REV . CHIM. (București) 60 Nr. 12 2009 http:www.revistadechimie.ro 1357Molecular Descriptors for Quantitative Structure-Toxicity [631804]

REV . CHIM. (București) ♦ 60♦ Nr. 12 ♦ 2009 http://www.revistadechimie.ro 1357Molecular Descriptors for Quantitative Structure-Toxicity
Relationship (QSTR).
II. Three Ovality Molecular Descriptors and Their Use in Modeling the Toxicity
of Aliphatic Alcohols on Tetrahymena pyriformis
VICENTIU VLAIA1*, TUDOR OLARIU1, CIPRIAN CIUBOTARIU2, MIHAI MEDELEANU3, LAVINIA VLAIA1, DAN CIUBOTARIU1
1 “Victor Babes” University of Medicine and Pharmacy, Faculty of Pharmacy, Department of Organic Chemistry,
2 P-ta Eftimie Murgu, 300041, Timisoara, Romania
2 University Politehnica Timisoara ,Department of Computer Sciences, 2 P-ta Victoriei, 300006, Timisoara, Romania
3 University Politehnica Timisoara, Department of Organic Chemistry, 2 P-ta Victoriei, 300006, Timisoara, Romania
The molecular descriptors reported in this paper,
iD, i=1,2,3 were constructed on the basis of the molecular
van der Waals (vdW) space, considered homogeneous, isotropic, and compressible in some extent. They
were calculated as the ratios of the radii
1D), surfaces (
2D), and volumes (
3D) of the greatest molecular
sphere, corresponding to the vdW surface area of a molecule, and those of the smallest molecular sphere,
corresponding to the vdW volume of the same molecule. Ovality measures of the vdW molecular shape,
D,
were tested with good results (r>0.980, r2
adj>0.960, q2
LOO>0.950) on a series of 35 aliphatic alcohols exhibiting
toxicity to Tetrahymena pyriformis, measured as A=Log(1/IGC50-), where IGC50 is the concentration which
inhibits a 50% growth. The predictive ability of the QSTR models was estimated also by bootstrapping and
LHO statistical procedures. The best model was obtained for the
3D predictor variable:r>0.986, r2
adj>0.971,
q2
LOO>0.968. The ovality molecular descriptors
iD, i=1,2,3 can be easily calculated for any molecule however
complex the structure is. They are good measures of the shape feature of toxicant molecule.
Keywords : QSTR, Tetrahymena pyriformis, aliphatic alcohols, molecular ovality
Quantitative structure-toxicity relationships (QSTR)
attempt to correlate structural molecular properties
(descriptors) with toxicities for a set of similar compounds,
by means of statistical methods. As a result, a simplemathematical relationship is established [1]. The main idea
that underlies this method is that there are several
molecular features, the so-called molecular descriptors(MDs) that represent the properties of the molecule in its
interaction with other systems [2]. Ideally, MDs used in
QSTRs should be capable of mechanistic evaluation, thatis, a QSTR should be interpretable in terms of the
parameters included. Unfortunately, there are many
molecular descriptors that are not so easy to interpret.
There is an increased emphasis in predicting the toxic
effects of the chemical compounds from molecular
structure. The ability to use a QSTR analysis to estimateaccurately the relative toxicity of chemicals would be of
value to chemical and pharmaceutical industry. A variety
of toxicity data sets have been compiled for QSTR studies.Of these, the population growth inhibition of the freshwater
ciliate Tetrahymena pyriformis is among the largest. These
toxicity data have been derived for the express purposesof the QSTR development and validation [3].
Among the most widespread industrial organic
chemicals in the world are the aliphatic alcohols, asindicated by the high production volume chemical list [4].
The alcohols exhibit their toxic effect by means of narcosis,
which is a general term that describes non-covalentinteractions between xenobiotics and cellular membranes.
When accumulating, they disturb the function of cellular
membranes, and over a certain concentration they maycause the death [5].
* email.: vlaiav@yahoo. comCentral to the creation of a QSTR is the choice of
structural descriptors [6]. The purpose of a molecular
descriptor in a QSTR application is to provide a measure ofa particular feature of the structures of the compounds
being studied. The goal is simply to measure the feature in
question as accurately and unambiguously as possible. Atpresent, many structural descriptors are available, ranging
from simple whole-molecule properties to quantum
mechanical indices [7]. For example, many MDscalculated by means of DRAGON software have been
extensively used with good results in various QSAR studies
[8-10].
The ovality index, O, was introduced
[11] as a measure
of the deviation of a molecule from the spherical shape,
taking into account the fact that for a given volume, thespherical shape presents the minimum surface. It has been
calculated from the ratio between the actual molecular
surface area, S
w, and the minimum surface area, SV,
corresponding to the actual van der W aals (vdW) volume,
Vw, of that molecule [7, 12]:
(1)
In relation (1) r represents the vdW radius of the given
molecule, calculated from its actual vdW volume. The
ovality index is equal to 1 for spherical top molecules and
increases with increasing linearity of the molecule.
In fact, the reciprocal of the ovality index, Ψ=O-1, was
introduced before [13], in 1935, as sphericity index, to
measure how spherical (or round) an object is. The

REV . CHIM. (București) ♦ 60♦ Nr. 12 ♦ 2009 http://www.revistadechimie.ro 1358sphericity, Ψ, is the ratio of the surface area of a sphere
(with the same volume as the given object) to the surface
area of the object.
The aims of this investigation were to extend the ovality
vdW MDs defined by relation (1) and to analyze the
capability of these new shape MDs to relate the structureof chemical compounds to their toxicity. Taking into
account the fact that for a given volume the spherical shape
presents the minimum surface, the
iD, i=1,2,3 ovality MDs
were introduced [14] as a measure of the deviation of a
molecule from the spherical shape. It was assumed, as in
our previous paper of this series [15], that a molecule can
be characterized by two spheres corresponding,respectively, to its vdW volume (V
w) and surface (SW). The
descriptors
iD were defined on the basis of the
characteristics of the greatest sphere, corresponding to
SW, and those of the smallest one, corresponding to VW [14,
15]. The values of
iD can be easily computed, and their
physical meaning is clear:
1D,
2D, and
3D describe the
molecular shape in one-, two-, and three-dimensional
space, respectively.
The work also describes a QSTR study carried out on a
series of 35 alcohols which show toxic effects on the
Tetrahymena pyriformis . The experimental toxic activities
were taken from literature [3]. They represent the
concentration which inhibits a 50% growth, expressed in
millimoles. The calculations were carried out with theMobyDigs software [16], and the resulted statistical QSTR
models were reported on in this paper.
Material and Methods
Toxicity Data
Protozoa are real eukaryotic cells and ubiquitous in the
aquatic and terrestrial environment. Their normal
behaviour in nature may be related to the presence of
pollutants and to air, soil and water quality. This fact has
led toxicologists and ecotoxicologists to use protozoa as
test systems for studies on xenobiotics and health riskassessment. Among protozoa , Tetrahymena pyriformis is
the most commonly ciliated model used for laboratory
research and QSTR studies.
The data set for the present study has been collected
from a series of 500 aliphatic chemicals that include
different structural classes such as saturated alcohols,ketones, nitriles, esters, and sulfur-containing compounds
[3]. The data set is limited only to 35 aliphatic alcohols for
testing only the capability of the ovality descriptors aspredictive variables in QSTR studies. The toxicities of the
studied alcohols are expressed in terms of inhibitory growth
concentration, IGC
50 (measured millimolar), for T.
pyriformis and taken from ref. [3]. The T . pyriformis toxicity
data for various chemicals are also available at the Tetratox
database Web site [17].
We used as experimental biological (toxic) activity,
denoted by A, the logarithm of the inverse of concentration
that produces 50% growth inhibition to T. pyriformis ,
A=Log(1/IGC50). The values of A for the studied series of
35 alcohols used in this QSTR study are presented in table
1.
Ovality van der W aals molecular descriptors
In the hard sphere approximation a molecule, M, can be
viewed as a collection of atomic spheres centered in the
equilibrium positions of the atomic nuclei; each sphere
has a radius equal with its vdW radius, rW. An envelope, Γ,
may be defined as the outer surface of the intersected
atomic spheres of M. Γ represents the van der Waals
surface of a molecule M, which embeds an associatedmolecular body with a well defined boundary. Van der Waals
surfaces are models based on the above assumption and
they are exceptionally useful tools for the approximaterepresentations of molecules [18].
The points (x,y,z) inside the envelope Γ satisfy at least
one of the following inequalities:
(2)
where m represents the number of atoms in a given M
molecule, and Xi, Yi, Zi are the Cartesian coordinates of i
atom. Obviously, this envelope is a surface.
Therefore, the total volume embedded by this envelope
Γ is the molecular vdW volume of M, noted by Vw, and the
area of this envelope was noted by Sw. Vw and SW can be
estimated by analytical integration, but the algorithms areprohibitively complicated [19]. Therefore, we developed
some methods for calculating V
W and SW with the aid of
Monte Carlo integration methods [19-22].
Molecules are dynamic objects undergoing continuous
internal motion. Some finite range of possible deformations
with respect to the formal equilibrium shape of themolecule is an inseparable aspect of any realistic molecular
model. Consequently, it is important to use techniques for
molecular shape characterization which can account forthe deformability and the dynamic features of molecular
shapes. One must be able to distinguish the essential shape
deformations from those having little chemical significance[23a].
Therefore, we consider that a molecule, M, can be
compressed in a range comprised between its maximumand minimum surface area. Consequently, the
deformability of a molecule M may be described by two
spheres, corresponding, respectively, to the molecular vdW
volume V
W – the smallest molecular sphere, SS, and to
molecular vdW surface, SW – the greatest molecular sphere,
SG [14, 15]. The vdW radius, w
Sr, and the vdW volume,w
SV,
of the molecular SG sphere are calculated using the
following relations:

The vdW radius, rw
V, and the vdW surface area Sw
V of the
molecular SS sphere are calculated with the following
relations:
Thus, the molecular SG and SS spheres are described by
the following two triplets:

Here we present an extension of the ovality molecular
descriptor defined by relation (1) to three molecular vdW
ovality descriptors, denoted by
iD, i=1,2,3. Thus, taking
into account the characteristics of the greatest and the
smallest molecular sphere, SG (relation 7), and SS (relation
8), respectively, the ovality descriptors have been definedas follows [14]:(3)
(4)
(5)
(6)
(7)
(8)

REV . CHIM. (București) ♦ 60♦ Nr. 12 ♦ 2009 http://www.revistadechimie.ro 1359
One may observe that the relations (1) and (10) are the
same. Consequently, the two-dimensional (2D) ovality
molecular vdW descriptor,
2D , is identical with the ovality
index, O [11, 12]. The relations (9) and (11) extend the
index O so that one can also measure the deviation of a
molecule from the spherical shape on one- (1D) and on
three-dimensions (3D) of the vdW space. The values of
iD, i=1,2,3 descriptors systematized in table 1 were
computed with the aid of the IRS software package [24].
Because of the reference elements of the two sphereswith respect to units proportional to the size of a molecule
M (Å, Å
2, Å3), the shape characterization by the three ovality
descriptors (relations 9, 10, and 11) is size-invariant, thatis, a “pure” shape characterization is obtained [23b]. Infact, these descriptors are dimensionless measures of the
molecular shape.
Statistical analysis
Statistical analysis was performed by means of
MobyDigs software [16]. The goodness of fit of the linearQSTR models A vs.
iD descriptors was evaluated with the
aid of the following statistics: the correlation coefficient
(r) and the coefficient of determination (r2), adjusted for
the degree of freedom (2
adjr). The uncertainty in the model
was quantified by standard error ( s), and the reliability by
the F (Fisher) and t (Student) statistics. The t-test was
used to determine the 95% confidence limits of the QSTR
models.
In order to discriminate the statistical fit from the ability
of a model to make predictions, we used the leave-one-
out (LOO) and the leave-n-out (L-n-O) cross-validation
method to estimate the predictive ability of the obtainedQSTR model, via the cross-validation coefficient (also
called coefficient of predictions), q
2. In the LOO procedure
one compound is removed from the training set, the QSTRis reconstructed using the remaining compounds, and the
toxicological activity of the deleted compound is then
predicted with the new QSTR model. The deletedcompound is then reinstated and the procedure is repeated
until each compound in turn has been left out. A q
2 value of
Table 1
VALUES OF BIOLOGICAL (TOXIC) ACTIVITY
(A=LOG1/IGC50) AND OVALITY (
ID,i=1-3 )
MOLECULAR DESCRIPTORS FOR THE ALIPHATIC
ALCOHOLS USED IN THIS QSTR STUDY
(9)
(10)
(11)

REV . CHIM. (București) ♦ 60♦ Nr. 12 ♦ 2009 http://www.revistadechimie.ro 1360>0.5 is acceptable [25]. However, the LOO technique has
come in for criticism [26, 27]. A better procedure is to leave
an appreciable proportion (20-50%) of compounds out ofthe training set and to use them as an external test set.
This L-n-O procedure may be viewed as an external method
for validation: the chemical structures not used in thetraining set were selected for inclusion in the validation set
[28].
Finally a chance correlation can be checked by
scrambling the toxicological response values (Y-
scrambling)
[16] and trying to build a model using the
scrambled data. This procedure is then repeated severaltimes and the r
2 and q2 values are checked against that for
the real QSTR. One expect low r2
Y-s and low q2
Y-s values : if
only one of the r2 (or q2) values from the scrambled data is
as high as that from real QSTR, then there is a risk that the
real QSTR is a chance correlation [29].
Results and discussions
The ovality molecular descriptors for the 35 aliphatic
alcohols used for developing the QSTRs and their toxicityon T. pyriformis presented here are listed in table 1. The
compounds were sorted by activity, in its decreasing order.
The ovality descriptors were calculated with relations (3)-(6) and (9)-(11). The values were listed in table 1. One
may see that the domain of
3D values is greater than those
of
2D values. Consequently, one may expect that the
discrimination capability between the molecular shapes
of the congeners decreases as follows
3D>
2D >
1D. In
order to estimate the vdW volumes (wV) and surface areas
(wS) of aliphatic alcohols, the Monte Carlo technique [19-
22] was applied using our IRS computer software [24]. All
the statistical calculations were made with MobyDigscomputer program [16].
The linear QSTR models obtained by correlating toxicity
(A) versus ovality descriptors
iD, i=1,2,3, are the following:
The predictive ability of the models (12) – (14) was
estimated by means of CV leave-one-out (LOO) and
bootstrapping (BOOT) methods, using the coefficients ofprediction, q
2, the standard deviation error in calculation,
SDEC, and the standard deviation error in prediction, SDEP .
The values of these statistical indicators are systematizedin table 2.
The predictive power of these models is good, taking
into account the commonly accepted values for asatisfactory QSTR model, q
2 > 0.500. CV techniques
allowed the assessment of internal prediction, in addition
to the robustness of the linear models (12) – (14), i.e. thestability of these QSTR equations. Bootstrapping simulates
what would be happen if the population was resampled by
randomly resampling the data set from table 1. The risk ofchance correlation was verified by Y-scrambling procedure,
in which the dependent variable A (toxic activities of
alcohols on Tetrahymena pyriformis , logIGC
50-1) was
randomly shuffled and a new QSTR model was developed
using the
iD, i=1,2,3 independent variables. The process
was repeated 300 times and the resulting QSTR models
have the expected low r2
Y-s and low q2
Y-s values, which are
presented in table 2.
In addition, we applied a variant of the external
validation procedure L-n-O, where n=50%. The data set inTable 1 (sorted by toxicity values in decreasing order) was
split into test set and training set, assigning the compounds
alternately to test subset and training subset, and vice versa .
Afterwards, the QSTR model obtained for the odd ranking-
training subset was used to calculate the toxic activities of
the compounds in pair ranking-test subset, and, inversely,the QSTR model developed for the pair ranking-training
subset was used to estimate the toxic activities of the
compounds belonging to the odd ranking-test subset. Theresults of this procedure, referred to below as the Leave
odd-pair Out (Lo-pO) cross-validation technique [19, 28,
30], are as follows – see relations (15) and (16). We report
bellow only the results obtained for QSTR model (14), in
which
3D was used as predictor variable.
One may observe from the QSTR models (12) – (14)
that the shape of the aliphatic alcohol molecules affects
their toxicity. The toxicity is increasing as the values of
these
.iD molecular structural parameters are increasing.
Thus, the requirement for a low toxicity is a more spherical
shape of the molecule, which decreases the hydrophobic
interactions.
When we used the odd ranking subset as a training set
we obtained the following QSTR model:
(15)
Table 2
VALUES OF STATISTICS USED TO ASSES
PREDICTIVE POWER
OF THE QSTR MODELS A VS. OVALITY
DESCRIPTORS (
DS)#
Table 3
VALUES OF STATISTICS USED TO
ASSES PREDICTIVE POWER
OF THE QSAR MODELS (15)
AND (16)*(12)
(13)
(14)

REV . CHIM. (București) ♦ 60♦ Nr. 12 ♦ 2009 http://www.revistadechimie.roIf the pair ranking subset was used for training, the QSTR
model was:
(16)
The QSTR equations (15) and (16) were used to predict
the toxicity of the alcohols in the two test subsets – the pairranking subset, and the odd ranking subset, respectively.
Table 3 contains the values of statistical indicators used to
asses the predictive capacity of the models (15) and (16).One can see that the goodness of fit and the predictive
ability of these models are good.
Because the actual values of activities, A, are scattered
by measurement errors, the Lo-pO-CV procedure used in
this work can be considered as a pseudorandom division
of data sets. The method has the advantage that the activitydistributions of corresponding training sets and test sets
are very similar, and it should allow assessing the ability of
the model to interpolate [28].
Conclusions
Here we reported the extension of the ovality molecular
descriptor defined by relation (1) to three molecular vdW
ovality measures,
iD, i=1,2,3. The development of these
structural descriptors was made in the “hard spheretheory”, supposing that the molecular vdW space is
homogeneous, isotropic, and compressible in some extent.
Molecules are built from atoms and it is natural to relate
the formal concept of the “surface of a molecule” to the
formal atomic surfaces of the constituent atoms. Fused
sphere surfaces, such as fused sphere vdW surfaces aresimple approximations to molecular contour surfaces. By
specifying the locations of the centers (atomic nuclei) and
the radii (as vdW radii) of formal atomic spheres in amolecule, the fused sphere surface is fully defined as the
envelope surface of the fused spheres.
Molecular recognition and the interactions of reacting
molecules are determined by the three-dimensional shape
features of the molecules [31]. The interaction of a solute
molecule with the solvent has important influence on mostmolecular properties and reactions. Molecular shape is also
affected by such interactions, especially the biological
interactions.

iD are molecular shape parameters, which describe
the degree of deviation of a molecule from a spherical
(tetrahedral) shape. They well model the toxicity of a seriesof 35 aliphatic alcohols to Tetrahymena pyriformis .
The aliphatic alcohols act toward the cellular
membranes. The shape of the molecules, as measured by
iD, seems to be an important factor affecting the integrity
of these membranes. The hydrophobic interactions are
related with these molecular shape descriptors,
iD. They
influence the capacity of the alcohol molecules to
accumulate within cellular membranes and thus their
toxicity.
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