Cent. Eur. J. Chem. • 11(12) • 2013 • 2031-2039
DOI: 10.2478/s11532-013-0328-y
Central European Journal of Chemistry
Chemometric estimation of the RP TLC
retention behaviour of some estrane derivatives
by using multivariate regression methods
Research Article
Strahinja Z. Kovačević*, Lidija R. Jevrić,
Sanja O. Podunavac Kuzmanović, Eva S. Lončar
University of Novi Sad, Faculty of Technology,
Department of Applied and Engineering Chemistry,
21000 Novi Sad, Serbia
Received 7 April 2013; Accepted 17 July 2013
Abstract: Quantitative structure-retention relationship (QSRR) was developed for a series of estrane derivatives, on the basis of their retention data,
obtained in reversed-phase thin-layer chromatography (RP TLC), and in silico molecular descriptors. Physicochemical and topological
descriptors, as well as molecular bulkiness descriptors, were calculated from the optimized molecular structures. Full geometry
optimization was achieved by using Austin Model 1 (AM1) semi-empirical molecular orbital method. In the present study, QSRR analysis
was based on principal component analysis (PCA), multiple linear regression (MLR) and partial least squares (PLS) method. PCA was
applied in order to reveal similarities or dissimilarities between analytes, and MLR and PLS regression methods were carried out in
order to identify the most important in silico molecular descriptors and quantify their influence on the retention behaviour of studied
compounds. Physically meaningful and statistically significant structure-retention relationships were established.
Keywords: QSRR • Molecular descriptors • Partial least squares • Multiple linear regression • Reversed-phase thin-layer chromatography
© Versita Sp. z o.o.
1. Introduction
Estran is a steroid hydrocarbon that is the basis of
several female sex hormones, such as 17β-estradiol
and estriol. Steroid hormones have cyclopentanoperhydrophenanthrene structure that can be modified with
various substituents. Regardless of the similarities in
chemical structure and stereochemistry, every class of
steroid expresses specific physiological activity. Even
the smallest modifications in steroidal structure can
cause large changes in physicochemical properties and
physiological activity of these compounds, including their
retention behaviour.
Determination of the correlation between retention
behaviour of molecules in chromatographic systems
and molecular structure is the main task of quantitative
structure-retention relationships (QSRR) chemometric
method [1]. Cserhati and Forgacs have critically evaluated
how to calculate quantitative relationships between
retention data in thin-layer chromatography (TLC) and
molecular structure (physicochemical parameters) [2].
Although TLC is a relatively old analytical technique,
it is applied in the various QSRR studies of organic
molecules [3]. The technique of planar chromatography
provides a wide choice of adsorbents and solvents and
only requires exceedingly small amounts of analytes for
testing. In TLC, the QSRR studies are usually based on
the application of RM value defined by Bate-Smith and
Westall equation:
RM = log[(1/RF)–1]
(1)
where RF represents so-called retardation factor, defined
as the ratio of the distance traveled by the centre of
the spot to the distance simultaneously traveled by the
mobile phase. In reversed-phase (RP) TLC, RM value
* E-mail: [email protected]
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Chemometric estimation of the RP TLC retention behaviour
of some estrane derivatives by using multivariate regression methods
of the solute depends linearly on the concentration of
organic component in the mobile phase (φ), according
to the equation:
RM = RM0 + S ∙ φ
(2)
where RM0 is the intercept, that represents extrapolated
RM value to 0% v/v of organic solvent, and S is the slope.
Eqs. 1 and 2 are the basis for deriving data for the
QSRR studies. Extrapolation to pure water, based on
Soczewinski model, leads to the estimation of lipophilicity
of molecules, and that is the reason why the RM0 values
are sometimes preferably modeled and commonly used
as quantitative TLC retention descriptors instead of RM
values that are highly dependent on chromatographic
conditions [4].
In QSRR analysis, correlations between retention
data (mostly RM0 values) and various empirical, semiempirical and non-empirical structural parameters, are
usually examined by the linear modelling methods, such
as linear regression (LR), multiple linear regression
(MLR), principal component regression (PCR) and
partial least squares regression (PLS). In addition,
principal component analysis (PCA) is a very useful
tool in providing data overview. As a result of statistical
modelling, established QSRR models can be applied for
identification of the most useful structural descriptors,
prediction of the retention for new-synthesized
molecules and identification of unknown analytes [5].
QSRR can provide insight into the molecular mechanism
of separation in a selected chromatographic system
and quantitative comparison of separation properties of
individual types of chromatographic conditions [5].
Structure-retention relationships for some groups
of steroid compounds have already been presented
in several publications based on application of LR
[6,7], MLR [7-12], PLS [8,10,12-14] and ANN [12]
chemometric tools in liquid chromatography [6,8,13,14],
gas chromatography [9-12] and micellar electrokinetic
capillary chromatography [7]. However, our paper is
an extension of a previous study [15], which is based
on the simplest linear QSRR between logP values and
RM0 parameters, obtained in RP TLC with bonded C18
silica gel layer and methanol/water mobile phase, for a
series of variously substituted steroidal compounds with
estrane and secoestrane skeleton. In the present paper,
the main aim was to obtain the new QSRRs, by using
MLR and PLS chemometric methods, that can more
precisely predict retention of selected eighteen estrane
derivatives in listed chromatographic conditions on the
basis of 2D and 3D molecular descriptors, and identify
the most relevant descriptors that have the highest
influence on the RM0.
2. Experimental procedure
2.1. Studied compounds and retention data
The 2D chemical structures of estrane derivatives
investigated in this study are presented in Table 1.
Their IUPAC names are listed in Supplementary
Table 1 (Supplementary data). These compounds
contain hydroxyl, methyl, acetyl, benzyl, benzoyl and
propionyl functional groups as substituents. Complete
experimental procedure of RP TLC separation, with
bonded C18 silica gel plates and methanol/water mobile
phase, and obtained retention data (RM0) of the analyzed
compounds were reported previously [15].
2.2. Molecular geometry optimization and
molecular descriptors calculation
Obtaining the correct molecular structure is very
important for satisfactory calculation of descriptors,
so the appropriate software for molecular design is
required. In silico modelling of studied compounds was
performed by the following software: CS ChemBioDraw
Ultra 12.0 for drawing 2D molecular structures and
CS ChemBio3D Ultra 12.0 for 3D molecular modelling
running on AMD Sempron Processor 3000+ [16].
The formed 3D structures were subjected to energy
minimization using molecular mechanics force field
method (MM2). The cutoff for structure optimization was
set at a gradient of 0.1 kcal Å-1 mol-1. The Austin Model
1 (AM1) was used for full geometry optimization of all
structures until the root mean square (RMS) gradient
reached a value smaller than 0.0001 kcal Å-1 mol-1 using
Molecular Orbital Package (MOPAC) program [17].
The values of molecular descriptors for each
compound in the data set were calculated using the
software CS ChemBio3D Ultra 12.0 and MarvinSketch
5.11 [16,18]. This data is presented in Supplementary
Table 2. Determined descriptors of the examined
molecules were: (1) physicochemical descriptors
(boiling point – BP [K], melting point – MP [K], critical
pressure – CP [bar], critical temperature – CT [K], critical
volume – CV [cm3 mol-1], ideal gas thermal capacity –
IGTC [J mol-1 K-1], Gibbs free energy [kJ mol-1] – GE,
polarizability – PI, distribution coefficient – logD), (2)
molecular bulkiness descriptors (molar refractivity –
MR [cm3 mol-1], total energy – TE [kcal mol-1], van der
Waals surface area – vdWSA [Å2], molecular volume
[Å3]), and (3) topological descriptors (Wiener index – WI,
molecular topological index – MTI).
2.3. Multivariate linear modelling: PCA, MLR
and PLS approaches
To describe the relationships in a set of experimental and
calculated data, the most frequently used chemometric
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S. Z. Kovačević et al.
Table 1.
The chemical structures of the compounds studied.
Compound
No.
Chemical
structure
Compound
No.
Chemical
structure
OH
OH
10
1
O
O
HO
OH
O
O
O
O
OH
O
O
12*
3
HO
HO
O
OH
OH
4*
13
O
O
O
O
5
O
O
O
O
HO
O
O
O
O
15
6
O
O
O
HO
O
OH
7
O
14*
O
O
16
O
O
HO
O
8*
O
11
2
O
O
17*
O
O
O
O
O
9
O
18
O
HO
*External test set
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Chemometric estimation of the RP TLC retention behaviour
of some estrane derivatives by using multivariate regression methods
multivariate methods are MLR and PLS [19,20], and the
most often used explorative statistical method is PCA
[21].
The main objective of PCA is to substitute
the representation of the objects, from the initial
representation in the form of the n original intercorrelated
variables, into the new principal component coordinate
space [22]. Therefore, PCA can be defined as a
statistical technique for reducing the amount of data
when there is a correlation present. It is worth stressing
that it is not a useful technique if the variables are
uncorrelated [23]. Each PC is characterized by loadings
and scores, where scores are the new coordinates of
the projected objects and loadings reflect the direction
with respect to the original variables. The loadings plot
represents relationships between variables and can be
used to identify variables (molecular descriptors in the
present paper) that contribute to the positioning of the
objects on the scores plot. The scores plot provides a
data overview displaying patterns or groupings within
the data. Also, PCA is a very useful tool in determination
of the outliers among the analytes (data lying outside
the Hotelling T2 ellipse).
MLR is an extension of simple linear regression that
includes more than one independent or predictor variable.
General MLR model can be written in the following form:
y = a + b1 ∙ D1 + b2 ∙ D2 +…+ bn ∙ Dn
(3)
where y is the quantitative property to predict (dependent
variable), Dn an independent (descriptor) variable, a
is the intercept, and bn is the regression coefficient for
Dn. In MLR analysis it is very important to define the
optimal number of independent variables included in
the MLR model, this way the over-parametrization of
the mathematical model and the chance correlation
between the descriptors are avoided [24]. To select
descriptors for MLR, we applied multivariate variable
selection (MVS) routine. This is a heuristic algorithm
which seeks a subset that provides the maximum value
of R2.
In order to avoid multicollinearity, variance inflation
factor (VIF) is a useful diagnostic tool for checking the
impact of multicollinearity in the MLR models. VIF was
calculated for each molecular descriptor that configures
in established MLR models. The VIF factor was
calculated according to following equation:
VIFi = (1 – Ri2)-1
(4)
where Ri2 is the determination coefficient in a regression
of the Di independent variable on all other independent
variables in MLR model. The literature suggests that VIF
factor greater than 10 indicates multicollinearity in the
model [22,23].
The PLS method is established from the concept of
PCA. Just as with PCA, in PLS methodology the data
analysis is simplified by projecting the data into a low
dimensional latent variable space. PLS regression uses
linear combinations of the predictor variables rather than
the original variables. In PLS method, variables that
show a high correlation with the response variables are
given extra weight because they will be more effective
at prediction [25]. The PLS method enables analysis of
strongly collinear data, reducing the high-dimensional
data matrix to a much smaller and interpretable set of
latent variables.
The complete PCA and PLS calculation procedures
were conducted by using a demo version of PLS Toolbox
statistical package for MATLAB version 7.12.0.635
R2011a [26,27]. The MLR analysis was carried out by
using NCSS 2007 & GESS 2006 software [28].
2.4. Model validation
Validation of the developed mathematical models is an
important aspect of any QSRR study. Once a model is
obtained, it is necessary to determine its reliability and
statistical significance.
In this study, both internal and external validation
were conducted. As internal validation, in the case of
MLR a leave-one-out (LOO) cross-validation method
was applied. In PLS analysis cross-validation was
performed by splitting the entire calibration set into three
random subsets and one iteration. External validation
was carried out by using external validation set. This socalled ”test set” contains 5 randomly chosen compounds
(30% of the whole set of 18 compounds). This set was
applied after construction of MLR and PLS models in
order to compare the difference between experimental
and predicted RM0 values of the compounds contained
in it. The external test set can provide insight into the
real predicting possibility of the models. The optimal
complexity and predictivity of the MLR models are
usually determined by standard statistical measures
(correlation coefficient of calibration (Rcal), Fisher’s
value (F), standard deviation (S), coefficient of variation
(CV%)) and validation parameters (cross-validated
determination coefficient (R2cv), adjusted determination
coefficient (R2adj), correlation coefficient of prediction
(Rpred), predicted residual sum of squares (PRESS), total
sum of squares (TSS), standard deviation based on
predicted residual sum of squares (SPRESS)) [29]. In the
case of statistical validity and predictivity of PLS models,
the parameters mostly used are: cumulative sum of
squares of the Ys explained by all extracted components
(R2Ycum), root mean square error of calibration (RMSEC),
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(a)
Figure 1.
Score plot (a) and factor loadings (b) of molecular descriptors for the first two PCs.
root mean square error of prediction (RMSEP), root mean
square error of cross-validation (RMSECV), correlation
coefficient of calibration (Rcal), correlation coefficient of
prediction (Rpred) and determination coefficient of crossvalidation (R2cv) [30].
3. Results and discussion
3.1. PCA
(b)
PCA was carried out in order to determine the
presence of outliers among the analytes with 0.95
confidence level for T2 Hotelling limit for outliers, and to
overview the examined compounds for similarities and
dissimilarities. PCA resulted in a two-component model
that explains 94.49% of the data variation. The first
principal component (PC1) explains up to 80.20% of the
variability and the second accounts for up to 14.29%.
Fig. 1 shows the score plot and the mutual projections of
the loadings vectors for the first two PCs. The addition of
more PCs did not significantly change the distribution of
the molecules on the score plot. All the compounds are
lying inside the Hoteling T2 ellipse, suggesting that there
are no outliers among the analytes.
As it can be observed from the loading graph
(Fig. 1B), the majority of descriptors have a positive
influence on PC1, while only CP expresses a high
negative influence. Going along the PC2 axis, GE
descriptor has the dominant positive influence, while
TE has the highest negative influence. The loading
graph indicates the distribution of the molecules on the
score plot (Fig. 1A), which shows that PC1 separates
molecules according to their molecular volume.
Molecular volume (molecular size) was chosen as a
discriminating factor between compounds because the
majority of descriptors, that have the highest positive
and negative influence on the PC1, are very highly
correlated with molecular volume, as shown in the
Supplementary Table 3. Therefore, compound 11, as a
molecule with the largest volume, is positioned at the
positive end of the PC1 axis, and compound 16, as a
molecule with the smallest volume, is positioned at the
negative end of PC1 axis. Other compounds between
them are distributed from the negative toward positive
end of PC1 axis according to increase in molecular
volume. The order of molecules based on molecular
volume is presented in Supplementary Fig. 1. PC2 axis
distinguishes compounds 5, 8 and 15 from the others on
the basis of their TE and GE parameters.
3.2. MLR
MLR analysis was carried out to derive the best QSRR
models that can reliably predict retention constant (RM0)
in reversed-phase chromatographic system based on
selected molecular descriptors. In the present study,
according to number of compounds studied, models
that contain three independent variables were chosen.
In the next step, the low-correlated descriptors, obtained
by MVS routine which includes all possible regression
method, were selected as independent variables. All
possible regression method showed which combination
of the descriptors can be included in the MLR models
without expressed multicollinearity. As a result of MLR
analysis, two statistically significant equations, based
on calibration data set and free of multicollinearity
(VIF < 10), were obtained:
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Chemometric estimation of the RP TLC retention behaviour
of some estrane derivatives by using multivariate regression methods
Table 2.
and predictive ability, according to explanation of
the meaning of listed statistical parameters in the
subsection 2.4. However, model 2 has better statistical
parameters than model 1. The only advantage of model
1 over model 2 is better parameter of external validation
(Rpred value).
To confirm our findings, RM0 values were calculated
from the obtained MLR models and graphically compared
with experimental data (Fig. 2). Low scattering of points
around the linear relationship, significant slope (higher
than 0.95) and intercept close to zero (lower than
0.2228), indicate a very good concurrence between
experimental values of retention parameters and values
obtained by defined mathematical models.
The residuals vesus model predicted RM0 values plot
can be very informative regarding model fitting to a data
set. In the case of both MLR models, the residual values
are randomly distributed (low correlation). It implies that
the models fit the data well. In Supplementary Fig. 2
shows random pattern in distribution of the residuals.
The presented results indicate that MLR analysis
combined with a successful variable-selection procedure
enables forming of efficient QSRR models for predicting
the retention of studied estrane derivatives.
Statistical parameters of MLR models established.
Parameter
MLR model 1
MLR model 2
Rcal
0.9930
0.9956
Rpred
0.9875
0.9667
R2cv
0.9657
0.9820
R
0.9815
0.9883
S
0.2419
0.1925
F
212.68
337.69
2
adj
CV%
PRESS
4.28
3.41
1.2995
0.6811
TSS
37.87
37.87
PRESS/TSS
0.0343
0.0180
SPRESS
0.3162
0.2289
VIFGE
1.038
1.026
VIFCV
1.446
-
VIFMP
1.403
3.175
VIFMR
-
3.137
Table 3. Statistical parameters of the obtained PLS model.
Parameter
Value
R2Y(cum)
97.40%
RMSEC
0.1905
RMSECV
0.3707
RMSEP
0.2554
Rcal
0.9937
R2cv
0.9628
Rpred
0.9921
3.3. PLS
MLR model 1:
RM0 = 0.004033 ∙ GE + 0.013909 ∙
∙ CV – 0.014419 ∙ MP – 0.024739
(5)
MLR model 2:
RM0 = 0.002038∙ GE + 0.146148 ∙
∙ MR – 0.017372 ∙ MP + 1.571067
(6)
Positive values of regression coefficient indicate that
observed descriptor contributes positively to the value of
RM0, whereas negative values indicate that the greater
the value of descriptor, the lower the value of RM0. In the
model 1 the highest influence on the retention has MP,
while MR is the most important factor included in the
model 2.
The statistical characteristics of the established
models are listed in Table 2. The statistical analysis of the
models indicate their outstanding statistical performance
The PLS model calibration was carried out on the entire
calibration data set. The obtained model was evaluated
by using random subsets (three splits and one iteration)
cross-validation method. The number of the LVs was
chosen on the basis of the minimum RMSECV value,
which was obtained for three LVs model (Supplementary
Fig. 3). Three LVs captured 98.75% of the variance
in the descriptor variables space, indicating that the
information contained in the descriptors are effectively
used in the calibration model. After calibration, obtained
PLS regression model was applied on the external test
set. Statistical parameters of the obtained PLS model
are presented in Table 3.
Comparison of the experimentally obtained RM0
values and predicted RM0 values is presented in
Fig. 3. It shows low scattering of the points around
the linear relationship curve and slope close to 1.0,
indicating very good concurrence between predicted
and measured data. Residual versus predicted RM0
values plot for PLS model is presented in Supplementary
Fig. 4. As it can be seen from the Supplementary
Fig. 4, randomly distributed residual values suggest that
the PLS model fits adequately to all the data.
Depicted results indicate remarkable predictive
power of the established PLS model. Although MLR
model 2 shows the best characteristics according to
internal validation (the highest R2cv value), the external
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S. Z. Kovačević et al.
Figure 2. Graphs of experimental versus predicted RM0 values according to MLR models.
validation, which is much more reliable, confirmed that
PLS model has the best predictive ability (the highest
Rpred value). In general, PLS analysis formed highquality regression model, because this technique uses
two criteria: the direction of the highest variance in the
data set and the best correlation with the independent
variable scores in its search for the LVs in the X-variable
and Y-variable domain.
3.3.1. Contribution of the molecular descriptors to the
retention (RM0) in PLS model
Figure 3. Graph
of experimental versus predicted RM0 values
according to PLS model.
The assessment of the contribution of variables
(molecular descriptors) on RM0 in PLS model was
evaluated by using the variable importance in the
projection (VIP) value. The descriptors with a VIP score
higher than 1 were considered as the most relevant for
explaining RM0, and those with a VIP score lower than
0.5 were insignificant. The variables versus VIP scores
plot is shown in Supplementary Fig. 5. The plot of the
regression coefficients of descriptors is presented in
Fig. 4.
As it can be seen from the Supplementary Fig. 5 and
Fig. 4, the most significant descriptors influencing the
RM0 values of studied estrane derivatives are MP, CP,
CV, PI, MR, vdWSA, WI and MTI. These descriptors
have significant regression coefficients in PLS model,
as well as VIP value higher than 1. On the regression
coefficients plot the mentioned descriptors are denoted
by asterisks.
All these descriptors and retention constant depend
very strongly on molecular structure. Hence, as a result
of the conducted MLR and PLS analyses physically
meaningful and statistically significant mathematical
models were obtained.
Figure 4. Plot of the regression coefficients of molecular descriptors
in PLS model.
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Chemometric estimation of the RP TLC retention behaviour
of some estrane derivatives by using multivariate regression methods
4. Conclusions
This paper focuses on identifying the most significant
molecular descriptors that have the highest influence
on retention behavior of estrane derivatives in
reversed-phase liquid chromatography on a thin
layer of C18 bonded silica gel with methanol/water
mobile phase. Identification of the most influential
descriptors and quantification of their impact on the
retention were achieved by MLR and PLS multivariate
chemometric methods. The best relationships
between the set of calculated physicochemical,
topological and molecular bulkiness descriptors and
experimentally obtained retention parameters (RM0)
were chosen on the basis of comparison of the statistical
parameters.
The application of PCA revealed that analytes
could be classified with respect to their structural
characteristics, such as molecular volume. Regression
analysis, based on MLR and PLS approaches, produced
three mathematical models (two MLR equations and
one PLS model) that have the outstanding statistical
characteristics. External validation of models showed
that PLS model has the best predictive power. The
descriptors included in the obtained MLR and PLS
models are of a similar nature. All models confirmed
the importance of some physicochemical and molecular
bulkiness descriptors in the total retention mechanism
in the investigated chromatographic system. The PLS
model also confirmed the importance of calculated
topological descriptors and their influence on the
retention. Predictive ability of these models, based on
physically meaningful parameters, allows us to estimate
retention constants (RM0) for similar compounds and to
understand their behaviour in RP TLC system.
Acknowledgement
This paper was performed within the framework of the
research projects No.172012 and No.172014, supported
by the Ministry of Education, Science and Technological
Development of the Republic of Serbia and the project
No. 114-451-2373/2011, financially supported by the
Provincial Secretariat for Science and Technological
Development of Vojvodina.
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