V. K . Mukhomorov / Advances in Biolo gi cal Chemistry 1 (2011) 1-5

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( )

22

222 2

expAd abc

=+− π−

(4)

a2 = 69 .0 ± 1. 55, b2 = 5.50 ± 0.08, c2 = –1.40 ± 0.06, d2 =

6.90 ± 0.35, number of molecules m = 18, R2 = 0.85, F =

9.2 > ()

1,17;0.05

cr

F = 4.54.

Toxicity of the molecules has maximum in the range

of π = 5 – 7 (m = 10 – 14) (Figu re 1). Maxi mum of ra-

diopr otective activity (A) is in this range of m.

Hence, molecules for m > 14 and m < 5 (thus, for

example, m = 15, Z = 2.44 <

= 3.0) are likely to be

potential radioprotectors. However, both toxic and radi-

oprotective effect is limited by the hydrophobic proper-

ties of molecules.

The further research of linkage the structure of the

chemical preparations that presented in the Table 1 has

shown that electronic parameter Z is associated with

information function (entropy) of Shannon-Wiener

[9,10]: 2

log

i

= −

; here Nnp ii /= at what

, and

. Entropy function H r epre-

sents the integral characteristic of the object describi ng a

measure of a molecular structure diversity.

is a

number of atoms of kind i; N is a number of atoms in

molecule.

In this work is used Kolmogorov’s combinatory ap-

proach [9] for information function definition. The

quantity o f the infor mation in a mo lecule is turned out

onl y fu nc t ion o f n u mbe r o f fi ni te e l e me nt s o f a t o ms set.

Information measures are an integral index and are

defined for the whole sets of events. It does not con-

tradict representations about complex character of ra-

dioprotective action of radio protectors [10]. From

Ta b l e 1 follows that mean value of information func-

tion for radioprotectors equals to

bit (S1 =

0.16). Whereas for the chemical preparations which

are not po ssessin g protec tive activi ty this func tion it is

equal

bit (S2 = 0.15). Using t-criterion is

easy for checking up, whether distinction of means

information functions is statistically significant for

and

. Using t-criterion we can examine the

statisticall y difference for mean values of the informa-

tion functions

and

. Significant difference for

mean values of the information functions

and

Let’s preliminary define distinction between disper-

sio n s

and

by means of Fisher’s criterion:

( )

( )

31290 05

2

1 2,;

114 18

.

cr

F SS.F.= =<=

, that is distinction

in dispersions is statistically insignificant. Therefore

we can appl y t-c r ite r ion:

()()

( )

}

120 051122

1

12

0 1811

20 08

.

HH.tNS NS

NN N.

−

−= >⋅− +−

⋅+− =

(5)

Inequality (5) confirms the statistical significance of

distinction for averages values

and

. Thus,

character H as well as fa ctor Z allo w to separa te effec-

tive radio protectors from the preparations which are

not hav i ng e ffecti ve a ntir ad ia tio n ac tio n s.

We will verify the statistical significance of the

stated hypothesis, using a statistical method of com-

parison of qualitative characters: Φ = 0.77 ± 0.07,

2

()

;

20 051

35 6χ384

cr

.

..

χ

=≥=

. Thus, statistical criteria χ2

con firm t he exi stence of the linka ge bet ween c haracter

H and biological activity of chemical preparations.

Using methods of the statistical analysis it is possible

to show that entropy is coupled with parameter Z, and

the statistics will be followin g: the statistical sampli n g

is N = 60, the factor of linear correlation is R2 = 0.85

, Fish er’s criterion is

.

These inequalities confirm the statistical significance

of linkages between t he character s Z and H.

At the same time use of molecular characters Z and

H for separating the carcinogenic preparations from

non carcinogenic ones (in the Table 1 are noted by

signs + and –, accordingly) also leads to statistically

authentic results. Really, for most of carcinogens (Ta-

ble 1) the character

. For not carcinogens:

>. We have for information functions the follow-

ing inequalities: и

, accordingly. Here

=

1.6 bit is the mean value of information function for

chemical carcinogens. Distinction of mean values of

information function for the chemical preparations

possessing carcinogen activity

= 1.41 bit and not

posse ssi ng one s tha t 2

H= 1.86 bit, even more, than in

case of radio protectors. Hence, using t-criterion we

obtain that chemical preparations for which H ≤

and

belo ng to different sets, and the t hreshold

factor

is statis ticall y sign ifican t.

Thus regions of the characters Z and H are overlap-

ping with each other that obtained from different prin-

ciples for carcinogenic chemical compounds and for

effective radioprotectors. Hence, chemical prepara-

tions which are radioprotectors, can be carcinogen

dangerous.

3. CONCLUSIO NS

We have formulated two classification principles

which obtained as a result of the statistical analysis of

the experimental data using two kinds of biological

activity. Hypothesis are verified by means of its test

for chemical compounds which have not included in an

initial series of the preparations. There are chemicals

which have been examined both for radioprotective

efficacy [10,11], and for carcinogenicity [12]. Dithia-