A Model for Chemosensory Reception 
Rainer Malaka, Thomas Ragg 
Institut far Logik, Komplexit[tt und Deduktionssysteme 
Universit[tt Karlsruhe, PO Box 
D-76128 Karlsruhe, Germany 
e-mail: malaka@ira.uka. de, ragg@ira. uka.de 
Martin Hammer 
Institut fiJr Neurobiologie 
Freie Universit[tt Berlin 
D- 14195 Berlin, Germany 
e-mail: mhammer @ castor.zedat.fu-berlin.de 
Abstract 
A new model for chemosensory reception is presented. It models reacti- 
ons between odor molecules and receptor proteins and the activation of 
second messenger by receptor proteins. The mathematical formulation 
of the reaction kinetics is transformed into an artificial neural network 
(ANN). The resulting feed-forward network provides a powerful means 
for parameter fitting by applying learning algorithms. The weights of the 
network corresponding to chemical parameters can be trained by presen- 
ting experimental data. We demonstrate the simulation capabilities of the 
model with experimental data from honey bee chemosensory neurons. It 
can be shown that our model is sufficient to rebuild the observed data and 
that simpler models are not able to do this task. 
1 INTRODUCTION 
Terrestrial animals, vertebrates and invertebrates, have developed very similar solutions 
for the problem of recognizing volatile substances [Vogt et al., 1989]. Odor molecules 
bind to receptor proteins (receptor sites) at the cell membrane of the sensory cell. This 
interaction of odor molecules and receptor proteins activates a G-protein mediated second 
62 Rainer Malaka, Thomas Ragg, Martin Hammer 
' "   odor molecules 
...receptor proteins 'I second messengers 
aon potentials 
ion channels 
ionic Influx 
Figure 1: Reaction cascade in chemosensory neurons. Volatile odor molecules reach 
receptor proteins at the surface of the chemosensory neuron. The odor bound binding 
proteins activate second messengers (e.g. G-proteins). The activated second messengers 
cause a change in the conductivity of ion channels. Through ionic influx a depolarization 
can build an action potential. 
messenger process. The concentrations of cAMP or IP3 rise rapidly and activate cyclic- 
nucleotide-gated ion channels or IP3-gated ion channels [Breer et al., 1989, Shepherd, 
1991]. As a result of this second messenger reaction cascade the conductivity of ion 
channels is changed and the cell can be hyperpolarized or depolarized, which can cause the 
generation of action potentials. It has been shown that one odor is able to activate different 
second messenger processes and that there is some interaction between the different second 
messenger processes [Breer & Boekhoff, 1992]. 
Figure 1 shows schematically the cascade of reactions from odor molecules over receptor 
proteins and second messengers up to the changing of ion channel conductance and the 
generation of action potentials. 
Responses of sensory neurons can be very complex. The response as a function of the 
odor concentration is highly non-linear. The response to mixtures can be synergistic or 
inhibitory relative to the response to the components of the compound. A synergistic effect 
occurs, if the response of one sensory cell to a binary mixture of two odors A and A2 with 
concentrations [A], [A2] is higher than the sum of the responses to the odors A, A2 at 
concentrations [A], [A2] alone. An inhibitory effect occurs, if the response to the mixture is 
smaller than either response to the single odors. In bee subplacode and placode recordings 
both effects can be observed [Akers & Getz, 1993]. 
Models of chemosensory reception should be complex enough to simulate the inhibitory 
and synergistic effects observed in sensory neurons, and they must provide a means for 
parameter fitting. We want to introduce a computational model which is constructed 
analogously to the chemical reaction cascade in the sensory neuron. The model can be 
expressed as an ANN and all unknown parameters can be trained with a learning algorithm. 
A Model for Chemosensory Reception 63 
2 THE RECEPTOR TRANSDUCER MODEL 
The first step of odor reception is done by receptor proteins located at the cell membrane. 
There may be many receptor protein types in sensory cells at different concentrations and 
with different sensitivity to various odors. There is the possibility for different odors ligands 
Ai to react with a receptor protein/j, but it is also possible for a single odor to react with 
different receptor proteins. 
The second step is the activation of second messengers. Ennis proposed a modelling 
of these complex reactions by a reaction step of activated odor-receptor complexes with 
transducer mechanisms [Ennis, 1991]. These transducers are a simplification of the second 
messengers processes. In Ennis' model transducers and receptor proteins are odor specific. 
We generalize Ennis' model by introducing transducer mechanisms T that can be activated 
by odor-receptor complexes, and as with odors and receptor proteins we allow receptor 
proteins and transducers to react in any combination. Receptor proteins and transducer 
proteins are not required to be odor specific. 
The kinetics of the two reactions are given by 
Ai + j  Ai j 
Aitj + T  AitjT . (1) 
In a first reaction odor ligands Ai bind to receptor proteins/i and build odor-receptor 
complexes Ai 1, which can activate transducer mechanisms T in a second reaction. 
Affinities ki1 and 11  describe the possibility of reactions between odor ligands Ai and recep- 
tor proteins/j or between odor-receptor complexes Ai/j and transducers T, respectively. 
The mass action equations are 
[Ai lj] '- kij[Ai][lj] 
= tj[AiRI[T]. (2) 
The binding of odor-receptor complexes with transducer mechanisms is not dependent on 
the specific odor which is bound to the receptor protein, i.e. Ij  does not depend on i. It is 
only necessary that the receptor protein is bound. 
A sensory neuron can now be defined by the total concentration (or amount) of receptor 
proteins [/] and transducers []. The total concentration of either type corresponds to the 
sum of the free sites and the bound sites: 
[jl = + (3) 
i 
[hi = [Tk] + E[AiRjT,:] .1 (4) 
i,j 
Activated transducer mechanisms may elicit an excitatory or inhibitory effect depending 
on the kind of ion channel they open. Thus we divide the transducers Te into two types: 
inhibitory and excitatory transducers. With 
6e = { +11 , if transducer Te is excitatory 
- , if transducer Te is inhibitory (5) 
We use the simplification [j] = [Rj] + y.i[AiRj] instead of [Jl = [Rj] + y.i[AiRjl + 
i,n[AiRj'Tn], which is sufficient for [/s'] :> [2n], see also [Malaka & Ragg, 19931. 
64 Rainer Malaka, Thomas Ragg, Martin Hammer 
[A] 
tjk[/j] 
Figure 2: ANN equivalent to the full receptor-transducer model. The input layer corre- 
sponds to the concentration of odor ligands [Ai], the first hidden layer to activated receptor 
protein types, the second to activated transducer mechanisms. The output neuron computes 
the effect E of the sensory cell. 
the effect can be set to the sum of all activated excitatory transducers minus the sum of all 
inhibitory transducers relative to the total amount of transducers. An additive constant 0 is 
used to model spontaneous reactions. With this the effect of an odor can be set to 
With Eqs.(2,4) and the hyperbolic function hyp(z) = z/(1 + z) the effect E defined in 
Eq.(6) can be reformulated to 
1 ) 
E = 5-k[k] Ehyp Ijk[AiRj] 6k[k] + 0. (7) 
k \ i,j 
Analogously, we eliminate [A,jl and [Rj]: 
E- E,[,lhyp E/5[5]hyp ki5[A,] 6[]+0. (8) 
Equation (8) can now be regarded as an ANN with 4 feed-forward layers. The concentrations 
of the odor ligands [Ai] represent the input layer, the two hidden layers correspond to 
activated receptor proteins and activated transducers, and one output element in layer 4 
represents the effect caused by the input odor. The weight between the i-th element of the 
input layer to the j-th element of the first hidden layer is ki5 and from there to the k-th 
neuron of the second hidden layer 15 [/]. The weight from element k of hidden layer 2 to 
the output element is 6e [e]/5-e[e]. The adaptive elements of the hidden layers have the 
hyperbolic activation functions hyp. The network structure is shown in Figure 2. 
A Model for Chemosensory Reception 65 
error 
1 2 
1 2 3  5  4   5 transducer 
 - xu 20 50 v mecanisms 
receptor protein types 
Figure 3: Mean error in spikes per output neuron for the model with different network 
sizes. Network sizes are varied in the number of receptor protein types and the number of 
transducing mechanisms. 
3 SIMULATION RESULTS 
Applying learning algorithms like backpropagation or RProp to the model network, it is 
possible to find parameter settings for optimal (or local optimal) simulations of chemosen- 
sory cell responses with given response characteristics. In our simulations the best training 
results were achieved by using the fast learning algorithm RProp, which is an improved 
version of backpropagation [Riedmiller & Braun, 1993]. 
For our simulations we used extracellular recordings made by Akers and Getz from single 
sensilla placodes of honey bee workers applying different stimuli and their binary mixtures 
to the antenna (see [Akers & Getz, 1992] for material and methods). The data set for 
training the ANNs consists of responses of 54 subplacodes to the four odors, geraniol, 
citral, limonene, linalool, their binary mixtures, and a mixture of all of four odors each 
at two concentration levels and to a blank stimulus, i.e. 23 responses to different odor 
stimulations for each subplacode. 
In a series of training runs with varying numbers of receptor protein types and transducer 
types the full model was trained to fit the data set. The networks were able to simulate the 
responses of the subplacodes, dependent on the network size. The size of the first hidden 
layer corresponds to the number of receptor protein types (/) in the model, the size of the 
second hidden layer corresponds to the number of transducing mechanisms (T). 
Figure 3 shows the mean error per output neuron in spikes for all combinations of one to 
six receptor types and one to six transducer mechanisms and for combinations with ten, 
twenty and fifty receptor protein types. 
The mean response over all subplacode responses is 18.15 spikes. The best results with 
errors less than two spikes per response were achieved with models with at least three 
receptor protein types and at least three transducer mechanisms. A model with only two 
transducer types is not sufficient to simulate the data. 
For generalization tests we generated a larger pattern set with our model. This training set 
66 Rainer Malaka, Thomas Ragg, Martin Hammer 
a) 
e) 
spikes 
2 64 
[Ger&niol] 1 
0 0.06 
0.03 
[r=ol 1 .">.  2..' .. 
u.3_  ./ 0.25 [Ciral] 
0.06 V ........... 
spikes 
0.06 
O. 03 
spikes 
35 
30 
25 
20 
15 
I 
t..ol 0.%06 '50'% ...... 
' 0 v.uJ tci rall 
spikes 
.... U.&D 0.06. / 0.25 [Linalool] 
b) 0.03 0.06 
spikes T 
30 
25 
20 
15 
1 2 
0,06  ....... 
d) 
0.06 
0.03 
spikes 
o 
35 
30 
25 
20 
15 
1 
6,13216[. d  2.5 oo 2 6,1 
Figure 4: Simulation results of our model (a,b) and the Ennis model (c,d). The responses of 
simulated sensory cells is given in spikes. The left column (a,c) represents receptor neuron 
responses to mixtures of geraniol and citral, the right column (b,d) represents sensory 
cell responses to mixtures of limonene and linalool. The concentrations of the odorants 
are depicted on a logarithmic scale from 2 -5 to 26 micrograms (0.03 to 64 micrograms). 
Measurement points and deviations from simulated data are given by crosses in the diagrams. 
was divided in a set of 23 training patterns and 88 test patterns. The training set had the 
same structure as the experimental data. Training of new randomly initialized networks 
provided a mean error on the test set that was approximately 1.6 times higher than on the 
training set. An overfitting effect was not observable during the training sequence of 10000 
A Model for Chemosensot? Reception 67 
learning epochs. 
It is also possible to transform many other models for chemosensory perception into ANNs. 
We fitted the stimulus summation model and the stimulus substitution model [Cart & 
Derby, 1986] as well as the models proposed by Ennis [Ennis, 1991]. All of the other 
models were not able to reproduce the complex response functions observed in honey 
bee sensory neurons. Some of them are able to simulate synergistic responses to binary 
mixtures, but none were able to produce inhibitory effects. Figure 4 shows the simulation 
of a sensory neuron that shows very similar spike rates for the single odors geraniol and 
citral and to their binary mixture at the same concentration, while the mixture interaction 
of limonene and linalool shows a strong synergistic effect, i.e. the response to mixture of 
both odors is much higher than the responses to the single odors. As shown in Figure 4a) 
and b) our model is able to simulate this behavior, while the Ennis model is not sufficient 
to show the two different types of interaction for the binary mixtures geraniol-citral and 
limonene-linalool, as shown in Figure 4c) and d). The error for the Ennis model is greater 
than four spikes per output neuron and the error for our model with six receptor types and 
four transducer mechanisms is smaller than one spike per output neuron. The stimulus 
summation and stimulus substitution model have very similar results as the Ennis model, 
Figure 4 e) and f) show the simulation of the stimulus summation. 
4 CONCLUSIONS 
Artificial neural networks are a powerful tool for the simulation of the responses of chemo- 
sensory cells. The use of ANNs is consistent with theoretical modelings. Many previously 
proposed models are expressible as ANNs. The new receptor transducer model described 
in this paper is also expressible as an ANN. The use of learning algorithms is a means to 
fit parameters for the simulation with given experimental response data. With this method 
it is possible to create simulation models of chemosensory cells, that can be used in further 
modelings of olfactory and chemosensory systems. 
Applying data from honey bee placode recordings we could also investigate the necessary 
complexity of chemosensory models. It could be shown that only the full receptor transducer 
model is able to simulate the complex response characteristics observed in honey bee 
chemosensory cells. Most other models can show only low synergistic mixture interactions 
and none of the other models is able to simulate inhibitory effects in odor perception. 
The found parameters of the ANN do not have to correspond to physiological entities, such 
as affinities between molecules. The learning or parameter fitting optimizes the parameters 
in a way that the difference between experimental data and simulation results is minimized. 
If there are several solutions to this task, one solution will be found, which might differ 
from the actual values. But it can be said, that a model is not sufficient if the learning 
algorithm is not able to fit the experimental data. This implies that the smallest model, 
which is able to simulate the given data covers the minimum of complexity necessary. For 
honey bees this means that a competitive receptor transducer model is necessary with at 
least two transducer mechanisms and three receptor protein types. Any other model, such 
as the stimulus summation model, the stimulus substitution model and the Ennis model, is 
not sufficient. 
The model is not restricted to insect olfactory receptor neurons and can also be applied to 
many types of olfactory or gustatory receptor neurons in invertebrates and vertebrates. 
68 Rainer Malaka, Thomas Ragg, Martin Hammer 
Acknowledgments 
We want to thank Pat Akers and Wayne Getz for giving us subplacode response data to train 
the ANNs used in our model, Heinrich Braun and Wayne Getz for fruitful discussions on our 
work. This work was supported by grants of the Deutsche Forschungsgemeinschaft (DFG), 
SPP Physiologie und Theorie neuronaler Netze, and the State of Baden-Wiirttemberg. 
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