J Pharm Pharmaceut Sci (www.cspscanada.org) 8(3):586592, 2005
Quantitative Structure AntitumoralActivity Relationships of Thiadiazinthione Derivatives Using the Novel Hybrid Molecular Index ^{p}MRc
Ramón
Carrasco,^{a} Juan A. Padrón,^{b}
Rolando Pérez,^{c} Hortensia Rodríguez,^{c} Margarita Suárez,^{c}
Carmen Ochoa^{d}
^{a}Dept. Química,
Centro de Química
Farmacéutica, La Habana, Cuba
^{b}Laboratorio de Química Computacional y
Teórica, Facultad de Química, Universidad de La Habana
^{c}Laboratorio de Síntesis Orgánica, Facultad
de Química, Universidad de La Habana
^{d}Instituto de Química Médica (CSIC)
Madrid, España
Received October 26, 2005; Revised November 18, 2005, Accepted November 25, 2003, Published December 1, 2005
Corresponding
author: Ramon CarrascoVelar,
Dept. Química, Centro
de Química Farmacéutica, Ave. 21 y Calle 200, Apdo. 16042, La
Abstract
Purpose.
The recently defined
molarrefractivitypartition index was
applied to a family of 1,3,5
thiadiazin2thione derivatives in
order to establish quantitative
structureantitumoral models. The goal
of this effort is to establish the
relationships between the structure
and biological response of these
compounds.
Method. After the splitting of
the sample in two sets, their indices
were correlated against the measured
biological activity. The combined use
of our index with others had been able
to describe not only the topologic but
also the
3,5disubstitutedtetrahydro2H1,3,5thiadiazin2thione derivatives (I) have a wide spectrum of antimicrobial activity.[1] Several studies related to the antifungic, antiviral, antihelmintic, and tuberculostatic activity of these compounds have been extensively reported.[13] Previously, two series of 3,5disubstituted thiadiazinthiones have been synthesized and assayed in vitro and in vivo in order to obtain new antiparasitic chemical substances for assessment as potential antiprotozoal agents.[2] In a recent work the antitumoral activity of these compounds have been reported against several tumoral cell lines and also some features of the degradation pathways of this heterocycle[3] were outlined. Up to now, experimental evidence strongly suggests that the thiadiazinthione ring acts as a prodrug. [1] In a protic medium, the heterocycle undergoes a ring opening to form different active metabolites, which are indeed responsible of the biological activity [1]. The use of topologic and topographical indexes is widely accepted for molecular modeling. Recently, we reported the hybrid molarrefractivitypartition index (^{p}MRc)[4,5], based on Randic algorithm [6] and Ghose and Crippen partitioned molecular refractivity [7], that have the capability to portray London dispersive forces from a different perspective than the molecular refractivity. Then, the aim of this work is to test the index capability to relate structural features of this compound family with their antitumoral activity.
The molar refractivity is a constitutiveadditive property calculated by the LorenzLorentz formula:
(1)
where M is the molecular weight, n
is the refraction index and r the density, and its value depends only of the wavelength of the
light used to measure the refraction index. For a radiation of infinite
wavelength, the molar refractivity represents the real volume of the molecules
and its polarizability. Then, the molar refractivity is
related, not only to the volume of the molecules but also to the
Table
1. General
formula and substituents of the thiadiazinthiones employed


Sample # 1 
Sample # 2 

Compound 
R_{2} 
Compound 
R_{2} 
M1A 
(CH_{2})_{5}COOH 
M2A 
(CH_{2})_{5}COOH 
M1BS 
CH(COOH)CH_{2}COOH 
M2BS 
CH(COOH)CH_{2}COOH 
M1C 
CH_{2}COOH 
M2C 
CH_{2}COOH 
M1DS 
CH(CH_{2}Ph)COOH 
M2DS 
CH(CH_{2}Ph)COOH 
M1DRS 
CH(CH_{2}Ph)COOH 
M2DRS 
CH(CH_{2}Ph)COOH 
M1ES 
CH[CH(CH_{3})_{2}]COOH 
M2FS 
CH[(CH_{2})_{2}COOH]COOH 
M1FS 
CH[(CH_{2})_{2}COOH]COOH 
M2GS 
CH(CH_{3})_{2}COOH 
M1GS 
CH(CH_{3})_{2}COOH 
M2H 
CH_{2}CONHCH_{2}COOH 
M1H 
CH_{2}CONHCH_{2}COOH 
M2JS 
CH(CH_{2}CONH_{2})COOH 
M1IS 
CH[(CH_{2})_{2}SCH_{3}]COOH 
M2M 
CH_{2}CH_{2}COOH 
M1JS 
CH(CH_{2}CONH_{2})COOH 
M2NS 
C[CH_{2}CH(CH_{3})_{2}]COOH 
M1JR 
CH(CH_{2}CONH_{2})COOH 


M1K 
C[(CH_{3})_{2}]COOH 


M1M 
CH_{2}CH_{2}COOH 


M1NS 
C[CH_{2}CH(CH_{3})_{2}]COOH 


M1O 
Furfuryl 


Table
2. Atomic
refractivity values reported by Ghose et. al.
Atom
type 
Atomic Refractivity

Atom
type 
Atomic Refractivity

Csp_{3} 
2.8158 
N
(Ar) 
2.7662 
Csp_{2} 
3.8278 
NO_{2} 
3.5054 
Csp 
3.8974 
ArN=X 
3.8095 
C
(Ar) 
3.5090 
F 
1.0632 
C=X 
3.0887 
Cl 
5.6105 
H 
0.9155 
Br 
8.6782 
O 
1.6351 
I 
13.8741 
=O 
1.7956 
Ssp_{3} 
7.3190 
O=N 
2.1407 
Ssp_{2} 
9.1680 
Nsp_{3} 
3.0100 
RSOR 
6.0762 
Nsp_{2},
Nsp 
3.2009 
RSO_{2}R 
5.3321 
Ghose and Crippen defined 110 atom types, [7] representing most commonly occurring atomic states of carbon, hydrogen, oxygen, nitrogen, halogens, and sulphur in organic molecules to split the molar refractivity. They stated that this classification partially differentiates the polarizing effects of heteroatoms and the effect of overlapping with nonhydrogen atoms, although they accepted that this classification might be weak in differentiating the conjugation effects. The authors stated that the classification may not completely cover all organic molecules, and that addition of atom types is always feasible. Further on, the 110 atom types were reduced to 22 (table 2). They assumed that the sum of the atomic values (a_{i}) is the molecular value of the molar refractivity (eq. 2):
(2)
Graph theory is a branch of mathematics related to topology and combinatorial problems.[18] Different authors have reported a large number of topological and topographical indices as well as its broad and successful applicability in QSAR and QSPR studies. However, the principal problems of the use of this approach are related to the physical meaning and the information redundancy among indices of similar definition, commonly expressed by high correlation values. [19] In this sense, Randic postulated [20] that any novel molecular descriptor 1) need to be simple, 2) add more insights to the problem, 3) or to solve a unexplained problem by alternative schemes, among others features. Randic molecular connectivity index for path of order p (^{ p}c) is defined as [6]:
(3)
It was modified by Kier and Hall[21,22] by defining subgraphs G_{j }tree type in the G graph containing edges. To each vertex i of graph G is associated a term di (for example di = vi). After this, to each subgraph Gi with vertices j1,..., jh+1 is calculated the F magnitude (Eq. 4)
(4)
The numbers F(d_{i1}, d_{j(h+1)}) are then added in all the subgraph Gi.. To include the multiple bonds and heteroatoms, Kier and Hall suggested the employ of di as,
(5)
where Z_{i} is the total number of electrons, Z^{v}_{i} is the number of valence electrons and h_{i} is the hydrogen atoms number bonded to atom i. The connectivity indices obtained by this formula are known as valence indices [22] and represented by ^{p}c^{v}. A more detailed explanation of the graph theory and calculation procedures can be found elsewhere.[23]
Molar refractivity partition index[6,7] (^{p}MRc) use the Randictype graphtheoretical invariant, and is defined as follow (Eq. 6),
(6)
where the sum is all over adjacent vertices in the graph. dMR(v_{i}) is the atomic refractivity value of the v_{i} atom. The atomic refractivity values of bonded hydrogen to heavy atoms are also added to this term, to take into account their contribution in the graph.
Table 1 shows the compound sets. Reported antitumoral activity [3] is shown in tables 3 and 5. Biological activity is given as log IC_{50} against HeLa cells (logA). All structures were optimized to 0.01 convergence by the semiempirical method PM3 [9,10] implemented in MOPAC 6.0 program. [1113]
In all the indexes employed the superscript p and c indicates path and cluster order, respectively. Randić (^{p}c) and valence (^{p}c^{c}_{V}), based on the vertices connectivity matrix and ^{p}e Estrada indices, in the edge connectivity matrix [14] were used as topological descriptors. As topographic descriptors, the ^{p}W, ^{p}W_{q}, pW_{q}^{C} and ^{p}e_{r} Estrada indices [14] were employed. The W indices are based in the matrix of the vertices, weighted by the bond orders, the charge density and the charge density with spatial correction respectively. In the case of ^{p}e_{r}, the connectivity matrix of the edges is weighted with the bond orders. The c, c^{V}, W, W_{q}, W_{q}^{C}, e and e_{r} were calculated with the MODEST program [15]. Both the bond orders and the charge density were taken from the output of the semiempirical calculations.
^{p}MRc index was included to portray the importance of the
The 27 compounds in the sample were divided in two, according the nature of R_{1} substituent. Forward stepwise multiple regression analysis was employed to establish the quantitative regression models, using the STATISTICA package. [17] A statistical outlier was defined as any compound that failed in three of the several criteria included in the program. In such case it was excluded from the sample and the analysis was restarted. Both models were crossvalidated, reporting the Q^{2}^{ }value.
The mechanism of the antitumoral action of these compounds is not well established. It has been previously described that, in biological environment, the thiadiazinthione ring breaks to generate active metabolites.
Since only two different substituents in position 1 are represented in the series, it is possible to use an indicator (dummy) variable (taking values 1 or 0 for the presence or not of a given substituent) to described the whole set. However, we had preferred to treat the sample separately. Therefore the sample was divided in two: Sample #1 with R_{1}=furfuryl and Sample #2 with R_{1}=cyclohexyl.
This sample set includes
sixteen N1furfuryl derivatives. After the exclusion of the compound
M1JS as a statistical outlier (predicted value error > 55 %)
the regression analysis affords the equation 7:
(7)
The prediction results
are shown in
table 3. According to Kubinyi,[18] the analysis for
the exclusion of statistical outliers must be an arbitrary process.
As the
exclusion of compound
M1DRS (error =
16.67%)
as a statistical outlier does not improve the quality of the model it was
maintained in the sample. Although
the
Q^{2} value of
the cross validation is higher than 0.5 (suggesting that the equation has
predictive capability), it is decreased by more than 10% with respect to the
R^{2} value of the regression
model. For this reason, we consider the predictive capability of the equation
as low, although Golbraigkh and Tropsha [19] accept
Q^{2} values higher than 0.5. The mean contribution to the
activity of each variable is 3.149, 3.314 and –0.666 for
^{6}MRc,
^{3}c and
^{2}MR^{3}c respectively. The analysis of these values suggests that the
inclusion of long fragments in the structure decreases the antitumoral
activity. This could be due to an increase in the possibility to form
instantaneous dipoles, taking into account the presence of heteroatoms as S and
O. Then, an increased macromolecular union described by this variable could
explain the role of the
The most important features that determine the antitumoral activity are the presence of fragments of three atoms and pathclusters combinations as described by variables ^{3}c and ^{2}MR^{3}c respectively. Although it is risky to say that equation 7 is predictive, it was useful to evaluate which structural features are involved in the biological response of this compounds set in the HeLa assay.
The figures 1 and 2 show the plot of Predicted vs. Observed values and Residuals vs. Deleted Residuals from equation 7.
Figure
1.
Predicted vs. observed values for sample 1 with
equation 7
Figure
2.
Deleted vs. deleted residuals from equation 7
Summarizing, these results suggests that topological features and the dispersive forces described by the hybrid index ^{p}MRc affect the antitumoral activity of the compounds of sample 1, which can be associated to the presence of long fragments (up to six carbon atoms). These fragment types are also topologically described by the Randic index. The branching (^{2}MR^{3}c) and the size (^{6}MRc, ^{3}c) of the molecules in this sample may be the principal structural features that modulate the activity of these compounds.
The correlation matrix (table 4) demonstrates that correlation between variables in eq. 7 is less than 0.88, which is a good performance taking into account the nature of the variables employed in the analysis. [7]
If this equation is used only for classification as active or inactive, and the threshold of the error is accepted as 10 %, it can be concluded that 80% of the sample was correctly predicted.
Table
3.
Results, sample 1 with R1=
furfuryl
Compound 
R_{2} 
Exp. 
Pred. 
Res. 
% Error 
M1A 
(CH_{2})_{5}COOH 
0.60 
0.59 
0.01 
1.67 
M1BS 
CH(COOH)CH_{2}COOH 
0.96 
0.97 
0.01 
1.04 
M1C 
CH_{2}COOH 
0.99 
1.05 
0.06 
6.06 
M1DS 
CH(CH_{2}Ph)COOH 
1.06 
0.98 
0.09 
8.49 
M1DRS 
CH(CH_{2}Ph)COOH 
0.84 
0.98 
0.14 
16.67 
M1ES 
CH[CH(CH_{3})_{2}]COOH 
0.90 
0.90 
0.00 
0.00 
M1FS 
CH[(CH_{2})_{2}COOH]COOH 
1.47 
1.43 
0.04 
2.72 
M1GS 
CH(CH_{3})_{2}COOH 
0.97 
0.88 
0.09 
9.28 
M1H 
CH_{2}CONHCH_{2}COOH 
0.79 
0.77 
0.01 
1.27 
M1IS 
CH[(CH_{2})_{2}SCH_{3}]COOH 
0.88 
0.96 
0.08 
9.09 
M1JS 
CH(CH_{2}CONH_{2})COOH 
0.53 
Outlier


M1JR 
CH(CH_{2}CONH_{2})COOH 
0.88 
0.96 
0.08 
9.09 
M1K 
C[(CH_{3})_{2}]COOH 
0.92 
1.02 
0.10 
10.87 
M1M 
CH_{2}CH_{2}COOH 
0.85 
0.90 
0.06 
7.06 
M1NS 
C[CH_{2}CH(CH_{3})_{2}]COOH 
1.09 
0.93 
0.15 
13.76 
M1O 
Furfuryl 
1.13 
1.02 
0.11 
9.73 
Mean 




7.12 
Table
4.
Correlation
matrix of variables in eq. 7.

Log A 
^{3}c 
^{6}MRc 
^{2}MR^{3}c 
Log A 
1.000 



^{3}c 
0.237 
1.000 


^{6}MRc 
0.361 
0.865 
1.000 

^{2}MR^{3}c 
0.321 
0.668 
0.875 
1.000 
This sample set includes the 11 derivatives where R_{1} = cyclohexyl. The regression analysis allows us to obtain the equation 8, which includes ^{1}c_{v}^{3} and ^{3}MR^{3}c indices. Both of them describe the role of molecular branching, but with different sign and fragments. The mean contribution values of each variable to the activity are 2.779 and 0.682 respectively.
This result suggests that
in this compound set topological features given by variable ^{1}c_{v}^{3}
are more important than dispersive forces.
(8)
Activity prediction for sample 2 is shown in table 5.
Table
5.
Results, sample 2 with
R1= cyclohexyl
Compound 
R_{2} 
Exp. 
Pred. 
Res. 
% Error 
M2A 
(CH_{2})_{5}COOH 
1.48 
1.42 
0.06 
4.05 
M2BS 
CH(COOH)CH_{2}COOH 
1.66 
1.64 
0.01 
0.60 
M2C 
CH_{2}COOH 
1.46 
1.55 
0.08 
5.48 
M2DS 
CH(CH_{2}Ph)COOH 
1.14 
1.29 
0.16 
14.04 
M2DRS 
CH(CH_{2}Ph)COOH 
1.37 
1.29 
0.08 
5.84 
M2FS 
CH[(CH_{2})_{2}COOH]COOH 
1.46 
1.42 
0.04 
2.74 
M2GS 
CH(CH_{3})_{2}COOH 
1.14 
1.14 
0.00 
0.00 
M2H 
CH_{2}CONHCH_{2}COOH 
1.66 
1.64 
0.02 
1.20 
M2JS 
CH(CH_{2}CONH_{2})COOH 
1.18 
Outlier 

M2M 
CH_{2}CH_{2}COOH 
1.54 
1.54 
0.00 
0.00 
M2NS 
C[CH_{2}CH(CH_{3})_{2}]COOH 
1.18 
1.16 
0.02 
1.69 
Mean 




3.24 
Figure 3.
Predicted
vs. observed values calculated with equation 8 for sample 2.
Figure 4. Residuals vs. deleted
residuals obtained from equation 8.
Figures 3 and 4 show the plots of the predicted vs. observed values with equation 8, and the graph of residuals vs. deleted residuals.
This last graph (fig. 4) suggests that this regression model is more stable than that given with equation 7 for the first compounds set. This can be explained from the definition of deleted residuals. They are the residuals that one would obtain if the respective case would be excluded from the estimation of the multiple regression (i.e., the computation of the regression coefficients).
Thus, if there are large discrepancies between the deleted residuals and the regular standardized residuals, then it can be concluded that the regression coefficients are not very stable, that is, they are greatly affected by the exclusion of single cases. If these results are analyzed in the same manner as for sample 1, it may be concluded that, qualitatively speaking, 90% of the sample was correctly predicted.
As a general remark, when the substituent in R1 is furfuryl, an increased activity is obtained except when R is CH[(CH_{2})_{2}COOH]COOH. Equations 7 and 8 suggest that the presence of pathcluster fragments type (^{2}MR^{3}_{c} and ^{3}MR^{3}_{c} respectively) in both series also increases the activity. These two features suggest that this pattern of substitution affords leads compounds in both series. On the other hand, it was determined that the ^{p}MRc index is useful to describe the antitumoral activity of the thiadiazinthiones set studied in this work. The index was able to discriminate between pure topological features and those related to dispersive forces.
This work has been partially supported by Ministry of Public Health of Cuba grants. The authors wish to thanks the referees and the editorial board for their useful comments and kindly patient.
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Published by the Canadian Society for Pharmaceutical Sciences.
Copyright © 1998 by the Canadian Society for Pharmaceutical Sciences.