A NEURAL NETWORK MODEL OF THE OLFACTORY SYSTEM

FOR GLOMERULAR ACTIVITY PREDICTION

Zu Soh, Ryuji Inazawa, Toshio Tsuji

Graduate School of Engineering, Hiroshima University, Hiroshima, Japan

Noboru Takiguchi

Graduate School of Natural Science and Technology, Kanazawa University, Ishikawa, Japan

Hisao Ohtake

Graduate School of Engineering, Osaka University, Osaka, Japan

Keywords:

Glomerular activity prediction, Odor qualities, Olfactory system, Neural network model.

Abstract:

Recently, the importance of odors has begun to be emphasized as well as methods for their evaluation, espe-

cially in the fragrance and food industries. Although odors can be characterized by their odorant components,

their chemical information cannot be directly related to the ﬂavors we perceive. Recent research has revealed

that neuronal activity related to glomeruli (which form part of the olfactory system) is closely connected to

odor qualities. In this paper, we propose a neural network model of the olfactory system in mice to predict

glomerular activity from odorant molecules. To adjust the parameters included in the model, a learning al-

gorithm is also proposed. The results of simulation proved that the relationship between glomerular activity

and odorant molecules could be approximated using the proposed model. In addition, the model could predict

glomerular activity to a certain extent. These results suggest that the proposed model could be utilized to

predict odor qualities for future application.

1 INTRODUCTION

As considerable evidence has been presented to show

that odours have an effect on memory and emotions,

the importance of smells has begun to be recognized

beyond their role as components of ﬂavor (Herz and

Engen, 1996). Gas chromatography is a useful tech-

nique used to detect the odorant molecules (or simply

odorants) contained in an odour (van Ruth, 2001), and

the analyzed data are used to characterize the odour

(Aznar et al., 2001; Semmelroch and Grosch, 1995).

However, it is impossible to relate information about

odorant molecules to odour qualities without the pro-

cess of evaluation by human senses. One solution to

this problem is to build a regression model to con-

vert the data obtained from gas chromatographyto the

indices of sensory evaluation (Limpawattana et al.,

2001). In this case, the regression model is special-

ized to the objective odorants, making it necessary to

build different models for different kinds of odour.

Another solution is to build a model of the ol-

factory system based on biological insight. The re-

lationship between odorants and odour qualities is

mostly investigated from the ﬁeld of biological re-

search. The most widely supported stereochemical

theory (Amoore, 1963) suggests that odour qualities

largely depend on the shape of the odorant molecules

involved. This theory is consistent with recent ﬁnd-

ings regarding the olfactory receptor gene family

(Buck and Axel, 1991). The most important informa-

tion directly related to odour qualities is considered

to be that regarding activity on the glomeruli, which

are distributed over the surface of the olfactory bulb

(Mori and Yoshihara, 1995). Moreover, glomerular

activity evoked by input from olfactory receptors is

odour-speciﬁc, and odour qualities can be predicted

from the activated region of the glomeruli (Youngen-

tob et al., 2006).

Outside the ﬁeld of biological research, there are

few approaches that reveal the relationship between

379

Soh Z., Inazawa R., Tsuji T., Takiguchi N. and Ohtake H. (2009).

A NEURAL NETWORK MODEL OF THE OLFACTORY SYSTEM FOR GLOMERULAR ACTIVITY PREDICTION.

In Proceedings of the International Joint Conference on Computational Intelligence, pages 379-385

DOI: 10.5220/0002320203790385

 SciTePress

Octanal

Glomerular activity

(Leon et al.)

Odorant

molecule

-2 5

Activity strength

(z-score)

Receptor

cells

Piriform

cortex

Olfactory

bulb

Figure 1: Structure of the olfactory system of rats.

Glomerular activity downloaded from the Glomerular Re-

sponse Archive (Leon and Johnson, 2009).

odour qualities and odorants from the ﬁeld of engi-

neering. Most related engineering researches have

focused on developing biomimetic algorithms to dis-

criminate similar odours (Gutierrez-Osuna,2002), but

not to predict qualities for unknown odorants. This

may be because a considerable data set is needed to

approximate odorants to odour qualities, especially

for the human senses. In regard to the olfactory sys-

tem of rats, however, more than 300 types of glomeru-

lar activity evoked by different odorants are provided

online (Leon and Johnson, 2009).

Against this background, we report on a neural

network model of the olfactory system of rats to en-

able prediction of glomerular activity from odorant

molecules, since the basic structure of the olfactory

system in rats has a lot in common with that of hu-

man. We also propose a learning algorithm to adjust

the parameters included in the model. This consists

of a training algorithm for radial basis function (Chen

et al., 1991) and the Nelder-Mead (simplex) method

(Nelder and Mead, 1965).

This paper is organized as follows: In Section 2,

biological knowledge regarding the olfactory system

of rats is brieﬂy explained. Section 3 proposes an ol-

factory model and a parameter-setting algorithm for

parameter adjustment. Section 4 details simulations

of parameter settings and prediction of glomerular ac-

tivity in rats. Finally, Section 5 concludes the paper

and outlines work planned for the future.

2 THE OLFACTORY SYSTEM OF

RATS

Figure 1 shows the basic structure of the olfactory

system in rats, which consists of three parts: recep-

tor neurons, the olfactory bulb and the piriform cor-

tex. Receptor neuronsare distributed on the surface of

the nasal chamber, expressing single receptor protein

from among thousands of different varieties (Buck

and Axel, 1991); these neurons are activated and send

Caudal

Rostral

Ve ntral

Dorsal

Orientation of

unrolled map of glomeruli

Figure 2: Glomerular module arrangement adapted from the

Glomerular Response Archive (Leon and Johnson, 2009).

signals to the olfactory bulb. The axons from the re-

ceptors that express the same receptor terminate at the

same point on the surface of the olfactory bulb (Mori

and Yoshihara, 1995). The terminals of these axons

form a small, round cluster called a glomerulus. A 2D

map of glomerular distribution can be associated with

receptor genes as well as with odorants, and is called

an odour map (Mori and Yoshihara, 1995). The ac-

tivity of the glomeruli is thus odour-speciﬁc. This ac-

tivity is then communicated to the deeper layer of the

olfactory bulb, which mainly consists of mitral and

granule cells. The piriform cortex performs odour

recognition based on the output of the mitral cells,

whose information is modiﬁed according to glomeru-

lar activity. It has been reported that this activity rep-

resents important information that is closely related

to the sense of smell in animals (Youngentob et al.,

2006).

Glomerular activity for more than 300 kinds of

odorant has been measured by Leon et al (Leon and

Johnson, 2009), and is shown very clearly using color

contour charts. From the results of this measurement,

Johnson et al. (Johnson et al., 2005) deﬁned assem-

blies of glomeruli as a glomerular modules, which

respond to a speciﬁc molecular features such as the

functional group. Figure 2 shows an unrolled map

of glomeruli; the boundaries and unique letters de-

note the areas and symbols of the glomerular mod-

ules. More minor features, such as the length of the

carbon chain, are coded within a module (Johnson and

Leon, 2007). Accordingly, if these rules can be sys-

tematically approximated, glomerular activity evoked

by untested odorants could be predicted.

3 MODEL

We assumed that glomerular activity can be expressed

by a summation of Gaussian functions whose param-

eters are modulated by the activity of the receptors.

Under this assumption, the radial basis function-like

model shown in Figure 3 is proposed. The model con-

IJCCI 2009 - International Joint Conference on Computational Intelligence

380

Exponetial-Gaussian

layer

Gaussian

layer

Receptor

layer

( x , y )

K(Gl,G1)

䊶䊶

䊶䊶䊶

1,1 1,1

( x , y )

M,N

M,2

M,1

1,1

1,2

1,1

1,N

M,N

M,1

M,N

K(Gl,GM)

Glomeruli

layer

Figure 3: The proposed model for the olfactory system of

rats.

Odorant molecule

Receptor

(=A representative odorant)

l Gm

Figure 4: Labeled graphic expression of odorants for the

graph kernel function.

sists of four layers: receptor, exponential-Gaussian,

Gaussian, and glomeruli. This section describes the

processes in each layer and the learning algorithm

used.

3.1 Model Structure

The receptor layer consists of M units corresponding

to the number of arbitrarily deﬁned odorants (repre-

sentative odorants), and each receptor unit is most

strongly activated by a representative odorant. Since

actual receptors are also activated by odorants with a

structure similar to that of the representative odorant,

the output of the receptor unit is deﬁned as the simi-

larity between the representative and input odorants.

In this model, the graph kernel function K(G

, G

)

proposed by Kashima et al (Kashima et al., 2004) is

introduced to calculate structural similarity between

the molecules. In this function, the input odorant and

representative odorant are expressed by the graphs G

and G

in Figure 4, where the atoms correspond to

nodes and the bonds to edges. In addition, unique la-

bels are allocated to the types of atoms and bonds.

For example, hydrogen atoms (H) are labeled as N3

in Figure 4. The kernel function is then deﬁned as:

0.5

0.5 1

Receptor unit Output ( U

m(Gl))

Measured glomerular

activity

(Normalized)

Fitting by exponential function

Fitting by exponential-Gaussian function

Measured activity

Figure 5: Example of exponential-Gaussian function ﬁtting.

K(G

, G

)

∑

p(h

)p(h



b(h

), b(h

)



(1)

where h

and h

are arbitrary paths in the graphs of G

and G

respectively, and p(h

) and p(h

) are

the probabilities of the paths to be selected by the ran-

dom walk algorithm. K

(b(h

), b(h

)) is a function to

compare the path selection as shown below:

(b(h

), b(h

)) =



1, b(h

) = b(h

)

0, b(h

) 6= b(h

)

(2)

where b(h

) and b(h

) are the labels of path h

and

, respectively. The output of the receptor layer

) is deﬁned as the generalized value calculated

by Equation (3):

) =

K(G

, G

)

(K(G

, G

)K(G

, G

))

, (3)

where

) becomes 1 when the representative

odorant is input (G

= G

The output of each Receptor unit is input into

N exponential-Gaussian units so that the unit num-

ber in the exponential-Gaussian layer becomes MN.

Exponential-Gaussian units play a role in control-

ling activity strength at the connected region on the

Glomeruli layer. Figure 5 shows an example of the

relationship between the output of a Receptor unit

and the measured activity strength at the region of

the glomeruli to which the Receptor unit is con-

nected through the subsequent exponential-Gaussian

and Gaussian units. As shown in Figure 5, the activity

strength grows exponentially at ﬁrst, then drops when

the value of U

approaches to 1. This trend may be

caused by the structure of the glomeruli. Glomeruli

that are topologically close to each other respond to

similar odorants (Johnson and Leon, 2007), but also

send inhibitory signals to each other (Aungst et al.,

2003). As a result, when an odorant similar to the rep-

resentative one is input, inhibitory signals from sur-

roundingglomeruli suppress the excitatory input from

A NEURAL NETWORK MODEL OF THE OLFACTORY SYSTEM FOR GLOMERULAR ACTIVITY PREDICTION

381

the receptors. Hence, the exponential-Gaussian unit

is deﬁned by the following equation to convert the re-

ceptor unit output into the activity of the glomeruli:

m,n

= a

exp



)



− a

exp{−(10

)



) − a



(4)

where the ﬁrst term on the right is an exponential

function, the second term is the Gaussian function,

and a

...a

are the parameters deﬁned by the learning

algorithm described in Section 3.2.

The output of the exponential-Gaussian layer is

input to the Gaussian layer through the connective

weight C

m,n

as follows:

m,n

= C

m,n

, (5)

The Gaussian layer diffuses the activity to the

neighboring region on the Glomeruli layer. The out-

put of the Gaussian function is given by the following

equation:

m,n

(x, y)

m,n

exp

(

m,n

−x

)

m,n

(

m,n

−y

)

m,n

)

(6)

where the parameters α

m,n

and β

m,n

control the width

of the Gaussian curve.

The connections from the Gaussian layer to the

glomeruli layer allocate the output of the Gaussian

units to proper center coordinates (

m,n

) on the

glomeruli layer. The inputs to each of the coordinates

are added by

V(x, y) =

∑

m=1

∑

n=1

m,n

(x, y), (7)

from which the estimated glomerular activity is ob-

tained.

3.2 Learning Algorithm

To ﬁnd proper parameters for the model, this section

proposes a learning algorithm consisting of two steps.

The adjustable parametersare the representativeodor-

ants G

of the Receptor units, the parameters in the

exponential-Gaussian units a

(i = 1, 2, ..., 5), the con-

nective weights C

l,m

from the exponential-Gaussian

layer to the Gaussian layer, and the center coordi-

nates (

m,n

) to which the Gaussian units are

connected. The ﬁrst step determines the parameters

Gm, C

l,m

and (

m,n

), and the second step ad-

justs a

(i = 1, 2, ..., 5). Note that, for simpliﬁcation,

the width of the Gaussian curves α

m,n

and β

m,n

ﬁxed in this paper. To implement the algorithm, M

representative odorants (G

T,1

...G

T,M

) and the corre-

sponding glomeruli activities (V

T,1

(x, y)... V

T,M

(x, y))

measured by Leon and Johnson (2009) are chosen in

advance as a learning data set. Since the original ac-

tivity patterns consist of graphical data in png format,

they were converted to numerical data according to

the color scale shown on the website (Leon and John-

son, 2009). The converted data were then normalized

to a value range of [0,1].

First Step. First, the receptor units responding to

each representative odorant are deﬁned, thus G

T,m

Then, each instance of glomerular activity evoked

by a representative odorant is approximated by the

Gaussian functions using the learning algorithm for

the radial basis function (RBF) (Chen et al., 1991).

This approximation gives the center coordinates

(

m,n

) and the peak value of the Gaussian unit.

The peak obtained value is assigned toC

m,n

. Note that

the number of Gaussian function N is also an impor-

tant parameter, and is analyzed in the next simulation

section.

Second Step. The parameters included in each

exponential-Gaussian unit are determined using the

Nelder-Mead (simplex) method (Nelder and Mead,

1965); this algorithm minimizes the objective func-

tion deﬁned below:

m,n

∑

l=1



T,m

m,n

, y

m,n

) −

)



. (8)

4 SIMULATION

This section reports on veriﬁcation of the learning al-

gorithm and the prediction ability of the model by

comparingthe output of the glomeruli layer with mea-

sured glomerular activity.

4.1 Learning

First, learning data as shown in Figure 6(a) were pre-

pared to implement the learning algorithm. This data

set consists of M = 8 kinds of representative odorants

, m ∈ 1, 2, ..., 8) that share the functional group

of alcohol with different carbon numbers and the cor-

responding measured glomerular activity (V

T,o

(x, y),

o = m). This set was chosen because large shifts of

the activation area in the glomeruli can be observed

with increases in the carbon number. From Figure

6(a), it can be conﬁrmed that the activation area shifts

from the caudal to the rostral side (left to right) as the

carbon number increases.

IJCCI 2009 - International Joint Conference on Computational Intelligence

382

1-propanol

1-butanol

1-pentanol

1-hexanol

1-heptanol

OHOH

1-octanol

OHOH

1-nonanol

OHOH

1-decanol

OHOH

(a) Learning data set adapted from Glomerular Response Archive (Leon and Johnson, 2009)

(b) Binarized measured activity

Figure 6: Learning results.

To ﬁnd the best Gaussian function number N,

learning simulation was performed with N = 1, 10,

20, ..., 70. The other parameters were determined us-

ing the learning algorithm described in the previous

section. To facilitate visual comparison of the outputs

of the glomeruli layer V

(x, y) with the measured ac-

tivities V

T,o

(x, y), both values are binarized; the top

5% of the values are converted to 1, and the others to

0. In addition, for quantitative comparison, the corre-

lation of the glomeruli module activation rate is cal-

culated between the binarized output of the glomeruli

layer and the binarized measured activity. The activa-

tion rateV

′

o,µ

in the module µ is deﬁned by the follow-

ing equation:

′

o,µ

(µ ∈ a, ..., p, A, ..., M, P) (9)

where S

o,µ

denotes the activated area, and S

o,µ

is the

whole area of the module µ.

After implementation of the learning algorithm,

each representative odorant in the learning data set

was input to the model, and the correlation outlined

above was calculated. This procedure was repeated

with different values of Gaussian function number N.

Figure 7 shows the relationship between N and the av-

erage correlation over the learning data set. It can be

seen that this correlation rises along with increases in

N until N = 50, then gradually drops. From this re-

sult, N = 50 is determined as the best Gaussian func-

tion number for this learning data set. One of the rea-

1 10 20 30 40 50 60 70

0.2

0.4

0.6

0.8

Gaussian unit number N

Glomerular module-

based correlation

Figure 7: Relationship between glomerular module-based

correlation and the Gaussian unit number.

sons for the decrease in correlation after N = 50 could

be that the activity at the center of the extra Gaussian

units does not obey the assumed relationship shown

in Equation (4) and Figure 5.

Figure 6(b) and (c) show the measured activity and

output of the glomeruli layer when N = 50, respec-

tively. Comparing the ﬁgures shows that the model

successfully reproduce the features seen in the mea-

sured activity. Speciﬁcally, the glomeruli layer output

shows the same trend in the shift of activated area.

These results suggest that the proposed learning algo-

rithm can approximate the learning data set.

4.2 Prediction

Using the parameters determined in the learning sim-

ulation, odorants not included in the learning data set

A NEURAL NETWORK MODEL OF THE OLFACTORY SYSTEM FOR GLOMERULAR ACTIVITY PREDICTION

383

2-hexanol

2-octanol

2-nonanol

2-pentanol

(b) Binarized measured activity

(a) Prediction data set adapted from Glomerular

Response Archive (Leon and Johnson, 2009)

Corre-

lation

0.42 0.470.620.51

Figure 8: Prediction results.

were input to the model. The odorants for predic-

tion are shown in Figure 8 (a). These data were cho-

sen because they are structurally close to those of the

learning data set. The binarized measured activitiy

is shown in Figure 8 (b) and the binarized Glomeruli

layer output is shown in Figure 8 (c). Although the

predicted results are not as precise as the output for

the odorants in the learning data set, this activity, es-

pecially on the lower side, captured the features of

the measured activity. In addition, the shift of the ac-

tivated area from the caudal to the rostral side (left

to right) along with increases in the carbon number

seems to be preserved. These results imply the feasi-

bility of predicting glomerular activity using the pro-

posed model.

5 CONCLUSIONS

In this paper, we proposed an olfactory model aimed

at developing a novel algorithm to relate odorant

molecules to odour qualities. The proposed model

takes odorants as the input, from which glomerular

activity is produced. In the model, odorants are ex-

pressed in graph form, and a graph kernel function is

employed to estimate the response of of receptors to

the odorants. A learning algorithm was also proposed

to set the parameters included in the model. Using

the model and this learning algorithm, we performed

simulation to learn a set of glomerular activities. The

results indicated that the model could approximate

the features of the learning data set. Further, we

performed a prediction simulation using the param-

eters determined by the learning algorithm. Although

the correlation between the output of the model and

the measured activity was not as high as that of the

learned data, it was observed that the features in the

measured activity were captured. This indicates the

feasibility of predicting glomerular activity.

In future work, we aim to improve the prediction

ability of the model to enable the ﬂavor of an odor-

ant to be predicted. To achieve this, we plan to intro-

duce other learning algorithms for feed-forward neu-

ral networks. In addition, the simulation needs to be

performed using a larger data set.

ACKNOWLEDGEMENTS

This work was partially supported by a Grant-in-Aid

for Scientiﬁc Research (21-9124) from the Research

Fellow-ships of the Japan Society for the Promotion

of Science (JSPS) for Young Scientists, and Grant-

in-Aid for Scientiﬁc Research on Innovative Areas

(20115010).

REFERENCES

Amoore, J. (1963). Stereochemical theory of olfaction. Na-

ture, 198:271–272.

Aungst, J. L., Heyward, P. M., Puche, A. C., Karnup,

S. V., Hayar, A., Szabo, G., and Shipley, M. T.

(2003). Centre-surround inhibition among olfactory

bulb glomeruli. Nature, 426:623–329.

Aznar, M., Lopez, R., Cacho, J., and Ferreira, V. (2001).

Identiﬁcation and quantiﬁcation of impact odorants

of aged red wines from rioja. gc-olfactometry, quan-

titative gc-ms, and odor evaluation of hplc frac-

tions. Journal of Agricultural and Food Chemistry,

49(6):2924–2929.

Buck, L. and Axel, R. (1991). A novel multigene family

may encode odorant receptors: a molecular basis for

odor recognition. Cell, 65:175–187.

Chen, S., Cowan, C., and Grant, P. (1991). Orthogonal least

squares learning algorithm for radial basis function

networks. IEEE Transactions on Neural Networks,

2(2):302–309.

Gutierrez-Osuna, R. (2002). Pattern analysis for machine

olfaction: A review. IEEE Sensors Journal, 2(3):189–

202.

Herz, R. and Engen, T. (1996). Odor memory review and

analysis. Psychonomic Bulletin and Review, 3(3):300

– 313.

IJCCI 2009 - International Joint Conference on Computational Intelligence

384

Johnson, B. A., Farahbod, H., and Leon, M. (2005). Interac-

tions between odorant functional group and hydrocar-

bon structure inﬂuence activity in glomerular response

modules in the rat olfactory bulb. The Journal of Com-

parative Neurology, 483(2):205–216.

Johnson, B. A. and Leon, M. (2007). Chemotopic odor-

ant coding in a mammalian olfactory. The Journal of

Comparative Neurology, 503(1):1–34.

Kashima, H., Tsuda, K., and Inokuschi, A. (2004). Kernels

for graphs. MIT Press.

Leon, M. and Johnson, B. A. (2009). Glomerular response

archive: http://leonserver.bio.uci.edu/.

Limpawattana, M., Yang, S., Yang, D., Kays, S., and

Shewfelt, R. (2001). Relating sensory descriptors to

volatile components in ﬂavor of specialty rice types.

Journal of Food Science, 73(9):S456–S460.

Mori, K. and Yoshihara, Y. (1995). Molecular recognition

and olfactory processing in the mammalian olfactory

system. Progress in Neurobiology, 45:585–619.

Nelder, J. and Mead, R. (1965). A simplex method for func-

tion minimization. The Computer Journal, 7(4):308–

313.

Semmelroch, P. and Grosch, W. (1995). Analysis of roasted

coffee powders and brews by gas chromatography-

olfactometry of headspace samples. Food Science and

Technology, 28(3):310 – 313.

van Ruth, S. (2001). Methods for gas chromatography-

olfactometry: a review. Biomolecular Engineering,

17(4-5):121 – 128.

Youngentob, Johnson, B., Leon, M., Sheehe, P., and

Kent, P. (2006). Predicting odorant quality per-

ceptions from multidimensional scaling of olfactory

bulb glomerular activity patterns. Behavioral Neuro-

science, 120(6):1337–1345.

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