Environ. Sci. Technol. 2007, 41, 2414-2421
Chemical Indices and Methods of Multivariate Statistics as a Tool for Odor Classification I N G O T . M A H L K E , * ,† PETER H. THIESEN,† AND B E R N D N I E M E Y E R †,‡ Helmut-Schmidt-University / University of the Federal Armed Forces Hamburg Institute of Thermodynamics, 22043 Hamburg, Germany, and Institute for Coastal Research, GKSS Research Center, 21502 Geesthacht, Germany
Industrial and agricultural off-gas streams are comprised of numerous volatile compounds, many of which have substantially different odorous properties. State-of-the-art waste-gas treatment includes the characterization of these molecules and is directed at, if possible, either the avoidance of such odorants during processing or the use of existing standardized air purification techniques like bioscrubbing or afterburning, which however, often show low efficiency under ecological and economical regards. Selective odor separation from the off-gas streams could ease many of these disadvantages but is not yet widely applicable. Thus, the aim of this paper is to identify possible model substances in selective odor separation research from 155 volatile molecules mainly originating from livestock facilities, fat refineries, and cocoa and coffee production by knowledge-based methods. All compounds are examined with regard to their structure and information-content using topological and information-theoretical indices. Resulting data are fitted in an observation matrix, and similarities between the substances are computed. Principal component analysis and k-means cluster analysis are conducted showing that clustering of indices data can depict odor information correlating well to molecular composition and molecular shape. Quantitative molecule describtion along with the application of such statistical means therefore provide a good classification tool of malodorant structure properties with no thermodynamic data needed. The approximate look-alike shape of odorous compounds within the clusters suggests a fair choice of possible model molecules.
Introduction Densely populated areas grant job opportunities as well as sources of recreation and recovery in order to remain attractive to its inhabitants and taxpayers. These ideals sometimes result in the conflicting interests of odorless ambient air and nearby industrial jobs. However, the tolerance toward odorous disturbances in the vicinity of production or processing facilities is decreasing and companies have to run expensive campaigns to compensate for their emissions during the production process and to develop * Corresponding author phone: +49-511-2282329; fax: +49-4065412008; e-mail:
[email protected]. † Helmut-Schmidt-University. ‡ GKSS Research Center. 2414
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credible odor management systems (1). Moreover, recent legislation in many countries is also influenced more and more by stricter licensing procedures for both new and already working complexes (2-5). The fact that process parameters at waste-gas emitting plants are often varying in combination with climatic factors and a very low detection level of some substances in the human olfactory system make any off-odor quite an environmental burden. In a mutual cooperative project of industry and research facilities, new methods of odor detection, analysis and selective odor reduction are being developed (6). From the view of process engineering, malodorous air streams frequently can be assigned to one of two common cases: Either the waste-gas is dominated by one distinct odor which cannot be treated sufficiently biologically or the off-gas poses a multicomponent system yielding a large number of odor-active molecules of different smells (7). For the first case, it seems reasonable to synthesize and utilize surface modified selective adsorbents tailor-made for the actual purpose (8, 9). By measuring the adsorbed and desorbed loads of eight different representative volatile compounds in two consecutive cycles adsorption profiles have been established for each of the adsorbents (10, 11). Examining the surface-modified samples against unmodified carriers, adsorption and desorption processes have repeatedly shown better results (12, 13). Finally, this method has been applied to industrial scale problems (14). For the second case, a “one choice fits all” solution seems rather unsatisfactory and economically unfeasible. These air streams usually consist of a mixture of nonodorous molecules with several substances contributing to odor perception. In fact, thermodynamic data for a lot of these compounds are totally unknown, which makes it even harder to evaluate the odorous potential of such compounds or to design effective separation techniques to eliminate them from the off-gas. Not surprisingly, attempts to instrumentally identify odorrelevant molecules mimicing human sensory detection have, repeatedly, not been successful (15). However, the purpose of this work is to classify 155 volatile compounds by knowledge-based methods leading to the identification of possible model substances for further investigations and eventually to the introduction of an “adsorbent library”, matching classified groups of odors to unmodified or modified adsorbents depending on their speciality.
Theoretical Background In order to “translate” molecular properties of odorants into quantitative values, the use of chemical indices and graph theory is suggested. This is by representing the structural formula of a given molecule by a chemical graph, where the atoms are replaced by numbered vertices, and the molecular bonds are replaced by edges (Figure 1). Only so-called simple molecular graphs are used, which means that multiple bonds do not result in loops or multiple links in the chemical graph. In contrast to standard procedures we decided not to strip off the hydrogen atoms when transforming the molecule into the labeled graph. In our view, this contributes to a better topological representation of the molecules. Due to the fact that in computational chemistry QSAR/ QSPR-models (quantitative structure-activity/property relationships) using these methods have been already successfully applied in the prediction of molecular systems in different fields of research (16), an attempt of quantifying molecular properties which should contribute to the odor 10.1021/es060512z CCC: $37.00
2007 American Chemical Society Published on Web 02/20/2007
number 9 is 3 neglecting any multiple or aromatic bonds. The Zagreb Group Index measures the connectivity of a molecular graph by summing up the square values of each vertex’s degree. It is defined as N
M)
∑d
2
i
i)1
FIGURE 1. Indole-3-acetic acid as a labeled graph. Atoms are displayed as numbered vertices; bonds are labeled as connecting edges. impression is proposed. Subsequently the compounds in this study are classified by means of pattern analysis techniques. Tools of multivariate statistics have proven helpful in molecular description in a growing number of recent publications. Go¨tz et al. used hierarchical cluster analysis to attribute dioxin contaminated sediment samples to pollution sources along the Elbe river in Germany (17). Goodner et al. classified citrus juices on the basis of carotenoid profiles by principal component analysis (18), and Park et al. eventually examined insects’ odor dicrimination using hierarchical cluster analysis as well (19). Even though it has not been finally determined whether the odorous potential of a volatile compound is due to its’ stereochemistry (20) or to molecular vibration (21), strucutural properties apparently play a major role in the binding of the odorous molecule (22), thus the used indices had to reflect this requirement. Therefore, topological indices are applied to the molecules with each index stressing different structural features. Furthermore, the idea that, like in all systems that contain multiple possibilities of interaction with the environment, on an abstract basis the odorous molecule possesses an uncertainty value enabling interactions in various ways led us to the conviction to include a measure of complexity. According to Shannon’s information theory, the information content of a system increases if the number of different possible states of the system rises as well (23). The amount of information carried by distinct properties of the odorant can be correlated to the intramolecular variety of this property and, therefore, takes the same form as the entropy in statistical thermodynamics (24). It can be given as n
I ) -k
∑ p log i
2
pi
i)1
with the vertices running from 1 to N. However, one disadvantage of the Zagreb Index is that it does not weight the vertices evenly giving greater weight to the inner vertices (27). Wiener Index. One of the first topological indices that was introduced is the Wiener Index which gives a good measure on the compactness of molecules, and is larger for long chains and smaller for branched molecules. It gives half of the distance between all vertices to all other vertices of the compound and is obtained by summation over all edges w separating each pair of vertices on the shortest path (e.g., with indole-3-acetic acid, the distance between vertex number 1 and vertex number 14 is 5). It also equals the sum of all inputs to the triangular distance submatrix of the molecular graph (28).
W)
N
1
∑w
2
ij
(i,j)
Randic´ Connectivity Index. This index once more emphasizes the connectivity of the molecule. The calculation always involves a pair of adjacent vertices, thus being referred to as a second-generation index (16). This index is generated by the sum over all edges in combination with the inverse square root of the vertices’ degrees being incident to the edge. It is defined as (29)
Χ)
∑ (d d )
-0.5
i j
; ∀ di, dj adjacent
edges
For example, with indole-3-acetic acid, the contribution of vertex number 1 and vertex number 2 is 0.7071. Contrary to the Zagreb index, the Randic´ Connectivity Index does not overvalue the interior but the outer vertices or edges, which is due to the inverse of the square root. Balaban Distance Connectivity Index. This index resembles the Wiener index as well as the Randic´ Connectivity Index. It introduces a factor c ) b/(µ + 1) with b being the number of bonds and µ being the cyclomatic number of the graph, thus discriminating easily between cyclic and noncyclic molecules. It makes use of the distance sums of all adjacent vertices because only these vertices contribute with a value other than zero. The Balaban Index is defined as (29)
J)c
∑ (v v ) i j
-0.5
; ∀ vi, vj adjacent
edges
where p denotes the probability of the state i, and k amounts to a unit constant. Thus, information-theoretical indices were applied to the molecules as well.
Materials and Methods We selected 155 different waste-gas components from livestock facilities, fat refineries (25), and cocoa and coffee production plants (26). Indices calculated for each of these compounds belong either to the group of strictly topological indices, strictly information-theoretical indices, or indices measuring aspects of both groups. The indices used for the present work are described below: Zagreb Group Index. The degree d of a vertex is defined as the number of edges incident with this vertex. In the case of indole-3-acetic acid (see Figure 1), e.g., the degree of vertex
At the sample molecule, indole-3-acetic acid, the contribution of vertex number 1 and vertex number 2 is 0.0095. Information Index on Atomic Composition. This index takes into account the number of different elements within the molecule. As stated above, according to the information theory the information content is dependent on the intramolecular variety. The index formula can be given as (30) n
Iac ) N *log2 N -
∑ (N *log i
2
Ni)
i)1
where N denotes the total number of atoms and Ni the number of atoms of type i. For indole-3-acetic acid, the index’s value amounts to 34.3589. VOL. 41, NO. 7, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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Information Index on the Kind of Molecular Bonds. Quite similar to the index on atomic composition, this index is defined as n
Ib ) B *log2 B -
∑ (B *log i
2
Bi)
i)1
with B indicating the total number of bonds and with Bi distinguishing in single, double, triple, and aromatic bonds. For example, with indole-3-acetic acid, the index equals 27.8031. The Orbital Information Index. This index applies topological aspects as first criteria. The aim is to generate equivalent classes of graph elements, i.e., vertices, which can be substituted among each other without destroying any of the graph properties. Thus, in a first approximation, all vertices having the same valence as well as having same degree neighbors are considered equivalent which indicates an isomorphism in graph theory. Edge structure and the vertices’ degree must be preserved in all graphs when substitution is carried out. Even though an isomorphism is necessary it is not sufficient for vertices to be grouped into the same equivalent class, yet. Furthermore, graphs with substitutable vertices are required to be automorph, which means that a permutation of vertices mapping the graph to itself must exist. Only if this requirement is fulfilled vertices are grouped into one equivalent class, so-called orbits. Now, the information-theoretical equation comes into play (31) k
Ic ) C *log2 C -
∑ (C *log i
2
Ci)
i)1
where C denotes the total number of atoms and Ci the number of atoms grouped into the ith class, respectively. For indole3-acetic acid, the index equals 96.1075. Electropy Information Index. The Electropy Information Index considers the electron configuration of the molecule and splits up the electron distribution around the nucleus into different partial bond spaces, while the molecule is considered to form a finite bond space S. A first distinction is made between the valence bond space Sv containing all electrons contributing to the molecular bonding and those electrons which constitute the non-valence space Sn in closer proximity to the nucleus. The valence bond space is further divided into σ- and π-partial spaces, so that
S ) Sv + Sn ) Sσ + Sπ + Sn is valid. Finally, all partial bond spaces are further separated according to the type of atoms they link forming individual bond spaces. Solely, the carbon skeleton of a molecule must be considered as one common bond space if not fragmented by any heteroatom. After defining all partial bond spaces the information content becomes important. The electrons are distributed to the partial bond spaces in such manner that eventually the number of electrons equals that of the molecule’s electron configuration in every partial bond space. This process of distribution (P) resembles a popular combinatorial problem. If N numbered balls were to be distributed to k baskets of not necessarily equal size, then
k
I ) log2 P ) log2(N!/
∏ N !) i
i)1
For the sample molecule indole-3-acetic acid, the index’ value amounts to 369.7813. So far, eight different index values have been calculated for each compound. Due to the fact that odorous capacities seem to be restricted by any molecule’s size (32) the molecular weight is also added to the data. All quantities are standardized by dividing by the number of atoms of each molecule. The obtained values for all substances and indexes are fitted into an observation matrix M.
In these data, two different methods of multivariate statistics are carried out. First, to discover any linear relations in the data, a principal component analysis is performed. To avoid different weights of variables, all columns are standardized to mean 0 and a variance of 1. The calculations are executed using MAPLE 7.0. Second, a hierarchical k-means cluster analysis is conducted using Clustan Graphics 6.0 and choosing Ward’s method as clustering method. All values are standardized to z-scores before computing proximities to avoid unequal variable weights.
Results and Discussion For this work, results of the principal component analysis (PCA) give a first visualization of how different groups of odorants are arranged in relation to one another with different symbols and colors indicating different groups of substances (Figure 2). However, since only 73.6% of the original variance of the given information are represented by the first two principal components, this method does not lead to satisfactory results. Even if a third principal component was taken into account the system does not exceed 83.4% in representation of the original variance. Furthermore, it becomes obvious that no sufficient heterogeneity distinguishing different groups of molecules can be discovered by this method. Applying hierarchical cluster analysis leads to better results because none of the original variance is lost. A so-called dendrogram is the result of such a hierarchical cluster analysis starting on one side with as many classes as there are objects and aggregating these classes according to their similarity. In this case k-means analysis is used because it was intended to create 20 classes showing a good homogeneity of objects within each cluster and a good heterogeneity between
k
P ) N!/
∏N! i
i)1
different possibilities of distribution are existing. Thus, back to the chemical molecule, the information content according to the molecule’s electron configuration can be given by (29) 2416
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FIGURE 2. Two-dimensional PCA leads to unsufficient heterogeneity between clusters.
FIGURE 3. Dendrogramm of the 155 volatile compounds. different clusters (Figure 3). One measure for homogeneity is the fusion level at which objects unite grouping together into a cluster. Generally more homogeneous clusters are obtained when the fusion level is reduced with more classes being generated. In our examination, objects are distinct enough to fairly discriminate among them at the level of 20 clusters. Even though the discussion whether human odor detection is mainly due to shape or molecular vibration has not been decided, it is a common agreement that topological aspects play a role in selective odor separation. While Schiffman has linked Raman spectra to the olfactory quality of topologically similar molecules (33) we provide an effective
[
1 0.41 -0.09 0.72 R ) -0.17 -0.38 0.35 0.07 0.67
0.41 1 0.21 0.60 0.07 -0.12 0.71 -0.57 0.51
-0.09 0.21 1 0.19 0.58 0.67 -0.02 -0.60 -0.25
0.72 0.60 0.19 1 0.04 0.02 0.52 -0.40 0.80
tool for molecule classification via different indices with no thermodynamic data being needed. The dominant feature in most of the clusters that have been created is the approximate look-alike-shape of the odorants within any respective cluster. To ensure that this topological similarity is not due to a high correlation in the original data we performed a correlation analysis on the standardized data matrix. Results (see matrix R below) show no particular correlation among the indices utilized. A closer look at the members of single clusters, e.g., cluster 11, confirms the similarity in shape (Table 1). Consisting of a total of 17 molecules of various functional groups (ketones, aldehydes, carboxylic acids, alcohol, and esters) all members of this
-0.17 0.07 0.58 0.04 1 0.54 -0.22 -0.68 -0.43
-0.38 -0.12 0.67 0.02 0.54 1 -0.28 -0.53 -0.43
0.35 0.71 -0.02 0.52 -0.22 -0.28 1 -0.25 0.61
0.07 -0.57 -0.60 -0.40 -0.68 -0.53 -0.25 1 0.01
0.67 0.51 -0.25 0.80 -0.43 -0.43 0.61 0.01 1
]
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TABLE 1. Members of Cluster 11 Display a High Degree of Topological Similarity
cluster are long-chained and slightly branched molecules. Even though these compounds very likely are still too diverse to practically allow selective separation, the various subgroups of this cluster reveal another feature. It becomes evident that the clustering process has resulted in partly 2418
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homogeneous subgroups also with regard to the olfactory quality of the molecules (Figure 4). The first subgroup of the top seven substances, except for 1-octen-3-ol, can be described as having a green-herbal and fruity note. The second subgroup is a bit more diverse. While heptanoic acid
FIGURE 4. Olfactory qualities of the compounds merged into cluster 11. The subgroub of fruity and green-herbal substances includes the first seven subtances except for 1-octen-3-ol. Despite its homogeneous fusion level, the second subgroup containing the next four compounds cannot be described by a completely uniform olfactory descriptor. The third subgroup then is dominated by molecules with a fatty and waxy smell.
FIGURE 5. Mean values vary significantly across the clusters due to different electronegative contribution of functional groups in the existing clusters. and octanoic acid dispense the rancid and fatty smell that is typical for carboxylic acids, 2-butoxyethanol is attributed to an ether-like odor and 3-methylbutyl acetate to a bananalike note. Even though the lower six members of cluster 11 do not form such a homogeneous subgroup as the other substances the odor of the lower five members of cluster 11 is mainly described as fatty and waxy, whereas the note of the last compound is unknown. In this paper we focused on indices describing molecule topology, structure, and information content, but classification procedures offer the possibility to introduce indices
related to other properties as well. Abul-Kassim and Simoneit have identified quite a few “most important properties of an organic pollutant” for adsorption mechanisms pointing out that the mode of interaction is dependent on a number of properties, molecular polarity being one of them (45). In order to evaluate the usefulness of the classification so far, we tested our results against another, not closely related, index. Polarity for polyatomic molecules cannot be easily calculated, thus we created an index which takes into account the difference in electronegativity of adjacent atoms and the strength of attraction on valence electrons by the nucleus as VOL. 41, NO. 7, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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a function of the radius. We defined
E)
1
∑
N edges
(
χi - χj +
rj
)
ri
; ∀ χi > χj
with N being the total number of atoms. We applied this index to all compounds and calculated how its means, medians, and standard deviations vary across the clusters we previously obtained. We plotted the standard deviation versus the mean of each cluster (Figure 5), and found that the mean values vary significantly. These differences can be explained by the different polar contributions of different functional groups in the existing clusters. This supports the thesis that the clusters we obtained are not random but meaningful for separation under this viewpoint. With respect to cluster 11, the figure displays two other clusters with a similar mean value. One of them, cluster 5, is mainly composed of similar functional groups but slightly shorter carboxylic acids and aldehydes than in cluster 11 (see the Supporting Information). The other, cluster 18, is solely comprised of aromatic structures thus clearly distinguishing it topologically from cluster 11, and also displaying a larger standard deviation. In this first step, we conclude that the quantitative description of different molecular properties via indices proved to provide a good classification of odorant structure properties and, in parts, the olfactory qualities of the investigated molecules. In the sample cluster 11, we suggest 2-heptanone as model substance for the upper seven compounds and nonanal for the lower molecules due to their “easy to handle” odorous intensity. Thus, the described method can generally be used to generate model substances for actual industrial multicomponent off-gas streams and will allow the testing of an adequate set of selective tailormade filtering devices for each cluster. Furthermore, the data can support the feature selection in the teaching process of electronic noses applied for process control.
Acknowledgments We thank the Bundesministerium fu ¨ r Bildung and Forschung (German Federal Department on Research) for the financial support which enabled this study. This integrated project of 18 partners and its fourth subproject is funded under the no. 0330236.
Supporting Information Available All 155 substances with calculated indices are listed to give a better estimation of the degree of separation reached by this method. Additionally, the members of four additional clusters with their odor descriptors and a close-up of the respective clusters are depicted. This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review March 4, 2006. Revised manuscript received January 7, 2007. Accepted January 10, 2007. ES060512Z
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