Pharmaceutical Chemistry Journal, Vol. 28, No. 10, 1994

N E W P A R A M E T E R S IN Q U A N T I T A T I V E S T R U C T U R E - A C T I V I T Y

R E L A T I O N S H I P S

1~. T. Oganesyan, S. Kh. Chomaeva, A. V. Ivchenko, and L. S. Sarkisov

UDC 615.2/3.015.11.07

A study of the relationships between the structure and biological activity of chemical compounds provides a basis for the directed synthesis of novel pharmaceuticals with given properties and includes an assessment of their toxicity. A study of

this problem in relation to current medicinal chemistry clearly leads to research into quantitative structure-activity relationships

(QSARs). The parameters used for QSARs take into account changes in the electronic configuration, hydrophoby, and steric

properties of the molecules [8] that occur in a series of related compounds when substituents are introduced. Research into

suitable numerical values that reflect these properties and a study of their functional relationships on model systems make it

possible to develop a strategy for directed synthesis. A number of parameters are currently used in the regression equations employed for studying QSARs. Amongst these

should be included the parameter of hydrophoby [6], which is determined experimentally by extractive photometry. This method

is known to have quite a high margin of error for tow values of the distribution constant [6], which in the end has quite a significant effect on the final result in the determination of the correlation coefficient. This can account for the fact that in a

study of QSARs the correlation coefficient using this parameter is equal to 0.7. �9 Other parameters used in correlative equations are the Taft and Hammett constants, which are widely used for aromatic

systems but have serious limitations for heterocycles and cannot be used in aliphatic and alicyclic compounds [8]. The UV, IR, NMR and mass spectrometric properties of the compounds being studied are also widely used for this

purpose [3, 5, 10-12]. The experimenter frequently needs to obtain rapid information about QSAEs so that on the basis of these

data the molecules of biologically active compounds can be refined. All of the above has provided a basis for research on parameters, calculation of which would involve the partial

application of experimental methods or completely exclude their use. Quantum-chemical theories suggest that the approach to any molecule should be the same as to a complete system

whose external properties reflect its internal composition [2]. In our opinion, one parameter not requiring experimental determination could be the factor relating the valence

electrons (Z) to the nuclei (N) in a. given molecule, namely, Z/N. Since the molecules of many biologically active compounds are systems that incorporate unsaturated, aromatic, and

heterocyclic residues, it is reasonable to take into account these structural features. Therefore, we propose to use the ratio of

the number of 7r bonds to the number of a bonds Or~a) as a parameter that indicates the degree of r-coherence. The validity of this approach is based on the fact that xenobiotics when undergoing metabolism interact with a

biological substrate and the 7r electrons in the resulting substrate-substance complex play a significant role [4]. Unshared electron pairs on the substituents in unsaturated systems cause characteristic electronic effects, as indicated

by the specific types of electronic transitions in the UV spectra. At the same time the unshared electron pairs participate in a donor-acceptor interaction with the substrate, hence establishing the complementary nature of the substance with a receptor. From all these arguments we can develop the parameter ~ , which is the number of unshared electron pairs in the atoms of a' given molecule.

Pyatigorsk Pharmaceutical Institute. Translated from Khimiko-farmatsevticheskii Zhurnal, Vol. 28, No. 10, pp. 53-56,

October, 1994. Original article submitted June 29, 1993.

0091-150X/94/2810-0759512.50 o1995 Plenum Publishing Corporation 759

TABLE 1. Parameters for 2-Styrylchromone Derivatives

Z ,9

0

Compound

a( a 2 4-OH a 3 2,4-,di(OH) a4 3-OCH3-4-OH as 3.4-di (OCH3) a6 2-OCH 3 a7 4-OCH 3 a~ 3-OCH 3 ao 2,4-.di (OCH0 a(o 3-OH all 2,5-,di (OH) at2 2-OH

ZtlK i I g - - - -

ZoINll

0.0180 -0,0315 -0.0280 -0,0189 0,0253

-0,0077 -0,0077 -0,0077 0.0253

-0,0315 -0.0280 -0.0315

~nE l I g - - -

~.~0

1.1396 1,5549 0,3323 2.0624 2.0294 2,7310 1,9586 2,3452 1.5057 2,1956 2,5160 2,8364

It/tt i Ig - - - - "

-0,0377 0,5772 0.0334

-0,0023 0,658h 0.0093 0.0093 0,0093 0,658~ 0.5772 (-1,0334 0,5772

&i

a l l

0 0,1761 11.3(I 10 0.3(-110 0.3010 0,1761 0,1701 0.1761 0,3010 ('1.1761 (-1.3(110 0,17ol

11"

1,1216 1.5803 0,3603 2,0814 2.01142 2,7393 1.9005 2.3529 1.48(14 2,2271 2.5441] 2.8679

K*

1,1773 11,9777 0.2989 2.0047 1,3708 2.7223 1.9495 2.3359 0.8471 1,~184 2,4820 2,2592

A i

i~.-~ anti-

allergic 0.2540 0.3332 0.3739

�9 0,39116 0.4022 0,2540 0,3505 0,2947 I).3598 0.2751 0,3487 0.3010

,4/ ,~ .j~ anti-

hypoxie

0.0185 0,0532 0.1434 0,1125 o. 1799 o, 1007 0.069o 0,0931 1-1.15o8 0.0776 0.136O 0.0992

.4. # ,,.~ ~ - eptie

-0,1354 -0.2199 -0.2711 -0,8451 -0.4158 -0.3805 -0,291 s -0.3168 -0.4472 -0,2430 -0.2O39 -0.2858

A large number of molecules that belong to the same structural group but which are isomers of each other will have the same values of Z/N, w/o, and d , and they are called isosteric, forming an isosteric set.

Both the isolated molecule and a substance formed by it will be characterized by the same value of Z/N. In other words, Z/N is invariant in relation to association.

The widely used concept of a "functional group" in organic chemistry acquires a new shade of meaning when viewed in terms of the ratio Z/N. A functional group is usually regarded as a univalent radical, therefore, the development of a radical subspaee (molecules with odd values of Z) indicates at the same time an attempt to develop a natural system of functional groups. Resonance electron-donor groups (alkyl, amino, or alkoxy groups, for example) have lower values of Z/N, whereas resonance electron-acceptor groups (nitro, cyano, and carbonyl groups) have correspondingly higher values. It is a similar picture with inductive acceptors and donors. These trends are, of course, qualitative. An accurate differentiation of isomers and isosteres within a set is required for a study of quantitative relationships. Therefore, the main problem is to find natural criteria to distinguish the objects within a set.

The presence of isosteric sets in correlated series does not take into account the position of substituents that have the same structure and values of Z/N, ~r/a, and ~ but have different properties. It is clear that this requires suitable corrections to be made to the proposed parameters. Therefore, the information content of the new parameters can increase substantially if they are combined with the UV spectroscopic properties, which are required to be determined in the synthesis and identification of any new compound. Since the UV spectnma reflects the totality of electronic transitions in the molecules as a whole, it is, in our opinion, useful to determine the contribution of separate structural criteria to the molar extinction coefficient (e). This can be used to differentiate the isomers within an isosteric series with reasonable accuracy.

In our opinion the composite parameter D* can be used as a relationship incorporating the parameters e and Z/N. This parameter can be used to distinguish the compounds at the limits of any isosteric series and its significance lies in the fact that it indicates the specific contribution of the electron-nuclide shell of a molecule to the value of e.

Molecules that have the same total number of 7r electrons but are structural isomers in relation to each other can be differentiated if the specific contribution of the ~'-coherence factor to e is taken into account (K* parameter).

The calculation procedure is of considerable significance in elucidation of the QSARs. In our case we have used a four- parameter multiple correlation model. The choice of this particular calculation procedure makes it possible to determine most effectively the contribution of each parameter with a minimum number of input series. Therefore, in our opinion, the introduction of composite parameters extends the boundaries of any rigid calculation procedure and allows a more flexible and multiplanned approach towards solving the problems associated with QSAR8.

Thus, for the correlation analysis we have proposed the following new parameters, which have been given logarithmic values for greater convenience in the mathematical treatment, as indicated below:

760

TABLE 2. Multiple Correlation Coefficients for Freshly Synthesized Compounds

Activity of 2-styrylchromone derivatives ~t~ Correlated parameters antiallergic antihypoxic

ZilNi *tilai ai l g - - - - - ; l g - - : l g 7

Z0/N 0 ~t0/o 0 ~ 0

Xnsi nil r a i lg ; lg ; Ig L"

Zns 0 nOI~ 0 a 0

Zil Ni T-'n~i " i Ig ; Ig ; Ig ~-

ZoIN 0 Zns 0 a 0

Itileti ai D*; 1 s - : lg 7

7tol~ 0 a 0

Zi lN i b i K*: l g - - : Ig-;--

ZoIN 0 a 0

h i D*; K*: lg -c-

o 0

0.821

0,797

0,835

0.806

0,840

0.810

(I,943

0,891

0.944

0,903

0.911

0.908

analeptic

0,778

0,657

0,968

0.872

0.997

0.830

Zi/,u i 1. Ig Zo/Nll

"~n~ f

" I g - Z n~ 0

~ i / ~ i

lg ltO/~O

v o i

Ig- - - v (t o

5. D* = I g l - - - / . . . . I kYns o Zo/N o) - -

( v-me. i t / ,~. "~ 6 1," = t ~ | - - ' i ' ' | -

kXn% =0/~0 )

logarithm of the ratio of Zi/N of a given compound to Z0/N 0 of the base structure!

logarithm of the ratio of the sum of the molar coefficients of the absorption bands for a given compound(~ne i) to the corresponding sum for the base structure (Ene.o);

-- logarithm of the ratio of the degree of r-coherence ~rla of a given compound to the degree of 7r- c~hdrence of the base structure ~ro/o0, where *r/~ is the ratio of the number of ~r bonds to a bonds in a molecule;

logarithm of the ratio of the number of unshared electron pairs of the atoms in the molecule of a given compound to the number of unshared pairs in the atoms of the base molecule;

composite parameter that incorporates the values of parameters 2 and 1;

composite parameter that incorporates the values of parameters 2 and 3.

In Table 1 calculation parameters that were used in correlative equations are shown in the case of a specific group of

compounds - 2-styrylchromone derivatives [7].

It should be noted that this group of compounds constitutes a conjugated system that includes vinyl and aromatic r

electrons, indicating a high degree of r -coherence, as is reflected in the UV spectra.

From the data of Table 2, in which the multiple correlation coefficients are given for the group of compounds being

analyzed, a number of significant trends may be noted.

The proposed new parameters more completely reflect the characteristics of a molecule as a nuclide-electronic system.

The use of new calculation parameters features high values of the multiple correlation coefficients, which in turn provides an

indication of their validity and internal relationship (see Table 2, No. 1).

The nature of the interaction within a nuclide-electronic system as a whole is reflected in the UV spectra. The degree

of r -coherence introduces additional refinements to the intensity and positions of the absorption band maxima.

761

The use of the composite parameters D* and K*, which introduce additional corrections for a more complete division of the criteria of isostere molecules is fully justified, and this is borne out by the higher multiple correlation coefficients.

- - / - it We can discuss the possibility of calculating another composite parameter - M*, which is equal to Is ~"% ~0

is probably more appropriate to use this parameter in combination with D* and K* to study the QSARs of more extensive series of isostere molecules.

By analyzing the multiple correlation coefficients it may be concluded overall that the lower values of antiallergic activity are due to the considerable degree of error in the biological test itself. Thus, the normal limk for the standard deviation in physicochemieal experiments is + 0.02. However, the biological results vary over a considerably wider range, so much higher standard deviations are accepted in the regression equations (usually + 0.15) [1].

It should be noted in conclusion that the choice of a specific parameter should be related in logical manner to the structure of the compounds being analyzed. The more informative and interactive analysis of the molecule by the experimenter,

the more objective are the cause-and-effect links between the parameter used and the structure of the compound.

EXPERIMENTAL

The studies were conducted on a number of freshly synthesized 2-styrylchromone derivatives, the preparation of which is described in [7].

The biological tests were carried out using the known methods of M. N. Ivashev and A. S. Saraf, to whom we express our sincere gratitude.

The mathematical calculations were performed using a program in PL/1 developed by L. S. Sarkisov on a TURBO-86 M "Iskra" computer.

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2. 3. 4. 5.

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I. M. Korenman, Extraction in the Analysis of Organic Compounds [in Russian], Moscow (1977). I~. T. Oganesyan, A. S. Saraf, and A. V. Ivchenko, Khim.-farm. Zh., No. 1, 41-43 (1993). Chemist's Handbook [in Russian], Moscow-Leningrad (1964), Vol. 3. K. Khench, Khim.-farm. Zh., 14, No. 10, 15-30 (1980). T. J. Batterham and R. J. Hifhet, Aust. J. Chem., 17, No. 4, 428-439 (1984). T. Marbu, J. Kagan, and H. R/Ssler, Phytochemistry, 4, 177-183 (1965). F. Solcaniova and S. Toma, Org. Magn. Reson., 14, No. 2, 138-140 (1980).

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