Vol. 49 No. 1/2002 157–168 QUARTERLY

A new 4D-QSAR approach has been considered. For all investigated molecules the 3D structural models have been created and the set of conformers (fourth dimension) have been used. Each conformer is represented as a system of different simplexes (tetratomic fragments of fixed structure, chirality and symmetry). The investigation of influence of molecular structure of macrocyclic pyridinophanes, their analogues and certain other compounds on anticancer and antiviral (anti-influenza, antiherpes and antiadenovirus) activity has been carried out by means of the 4D-QSAR. Statistic characteristics for QSAR of PLS (partial least squares) models are satisfactory (R = 0.92-0.97; CVR = 0.63-0.83). Molecular fragments increasing and decreasing biological activity were defined. This information may be useful for design, and direct synthesis of novel anticancer and antiviral agents.

Prevention and treatment of oncologic diseases and viral pathology are the top problems.The above problems are interdependent, since oncogenicity of some viruses (including adenoviruses and viruses of the herpes group) has been established.We have shown that the well-known medicinal agent e-aminocapronic acid, which decreases experimental tumours growth and inhibits metastasis dissemination, has the wide spectrum of antiviral activity including anti-influenza, antiadenoviral and antiherpetic actions [1][2][3].New type of MCP-macrocyclic Schiff bases and their analogues that contain different structural fragments are very promising.We have established that some of them have anticancer and/or antiviral activity [4][5][6].
The structure-anticancer activity relationship of MCP within the topologic model was analyzed [4,7].The good agreement between observed and predicted values of activity against some cell cultures was observed for regression models.Thus, even within the simple topologic model it is possible to detect some patterns of relationship between structure of MCP and its activity.Assuming that more adequate QSAR models, taking into account a spatial structure of molecules and their conformational variety, should give more reliable results, we used a novel 4D QSAR approach, based on simplex representation of molecular structure.Anticancer activity of investigated compounds was tested in vitro at the National Cancer Institute (Bethesda, U.S.A.).The panel includes 60 cell lines of the following 9 human malignant tumors: leukemia, CNS cancer, prostate cancer, breast cancer, melanoma, non-small cell lung cancer, colon cancer, ovarian cancer, renal cancer.

Structures
The compounds were tested at 5 concentrations, resulting from a series of 10-fold dilutions (10 -8 -10 -4 M).Dimethylsulphoxide was used for preliminary dissolving of the compounds.A 48 h continuous drug exposure protocol and a sulforhodamine B (SRB) protein assay is used to estimate cell growth or cell death [8].We have compared results of the anticancer activity tests of the above macrocycles at the concentration 1 ´10 -4 M only, since the highest activity was demonstrated at this concentration.Anticancer activity is expressed as percent of control cell growth.Negative numbers testify that not cell growth, but cell destruction, takes place.
Anti-influenza activity in vitro was studied by inhibition of reproduction of A/Hong Kong/1/68 (H3N2) virus in tissue cultures of chorioallantoic membranes (CCM) of 12-14 days old chick embryos.Samples of compounds under examination (structures 1-33, Fig. 1) were dissolved in a special medium at 10 -3 M concentration.CCM were infected with 1000 TID 50 (tissue infection dose) of influenza virus.CCM cultures containing studied compounds were called "experimental" and those without them "control".Control and experimental samples were tested on viral infective titres after incubation (24 h, 37°C) [1].At least 5 experiments were done while investigating each compound.Anti-influenza activity was expressed as lgTID 50 and  reflected suppression of viral replication in "experimental", as compared to "control" samples.
Antiherpetic and antiadenoviral actions of investigated compounds were studied using cytomorphological method, based on calculation of the number of infected cells that contained intranuclear viral DNA inclusions [9].The inclusions were revealed by the luminescent microscopy method.A scheme of an experiment allowing determination of antiherpes activity was as follows.Two-day Hep-2 cell culture was infected with herpes simplex virus type 1 (HSV-1) strain US or adenovirus type 5 (Ad 5).Treatment of infected cells by compounds at the non-cytotoxic concentration (10 -4 M) suggested their action on the adsorption and reproduction of the viruses.Adsorption of viruses was allowed for 2 h on Hep-2 cells in the presence of studied compounds.Then all cells were washed from non-adsorbed viruses.Reproduction of adenoand herpesviruses was allowed for 48 h in the presence of studied compounds.Infected cells not treated by studied compounds were used as virus control.Then cells were washed and fixed by ethanol.After that infected cells were stained by a 0.01% solution of acridine orange and studied by luminescent microscopy method.Five hundred cells were counted in each of three parallel experiments.
The compounds ability to inhibit adenoviral or herpetical reproduction was estimated as reduction of the percentage of infected cells in treated, as compared with untreated, cell cultures.

4D QSAR approach, based on simplex representation of molecular structure
In the present work a new 4D-QSAR approach has been considered.For all investigated molecules the 3D structural models have been created and sets of conformers (fourth dimension) [10] have been used.Each conformer is represented as a system of different simplexes (tetratomic fragments of fixed structure, chirality and symmetry) (see Fig. 2).An example is presented on Scheme 1.
The simplex representation of molecular structure for biologically active substances allows unifying the description of spatial structure of compounds with saving of the complete stereochemical information [11][12][13].It enables to determine easily common fragments of spatial structure both promoting given biological activity and interfering with it.Thus, molecular structure descriptors in such a model are simplexes (fixed topology and stereochemical configuration) and their various combinations.The molecular design of compounds with the given level of activity is possible by means of generating of the allowed combinations of such types simplexes, which determine investigated property.
The developed approach has not the limitations of CoMFA (comparative molecular field analysis) [14].In the CoMFA only single fixed conformer is considered for each compound and a choice of such a conformer is often accidental.Moreover, in CoMFA there is a problem of optimal alignment of a set of considered molecules.
The approach developed in this work is similar to HQSAR (holographic QSAR) [15] but has none of its restrictions, connected with only topological representation of molecular structure and lacks ambiguity of descriptors formation when procedure of hashing of molecular holograms is realized.

Simplexes as descriptors of molecular structure
For any molecule there are 11 base types of molecular simplexes with all possible variants Stereochemical configuration of simplexes is defined by modified Kahn-Ingold-Prelog rules [12].
The structure of each simplex in molecule has been determined, with differences in atom and bond types considered.All atoms in a simplex are differentiated, based on the following characteristics: 1) element; 2) partial charge; 3) lipophility; 4) atomic refraction; 5) electronegativity of atom; 6) donor/acceptor of hydrogen in H-bond; etc.
Based on characteristics, expressed by real values (Nos.2-5 in the list), preliminary division into a definite discrete number of atom groups, characterized by different ranges of those values, is made. 1hemical bonds are differentiated by its nature: single, double, triple, aromatic.
The subsequent examples (see Fig. 2) demonstrate different systems of the representation of molecules as simplex sets.Thus molecule of acetic acid can be represented as a set of 13 simplexes (3 right, 3 left, 2 symmetrical, 5 plane).The differentiation of atom by element gives 7 types of simplexes, but differentiation of atom by charge gives only 4 types of simplexes.
In the proposed model a number of simplexes of specific type is a descriptor of the molecular structure.

Descriptors calculation in 4D QSAR models
In the 4D QSAR models each molecular structure parameter (D, descriptor) is calculated by summing products of descriptor value for each conformer (D k )2 and probability of the corresponding conformer (P k ).
where N is the number of conformers being considered, D k is the descriptor value for conformer k.
As it is well known [16], a probability of conformation P k is defined by its energy: where E i , E k is the energy of conformations i and k.The conformers are analyzed within energy band of 5-7 kcal/mol.

An example of descriptors calculation in 4D
QSAR has been demonstrated on Fig. 3.The calculation of descriptor value for one of all possible simplexes of alanine has been shown.Thus, 4D QSAR procedure consists of the following stages: 1. Formation of training set.2. Total conformational analysis of each compound and choice of more stable conformers within specified energy diapason (see Fig. 3).3. Fragmentation of each conformer into simplexes.Identification of type of each simplex and defining its stereochemical configuration (see Fig. 2).4. Descriptor value calculation for each concrete type of simplex, taking into account probability of its realization in a given compound (see Fig. 3). 5. Choice of significant structural parameters (descriptors) and QSAR analysis using statistical methods such as regression analysis, PLS (partial least squares), neural networks, etc. 6. Verification of QSAR models using leaveone-out cross-validation procedure and test set.7. Off-experimental screening of novel compounds.Molecular design of effective agents.
It should be noted that stages 1, 5, 6 and 7, are obligatory for any QSAR research.

Results of the QSAR modeling
As compared to the previously used QSAR approaches, based on topologic modeling of molecular structure [4,7], a more adequate «structure-activity» model has been constructed with the use of a training set representative for anticancer and various types of *Kinds of simplexes: R, right configuration; L, left configuration (chiral, see [12]); S, symmetrical (achiral); P, plane (achiral); A, any (configuration has not been considered); ** q A < = 0, q B > 0, where q is partial atom charge.antiviral activity and using 4D QSAR approach.It is noteworthy that the training set (Fig. 1) encompasses a broad structural variety: different MCP and their acyclic analogues, and also some of synthetic nucleosides (SN) and well-known antiviral agents (ambenum, deiteforin and other) representing various classes of organic compounds.3D QSAR approaches, such as CoMFA [14], HASL [17], lattice model [18] presumably cannot to be applied for this set.The main reason is that one-valued and optimal alignment of such heterogeneous structures for calculation of molecular field parameters is impossible.
As mentioned above, such limitation does not exist for simplex representation of molecular structure.In the present work the PLS method [19] was used for QSAR solutions.Quite adequate (R = 0.92-0.97)"structure-activity" models (Tables 2, 3) were obtained using PLS, by considering sets of conformers (4D-QSAR) instead of one fixed conformation.It is of note that all models have satisfactory predictive ability (CVR 2 > 0.4, Table 3).Observed and predicted values of considered types of biological activities are presented in Table 2.The new approach allowed to analyze the contributions to appropriate activity of all possible simplexes for each molecule.These contributions were calculated for each atom.Contribution of an atom is defined as an arithmetic mean of contributions of all simplexes3 , containing this atom.Thus, for each molecule it is possible to analyze an influence of various fragments on considered biological activity.Examples of such analyses for active and inactive molecules are presented in Fig. 4.
Analysis of simplexes combinations allowed to select appropriate molecular fragments (Table 4) which have positive and negative influence on values of each type of considered biological activity.This information may be useful for design and direct synthesis of novel antiviral and anticancer agents.The results suggested to synthesize and investigate the following molecular structures, expected to shown different biological activities.
The results of investigation of these compounds will be discussed in separate publications.Thus, developed 4D QSAR approach can be used for effective solution of the most different "structure-activity" tasks and molecular design of perspective drugs.
of investigated compounds (most of those compounds were previously synthesized and identified by G.L. Kamalov, R.N. Lozytska, D.N. Kryzhanovsky from the A.V. Bogatsky Physico-Chemical Institute of NAS of Ukraine and I.V. Alekseeva, L.I. Palchikovskaya from the Institute of Mo-lecular Biology and Genetics NAS of Ukraine) are presented in Fig. 1.

Figure 2 .
Figure 2. Examples of fragmentation by element (a) and by atom charge (b) of acetic acid into simplexes using base types 5 and 6 only.

Figure 3 .
Figure 3.An example of descriptor value calculation in 4D QSAR.

Figure 4 .
Figure 4.The influence of molecular fragments on value of activity.Dark colour, negative influence on antiviral activity and positive influence on anticancer activity; light colour -positive influence on antiviral activity and negative influence on anticancer activity.

Table 3 . Analysis of antiviral and anticancer activity by PLS-method
PLS, partial least squares; R, correlation coefficient.