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Chromatographic Retention Times of Polychlorinated Biphenyls: from Structural Information to Property Characterization

Lorentz Jäntschi
Sorana D. Bolboaca
2,* and
Mircea V. Diudea
Technical University of Cluj-Napoca, 103-105 Muncii Bvd, Cluj-Napoca, 400641 Romania
“Iuliu Hatieganu” University of Medicine and Pharmacy Cluj-Napoca, 6 Louis Pasteur, Cluj-Napoca, 400349 Romania
Babes-Bolyai University, 11 Arany Janos, Cluj-Napoca, 400028, Romania
Author to whom correspondence should be addressed.
Int. J. Mol. Sci. 2007, 8(11), 1125-1157;
Submission received: 16 August 2007 / Revised: 9 November 2007 / Accepted: 13 November 2007 / Published: 22 November 2007
(This article belongs to the Special Issue The Chemical Bond and Bonding)


The paper presents a unitary approach of the use of a Molecular Descriptors Family in structure-property/activity relationships, particularly in modelling the chromatographic retention times of polychlorinated biphenyls. Starting from molecular structure, viewed as a graph, and considering the bonds and bond types, atom types and often the 3D geometry of the molecule, a huge family of molecular descriptors called MDF was calculated. A preliminary selection of MDF members was done by simple linear regression (LR) against the measured property. The best fitted MDF subset is then submitted to multivariate linear regression (MLR) analysis in order to find the best pairs of MDF members that produce a reliable QSPR (Quantitative Structure-Property Relationship) model. The predictive capability was finally tested by randomly splitting of data into training and test sets. The best obtained models are presented and the results are discussed.

1. Introduction

Polychlorinated biphenyls (PCBs), organic compounds with 1 to 10 chlorine atoms attached to biphenyl, have the general chemical formula C12H10-xClx. First manufactured by Monsanto in 1929, the PCBs production was banned in the 1970th due to the high toxicity of most PCBs (209) and mixtures [1]. PCBs were used as insulating fluids for industrial transformers and capacitors, and are known as persistent organic pollutants. Even if the production of the PCBs was stopped, they still have an influence on the human [24] and animal [5] health due to their accumulation in the environment. Moreover, the toxicity and carcinogenicity of PCBs could be related to mechanistic studies of their truncated analogue vynil chloride [6]. Ecological and toxicological aspects of polychlorinated biphenyls (PCBs) in the environment are under investigation due to their worldwide distribution [710].
Starting with the 20th century, several mathematical approaches, that link chemical structure and property/activity in a quantitative manner, have been introduced [11]. Nowadays, quantitative structure-property/activity relationships (QSPRs/QSARs) are currently used in pharmaceutical chemistry, toxicology and other related fields [12].
A series of properties and activities of PCBs have been investigated by QSPR/QSAR modelling: aqueous solubility [13], gas/particle partitioning in the atmosphere [14], photo degradation half-life in n-hexane solution under UV irradiation [15], n-octanol/water partition coefficients [16,17], vaporization [18,19], and sublimation enthalpy [20]. The retention time of PCB congeners has also been previously investigated and reported [2125]. Some of the reported results are: • Hasan and Jurs [22] - five-variable regression equation with R2 = 0.997 and standard deviation of 0.017; • Liu et. all [24] - five-variable regression equation with the correlation coefficient of 0.9964 (R2 = 0.9928); • Ren et. all [25] - four descriptors regression model with a correlation coefficient of 0.988 (R2 = 0.9761) for the test set and an average absolute relative deviation of 3.08%.
The family of molecular descriptors MDF, designed by treating the interactions among fragments of a molecular structure with the formalism of electrostatic fields and potentials, and molecular topology as well, was developed and tested in QSPR/QSAR studies [2629].
The aim of the present study was to investigate the ability of our MDF in modelling the retention times of 209 polychlorinated biphenyls.

2. Materials and Methods

2.1 Polychlorinated Biphenyls (PCBs)

The relative response times of all PCBs obtained by using temperature-programmed, highresolution gas chromatography on a capillary column of SE-54, reported by Mullin et al. [30] served as experimental data in this study.
Molecular structure of PCBs was drawn by using HyperChem software [31] and their 3D geometry optimised at the Extended Hückel level of theory. These calculations also provided partial charges of atoms inside the molecules. The output files *.hin files, which store the information about topology, geometry and charge distribution of the PCBs, represented the primary data for the generation of the molecular descriptors family.

2.2 Methodology of using Molecular Descriptors Family in QSPR/QSAR

Our MDF implements three criteria of fragmentation, related to pairs of atoms, in order to generate molecular fragments. Let i and j be the atoms forming a pair. The criteria are as follows:
A minimal fragment is that one containing only the atom i, while a maximal fragment will contain all the atoms connected to i, excluding the atom j.
A Szeged fragment is the set of vertices located closer to i than j (a distance-based criterion), the distance d(i, k) being lesser than d(k, j), and
A Cluj fragment is generated by excluding the path from i to j (except its terminal points) and then applying the above Szeged criterion.
Every MDF member is named with seven ordered case sensitive letters: lMfOIpd, every letter encoding an operator, as follows.
The 7th letter (d) encodes the distance metric and is either ‘g’ (geometric) or ‘t’ (topological). The 6th letter (p) encodes the atomic property and can be ‘M’ (mass), ‘Q’ (charge), ‘C’ (cardinality), ‘E’ (electronegativity), ‘G’ (group electronegativity), or ‘H’ (number of attached hydrogens). The 5th letter (I) encodes the interaction descriptor (involving two participants): ‘D(d)’, ‘d(1/d)’, ‘O(p1)’, ‘o(1/p1)’, ‘P(p1p2)’, ‘p(1/p1p2)’, ‘Q(√p1p2)’, ‘q(1/√p1p2)’, ‘J(p1d)’, ‘j(1/p1d)’, ‘K(p1p2d)’, ‘k(1/p1p2d)’, ‘L(d√p1p2)’, ‘l(1/d√p1p2)’, ‘V(p1/d)’, ‘E(p1/d2)’, ‘W(p12/d)’, ‘w(p1p2/d)’, ‘F(p12/d2)’, ‘f(p1p2/d2)’, ‘S(p12/d3), ‘s(p1p2/d3)’, ‘T(p12/d4)’, ‘t(p1p2/d4)’. The 4th letter (O) encodes the type of overlapping interactions, which are either scalar (‘R’, ‘r’, ‘M’, ‘m’) or vectorial (‘D’, ‘d’). The 3rd letter (f) encodes the fragmentation algorithm and can be: ‘m’ (minimal), ‘M’ (maximal), ‘D’ (Szeged, distance based), and ‘P’ (Cluj, shortest paths based). The 2nd letter (M) encodes overlapping fragmental descriptors, which are of the type: sized group ( ‘m’, smallest; ‘M’, largest; ‘n’, smallest absolute; ‘N’, largest absolute); averaged group ( ‘S’, sum; ‘A’, average over all values; ‘a’, S divided by the number of all fragments; ‘B’, average first by atom group and then by the whole molecule; ‘b’, by bond); geometric group (‘P’, multiplication; ‘G’, geometric mean, by fragments; ‘g’, adjusted G; ‘F’, geometric mean by atom group and then by the whole molecule; ‘f’, by bond); harmonic group (‘s’, harmonic mean, ‘H’ harmonic mean, by fragments, and similarly to above ‘h’, ‘I’, and ‘i’).
MDF values enter in QSPR/QSAR modelling after a transformation (linearization procedure), one of: ‘I’ (identity), ‘i’ (inverse), ‘A’ (absolute), ‘a’ (inverse of absolute), ‘L’ (logarithm of absolute), ‘l’ (logarithm), which are encoded by the 1st letter.
MDF use a genetic algorithm for QSPR/QSAR modelling (genetic algorithms are a particular class of evolutionary algorithms, being categorized as global search heuristics [32]). The peculiarities of the genetic algorithm used are:
  • – Step 1 (implies inheritance and mutation). To the solution domain (2×6×24×6×4×19 MDF members) having the genetic representation with six letters words) are applied the linearization procedure from above, when every descendent is obtained from a parent (inheritance) through a transformation (mutation). Six times more (than parents) descendants are obtained. In this step, the fitness function is defined as “have real and distinct values”. A number of 490030 descendants dye due to mutation on PCB data set (remaining 297938 descendants, having genetic representation with seven letters words now).
  • – Step 2 (implies selection). To the solution domain (MDF descendants from Step 1) a bias procedure (selection) is applied. In this step, the fitness function is defined as “have distinct first nine digits of determination coefficient with measured property”. For PCBs data set, only 99806 members pass selection. From this solution domain another selection is made: best descriptor (which correlates the best with measured property (for PCBs result being presented in Eq(1)).
  • – Step 3 (implies crossover). Pairs of MDF members are crossover in order to obtain models with two descriptors. Two fitness functions are used here: “have better determination coefficient” and “have better cross-validation leave-one-out score”. The result for PCBs data set is given in Eq(2).

2.3 Computational Details

The MDF is calculated by a set of original programs written in PHP (Pre Hypertext Processor, [33]) and stored into a MySQL database [34] under a FreeBSD server [35]. This set of programs completes the MDF generation task. The programs create tables, insert, drop, delete, and select grants on ‘MDF’ database (Figure 1). All programs run in a directory with the name of the set of selected compounds (actually, PCB).
The first program, a_mdf_prepare.php, orders the molecules, contained as *.hin files in a ‘data’ subdirectory, in the same ordering as the measured property, contained in a ‘property.txt’ file. The names of *.hin files and corresponding property are used to create a temporary ‘PCB_tmpx’ table and finally the ‘PCB_data’ table. The second program, b_mdf_generate.php (the most time consuming procedure) it stores thousands records into the ‘PCB_tmpx’ table.
The third program, c_mdf_linearize.php, completes the ‘PCB_data’, ‘PCB_xval’, and ‘PCB_yval’ tables with linearized MDF members and statistical parameters. Note that, only real and distinct values are stored into the database. The fourth program, d_mdf_bias.php applied a bias procedure for data reduction. Finally, the fifth program, e_mdf_order.php, re-arrange the data from the ‘PCB_xval’, and ‘PCB_yval’ tables in descending order of the squared correlation coefficient. When the task is complete, the fifth program writes in the ‘ready’ table a record with the set name (Figure 2).
The QSPR/QSAR finding procedure is made by a client programs built in Delphi programming language [36]. Bivariate correlations are performed, one with any other MDF members.
A client program (Figure 3) connects the ‘MDF’ database, query the ready tables all together, for the ready set (now PCB set is ready), and runs for finding the best QSAR/QSPR model. Every new better QSPR/QSAR is stored into a table called ‘qspr_qsar’, within the same ‘MDF’ database.
This program, called i_mdf_query.php, provides complete statistical analysis of models. The user of MDF can modify, by means of this i_mdf_query.php program, the criteria for the best QSPR/QSAR models.

3. Results and Discussion

The above described procedure was used for finding the best QSPR model of the PCBs relative chromatographic retention times.
In monovariate correlation, the best MDF QSPR model was provided by the iIDRwHg MDF member, Eq(1):
Y ^ 1 d = - 0.16 + 0.09 · iIDRwHg R 2 = 0.9840 ; 95 % CI R [ 0.9894 - 0.9939 ] ; StErr = 0.02 ; F = 12806 ; p < 0.0001 Q 2 cv - loo = 0.9838
where Ŷ1d = estimated retention time by MDF-SAR equation with one descriptor; iIDRwHg = molecular descriptor; R2 = square correlation coefficient; 95%CIR = 95% confidence interval for correlation coefficient; Q2cv-loo= cross-validation leave-one-out score.
The quality of statistics is given by R2 (the square correlation coefficient), StErr (standard error of estimate), F (Fisher parameter) and p (type I error, or α error). The cross-validation leave-one-out score is given as Q2. Clearly, the model shows a good predictability. The type I error of the model from Eq(1) is very small, showing a very small error of rejecting the null hypothesis when it is actually true.
About ninety-eight percents of variation in PCBs chromatographic retention time can be explained by its linear relation with a single MDF member, iIDRwHg, which accounts for the actual geometry (by the geometric distance operator (‘g’)) and the number of directly bonded hydrogen atoms (‘H’).
The best model with two descriptors was:
Y ^ 2 d = - 5.96 + 0.024 · ISDmsHt - 1.02 · lADrtHg R 2 = 0.9967 ; 95 % CI [ 0.9977 - 0.9987 ] ; StdErr = 0.01 ; F = 30752 ; p < 0.0001 Q 2 cv - loo = 0.9962
where Ŷ2d = estimated retention time by MDF-SAR equation with two descriptors.
The multi-colinearity analysis shown that the two descriptors used by Eq(2) rather inter-related (R2(ISDmsHt, lADrtHg) = 0.944) and each of them (R2(Y, ISDmsHt) = 0.907; rank = 12614; R2(Y, lADrtHg) = 0.973; rank = 277) are not the best descriptor in monovariate regression model (see Eq(1)). The ISDmsHt descriptor is built by a topological distance operator (‘t’) while lADrtHg takes into account the genuine distance (‘g’). Both of them consider the directly bonded hydrogen atom (‘H’). The topological description explains more than 90% of the variance, the remaining 9.7% being completed by the information on molecular geometry.
The plot corresponding to Eq(2) is illustrated in Figure 4.
The values of the best descriptors in uni and bivariate regressions (Eq(1)&(2)), the experimental and estimated chromatographic retention time, and residuals for the PCBs set are listed in Table 1.
The accuracy of description is extremely high, even as the set of molecules is quite large. The excellent model (Eq(2)), derived for such a large set, is by itself a test of predictive ability. Indeed, if various ratios training/testing selections were considered, the quality of statistics remained very high (Table 2).
As it can be observed from Table 2, the lowest R2 is about 0.996 in both training and test sets, which demonstrates the ability of (ISDmsHt, lADrtHg) MDF pair to described the PCBs relative retention time (Eq(2)). Note that, R2 exceeds the upper bond of the confidence interval of Eq(2) in almost 20% of cases and is less then the lower bond in other 20% of cases. In the test set, in four cases the values of Q2 were greater than the upper confidence boundary.
By analysing of the obtained models (Eq(1) and Eq(2)) in the light of the previously reported models, it can be observed that with a single exception ([25], p = 0.3528) out of three the model with one descriptor - Eq(1) - did not obtains a greater squared correlation coefficient compared with models reported in the references [22] and [24] (the differences are of −0.0064 [22], and of −0.0043 [24] respectively).
Analyzing the model with two molecular descriptors it was identified a statistical significant differences between correlation coefficient of this model and of the model reported by [24] (p < 0.0001) or by [25] (p < 0.0001). There was not identified a statistical difference between the Eq(2) and the model reported by [22] (p = 0.7263). The following remarks can be revealed by summarizing the above results:
  • ○ The MDF model obtained by Eq(1) is a better model comparing with previously reported ones [22, 24,25] in terms of number of variables used (one descriptor for the model from Eq(1), five descriptors for the model reported in [22] and [24], four descriptors for the model reported in [25]).
  • ○ The MDF model obtained by Eq(2) is significantly better models comparing with models reported in [24] and [25] in terms of correlation coefficients. Moreover, it is a better model comparing with model reported in [22] in terms of number of variables used (two descriptors used by the Eq(2), and five descriptors used by the model reported in [22]).

4. Conclusions

The MDF methodology provides excellent QSPR models, with good stability and predictive ability. It has the disadvantage to be time consuming (it calculates a huge pool of molecular descriptors and provides exhaustive mono- and bivariate regressions) but this is compensated by the high quality of the QSPR models.
Thus, the variance of chromatographic retention time of PCBs is 99.7% explained by two molecular descriptors, showing us that the property is related with geometry and topology, as well as with directly bounded hydrogen’s of PCBs.
The selection of the MDF members from a huge family offers not only a QSPR model, but also a strong instrument to investigate the structural causality of a measured property. Thus, the chromatographic property of PCBs is determined by the molecular topology, geometry and the nonchlorinated (i.e., the remained hydrogenated) positions on the PCB structure.
Virtual library of QSPR/QSAR models:
Figure 1. ‘MDF’ database for PCBs.
Figure 1. ‘MDF’ database for PCBs.
Ijms 08 01125f1
Figure 2. Preparing data for Multiple Linear Regression analysis.
Figure 2. Preparing data for Multiple Linear Regression analysis.
Ijms 08 01125f2
Figure 3. MLR MDF QSPR client-server.
Figure 3. MLR MDF QSPR client-server.
Ijms 08 01125f3
Figure 4. The plot of experimental vs chromatographic retention time (CRT) by Eq(2).
Figure 4. The plot of experimental vs chromatographic retention time (CRT) by Eq(2).
Ijms 08 01125f4
Table 1. PCBs MDF descriptors, estimated and residuals obtained by Eq(1)&Eq(2).
Table 1. PCBs MDF descriptors, estimated and residuals obtained by Eq(1)&Eq(2).
MolPCB structureYiIDRwHgŶ1dY-Ŷ1dISDmsHtlADrtHgŶ2dY-Ŷ2d
PCB001Ijms 08 01125f50.099710.02−0.0122−0.5363133.20−3.420.1119−0.0122
PCB002Ijms 08 01125f60.154410.600.00410.1800134.27−3.470.15030.0041
PCB003Ijms 08 01125f70.19379.960.03761.6541135.23−3.400.15610.0376
PCB004Ijms 08 01125f80.224510.140.00540.2377134.89−3.420.21910.0054
PCB005Ijms 08 01125f90.27859.750.02511.1035133.36−3.410.25340.0251
PCB006Ijms 08 01125f100.270910.15−0.0193−0.8496136.72−3.380.2902−0.0193
PCB007Ijms 08 01125f110.256610.720.00280.1234134.60−3.480.25380.0028
PCB008Ijms 08 01125f120.278310.27−0.0048−0.2094133.35−3.430.2831−0.0048
PCB009Ijms 08 01125f130.257011.120.03481.5315134.95−3.550.22220.0348
PCB010Ijms 08 01125f140.224311.750.03331.4623133.57−3.570.19100.0333
PCB011Ijms 08 01125f150.323811.260.01680.7378133.12−3.520.30700.0168
PCB012Ijms 08 01125f160.329811.520.04421.9425132.24−3.570.28560.0442
PCB013Ijms 08 01125f170.331511.090.00650.2857134.24−3.490.32500.0065
PCB014Ijms 08 01125f180.237310.98−0.0393−1.7268133.10−3.500.2766−0.0393
PCB015Ijms 08 01125f190.338710.980.00360.1567131.58−3.510.33510.0036
PCB016Ijms 08 01125f200.362510.450.01930.8481132.74−3.450.34320.0193
PCB017Ijms 08 01125f210.339810.97−0.0184−0.8086133.06−3.510.3582−0.0184
PCB018Ijms 08 01125f220.337810.72−0.0125−0.5510131.64−3.500.3503−0.0125
PCB019Ijms 08 01125f230.304510.160.00420.1849132.62−3.440.30030.0042
PCB020Ijms 08 01125f240.417011.560.00150.0644132.66−3.570.41550.0015
PCB021Ijms 08 01125f250.413511.09−0.0179−0.7855133.32−3.500.4314−0.0179
PCB022Ijms 08 01125f260.426711.050.00050.0212131.66−3.520.42620.0005
PCB023Ijms 08 01125f270.377011.05−0.0239−1.0517132.19−3.510.4009−0.0239
PCB024Ijms 08 01125f280.350810.520.00420.1838131.49−3.460.34660.0042
PCB025Ijms 08 01125f290.393710.80−0.0283−1.2445133.28−3.480.4220−0.0283
PCB026Ijms 08 01125f300.391110.24−0.0015−0.0653133.94−3.420.3926−0.0015
PCB027Ijms 08 01125f310.352110.750.00560.2482132.13−3.500.34650.0056
PCB028Ijms 08 01125f320.403110.23−0.0294−1.2916131.25−3.450.4325−0.0294
PCB029Ijms 08 01125f330.382012.03−0.0161−0.7060132.78−3.650.3981−0.0161
PCB030Ijms 08 01125f330.316511.48−0.0323−1.4195133.66−3.570.3488−0.0323
PCB031Ijms 08 01125f340.409411.550.00860.3793132.00−3.600.40080.0086
PCB032Ijms 08 01125f350.363611.220.00890.3932131.75−3.570.35470.0089
PCB033Ijms 08 01125f360.416311.250.00570.2490132.12−3.580.41060.0057
PCB034Ijms 08 01125f370.378212.89−0.0103−0.4521130.80−3.730.3885−0.0103
PCB035Ijms 08 01125f380.473812.320.01380.6063131.52−3.670.46000.0138
PCB036Ijms 08 01125f390.437512.420.00270.1167130.24−3.680.43480.0027
PCB037Ijms 08 01125f400.485811.870.01840.8096129.97−3.610.46740.0184
PCB038Ijms 08 01125f410.510212.090.06352.7897130.07−3.660.44670.0635
PCB039Ijms 08 01125f420.448811.530.00410.1782131.14−3.590.44470.0041
PCB040Ijms 08 01125f430.510211.580.00120.0545129.81−3.600.50900.0012
PCB041Ijms 08 01125f440.499012.15−0.0127−0.5568130.26−3.670.5117−0.0127
PCB042Ijms 08 01125f450.487011.30−0.0324−1.4222129.77−3.590.5194−0.0324
PCB043Ijms 08 01125f460.458712.11−0.0267−1.1744130.59−3.660.4854−0.0267
PCB044Ijms 08 01125f470.483211.60−0.0088−0.3869129.80−3.610.4920−0.0088
PCB045Ijms 08 01125f480.433412.570.00040.0168130.50−3.740.43300.0004
PCB046Ijms 08 01125f490.445013.430.00880.3881128.67−3.820.43620.0088
PCB047Ijms 08 01125f500.463912.87−0.0562−2.4723128.32−3.760.5201−0.0562
PCB048Ijms 08 01125f510.465112.62−0.0098−0.4320128.24−3.750.4749−0.0098
PCB049Ijms 08 01125f520.461014.04−0.0314−1.3821126.70−3.900.4924−0.0314
PCB050Ijms 08 01125f530.400710.02−0.0122−0.5363133.20−3.420.1119−0.0122
PCB051Ijms 08 01125f540.424210.600.00410.1800134.27−3.470.15030.0041
PCB052Ijms 08 01125f550.45579.960.03761.6541135.23−3.400.15610.0376
PCB053Ijms 08 01125f560.418710.140.00540.2377134.89−3.420.21910.0054
PCB054Ijms 08 01125f570.38009.750.02511.1035133.36−3.410.25340.0251
PCB055Ijms 08 01125f580.556210.15−0.0193−0.8496136.72−3.380.2902−0.0193
PCB056Ijms 08 01125f590.567610.720.00280.1234134.60−3.480.25380.0028
PCB057Ijms 08 01125f600.551510.27−0.0048−0.2094133.35−3.430.2831−0.0048
PCB058Ijms 08 01125f610.526711.120.03481.5315134.95−3.550.22220.0348
PCB059Ijms 08 01125f620.486011.750.03331.4623133.57−3.570.19100.0333
PCB060Ijms 08 01125f630.567611.260.01680.7378133.12−3.520.30700.0168
PCB061Ijms 08 01125f640.533111.520.04421.9425132.24−3.570.28560.0442
PCB062Ijms 08 01125f650.468511.090.00650.2857134.24−3.490.32500.0065
PCB063Ijms 08 01125f660.529010.98−0.0393−1.7268133.10−3.500.2766−0.0393
PCB064Ijms 08 01125f670.499910.980.00360.1567131.58−3.510.33510.0036
PCB065Ijms 08 01125f680.467110.450.01930.8481132.74−3.450.34320.0193
PCB066Ijms 08 01125f690.544710.97−0.0184−0.8086133.06−3.510.3582−0.0184
PCB067Ijms 08 01125f700.521410.72−0.0125−0.5510131.64−3.500.3503−0.0125
PCB068Ijms 08 01125f710.504010.160.00420.1849132.62−3.440.30030.0042
PCB069Ijms 08 01125f720.451011.560.00150.0644132.66−3.570.41550.0015
PCB070Ijms 08 01125f730.540711.09−0.0179−0.7855133.32−3.500.4314−0.0179
PCB071Ijms 08 01125f740.498911.050.00050.0212131.66−3.520.42620.0005
PCB072Ijms 08 01125f750.498411.05−0.0239−1.0517132.19−3.510.4009−0.0239
PCB073Ijms 08 01125f760.455410.520.00420.1838131.49−3.460.34660.0042
PCB074Ijms 08 01125f770.534110.80−0.0283−1.2445133.28−3.480.4220−0.0283
PCB075Ijms 08 01125f780.464310.24−0.0015−0.0653133.94−3.420.3926−0.0015
PCB076Ijms 08 01125f790.540810.750.00560.2482132.13−3.500.34650.0056
PCB077Ijms 08 01125f800.629510.23−0.0294−1.2916131.25−3.450.4325−0.0294
PCB078Ijms 08 01125f810.602412.03−0.0161−0.7060132.78−3.650.3981−0.0161
PCB079Ijms 08 01125f820.589411.48−0.0323−1.4195133.66−3.570.3488−0.0323
PCB080Ijms 08 01125f830.546411.550.00860.3793132.00−3.600.40080.0086
PCB081Ijms 08 01125f840.614911.220.00890.3932131.75−3.570.35470.0089
PCB082Ijms 08 01125f850.645311.250.00570.2490132.12−3.580.41060.0057
PCB083Ijms 08 01125f860.602912.89−0.0103−0.4521130.80−3.730.3885−0.0103
PCB084Ijms 08 01125f870.574412.320.01380.6063131.52−3.670.46000.0138
PCB085Ijms 08 01125f880.622412.420.00270.1167130.24−3.680.43480.0027
PCB086Ijms 08 01125f890.610511.870.01840.8096129.97−3.610.46740.0184
PCB087Ijms 08 01125f900.617512.090.06352.7897130.07−3.660.44670.0635
PCB088Ijms 08 01125f910.548611.530.00410.1782131.14−3.590.44470.0041
PCB089Ijms 08 01125f920.577911.580.00120.0545129.81−3.600.50900.0012
PCB090Ijms 08 01125f930.581412.15−0.0127−0.5568130.26−3.670.5117−0.0127
PCB091Ijms 08 01125f940.554911.30−0.0324−1.4222129.77−3.590.5194−0.0324
PCB092Ijms 08 01125f950.574212.11−0.0267−1.1744130.59−3.660.4854−0.0267
PCB093Ijms 08 01125f960.543711.60−0.0088−0.3869129.80−3.610.4920−0.0088
PCB094Ijms 08 01125f970.533112.570.00040.0168130.50−3.740.43300.0004
PCB095Ijms 08 01125f980.546413.430.00880.3881128.67−3.820.43620.0088
PCB096Ijms 08 01125f990.505712.87−0.0562−2.4723128.32−3.760.5201−0.0562
PCB097Ijms 08 01125f1000.610012.62−0.0098−0.4320128.24−3.750.4749−0.0098
PCB098Ijms 08 01125f1010.541514.04−0.0314−1.3821126.70−3.900.4924−0.0314
PCB099Ijms 08 01125f1020.588010.02−0.0122−0.5363133.20−3.420.1119−0.0122
PCB100Ijms 08 01125f1030.521210.600.00410.1800134.27−3.470.15030.0041
PCB101Ijms 08 01125f1040.58169.960.03761.6541135.23−3.400.15610.0376
PCB102Ijms 08 01125f1050.543110.140.00540.2377134.89−3.420.21910.0054
PCB103Ijms 08 01125f1060.51429.750.02511.1035133.36−3.410.25340.0251
PCB104Ijms 08 01125f1070.475710.15−0.0193−0.8496136.72−3.380.2902−0.0193
PCB105Ijms 08 01125f1080.704910.720.00280.1234134.60−3.480.25380.0028
PCB106Ijms 08 01125f1090.668010.27−0.0048−0.2094133.35−3.430.2831−0.0048
PCB107Ijms 08 01125f1100.662811.120.03481.5315134.95−3.550.22220.0348
PCB108Ijms 08 01125f1110.662611.750.03331.4623133.57−3.570.19100.0333
PCB109Ijms 08 01125f1120.601611.260.01680.7378133.12−3.520.30700.0168
PCB110Ijms 08 01125f1130.631411.520.04421.9425132.24−3.570.28560.0442
PCB111Ijms 08 01125f1140.618311.090.00650.2857134.24−3.490.32500.0065
PCB112Ijms 08 01125f1150.598610.98−0.0393−1.7268133.10−3.500.2766−0.0393
PCB113Ijms 08 01125f1160.586210.980.00360.1567131.58−3.510.33510.0036
PCB114Ijms 08 01125f1170.682810.450.01930.8481132.74−3.450.34320.0193
PCB115Ijms 08 01125f1180.617110.97−0.0184−0.8086133.06−3.510.3582−0.0184
PCB116Ijms 08 01125f1190.613210.72−0.0125−0.5510131.64−3.500.3503−0.0125
PCB117Ijms 08 01125f1200.615010.160.00420.1849132.62−3.440.30030.0042
PCB118Ijms 08 01125f1210.669311.560.00150.0644132.66−3.570.41550.0015
PCB119Ijms 08 01125f1220.596811.09−0.0179−0.7855133.32−3.500.4314−0.0179
PCB120Ijms 08 01125f1230.625611.050.00050.0212131.66−3.520.42620.0005
PCB121Ijms 08 01125f1240.551811.05−0.0239−1.0517132.19−3.510.4009−0.0239
PCB122Ijms 08 01125f1250.687110.520.00420.1838131.49−3.460.34660.0042
PCB123Ijms 08 01125f1260.665810.80−0.0283−1.2445133.28−3.480.4220−0.0283
PCB124Ijms 08 01125f1270.658410.24−0.0015−0.0653133.94−3.420.3926−0.0015
PCB125Ijms 08 01125f1280.614210.750.00560.2482132.13−3.500.34650.0056
PCB126Ijms 08 01125f1290.751210.23−0.0294−1.2916131.25−3.450.4325−0.0294
PCB127Ijms 08 01125f1300.707812.03−0.0161−0.7060132.78−3.650.3981−0.0161
PCB128Ijms 08 01125f1310.776111.48−0.0323−1.4195133.66−3.570.3488−0.0323
PCB129Ijms 08 01125f1320.750111.550.00860.3793132.00−3.600.40080.0086
PCB130Ijms 08 01125f1330.718411.220.00890.3932131.75−3.570.35470.0089
PCB131Ijms 08 01125f1340.685311.250.00570.2490132.12−3.580.41060.0057
PCB132Ijms 08 01125f1350.703512.89−0.0103−0.4521130.80−3.730.3885−0.0103
PCB133Ijms 08 01125f1360.687112.320.01380.6063131.52−3.670.46000.0138
PCB134Ijms 08 01125f1370.679612.420.00270.1167130.24−3.680.43480.0027
PCB135Ijms 08 01125f1380.656311.870.01840.8096129.97−3.610.46740.0184
PCB136Ijms 08 01125f1390.625712.090.06352.7897130.07−3.660.44670.0635
PCB137Ijms 08 01125f1400.732911.530.00410.1782131.14−3.590.44470.0041
PCB138Ijms 08 01125f1410.740311.580.00120.0545129.81−3.600.50900.0012
PCB139Ijms 08 01125f1420.670712.15−0.0127−0.5568130.26−3.670.5117−0.0127
PCB140Ijms 08 01125f1430.670711.30−0.0324−1.4222129.77−3.590.5194−0.0324
PCB141Ijms 08 01125f1440.720012.11−0.0267−1.1744130.59−3.660.4854−0.0267
PCB142Ijms 08 01125f1450.684811.60−0.0088−0.3869129.80−3.610.4920−0.0088
PCB143Ijms 08 01125f1460.678912.570.00040.0168130.50−3.740.43300.0004
PCB144Ijms 08 01125f1470.656313.430.00880.3881128.67−3.820.43620.0088
PCB145Ijms 08 01125f1480.614912.87−0.0562−2.4723128.32−3.760.5201−0.0562
PCB146Ijms 08 01125f1490.695512.62−0.0098−0.4320128.24−3.750.4749−0.0098
PCB147Ijms 08 01125f1500.660814.04−0.0314−1.3821126.70−3.900.4924−0.0314
PCB148Ijms 08 01125f1510.624310.02−0.0122−0.5363133.20−3.420.1119−0.0122
PCB149Ijms 08 01125f1520.667210.600.00410.1800134.27−3.470.15030.0041
PCB150Ijms 08 01125f1530.59699.960.03761.6541135.23−3.400.15610.0376
PCB151Ijms 08 01125f1540.649910.140.00540.2377134.89−3.420.21910.0054
PCB152Ijms 08 01125f1550.60629.750.02511.1035133.36−3.410.25340.0251
PCB153Ijms 08 01125f1560.703610.15−0.0193−0.8496136.72−3.380.2902−0.0193
PCB154Ijms 08 01125f1570.634910.720.00280.1234134.60−3.480.25380.0028
PCB155Ijms 08 01125f1580.566610.27−0.0048−0.2094133.35−3.430.2831−0.0048
PCB156Ijms 08 01125f1590.810511.120.03481.5315134.95−3.550.22220.0348
PCB157Ijms 08 01125f1600.818411.750.03331.4623133.57−3.570.19100.0333
PCB158Ijms 08 01125f1610.742911.260.01680.7378133.12−3.520.30700.0168
PCB159Ijms 08 01125f1620.765511.520.04421.9425132.24−3.570.28560.0442
PCB160Ijms 08 01125f1630.739611.090.00650.2857134.24−3.490.32500.0065
PCB161Ijms 08 01125f1640.696810.98−0.0393−1.7268133.10−3.500.2766−0.0393
PCB162Ijms 08 01125f1650.773710.980.00360.1567131.58−3.510.33510.0036
PCB163Ijms 08 01125f1660.739610.450.01930.8481132.74−3.450.34320.0193
PCB164Ijms 08 01125f1670.739910.97−0.0184−0.8086133.06−3.510.3582−0.0184
PCB165Ijms 08 01125f1680.692010.72−0.0125−0.5510131.64−3.500.3503−0.0125
PCB166Ijms 08 01125f1690.757210.160.00420.1849132.62−3.440.30030.0042
PCB167Ijms 08 01125f1700.781411.560.00150.0644132.66−3.570.41550.0015
PCB168Ijms 08 01125f1710.706811.09−0.0179−0.7855133.32−3.500.4314−0.0179
PCB169Ijms 08 01125f1720.862511.050.00050.0212131.66−3.520.42620.0005
PCB170Ijms 08 01125f1730.874011.05−0.0239−1.0517132.19−3.510.4009−0.0239
PCB171Ijms 08 01125f1740.808910.520.00420.1838131.49−3.460.34660.0042
PCB172Ijms 08 01125f1750.827810.80−0.0283−1.2445133.28−3.480.4220−0.0283
PCB173Ijms 08 01125f1760.815210.24−0.0015−0.0653133.94−3.420.3926−0.0015
PCB174Ijms 08 01125f1770.796510.750.00560.2482132.13−3.500.34650.0056
PCB175Ijms 08 01125f1780.761110.23−0.0294−1.2916131.25−3.450.4325−0.0294
PCB176Ijms 08 01125f1790.730512.03−0.0161−0.7060132.78−3.650.3981−0.0161
PCB177Ijms 08 01125f1800.803111.48−0.0323−1.4195133.66−3.570.3488−0.0323
PCB178Ijms 08 01125f1810.753711.550.00860.3793132.00−3.600.40080.0086
PCB179Ijms 08 01125f1820.720511.220.00890.3932131.75−3.570.35470.0089
PCB180Ijms 08 01125f1830.836211.250.00570.2490132.12−3.580.41060.0057
PCB181Ijms 08 01125f1840.796812.89−0.0103−0.4521130.80−3.730.3885−0.0103
PCB182Ijms 08 01125f1850.765312.320.01380.6063131.52−3.670.46000.0138
PCB183Ijms 08 01125f1860.772012.420.00270.1167130.24−3.680.43480.0027
PCB184Ijms 08 01125f1870.701611.870.01840.8096129.97−3.610.46740.0184
PCB185Ijms 08 01125f1880.784812.090.06352.7897130.07−3.660.44670.0635
PCB186Ijms 08 01125f1890.741611.530.00410.1782131.14−3.590.44470.0041
PCB187Ijms 08 01125f1900.765411.580.00120.0545129.81−3.600.50900.0012
PCB188Ijms 08 01125f1910.692012.15−0.0127−0.5568130.26−3.670.5117−0.0127
PCB189Ijms 08 01125f1920.914211.30−0.0324−1.4222129.77−3.590.5194−0.0324
PCB190Ijms 08 01125f1930.874012.11−0.0267−1.1744130.59−3.660.4854−0.0267
PCB191Ijms 08 01125f1940.844711.60−0.0088−0.3869129.80−3.610.4920−0.0088
PCB192Ijms 08 01125f1950.826912.570.00040.0168130.50−3.740.43300.0004
PCB193Ijms 08 01125f1960.839713.430.00880.3881128.67−3.820.43620.0088
PCB194Ijms 08 01125f1970.962012.87−0.0562−2.4723128.32−3.760.5201−0.0562
PCB195Ijms 08 01125f1980.932112.62−0.0098−0.4320128.24−3.750.4749−0.0098
PCB196Ijms 08 01125f1990.893814.04−0.0314−1.3821126.70−3.900.4924−0.0314
PCB197Ijms 08 01125f2000.829310.02−0.0122−0.5363133.20−3.420.1119−0.0122
PCB198Ijms 08 01125f2010.884510.600.00410.1800134.27−3.470.15030.0041
PCB199Ijms 08 01125f2020.84949.960.03761.6541135.23−3.400.15610.0376
PCB200Ijms 08 01125f2030.819710.140.00540.2377134.89−3.420.21910.0054
PCB201Ijms 08 01125f2040.88759.750.02511.1035133.36−3.410.25340.0251
PCB202Ijms 08 01125f2050.808910.15−0.0193−0.8496136.72−3.380.2902−0.0193
PCB203Ijms 08 01125f2060.893810.720.00280.1234134.60−3.480.25380.0028
PCB204Ijms 08 01125f2070.821710.27−0.0048−0.2094133.35−3.430.2831−0.0048
PCB205Ijms 08 01125f2080.967811.120.03481.5315134.95−3.550.22220.0348
PCB206Ijms 08 01125f2091.010311.750.03331.4623133.57−3.570.19100.0333
PCB207Ijms 08 01125f2100.942311.260.01680.7378133.12−3.520.30700.0168
PCB208Ijms 08 01125f2110.932011.520.04421.9425132.24−3.570.28560.0442
PCB209Ijms 08 01125f2121.049611.090.00650.2857134.24−3.490.32500.0065
iIDRwHg, ISDmsHt, and lADrtHg = the value of the descriptor - Eq(1)& Eq(2); Ŷ1d, 2d = relative retention time: estimated by Eq(1) and Eq(2), respectively; Y = relative retention time: experimental [30]; Y- Ŷ1d, 2d = residuals.
Table 2. Training vs Test Experiments: Results.
Table 2. Training vs Test Experiments: Results.
Training setTest set
No PCBsCoefficientsStatisticsNo PCBsStatistics
p < 0.0001


The research was partly supported by UEFISCSU Romania through research projects.


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Jäntschi, L.; Bolboaca, S.D.; Diudea, M.V. Chromatographic Retention Times of Polychlorinated Biphenyls: from Structural Information to Property Characterization. Int. J. Mol. Sci. 2007, 8, 1125-1157.

AMA Style

Jäntschi L, Bolboaca SD, Diudea MV. Chromatographic Retention Times of Polychlorinated Biphenyls: from Structural Information to Property Characterization. International Journal of Molecular Sciences. 2007; 8(11):1125-1157.

Chicago/Turabian Style

Jäntschi, Lorentz, Sorana D. Bolboaca, and Mircea V. Diudea. 2007. "Chromatographic Retention Times of Polychlorinated Biphenyls: from Structural Information to Property Characterization" International Journal of Molecular Sciences 8, no. 11: 1125-1157.

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