ijms International Journal of Molecular Sciences Int. J. Mol. Sci. 1422-0067 Molecular Diversity Preservation International (MDPI) 10.3390/ijms13066665 ijms-13-06665 Article Pharmacological Classification and Activity Evaluation of Furan and Thiophene Amide Derivatives Applying Semi-Empirical ab initio Molecular Modeling Methods BoberLeszek1 KawczakPiotr2 BaczekTomasz23* POLPHARMA SA Pharmaceutical Works, Starogard Gdanski 83-200, Poland; E-Mail: leszek.bober@plusnet.pl Department of Pharmaceutical Chemistry, Faculty of Pharmacy, Medical University of Gdansk, Gdansk 80-416, Poland; E-Mail: p99p@gumed.edu.pl Department of Health Sciences, Division of Human Anatomy and Physiology, Pomeranian University of Slupsk, Slupsk 76-200, Poland Author to whom correspondence should be addressed; E-Mail: tbaczek@gumed.edu.pl; Tel.: +48-58-349-31-33; Fax: +48-58-349-31-35. 2012 30 05 2012 13 6 6665 6678 23 04 2012 16 05 2012 21 05 2012 © 2012 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. 2012

This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Pharmacological and physicochemical classification of the furan and thiophene amide derivatives by multiple regression analysis and partial least square (PLS) based on semi-empirical ab initio molecular modeling studies and high-performance liquid chromatography (HPLC) retention data is proposed. Structural parameters obtained from the PCM (Polarizable Continuum Model) method and the literature values of biological activity (antiproliferative for the A431 cells) expressed as LD50 of the examined furan and thiophene derivatives was used to search for relationships. It was tested how variable molecular modeling conditions considered together, with or without HPLC retention data, allow evaluation of the structural recognition of furan and thiophene derivatives with respect to their pharmacological properties.

 furan derivatives thiophene derivatives HPLC molecular modeling structural analysis 1. Introduction

The process of searching for anticancer drugs involves consideration of different structures with different mechanisms of action. The methods of searching for the optimal structures (drug design, combinatorial synthesis, screening, etc.) also vary [1–3].

One can find an interesting approach in the work by Hollósy et al. [4] where two series of amide derivatives of 2-furanocarboxylic and 2-thiophenecarboxylic acids were selected for synthesis and testing. The authors obtained two sets of six derivatives of the acids (six pairs of compounds, a derivative of furan and an analogous derivative of thiophene in each pair). In the next step, they established the retention factor, log k, as a measure of lipophilicity in isocratic conditions for the studied compounds along with the use of the classical Hansch method [5]. They calculated also the logarithms of the partition coefficients, clog P, as an independent measure of lipophilicity. Finally, the authors studied the biological activity, the antiproliferative effect of the A431 cells expressed as LD50, and conducted a preliminary assessment of the statistical relationship between biological activity and lipophilicity arriving at a higher consistency for derivatives of thiophene and the calculated lipophilicity parameters (clog P).

Pondering the results obtained by the authors [4] we arrived at the question on how lipophilicity of the compounds and their antiproliferative activity related to structural parameters derived under the quantum chemistry calculation methods for molecules, when both isolated (in vacuo), and placed in an aqueous medium. If a dependence were to be statistically proven, it could allow an attempt at a preliminary explanation of the mechanism underlying the antiproliferative action of the analyzed compounds.

The object of this study was to conduct a statistical analysis of the data established by computational ab initio methods (for both isolated molecules, and molecules in aquatic environment conditions) and the parameters characterising lipophilicity and biological activity as presented in the work by Hollósy et al. [4] in order to confirm their chemometric dependence. The aim of this study was to demonstrate the common and the differentiating features of the considered compounds in terms of their physicochemical and pharmacological effects.

 2. Experimental Procedure 2.1. Analytes

The following compounds were used in the study: N-(3-triazolo)-amide furan-2-carboxylic acid (F1), N-(5-methyl)-2-amide furan-2-carboxylic acid (F2), N-(4-methoxyphenyl)-amide furan-2-carboxylic acid (F3), N-(4-fluorophenyl)-amide furan-2-carboxylic acid (F4), N-(4-bromophenyl)-amide furan-2-carboxylic acid (F5), N-(3,4-dichlorophenyl)-amide furan-2-carboxylic acid (F6), N-(3-triazolo)-amide thiophene-2-carboxylic acid (T1), N-(5-methylthiazol)-2-amide thiophene-2-carboxylic acid (T2), N-(4-methoxyphenyl)-amide thiophene-2-carboxylic acid (T3), N-(4-fluorophenyl)-amide thiophene-2-carboxylic acid (T4), N-(4-bromophenyl)-amide thiophene-2-carboxylic acid (T5) and N-(3,4-dichlorophenyl)-amide thiophene-2-carboxylic acid (T6). All structural formulas of the compounds studied are presented on Figure 1.

 2.2. Biological Activity Data

The study used the literature-quoted data of biological activity (antiproliferative for A431 cells) expressed as LD50. Based on previous experience [6,7] the values presented by the authors [4] were converted to their logarithmic form, log (1/LD50). The value of biological activity presented in this form is directly proportional to the force of action, hence better correlated with the structural parameters.

 2.3. Chromatographic Lipophilicity Data

The chromatographic data were expressed as log k and derived from the cited paper [4]. The authors obtained them using the Hypersil MOS (C8) column and a mobile phase containing 0.25 M triethylamine phosphate, pH 2.25, and 24% v/v acetonitrile. The analysis further included the semi-empirical values of log P (clog P) presented by the authors [4] and calculated by the Hansch method [5].

 2.4. Molecular Descriptors

The non-empirical structural indicators, i.e., quantum-chemical indicators, were calculated in the study. The structure of the tested compounds was examined by molecular modeling with the Gaussian 03W software (v03, Gaussian Inc., Wallingford, CT, USA, 2003). The geometry of molecules was optimized using the restricted Hartree-Fock 6–31G (d, p) method [8] also known as 6–31G** and then extended in addition with the method of polarization functions 6–31G (3d, 3p) [8], which assumes that there are three polarization functions—d and three polarization functions—p in the atom. The structure was optimized directly (in vacuo) and in the aquatic environment using the PCM method (Polarizable Continuum Model) [9–11].

The quantum-chemical indices considered were as follows: total energy (TE); electronic spatial extent (ESE), which is defined as the area covering the volume around the molecule beyond which electron density is less than 0.001 electron Bohr−3 and describes the sensitivity of the molecule to the electric field; the energy of the highest occupied molecular orbital (E_HOMO); the energy of the lowest vacant molecular orbital (E_LUMO), and the energy difference of HOMO and LUMO defined as the energy gap (EG). Moreover, the following values were used: the largest positive charge on the electron atoms (MAX_POS), the largest negative charge on the electron atoms (MAX_NEG), the difference between the largest positive and negative charge (DELTA_Q), the total dipole moment (TDM), and the isotropic polarizability (IPOL).

The values of total energy were expressed in atomic energy units a.u. or Hartree, energies of HOMO, LUMO and the energy gaps were expressed in eV and isotropic polarizability in Bohr−3. The values of the electron density and electron charges on atoms were expressed in units of elementary charge (ē), the dipole moment in Debye (D), and the electron spatial extent in eBohr−3.

For the optimized structures in aqueous environments the following parameters were also used: the polarized solute-solvent interaction energy (PSSIE), the cavitation energy (CE), the dispersion energy (DE), the repulsion energy (RE), and the total energy of non-electrostatic interaction (Tne), all values in kcal/mol.

 2.5. Statistical Analysis

The retention data of the compounds studied were related to their structural indicators under stepwise, progressive, and multiparametric regression analysis (multiple regression), and the analysis of partial least squares (PLS) was performed in Statistica 10 (v10, StatSoft, Tulsa, OK, USA, 2011) installed on a personal computer.

 3. Results and Discussion

The numerical values of all 10 structural parameters derived from the quantum-chemical calculations in vacuo with the use of the 6–31G (d, p) method for all 12 examined compounds are presented in Table 1. In Table 2 they are presented with the 6–31G (3d, 3p) method used.

The values of 15 structural parameters derived from the PCM calculations in the aquatic environment using 6–31G (d, p) are presented in Table 3. Table 4 presents the same for the 6–31G (3d, 3p) method.

The values of the parameters determining the lipophilicity and biological activity of the compounds in question are presented in Table 5.

A preliminary comparison, of the structural parameters calculated using the 6–31G (d, p) and 6–31G (3d, 3p) methods reveals that some differences in the values calculated for isolated molecules (in vacuuo) and molecules in an aqueous medium (PCM model) are only observed for the electron charge on the atoms (the largest positive charge MAX_POS, the largest negative charge MAX_NEG, and the difference between the charges ΔQ) standing at about 30%, and for IPOL (isotropic polarisability) ranging between 15–20%. Minor differences (within 5%) occur for the values of the total dipole moment. This comparison was only an approximate estimation of the values obtained directly from Gaussian software. In order to evaluate the usefulness of the calculations using 6–31G (d, p) and 6–31G (3d, 3p) it was necessary to conduct a multiregression analysis.

Before initiating the multiregression analysis, the data set was subject to cross-validation in the aggregate PLS analysis and in the traditional manner. i.e., by sequential removal of one case followed by a statistical analysis of the remaining 11 cases. Then, the mean values were calculated: the directional factors of the independent variables, the intercept and the regression coefficient based on those cases of the regression dependence where, the independent variables were most likely to repeat. Finally, the obtained values were compared with the values derived from the full set of cases (n = 12). The results of the multiregression analysis are presented in Tables 6–12.

Geometry optimization and calculation of the structural parameters of the enlarged function base (3d, 3p instead of d, p) does not yield any significant differences in the resulting multiregression relationships. This may be due to the fact that the structural parameters involving the highest observed differences (MAX_POS, MAX_NEG, ΔQ, and IPOL) do not occur at all, or appear sporadically as a third variable. The values of the structural parameters that have the greatest impact on the empirical parameters generally differ by less than 5%, and in some cases by even less than 1% for both functional bases.

The logarithm of the retention factor, log k, for isolated molecules (in vacuo) depends primarily on the electron spatial extent (ESE), than on the value of the total dipole moment (TDM). The best agreement (R~0.9) was obtained for those two independent variables (Figure 2). The situation is analogous in aqueous medium (R~0.9). During the cross-validation, dependence was found occasionally for three independent variables: ESE, TDM and MAX_POS (R~0.98) in 11 cases. The logarithm of the partition coefficient, clog P, calculated by the authors [4] under the classical Hansch method [5] also shows a very similar dependence for both the isolated molecules and those in the aquatic environment–ESE as a single variable, and ESE with TDM in the case of two variables (R~0.89). The relationship of two variables can be considered satisfactory. Occasionally, for all 12 cases, relationships of three variables were observed: ESE, TDM, and MAX_POS for isolated molecules, and ESE, TDM, and ΔQ for the particles in an aqueous medium (R~0.93–0.94).

The LD50 parameter was given for biological activity [4]. This was supplemented with the log (1/LD50) parameter being directly proportional to the force of action. The logarithm of the inverse of LD50 is proven in having slightly better correspondence with the structural parameters. Isolated molecules (in vacuo) demonstrated dependence on only one parameter—the lowest energy unoccupied molecular orbitals (E_LUMO) with R~0.89–0.90 (LD50) and R~0.91 (log (1/LD50)).

When the particles were optimized in the aquatic environment a shift of the structural parameters was recorded. This may be due to the fact that more parameters, not noted for isolated molecules, were taken into account for the aquatic environment. Moreover, there were more variables than cases so the calculation matrix became “oversquare”. The first important variable was the energy of dispersion (ED), although the dependence on E_LUMO for the log (1/LD50) occurred sporadically during cross-validation; the, R values were: ~0.83 (LD50) and ~0.84 (log (1/LD50)). A dependence was also found for two other variables: DE and E_LUMO with R~0.91–0.92 (LD50) and R~0.93–0.94 (log (1/LD50), presented on Figure 3). In addition, for log (1/LD50) a relationship was found between the following three variables: DE, E_LUMO, and the energy of interaction of the polarized solute-solvent (PSSIE), with R~0.96–0.97.

Among the parameters determining the lipophilicity of the molecules (chromatographic, log k, and calculated, clog P) those of the greatest impact are as follows: electron spatial extent (ESE) reflecting the particles’ dispersion ability and the London force interactions. Coming second in significance is the total dipole moment (TDM) reflecting the targeted electrostatic interactions. Incidentally, the influence of the electrical charges on the atoms (the largest positive difference MAX_POS and maximum positive and negative ΔQ) also appeared to be associated with more local electrostatic interactions. The coefficients of proportionality occurring for the ESE and TDM values are positive, which indicates that lipophilicity is directly proportional to these two parameters. The charges on atoms (or their difference) occasionally appearing in the equations as the third parameter show negative values for the proportionality coefficients, which leads to reduction of lipophilicity.

In the case of the parameters determining antiproliferative activity we observe competition between the energy of lowest unoccupied molecular orbitals and energy of dispersion. The energy of the LUMO orbitals, according to Koopman’s theorem, carries the physical sense of electron affinity (EA). A positive value of the LUMO energy in the thermodynamic convention denotes the energy, which must be supplied to the system in order to attach an additional electron to the molecule or otherwise convert it to an anion). On the other hand, negative LUMO energy denotes the energy provided by the system, which means that the process is exergonic. EA = −E_LUMO, and is the measure of electrophilicity of a molecule that is particularly important in the modeling of molecular properties and reactivity (radical reactions). The energy of dispersion (DE) denotes the share of the dispersive effect energy of the total energy of the solute-solvent interactions. The dispersion energy term is often collated with the repulsion into a unique term defining the so-called van der Waals contribution to the interaction energy of molecules [10,12]. The proportionality coefficients of the two independent variables (E_LUMO and DE) have negative signs (in the dependency for log (1/LD50)), the E_LUMO values are positive, while the DE values are negative. The exact numerical values are determined by the values of free expression. Increase of the LUMO energy leads to a reduction in antiproliferative activity, whereas increase of DE leads to growth in the antiproliferative activity. The third and incidentally occurring variable, i.e., the energy of the solute-solvent impacts, increases antiproliferative activity just like the energy of dispersion. The interaction energies of the solute and solvent, and particularly the dispersion component in the polar solvent, i.e., water, can serve as a model for interactions of substances demonstrating antiproliferative activity of cellular receptors. They represent non-specific interactions. This is indicated in the conclusions of the work [4] about the relationship between lipophilic and biological activities. The meaning of LUMO orbital energy should be interpreted differently. All examined compounds have positive values of LUMO orbital energy, which means that E_LUMO reduces the value of log (1/LD50) (the positive value of E_LUMO signifies that no anions are formed). If the E_LUMO values were negative, then the element described by this parameter would be positive and increase the value of log (1/LD50) (anions of the molecules in question would form, as well as possible additional interactions with the polar groups and the positively charged cellular structures).

As was shown in the cited work by Hollósy et al. [4], for the regressions between the parameters of lipophilicity and biological activity for each separate subset of the compounds under consideration, i.e, derivatives of furan and thiophene, it was decided to examine how the presented empirical parameters depend on the structural parameters in each subset. The presented results of those statistical analyses were only indicative and approximate due to the fact that they formed a small subset (n = 6) and the compounds contained in them differ in structure to a lesser degree than the full set of compounds.

In the subgroup of the furan derivatives, the lipophilicity parameters for the isolated molecules (in vacuo), just like the full set, depend mainly on the electron spatial extent (ESE) with R~0.85–0.90. The antiproliferative activity (only LD50 value) depends on the isotropic polarisability (IPOL), with R~0.82–0.85. Thus, the most important independent variables are: the structural parameters determining the possibility of dispersion and London force interactions.

In the aqueous medium all parameters, i.e., lipophilicity and biological activity, depend on the dispersive energy (ED), with R~0.93, and R~0.89 for the activity expressed as log (1/LD50). The correlation between LD50 and ED is therefore slightly closer than the correlation found by the authors [4] between LD50 and log k.

In the subgroup of the thiophene derivatives the lipophilicity parameters and biological activity for the isolated molecules (in vacuo) depend on the energy of the lowest unoccupied molecular orbitals (E_LUMO). However, with LD50, dependence on the electron spatial extent (ESE) occurred for the particles optimized on the (d, p) base alongside the two parametric dependencies on the ESE and the energy of the highest unoccupied molecular orbitals (E_HOMO). The regression coefficients characteristic for most of the dependencies are: R~0.85–0.89, R~0.92–0.93 for the log k dependencies, and R~0.99 for the two parametric dependencies for LD50.

In the aqueous medium all parameters, i.e., of both lipophilicity and proliferative activity, depend mainly on the energy of repulsion (repulsion between the solute and solvent particles)—RE. The values of regression coefficients were identified at R~0.93–0.96. The correlation between the biological parameters and the RE was also slightly better than that between the LD50 and log k presented in the work [4]. Furthermore, two-parametric dependencies developed with isotropic polarisability (IPOL) or total energy of non-electrostatic interactions (Tne) with the values of R~0.98–0.99 coming in as the prevailing second parameter.

The statistical analysis of the compound subsets indicates that the parameters of lipophilicity and biological activity are generally best correlated to the structural parameters describing the effect commonly referred as non-polar interactions, which confirms the conclusions drawn in the work by Hollósy et al. [4].

 4. Concluding Remarks

Based on the above overview of the results the following conclusions can be drawn.

Out of the considered 10 quantum-chemical parameters calculated for the isolated molecules the electron spatial extent (ESE) and the total dipole moment (TDM) prove to have the greatest impact on the lipophilicity parameters, whereas the energy of lowest unoccupied molecular orbitals (E_LUMO) proves to be most determinant of the biological activity.

In the aqueous medium of the PCM model and the considered 15 quantum-chemical parameters, ESE and TDM again proved to have the highest influence on lipophilicity (a third independent variable appearing occasionally). The biological activity, on the other hand, proved to be the closest related to the energy of dispersion (ED) with the E_LUMO variable coming second.

Concerning the subsets, including the furan derivatives and thiophene derivatives: the electron spatial extent (ESE) has the greatest impact on the lipophilicity parameters in the group of isolated furan derivative molecules; whereas isotropic polarisability (IPOL) proves to be the most potent determinant of biological activity. In the aquatic environment the dispersion energy (DE) proved to have the highest impact on both lipophilicity and biological activity.

In the group of thiophene derivatives E_LUMO and repulsion energy (RE) generally appear to have the greatest impact on the parameters of both lipophilicity and biological activity in isolated molecules.

The dependencies on the parameters derived from the quantum-chemical calculations confirm the earlier obtained dependencies between the parameters of lipophilicity and biological activity for the studied compounds.

Most of the quantum-chemical structural parameters, for which the relationship with the empirical parameters was determined, are related to dispersion and London force interactions, sometimes called non-polar interactions.

The structural parameters of the polar character are as follows: the total dipole moment (TDM), which is the second parameter of impact on the parameters of lipophilicity, and the energy of the lowest unoccupied molecular orbitals (E_LUMO) which affects the antiproliferative activity and most likely has an impact on the cellular redox processes.

 Supplementary Materials Acknowledgement

The work was supported by the Polish State Committee for Scientific Research Projects N N405 423839.

Conflict of Interest

No conflict of interest is declared.

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Structural formulas of compounds studied—amide derivatives of furan (1–6 F) and thiophene (1–6 T).

The relationships between observed and predicted values of the structures optimized in vacuo using 6–31G (3d, 3p) method; the regression equation: log k = k0 + k1ESE + k2TDM, where n = 12, R = 0.9001.

The relationships between observed and predicted values for the structures optimized in the aquatic environment using 6–31G (d, p) method; the regression equation: log (1/LD50) = k0 + k1DE + k2E_LUMO, n = 12, R = 0.9355.

The numerical values of 10 structural parameters derived from quantum-chemical calculations 6–31G (d, p) method in vacuo for all 12 analyzed compounds.

Compound TE ESE E_HOMO E_LUMO EG MAX_POS MAX_NEG ΔQ TDM IsoPol
1F −636.07 2474.06 −8.8656 3.0531 11.9187 0.8235 −0.8791 1.7026 5.7507 87.93
2F −1001.59 3710.12 −8.5739 2.7080 11.2819 0.8006 −0.8270 1.6276 3.1299 115.85
3F −739.85 5591.96 −7.7325 2.9755 10.7080 0.8003 −0.8511 1.6513 3.1471 128.70
4F −724.82 4490.71 −8.3135 2.7878 11.1013 0.8014 −0.8523 1.6537 5.3470 112.43
5F −3195.28 7208.03 −8.3334 2.6120 10.9454 0.8022 −0.8539 1.6562 5.7436 132.32
6F −1543.76 6490.64 −8.6180 2.4552 11.0732 0.8028 −0.8557 1.6584 7.4356 135.08
1T −958.73 2777.61 −8.9954 2.6150 11.6104 0.8444 −0.8786 1.7229 5.5502 100.73
2T −1324.25 4071.48 −8.6898 2.4139 11.1037 0.8321 −0.8227 1.6548 3.1543 129.02
3T −1062.52 6319.25 −7.7668 2.4014 10.1682 0.8648 −0.8471 1.7119 3.0444 141.97
4T −1047.49 5109.75 −8.3560 2.2433 10.5993 0.8660 −0.8484 1.7144 5.1907 125.55
5T −3517.94 8139.24 −8.3799 2.1845 10.5644 0.8504 −0.8388 1.6892 5.5362 145.53
6T −1866.43 7328.30 −8.6561 2.0044 10.6605 0.8674 −0.8521 1.7195 7.2734 148.25

The numerical values of 10 structural parameters derived from quantum-chemical calculations 6–31G (3d, 3p) method in vacuo for all 12 analyzed compounds.

Compound TE ESE E_HOMO E_LUMO EG MAX_POS MAX_NEG ΔQ TDM IsoPol
1F −636.11 2472.36 −8.8618 2.9557 11.8175 1.1067 −1.1117 2.2184 5.6098 100.19
2F −1001.63 3705.85 −8.5320 2.6370 11.4690 1.0726 −1.1213 2.1939 3.1582 130.05
3F −739.90 5583.02 −7.7293 2.9233 10.6526 1.2402 −1.2044 2.4446 3.1555 145.45
4F −724.86 4483.29 −8.3124 2.7255 11.0379 1.2511 −0.9106 2.1617 5.2793 127.78
5F −3195.37 7188.26 −8.3048 2.5410 10.8458 1.2533 −0.9057 2.1591 5.6901 151.90
6F −1543.80 6478.47 −8.5467 2.4014 10.9481 1.2472 −0.9830 2.2303 7.1568 156.68
1T −958.77 2772.40 −8.9709 2.5565 11.5274 1.0668 −0.8035 1.8704 5.4021 114.11
2T −1324.30 4066.11 −8.6341 2.3717 11.0058 0.8975 −0.7826 1.6801 3.1599 144.29
3T −1062.56 6305.01 −7.7687 2.4044 10.1731 1.1166 −1.2039 2.3205 3.0491 159.76
4T −1047.53 5097.75 −8.3606 2.2392 10.5998 1.1282 −0.8523 1.9805 5.1112 141.92
5T −3518.04 8111.85 −8.3584 2.1611 10.5195 1.1441 −0.8771 2.0212 5.4787 165.98
6T −1866.47 7311.38 −8.5883 2.0071 10.5954 1.1264 −0.8363 1.9626 6.9842 170.90

The numerical values of 15 structural parameters derived from quantum-chemical calculations 6–31G (d, p) method in water for all 12 analyzed compounds.

Compound TE ESE E_HOMO E_LUMO EG MAX_POS MAX_NEG ΔQ TDM IsoPol PSSIE CE DE RE Tne
1F −636.10 2476.66 −8.9881 2.7619 11.7500 0.8229 −0.8806 1.7036 7.6457 113.82 −25.85 23.55 −18.42 1.60 6.73
2F −1001.61 3716.68 −8.5840 2.5067 11.0907 0.8173 −0.8304 1.6477 3.7271 151.21 −16.24 28.29 −20.49 1.51 9.31
3F −739.88 5597.17 −7.8667 2.8430 10.7097 0.8075 −0.8491 1.6566 5.1573 165.53 −21.29 31.07 −21.70 1.45 10.81
4F −724.85 4494.59 −8.2972 2.7739 11.0711 0.8103 −0.8508 1.6611 7.6968 146.84 −20.90 27.38 −20.73 1.61 8.25
5F −3195.30 7215.63 −8.3282 2.6234 10.9516 0.8125 −0.8529 1.6754 8.1613 173.90 −21.10 29.10 −22.84 1.86 8.13
6F −1543.79 6494.17 −8.5334 2.5143 11.0477 0.8153 −0.8551 1.6704 10.5628 176.88 −22.14 30.57 −23.93 2.01 8.65
1T −958.76 2775.58 −9.1709 2.3586 11.5295 0.8521 −0.8797 1.7318 7.3680 134.38 −25.05 24.23 −20.12 1.75 5.86
2T −1324.26 4067.55 −8.6251 2.2294 10.8545 0.8480 −0.8244 1.6724 3.7027 172.15 −15.15 28.91 −22.11 1.65 8.45
3T −1062.53 6326.05 −7.8915 2.3497 10.2412 0.8704 −0.8467 1.7170 5.2606 186.30 −20.00 31.96 −23.50 1.65 10.10
4T −1047.51 5114.34 −8.3391 2.3029 10.6420 0.8734 −0.8485 1.7219 7.7298 167.51 −19.37 28.27 −22.52 1.80 7.55
5T −3517.97 8114.71 −8.4539 2.2653 10.7192 0.8564 −0.8266 1.6830 8.1202 193.59 −20.15 30.04 −24.66 2.09 7.47
6T −1866.45 7332.67 −8.5862 2.1467 10.7329 0.8787 −0.8528 1.7315 10.5812 197.49 −20.78 31.46 −25.72 2.20 7.94

The numerical values of 15 structural parameters derived from quantum-chemical calculations 6–31G (3d, 3p) method in water for all 12 analyzed compounds.

Compound TE ESE E_HOMO E_LUMO EG MAX_POS MAX_NEG ΔQ TDM IsoPol PSSIE CE DE RE Tne
1F −636.15 2473.06 −8.9785 2.6667 11.6452 1.1010 −1.1354 2.2365 7.7255 134.88 −25.71 23.53 −18.42 1.60 6.71
2F −1001.65 3709.09 −8.5494 2.4242 10.9736 1.0307 −1.1462 2.1769 3.9076 175.92 −16.26 28.26 −20.48 1.50 9.28
3F −739.92 5586.89 −7.8599 2.7799 10.6398 1.2236 −1.2102 2.4338 5.3148 192.94 −21.07 31.04 −21.70 1.45 10.79
4F −724.89 4486.57 −8.2969 2.7045 11.0014 1.2371 −1.0071 2.2442 7.8054 172.28 −21.04 27.35 −20.73 1.60 8.23
5F −3195.40 7192.27 −8.2934 2.5472 10.8406 1.2440 −1.0070 2.2510 8.2618 207.22 −20.82 29.05 −22.83 1.86 8.08
6F −1543.83 6482.36 −8.4792 2.4395 10.9187 1.2439 −1.0078 2.2517 10.4804 214.32 −21.84 30.54 −23.92 2.00 8.62
1T −958.81 2768.47 −9.1388 2.3061 11.4449 1.0647 −0.8626 1.9273 7.4300 158.67 −24.87 24.20 −20.12 1.75 5.83
2T −1324.32 4059.54 −8.5837 2.1815 10.7652 0.8650 −0.8381 1.7032 3.8445 199.93 −15.17 28.87 −22.11 1.65 8.41
3T −1062.59 6311.51 −7.8866 2.3355 10.2221 1.1045 −1.2101 2.3146 5.3958 216.82 −19.71 31.92 −23.50 1.64 10.06
4T −1047.55 5101.58 −8.3426 2.2822 10.6248 1.1179 −0.9097 2.0276 7.8160 196.09 −19.61 28.23 −22.51 1.80 7.51
5T −3518.06 8047.83 −8.5146 2.2754 10.7900 1.1365 −0.9033 2.0398 8.2146 228.33 −20.31 30.02 −24.65 2.10 7.47
6T −1866.49 7317.06 −8.5298 2.1233 10.6531 1.1253 −0.8986 2.0238 10.4847 238.03 −20.47 31.42 −25.72 2.20 7.90

The values of parameters of lipophilicity: the experimental one (log k). and calculated (clog P), and biological activity, expressed as the LD50 and the logarithm of inverse of LD50 (log (1/LD50)) value of antiproliferative activity for A431 cells.

Compound log k clog P LD50 (μg/mL) log (1/LD50)
1F −0.115 1.211 190 −2.279
2F 0.098 1.547 170 −2.230
3F 0.401 2.470 138 −2.140
4F 0.607 2.975 150 −2.177
5F 0.827 3.477 139 −2.143
6F 1.275 4.015 82 −1.914
1T 0.169 1.901 93 −1.968
2T 0.177 1.741 91 −1.959
3T 0.335 2.097 85 −1.929
4T 0.398 2.227 87 −1.940
5T 0.682 2.947 55 −1.740
6T 1.001 3.480 50 −1.699

The relationships for the structures optimized in vacuo and in the aquatic environment; statistical parameters: R, s, F and P of regression equation log k = k0 + k1ESE + k2TDM, where n = 12, for the series of model compounds.

k1 k2 R s F P
in vacuo 6–31G (d, p)
0.7822 ± 0.1970 - 0.7822 0.2645 15.7659 0.0026
0.6449 ± 0.1508 0.4689 ± 0.1508 0.9016 0.1936 19.5564 0.0005
in vacuo 6–31G (3d, 3p)
0.7826 ± 0.1969 - 0.7826 0.2643 15.8042 0.0026
0.6431 ± 0.1522 0.4661 ± 0.1522 0.9001 0.1950 19.2132 0.0006
aquatic 6–31G (d, p)
0.7831 ± 0.1967 - 0.7831 0.2640 15.8536 0.0026
0.5696 ± 0.1645 0.4858 ± 0.1645 0.8964 0.1983 18.4121 0.0006
aquatic 6–31G (3d, 3p)
0.7850 ± 0.1959 - 0.7850 0.2630 16.0537 0.0025
0.5726 ± 0.1652 0.4808 ± 0.1652 0.8957 0.1990 18.2513 0.0007

The relationships for the structures optimized in vacuo; statistical parameters: R, s, F and P of regression equation clog P = k0 + k1ESE + k2TDM + k3MAX_POS, where n = 12, for the series of model compounds.

k1 k1 k3 R s F P
in vacuo 6–31G (d, p)
0.7778 ± 0.1988 - - 0.7778 0.5753 15.3119 0.0029
0.6441 ± 0.1576 0.4566 ± 0.1576 - 0.8919 0.4363 17.5052 0.0008
0.7053 ± 0.1250 0.4692 ± 0.1229 −0.3139 ± 0.1201 0.9432 0.3398 21.5098 0.0003
in vacuo 6-31G (3d, 3p)
0.7781 ± 0.1986 - - 0.7781 0.5750 15.3420 0.0029
0.6412 ± 0.1580 0.4570 ± 0.1580 - 0.8919 0.4362 17.5094 0.0008

The relationships for the structures optimized in the aquatic environment; statistical parameters: R, s, F and P of regression equation clog P = k0 + k1ESE + k2TDM + k3ΔQ, where n = 12, for the series of model compounds.

k1 k1 k3 R s F P
aquatic 6–31G (d, p)
0.7786 ± 0.1984 - - 0.7786 0.5743 15.3962 0.0028
0.5681 ± 0.1695 0.4790 ± 0.1695 - 0.8896 0.4407 17.0703 0.0009
0.4928 ± 0.1378 0.6419 ± 0.1492 −0.3368 ± 0.1340 0.9399 0.3495 20.1994 0.0004
aquatic 6–31G (3d, 3p)
0.7803 ± 0.1695 - - 0.7803 0.5724 15.5705 0.0027
0.5697 ± 0.1959 0.4769 ± 0.1695 - 0.8899 0.4400 17.1306 0.0008

The relationships for the structures optimized in vacuo; statistical parameters: R, s, F and P of regression equation LD50 = k0 + k1E_LUMO, where n = 12, for the series of model compounds.

k1 R s F P
in vacuo 6–31G (d, p)
0.8978 ± 0.1393 0.8978 20.8614 41.5386 0.0001
in vacuo 6–31G (3d, 3p)
0.8876 ± 0.1457 0.8876 21.8155 37.1293 0.0001

The relationships for the structures optimized in the aquatic environment; statistical parameters: R, s, F and P of regression equation LD50 = k0 + k1DE + k2E_LUMO, where n = 12, for the series of model compounds.

k1 k2 R s F P
aquatic 6–31G (d, p)
0.8298 ± 0.1765 - 0.8298 26.4313 22.1060 0.0008
0.5274 ± 0.1620 0.5023 ± 0.1620 0.9216 19.3734 25.3801 0.0001
aquatic 6–31G (3d, 3p)
0.8301 ± 0.1763 - 0.8301 26.4053 22.1691 0.0008
0.5722 ± 0.1644 0.4593 ± 0.1644 0.9130 20.3672 22.5352 0.0003

The relationships for the structures optimized in vacuo; statistical parameters: R, s, F and P of regression equation log (1/LD50) = k0 + k1E_LUMO, where n = 12, for the series of model compounds.

k1 R s F P
in vacuo 6–31G (d, p)
−0.9141 ± 0.1282 0.9141 0.0788 50.8209 0.0001
in vacuo 6–31G (3d, 3p)
−0.9068 ± 0.1333 0.9068 0.0819 46.2899 0.0001

The relationships for the structures optimized in the aquatic environment; statistical parameters: R, s, F and P of regression equation log (1/LD50) = k0 + k1DE + k2E_LUMO + PSSIE, where n = 12, for the series of model compounds.

k1 k1 k3 R s F P
aquatic 6-31G (d, p)
−0.8440 ± 0.1696 - - 0.8440 0.1043 24.7644 0.0006
−0.5398 ± 0.1475 −0.5053 ± 0.1475 - 0.9355 0.0724 31.5427 0.0001
−0.5674 ± 0.1138 −0.5900 ± 0.1177 −0.2646 ± 0.0984 0.9666 0.0556 38.0013 0.0001
aquatic 6-31G (3d, 3p)
−0.8444 ± 0.1694 - - 0.8444 0.1041 24.8440 0.0005
−0.5844 ± 0.1509 −0.4629 ± 0.1509 - 0.9272 0.0768 27.5695 0.0001
−0.6239 ± 0.1196 −0.5482 ± 0.1232 −0.2756 ± 0.1074 0.9607 0.0603 31.9639 0.0001