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LIST OF CONTRIBUTORS
Lars Carlsen
Awareness Center, Linkøpingvej 35, Trekroner, DK-4000 Roskilde, Denmark
Alexandre Varnek
Department of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
Igor I. Bask i n
Laboratory of Chemoinformatics, UMR 7140 CNRS, University of Strasbourg, 4, rue B.
Pascal, Strasbourg 67000, France
George T. Hanson
Life Technologies, 501 Charmany Drive, Madison, Wisconsin, 53719, USA
Bonnie J. Hanson
Life Technologies, 501 Charmany Drive, Madison, Wisconsin, 53719, USA
Ye Fang
Biochemical Technologies, Science and Technology Division, Corning Incorporated,
Sullivan Park, Corning, NY 14831, USA
Maria Â. Taipa
Department of Bioengineering, Instituto Superior Técnico, Technical University of
Lisbon, Av.Rovisco Pais, 1049-001 Lisboa, Portugal
Cassia R. Overk
Department of Neurosciences, School of Medicine, University of California at San
Diego, La Jolla, California, CA 92093, USA
Judy L. Bolt o n
UIC/NIH Center for Botanical Dietary Supplements Research and Department of
Medicinal Chemistry and Pharmacognosy, College of Pharmacy, Uni versi ty of Illinois at
Chicago, 833 S.Wood St., M/C 781, Chicago, IL 60612, USA
Adam J. Kimple
Department of Pharmacology, Lineberger Comprehensive Cancer Center, and UNC
Neuroscience Center, The University of North Carolina at Chapel Hill, Chapel Hill, NC
27599-7365, USA
v
Adam Yasgar
NIH Chemical Genomics Center, National Center for Advancing Translational Sciences,
National Institutes of Health, Bethesda, MD 20892-3370, USA
Mark Hughes
BRITE Institute, North Carolina Central University, Durham, NC 27707, USA
Ajit Jadhav
NIH Chemical Genomics Center, National Center for Advancing Translational Sciences,
National Institutes of Health, Bethesda, MD 20892-3370, USA
Francis S. Willard
Department of Pharmacology, Lineberger Comprehensive Cancer Center, and UNC
Neuroscience Center, The University of North Carolina at Chapel Hill, Chapel Hill, NC
27599-7365, USA
Robin E. Muller
Department of Pharmacology, Lineberger Comprehensive Cancer Center, and UNC
Neuroscience Center, The University of North Carolina at Chapel Hill, Chapel Hill, NC
27599-7365, USA
Christopher P. Austin
NIH Chemical Genomics Center, National Center for Advancing Translational Sciences,
National Institutes of Health, Bethesda, MD 20892-3370, USA
James Inglese
NIH Chemical Genomics Center, National Center for Advancing Translational Sciences,
National Institutes of Health, Bethesda, MD 20892-3370, USA
Gordon C. Ibeanu
BRITE Institute, North Carolina Central University, Durham, NC 27707, USA
David P. Siderovski
Department of Pharmacology, Lineberger Comprehensive Cancer Center, and UNC
Neuroscience Center, The University of North Carolina at Chapel Hill, Chapel Hill, NC
27599-7365, USA
Anton Simeonov
NIH Chemical Genomics Center, National Center for Advancing Translational Sciences,
National Institutes of Health, Bethesda, MD 20892-3370, USA
vi
Christopher A. Johnston
Department of Pharmacology, Lineberger Comprehensive Cancer Center, and UNC
Neuroscience Center, The University of North Carolina at Chapel Hill, Chapel Hill, NC
27599-7365, USA
Francis S. Willard
Department of Pharmacology, Lineberger Comprehensive Cancer Center, and UNC
Neuroscience Center, The University of North Carolina at Chapel Hill, Chapel Hill, NC
27599-7365, USA
Kevin Ramer
Karo Bio USA, Durham, NC, 27703, USA
Rainer Blaesius
Karo Bio USA, Durham, NC, 27703, USA
Natalia Roques
Karo Bio USA, Durham, NC, 27703, USA
David P. Siderovski
Department of Pharmacology, Lineberger Comprehensive Cancer Center, and UNC
Neuroscience Center, The University of North Carolina at Chapel Hill, Chapel Hill, NC
27599-7365, USA
vii
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Advances in Combinatorial Chemistry & High Throughput Screening, 2013, Vol. 1, 3-35 3
CHAPTER 1
Assessing Chemicals Using Partial Order Ranking Methodology
Lars Carlsen
*,1,2
1
Awareness Center, Linkøpingvej 35, Trekroner, DK-4000 Roskilde, Denmark;
2
Center of Physicochemical Methods of Research and Analysis, al-Farabi Kazakh
National University, 96A Tole Bi st, Almaty 050012, Kazakhstan
Abstract: This review summarizes the use of selected partial order ranking (POR)
techniques for the assessment of chemicals. Simple partial order ranking may
advantageously be applied to give the single chemicals investigated an identity in relation to
other substances. Thus, it constitute s an ef fective tool for the prioritiza tion of chemicals, e.g.,
based on their PBT (Persistence, Bioaccumulating, Toxicity) characteristics. In more
elaborate cases where a larger number of descriptors are taken into account, e.g., comprising
physico-chemical characteristics, atmospheric parameters, geospecific factors and possibly
socio-economic factors hierarchical pa rtial order ranking (HPOR) may be applied. Thus, in a
first ordering step a series of meta-descriptors are generated that later subsequently being
used as descriptors in a subsequent ordering. HPOR allows a sensible ranking model even if
a relative high number of descriptors are included. Assessing chemicals can, taken the actual
situation into account, be based on a variety of parameters/descriptors. Thus, it might be
valuable information to know the mutual importa nce of the applied descriptor. This
information may appropriately be retrieved by a sensitivity study applying a designed
module in the PyHasse software package. Finally accumulation partial order ranking
(APOR) is illustrated. Accumulating partial APOR is a technique where data from a series
of individual tests of various characteristics are aggregated, however, maintaining the basics
of the partial order ranking methodology. APOR offers prioritization based on mutual
probabilities derived from the aggregated data. Alternatively prioritization may be achieved
based on average ranks derived from the APOR. The application APOR is demonstrated by
an assessment of a series of potential PBT substances. In contrast to simple ranking
techniques, partial order ranki ng does not automatical ly lead to an absolute rank of the single
substances being studied. However, a weak linear order may in all cases be achieved based
on the average ranks of the single substances. Additionally ranking probabilities can be
derived based on Monte Carlo si m ulati ons.
Keywords: Partial order ranking techniques, hierarchical partial order ranking,
accumulation partial order ranking, quantitative structure-activity relationships,
assessment of chemicals, prioritization of chemicals, decision support tool, PBT
substances.
*Address correspondence to Lars Carlsen: Awareness Center, Linkøpingvej 35, Trekroner, DK-4000
Roskilde, Denmark; Tel: +45 2048 0213; E-mail: LC@AwarenessCenter.dk
4 Advances in Combinatorial Chemistry & High Throughput Screening, Vol. 1 Lars Carlsen
1. INTRODUCTION
The assessment and regulation of chemicals has over the years developed to a
major issue in relation to assuring the human health as well as to protect our
environment. However, the vast majority of the chemicals available on the market
today has not been properly assessed and regulated. The simple explanation for
this is the obvious lack, or at least availability of the necessary data material. For a
discussion of data availability see, e.g., Voigt et al. [1-3].
A crucial point in the European chemical framework REACH [4] is the handling
of substances that meet the criteria for classification as dangerous in accordance
to Directive 67/548/EEC [5] or is assessed to be persistent, bioaccumulating and
toxic (PBT’s) or very persistent and very bioaccumulating (vPvB’s). For these
substances an assessment including an exposure assessment as well as a risk
characterization is mandatory. For the so-called CMR substances (carcinogens,
mutagens, and substances toxic to reproduction), endocrine disrupting substances
(ED’s), persistent organic pollutants (POP’s) and substances that are PBT’s or
vPvB’s, authorization must be obtained in order to use these substances ([4],
Article 57). However, this applies only in the cases where it is not possible to
determine a lower threshold for their action or for substances having PBT or vPvB
properties. For the latter type of substances the requirement for substitution
apparently is mandatory ([4]; article 57 and 59).
It must be emphasized t hat the above may well be undermined as authorization of
chemicals covered by Articles 55-59 in REACH [4] can be granted if the
manufacturer through a socio-economic analysis can show that, e.g., the socio-
economic benefits outwei gh the risks associated with the use of the substance ( [4],
Article. 60(4)(b)). It is worthwhile to not e that reco mmendations how to bal ance the
risks and the socio-economic analysis is not include d in the REACH framework.
In a proper assessment of the chemical substance, not only the physico-chemical
and toxicological characteristics (PBT) should be taken into account. I n addition a
series of environmental factors may advantageously be considered. Thus,
parameters like production tonnage [6], specific release scenarios [6, 7], and
geographical and site-specific factors [8] in addition to various substance
Assessing Chemicals Advances in Combinatorial Chemistry & High Throughput Screening, Vol. 1 5
dependent parameters should be taken into account. Further socio-economic
factors may be taken into consideration.
The present review will focus on the u se of partial order ranking methods as an
attractive supplement to assess chemicals. The study will include 1: a simple
ranking of substances based on their physico-chemical characteristics, possibly
based on QSAR generated data [9-13], 2: a more elaborate hierarchical partial
order ranking (HPOR) [14] method allowing to take a larger variety of
parameters, e.g., socio-economic factors into account, and 3: an assessment of
specific characteristics of chemical substances, e.g., PBT characteristics applying
the accumulating partial order (APOR) approach [15].
Further the use of sensitivity studies to disclose the relative importance of the
descriptor brought into play in the assessment of a group of chemicals will be
illustrated [16].
2. METHODS
The basic methodology applied for assessing chemical substances is partial order
ranking. Thus, in the following the basic concepts of partial order ranking,
including deriving linear extensions, ranking probability and average ranks are
summarized and the use of sensitivity calculations will be shown to elucidate the
relative importance of the single descriptors.. In addition two more elaborate
partial order ranking methodologies, i.e., hierarchical partial order ranking
(HPOR) and accumulating partial order ranking (APOR) are described.
As experimental data on physico-chemical characteristics and toxicology for
chemical substances in many cases are scarce, data for assessing chemicals may
often advantageously be derived based on quantitative structure-activity
relationships (QSARs). Thus, a short description of QSARs with focus on the so-
called ‘noise-deficient’ QSARs is included.
2.1. Partial Order Ranking
The theory of partial order ranking (POR) is pre sented elsewhere [17, 18]. I n brief,
Partial Order Ranking is a simple principle, which a priori includes “” as the only
6 Advances in Combinatorial Chemistry & High Throughput Screening, Vol. 1 Lars Carlsen
mathematical relation. If a system is considered, which can be described by a series of
descriptors p
i
, a given chemical A, characterized by the descriptors p
i
(A) can be
compared to another chemical B, characterized by the descriptors p
i
(B), through
comparison of the single descriptors, respectively. Thus, chemical A will be r anked
higher than B, i.e., B A, if at least one descriptor for A is higher than the
corresponding descriptor for B and no descriptor for A is lower than the
corresponding descriptor for B. If, on the other hand, p
i
(A) > p
i
(B) for descripto r i a nd
p
j
(A) < p
j
(B) for descriptor j, A and B will be denoted incomparable. Obviously, if all
descriptors for A ar e equal to the corre sponding descriptors for B, i.e., p
i
(B) = p
i
(A)
for all i, the two chemicals will have identical rank and will be considered as
equivalent, i.e., A = B. In mathematical terms this can be expressed as
B A p
i
(B) p
i
(A) for all i (1)
It further follows that if A B and B C then A C. If no rank can be
established between A and B these chemicals are denoted as incomparable, i.e.,
they cannot be assigned a mutual order. Theref ore POR is an ideal tool to handle
incommensurable attributes.
In partial order ranking - in contrast to standard multidimensional statistical
analysis - neither any assumptions about linearity nor any assumptions about
distribution properties are made. In this way the partial order ranking can be
considered as a non-parametric method. Thus, there is no preference among the
descriptors. However, due to the simple mathematics outlined above, it must be
emphasized that the method a priori is rather sensitive to noise, since even minor
fluctuations in the descriptor values may lead to non-comparability or reversed
ordering. A discussion on partial order ranking vs multicriteria decision analyses
can be found in Bruggemann and Carlsen [19].
A main point is that all descriptors have the same direction, i.e., “high” and “low”. As
an example bioaccumulation and toxicity can be mentioned. In the case of
bioaccumulation, the higher the number the higher a chemical substance tends to
bioaccumulate and thus the more probl ematic the substance, wher eas in the case of
toxicity, the lower the figure the more toxic the substance. Thus, in order to secure
identical directions of th e two descriptors, one of them, e.g., the toxicity figures, ha s
Assessing Chemicals Advances in Combinatorial Chemistry & High Throughput Screening, Vol. 1 7
to be multiplied by -1. Consequently, both in the case of bioaccumulation and in the
case of toxicity higher figures will now correspond to more problematic chemicals.
The graphical representation of the partial ordering is often given in a so-called
Hasse diagram [20-23].
The calculations are performed using the PyHasse software that today has
substituted the WHasse software [23] as the preferred tool for partial order
analyses. PyHasse has been developed (and currently being extended and
improved) by dr. R.Bruggemann (Berlin) and con sists close to 100 modules. The
software package is available on request from R. Bruggemann
1
and should be
considered as an experimental, non-professional software. An alternative is the
DART (Decision Analysis by Ranking Techniques) software that comprises
different kinds of order ranking methods, roughly classified as total - and partial
order ranking methods [24]. Beside DART [24] , the software pack age PyHa sse is
currently the only available one for applying ordinal analyses on data matrices.
2.2. Linear Extensions
The number of incomparable elements in the partial ordering may obviously
constitute a limitation in the attempt to rank, e.g., a series of chemical substance s
based on their potential environmental or human health hazard. To a certain extent
this problem can be remedied through the application of the so-called linear
extensions of the partial order ranking [25, 26]. A linear extension is a total order,
where all comparabilities of the partial order are reproduced [18, 20] . Due to the
incomparisons in the partial order ranking, a number of possible linear extensions
correspond to one partial order. If all possible linear extensions are found, a
ranking probability of the single substances can be calculated. Consequently, if all
possible linear extensions are found it is possible to calculate the average ranks of
the single elements in a partially ordered set [27, 28].
2.3. Average Ranks
As mentioned above the average rank of the singl e substances can be established
based on the linear extensions as the average of the ranks in all the linear
1
brg_home@web.de
8 Advances in Combinatorial Chemistry & High Throughput Screening, Vol. 1 Lars Carlsen
extensions. It has been demonstrated that the average rank of the single element in
the Hasse diagram can be obtained through deriving a large number of randomly
generated linear extensions [29-32]. The r andom linear extension approach allows
in addition to the determination of the average ranks of the single elements also
the determination of the ranking probability distribution of the single elements
[12, 13].
Alternatively average rank may be obtained directly. Thus, several approaches,
such as the lattice theoretical one [33-35] are developed in algorithmic oriented
literature. However, these methods are limited to relatively small datasets due to
the necessary computer power. Thus, appr oximate methods have been developed
based on loccal partial orders [36, 37].
2.4. Relative Descriptor Importance
Working with a multi-descriptor system as partial order ranking it is obviously of
significant interest to retrieve information about the relative importance of the
single indicators.
Hence, the sensitivity expresses how important any single descriptor is for the
structure of the partial order as visualized by the Hasse diagram. The PyHasse
software comprises a specific module that offers an estimation of the sensitivity
(for details on sensitivity analyses, see: [20]) as recently illustrated by a study of
30 chemicals comprising selected organo-phosphorous compounds and industri al
products [16] covered by the Stockholm Convention [38].
2.5. Hierarchical POR
Based on the average rank of the single substances, the most probable rank for
each element can be obtained and thus the most probably linear rank of the
elements studied can be established. This is done f or every dataset, e.g., physico-
chemical characteristics, atmospheric parameters, geospecific factors and socio-
economic factors each leading to an aver age r anking that subsequently are used as
so-called meta-descriptors. Thus, in the second stage the meta-descriptors
describe the meta-dimension are subsequently used as descriptors in a consecutive
partial order ranking. Obviously, the number of descriptors is significantly
Assessing Chemicals Advances in Combinatorial Chemistry & High Throughput Screening, Vol. 1 9
reduced and the ranking leading to the possible development of a robust model
[39] that in principle will contain all information based on the original set of
descriptors [14].
Since the meta-descriptors, as the descriptors, ar e ordered with the highest rank
being denoted “1”, the meta-descriptors must all be multiplied by -1 in order to
make sure that the elements with the highest rank, i.e., with the lowest attributed
number, will be ranked in the top of the Hasse diagram as a result of the ranking
based on the meta-descriptors. In Fig. (1) a graphical representation of the HPOR
approach [14] is depicted.
Dimension 1
d
,
d
,
…
,
d
Dimension N
d
,
d
,
…
,
d
• • • • •
Meta-dimension
md
1
, md
2
, ... , md
n
First
POR
Average
Rank
Final Rank
Dimension 2
d
,
d
,
…
,
d
First
POR
Average
Rank
First
POR
Average
Rank
Second
POR
Average
Rank
Fig. (1). Graphical representation of the hierarchical partial order ranking.
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