Activity Trends in Desoxy Anthrapyrazoles: The Influence of Molar Volume, Polarizability and Lipophilicity of N 2 C 5 Side Chains on Their Anticancer Response

QSAR methodology was used to assess the effects of lipophilicity (logP), molar volume (MV) and polarizability (pl) of the side chains at N 2 and C 5 of 20 known desoxy anthrapyrazoles on their in vitro anticancer activity expressed as the negative logarithm of the inhibitory concentration of 50% of L1210 murine leukemia cell line (1/logIC 50 ). The main data set shows poor correlations between biological response and the descriptors with exception of MV of the C 5 side chain, where a moderate correlation was discerned ( 2 n = 18, two outliers). To extract more information regarding mechanism, the main data set was visually classified to three clusters depending on N 2 side chain. Cluster 1 containing six 5-substituted 2-[(2-hydroxyethyl) amino] ethyl anthrapyrazoles; cluster 2 contains ten 5-subsitutes 2-(diethyl amino) ethyl anthrapyrazoles and cluster 3 contains four anthrapyrazoles with miscellaneous substituents at both N 2 and C 5 . For cluster 1, MV and pl of C 5 show high correlation with biological response (R 2 ’s

n = 18, two outliers). To extract more information regarding mechanism, the main data set was visually classified to three clusters depending on N 2 side chain. Cluster 1 containing six 5-substituted 2-[(2-hydroxyethyl) amino] ethyl anthrapyrazoles; cluster 2 contains ten 5-subsitutes 2-(diethyl amino) ethyl anthrapyrazoles and cluster 3 contains four anthrapyrazoles with miscellaneous substituents at both N 2 and C 5 . For cluster 1, MV and pl of C 5 show high correlation with biological response (R 2 's = 0.75 and 0.72 respectively) while logP gives a weak correlation (R 2 = 0.44). For cluster 2, the cor- ). This indicates mechanistic distinction between the three clusters. Derived descriptors which represent the difference between the descriptors of N 2 and C 5 side chains where used to explore the presence of interplay between these descriptors in affecting variability of the biological response.

Introduction
Anthrapyrazoles ( Figure 1) are totally synthetic anti cancer agents that exhibit a good efficacy in the treatment of breast cancer [1] [2]. They relate to the anthracene-9, 10-dione based family of anticancer agents which include anthracyclines, e.g., Daunorubicin and doxorubicin [3]. Duanorubicin and doxorubicin, in addition to alkylaminoalkyl anthracene-9, 10-diones such as ametantrne and mitoxantrone [4]. Different mechanisms had been suggested to account for anticancer activity of anthracenediones-based anticancer chemotherapeutic agent like DNA intercalation [5], Topoisomerase II inhibition [6], generation of reactive oxygen species (ROS) among others. ROS generation is associated with all quinone containing anticancer agent and is an outcome of flavoenzyme-assisted redox cycling inside biological systems [7]. This redox cycling plays an important role in cytotoxicity of these compounds [8]. Regardless of the mechanism by which a given class of quinonoid drugs exerts its activity, substituents do indeed modify this activity either by enhancing, retarding or even banning it altogether. This is evident from the fact that from the multitude known anthrapyrazoles, only piroxantrone and losoxantrone has surfaced as potent clinical agents [9]. Similar argument could be assumed for anthracyclines and indeed for all other drugs. We reason that some kind of interplay may exist between substituents restricted in N 2 and C 5 positions of the basic nucleus which lead eventually to the observed alteration of activity profile of individual compound relative the parent anthrapyrazole. Shwalter et al. [1] found that basic side chains with two to three carbon spacers between the nitrogens, at positions N 2 and C 5 of the anthrapyrazole ring structure, enhanced in vivo antitumor activity against P388 murine leukemia.
DNA binding and intercalation were also influenced by the side chains at N 2 and C 5 .
Quantitative structure activity relationships is a field of science inaugurated in 1964 by seminal two papers by Hansch and Fujita [10], on one hand, and Free and Wilson [11] in the other. Since then tremendous strides were made in   These include linear regression, partial least squire regression, neural networks among others [12]. The algorithm used in present study is non linear regression.
The physicochemical descriptors used in the present study are two geometrical parameters polarizability (pol) and molar volume (MV), in addition to lipophilicity parameter (logP).
Polarizabilty is a measure of the ease with which the electrons of a molecule are distorted. It is the basis for evaluating the nonspecific attraction forces (London dispersion forces) that arise when two molecules approach each other.
Each molecule distorts the electron cloud of the other and thereby induces an instantaneous dipole. The induced dipoles then attract each other [13]. Polarizability has been shown to play an important role in chemical-biological interactions. The first attempt to apply molecular refractivity in terms of the Polarizability was made by Pauling and Pressman [14]. Many empirical quantum mechanical methods of differing accuracy have been proposed for calculating molecular polarizabilities [15]- [20] and [21]. Molecular polarizability influences several other physical properties, including electronegativity [22] [23] [24] and [25], dipole moment [26] and ionization potential [27]. Molar volume (MV) is the geometrical-polarizability descriptor obtained from chemical structure according to the following formula: where Mw is the molecular weight and ρ is density. This parameter is closely related to the other two polarizability descriptors: molar refractivity and parachor but while the latters are additive, molar volume is strictly not. It is typically the volume enclosed within molecular surface area which is the area of outer surface of the volume from which water molecules are excluded [28].
logP is the calculated logarithm of octanol/water partition coefficient. It is the mostly used physicochemical parameters in QSAR studies [29]. It mimics the partitioning happening for xenobiotic between aqueous and lipid environments inside the body. The pharmokinetic stage in drug journey through various barriers inside the organism is monitored by this descriptor. This paper is a continuation of our customary interest in mechanistic aspect of quionoid anticancer drugs [30] [31].

Material and Methods
The biological data were taken from literature [1]. Molar volumes (MV), polarizabilities (pl) and lipophilicities (logP) were calculated using ACD lab chemsketch 15 freeware, Advanced Chemistry Development Toronto Canada (http://www.acdlabs.com/). ΔMV N2C5 , Δpl N2C5 , and ΔlogP N2C5 parameters were obtained by subtracting the value of molar volume of substituent at C 5 from that of N 2 on the anthrapyrazole ring system. Parent compound from which the side chain at N 2 and C 5 were derived, were used for calculating the molar volume. General chemical structure of anthrapyrazoles used in this analysis is illustrated in Figure 1 and their individual chemical structures are illustrated in Table 1. The calculated parameters (MV, pl and logP) and the derived parameters (ΔMV N2C5 , Δpl N2C5 , and ΔlogP N2C5 ) are reported in Table 2.
Initially the R 2 statistic were calculated for all the sets obtained by pairing each of the calculated and the derived parameters with anticancer activity (1/logIC 50 ) to specify if any correlation exists between them. Then regression analysis was carried out.

Results and Discussion
The dependence of biological activity of the 6 desoxy anthrapyrazoles in which R 2 = −CH 2 CH 2 NHCH 2 CH 2 OH on molar volume (MV R2 ) of the C 2 side chain was found to be parabolic as shown by the Equation (1)   biological activity and MV R2 is less than 5%. The standard deviation of the residuals calculated from the model (0.295) is smaller than the standard deviation of the original data (0.595). The correlation is depicted graphically in Figure 2. It is apparent from Equation (3) that anticancer activity of this particular series of anthrapyrazoles show excellent dependence on logP R2 . This is to be expected since logP is the parameter that encodes partitioning behaviors of xenobiotics via cell membrane.
MV R2 gives with 1/logIC 50 a good parabolic correlation (R 2 = 0.76) while pl R2 gives a weaker correlation (R 2 = 0.72). This suggests slightly higher contribution MV R2 to the observed activity compared to pl R2 . It well known that biological activity of anthrapyrazole is due to their capability to bind and to intercalate to DNA. The former is due largely to the effect of substituents at N 2 and C 5 and the latter is enhanced by certain features of the rigid chromophore, e.g., presence of hydroxyl group at Ring A. it may be suggested that MV R2 contributes to the capability of anthrapyrazoles to intercalate into DNA possibly by adding to the overall molar volume and modifying the orientation of the intercalator in-betweens DNA double helical structure. On the other hand, pl R2 contributes to DNA binding ability of anthrapyrazole since it is the basis for evaluating the nonspecific attraction forces (London dispersion forces) that may arise between the molecule and DNA.
The second subset where side chain at N 2 is fixed as 2-(diethylamino) ethyl (R 1 = −H 2 CH 2 NEt 2 ) contain compounds 11 -20. Upon similar treatment as above, the following correlations were found: ( )  As it is apparent from Equations (7)- (9), the third subgroup shows good correlations between MV R1 and pl R1 with activity while logP gives a moderate correlation.
The side chain at C 2 gives the following equations and metrics: Equations (10)- (12), shows poor correlation between MV R2 and logP R2 with activity while pl R2 gives a mild correlation. This indicates that N 2 substituent influence the activity more than C 2 substituents for this subgroup.
The present analysis shows that when N 2 side chains are held constant, the activity depends on C 2 side chains but when the N 2 substituents are varied, the activity depends on them rather C 2 side chains.
To explore the combined effect of both N 2 and C 5 substituents on biological activity, new parameters ΔMV N2C5 , Δpl N2C5 , and ΔlogP N2C5 , which represent the difference between MV, pl and log P of N 2 and C 5 side chains respectively, were introduced. Visual clustering yields poor results with these derived descriptors, in contrast to regression clustering which separates the original data set into 2 clusters for each descriptor, with expelling of a few data points as outliers. This indicates a kind of interplay between the two side chains in affecting the variability of the biological response.
For ΔMV N2C5 , Significant parabolic correlation were found to 1/logIC 50 for 13 out of the 20 anthrapyrazoles (R 2 = 0.816). Six of the remaining seven compounds which do not fit into above mentioned correlation give a parabolic cor-relation (R 2 = 0.88) while one compound was considered to be as an outlier. For Δpl N2C5 a parabolic correlation were discerned for 12 of them (R 2 = 0.778). Six of the remaining compound shows a different parabolic correlation (R 2 = 0.84) and two were considered as outliers. ΔlogP N2C5 show linear correlation for 15 compounds (R 2 = 0.717). The remaining 5 compounds correlate parabolically to 1/logIC 50 (R 2 = 0.846). This advocates the use of derived parameters such as ΔMV N2C5 , Δpl N2C5 and ΔlogP N2C5 to explore the interplay of local molecular descriptors on the global activity of different molecular entity.

Conclusion
For the desoxy anthrapyrazoles studied in the present paper, the side chain at N 2 determines the segregation of the compounds into three subgroups. One group contains six compounds with 2-hydroxyethylaminoethyl side chain at N 2 . The second group contains 2-(diethylamino)ethyl side chain at N 2 . The third group contains miscellaneous side chains at N 2 . The biological response of the first and the second subgroups depends parabolically on the molar volume, polarizability and logP of C 5 side chain while the third group shows poor dependence. There is an interplay between the two side chain at N 2 and C 5 through derived descriptor obtained by subtracting the MV's, pl's and logP's of the two side chains. The third subgroup shows strong dependence of descriptor/response correlation on the miscellaneous side chain at N 2 while the C 2 side chain has poor dependence. Such findings indicate mechanistic intricacies between the members of this group of desoxy anthrapyrazoles.