonly necessary that the receptor protein is bound. \n\nA  sensory neuron can  now  be defined by the total  concentration (or amount)  of receptor \nproteins [H]  and transducers [1'].  The total concentration of either type corresponds to the \nsum of the free sites and the bound sites: \n\n[Hj] \n\n[Rj] + I)AiRj] \n\n[T,,] + I)AiRjT,,] .1 \n\ni,j \n\n(3) \n\n(4) \n\nActivated transducer  mechanisms  may elicit an  excitatory or inhibitory effect depending \non the kind of ion channel they open.  Thus we divide the transducers T\"  into two types: \ninhibitory and excitatory transducers.  With \n\n{ + 1 \n-1 \n\n8\"  = \n\n, if transducer T\"  is excitatory \n, if transducer T\"  is inhibitory \n\n(5) \n\nIWe  use  the  simplification  [flj]  =  [Rj] + L:i[AiRJ' ]  instead of [flj]  =  [Rj] + L:.[AiRj] + \n\nL:i,k [AiRjTk], which is sufficient for [flj] > [tk], see also [Malaka &  Ragg, 1993]. \n\n\f64 \n\nRainer Malaka,  Thomas  Ragg, Martin  Hammer \n\nFigure 2:  ANN equivalent to  the full  receptor-transducer model.  The input layer corre(cid:173)\nsponds to the concentration of odor ligands [Ad, the first hidden layer to activated receptor \nprotein types, the second to activated transducer mechanisms.  The output neuron computes \nthe effect E of the sensory cell. \n\nthe effect can be set to the sum of all activated excitatory transducers minus the sum of all \ninhibitory transducers relative to the total amount of transducers.  An additive constant (J  is \nused to model spontaneous reactions.  With this the effect of an odor can be set to \n\n(6) \n\nWith Eqs.(2,4)  and the  hyperbolic function hyp(x)  = x/(l + x)  the effect E  defined in \nEq.(6) can be reformulated to \n\nE = \n\n1 A  2: hyp  (2: Ijk[AiRj ]) 15k ['h] + (J  . \n\n2::L[Tk] \n\n'\" \n\nL \n'\" \n\n\u2022 .  \nt ,) \n\nAnalogously, we eliminate [AiRj] and [Rj): \n\nE= \n\n1 A  2:hyp (2:Ijk[Rj]hYP(2:kij[Ad))  8k[Tk]+(J . \n\nLk[n]  k \n\nj \n\ni \n\n(7) \n\n(8) \n\nEquation (8) can now be regarded as an ANN with 4 feed-forward layers.  The concentrations \nof the  odor ligands  [Ad  represent  the  input  layer,  the  two  hidden  layers  correspond  to \nactivated receptor  proteins  and  activated  transducers,  and  one output element  in layer 4 \nrepresents the effect caused by the input odor.  The weight between the i-th element of the \ninput layer to  the j-th element of the first  hidden  layer is  kij  and  from  there to  the  k-th \nneuron of the second hidden layer Ij k [Hj].  The weight from element k of hidden layer 2 to \nthe output element is 15k [1'k]/ 2::k[1'k].  The adaptive elements ofthe hidden layers have the \nhyperbolic activation functions hypo  The network structure is shown in Figure 2. \n\n\fA  Model for  Chemosensory  Reception \n\n65 \n\n6 \n\n5 \n\n4 \n\n3 \n\n10 \nrecept or  protein  types \n\n6 \n\n20 \n\n50 \n\nmecanisms \n\nFigure  3:  Mean  error in  spikes  per output neuron  for  the  model  with different network \nsizes.  Network sizes are  varied in the number ofreceptor protein types and the number of \ntransducing mechanisms. \n\n3  SIMULATION RESULTS \n\nApplying learning algorithms like backpropagation or RProp  to  the  model network, it is \npossible to find parameter settings for optimal (or local optimal) simulations of chemosen(cid:173)\nsory cell responses with given response characteristics. In our simulations the best training \nresults  were  achieved  by using the fast  learning algorithm RProp,  which is  an  imprOVed \nversion of back propagation [Riedmiller &  Braun, 1993]. \n\nFor our simulations we used extracellular recordings made by Akers and Getz from single \nsensilla placodes of honey bee workers applying different stimuli and their binary mixtures \nto  the  antenna (see  [Akers  &  Getz,  1992]  for  material  and methods).  The data set  for \ntraining  the ANNs  consists  of responses  of 54 subplacodes  to  the  four  odors,  geraniol, \ncitral,  limonene,  linalool,  their binary  mixtures,  and a  mixture of all  of four  odors each \nat  two  concentration  levels  and  to  a  blank stimulus,  i.e.  23  responses  to  different odor \nstimulations for each subplacode. \n\nIn a series of training runs with varying numbers of receptor protein types and transducer \ntypes the full model was trained to fit the data set.  The networks were able to simulate the \nresponses  of the subplacodes, dependent on the network size.  The size of the first hidden \nlayer corresponds to the number of receptor protein types (R) in the model, the size of the \nsecond hidden layer corresponds to the number of transducing mechanisms (T). \n\nFigure 3 shows  the mean  error per output neuron in spikes for all combinations of one to \nsix receptor types  and one to  six transducer  mechanisms  and for  combinations with ten, \ntwenty and fifty receptor protein types. \n\nThe mean  response  over all  subplacode responses  is  18.15 spikes.  The best results with \nerrors  less  than  two  spikes  per response  were  achieved  with  models  with  at  least  three \nreceptor protein types  and at least three transducer mechanisms.  A  model  with only two \ntransducer types is not sufficient to simulate the data. \n\nFor generalization tests we generated a larger pattern set with our model.  This training set \n\n\fRainer Malaka,  Thomas  Ragg, Martin  Hammer \n\n66 \n\nspi kes \n\nspi kes \n\nFigure 4:  Simulation results of our model (a.b) and the Ennis model (c.d).  The responses of \nsimulated sensory cells is given in spikes.  The left column (a,c) represents receptor neuron \nresponses  to  mixtures  of geraniol  and  citral,  the  right  column  (b,d)  represents  sensory \ncell  responses  to  mixtures  of limonene and linalool.  The  concentrations  of the odorants \nare depicted on a  logarithmic scale from 2- 5  to 26  micrograms (0.03  to 64 micrograms). \nMeasurement points and deviations from simulated data are given by crosses in the diagrams. \n\nwas divided in a  set of 23  training patterns and 88  test patterns.  The training set had the \nsame structure as  the experimental  data.  Training of new  randomly initialized networks \nprovided a mean error on the test set that was approximately 1.6 times higher than on the \ntraining set.  An overfitting effect was not observable during the training sequence of 10000 \n\n\fA Model for  Chemosensory  Reception \n\n67 \n\nlearning epochs. \n\nIt is also possible to transform many other models for chemosensory perception into ANN s. \nWe  fitted  the  stimulus  summation  model  and  the  stimulus  substitution  model  [Carr  & \nDerby,  1986]  as  well  as  the  models  proposed by Ennis  [Ennis,  1991].  All  of the  other \nmodels  were  not  able  to  reproduce  the  complex  response  functions  observed  in  honey \nbee sensory neurons.  Some of them are  able to simulate  synergistic responses  to binary \nmixtures, but none were able to produce inhibitory effects.  Figure 4 shows the simulation \nof a  sensory neuron that shows  very  similar spike rates  for  the single odors geraniol and \ncitral and to their binary mixture at the same concentration, while the mixture interaction \nof limonene and linalool shows a strong synergistic effect, i.e.  the response to mixture of \nboth odors is  much higher than the responses to the single odors.  As shown in Figure 4a) \nand b) our model is able to simulate this behavior, while the Ennis model is not sufficient \nto show the two different types  of interaction for  the binary mixtures geraniol-citral and \nlimonene-linalool, as  shown in Figure 4c) and d).  The error for the Ennis model is greater \nthan four spikes per output neuron and the error for our model with six receptor types and \nfour transducer  mechanisms  is  smaller than  one spike per  output neuron.  The stimulus \nsummation and stimulus substitution model  have very  similar results as the Ennis model, \nFigure 4 e) and t) show the simulation of the stimulus summation. \n\n4  CONCLUSIONS \n\nArtificial neural networks are a powerful tool for the simulation of the responses of chemo(cid:173)\nsensory cells.  The use of ANNs is consistent with theoretical modelings. Many previously \nproposed models are expressible as ANNs.  The new receptor transducer model described \nin this paper is also expressible as  an  ANN.  The use of learning algorithms is a means  to \nfit parameters for the simulation with given experimental response data.  With this method \nit is possible to create simulation models of chemosensory cells, that can be used in further \nmodelings of olfactory and chemosensory systems. \n\nApplying data from honey bee placode recordings we could also investigate the necessary \ncomplexity of chemosensory models. It could be shown that only the full receptor transducer \nmodel  is  able  to  simulate  the  complex  response  characteristics  observed  in  honey  bee \nchemosensory cells.  Most other models can show only low synergistic mixture interactions \nand none of the other models is able to simulate inhibitory effects in odor perception. \n\nThe found parameters of the ANN do not have to correspond to physiological entities, such \nas affinities between molecules.  The learning or parameter fitting optimizes the parameters \nin a way that the difference between experimental data and simulation results is minimized. \nIf there  are  several  solutions to this task,  one  solution will be found,  which might differ \nfrom  the actual  values.  But it can  be said,  that a  model  is  not sufficient if the  learning \nalgorithm is  not able to fit  the experimental  data  This  implies that  the  smallest  model, \nwhich is able to simulate the given data covers the minimum of complexity necessary.  For \nhoney bees this  means  that a  competitive receptor transducer model  is necessary  with at \nleast two transducer mechanisms and three receptor protein types.  Any other model, such \nas the stimulus summation model, the stimulus substitution model and the Ennis model, is \nnot sufficient. \n\nThe model is not restricted to insect olfactory receptor neurons and can also be applied to \nmany types of olfactory or gustatory receptor neurons in invertebrates and vertebrates. \n\n\f68 \n\nRainer Malaka,  Thomas  Ragg, Martin  Hammer \n\nAcknowledgments \n\nWe want to thank Pat Akers and Wayne Getz for giving us subplacode response data to train \nthe ANNs used in our model, Heinrich Braun and Wayne Getz for fruitful discussions on our \nwork.  This work was supported by grants of the Deutsche Forschungsgemeinschaft (DFG), \nSPP Physiologie und Theorie neuronaler Netze, and the State of Baden-WUrttemberg. \n\nReferences \n\n[Akers & Getz,  1992]  R.P.  Akers & W.M. Getz. A test of identified response classes among \nolfactory receptor neurons  in the honeybee worker.  Chemical Senses,  17(2):191-209, \n1992. \n\n[Akers &  Getz, 1993]  RP. 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Springer, 1989. \n\n\f", "award": [], "sourceid": 935, "authors": [{"given_name": "Rainer", "family_name": "Malaka", "institution": null}, {"given_name": "Thomas", "family_name": "Ragg", "institution": null}, {"given_name": "Martin", "family_name": "Hammer", "institution": null}]}