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. ., . . () . , ­ -, . : , , , . ­ , . in vivo [1], . , . , , (A), , (C). , A, , , C, - . AC-. [1]. AC- , = N/N = N/N, + C = 1, N, N ­ , , N ­ AC-. C. , . , , . , AC- ...ACCACCCAACAAACACCA... ...AACCCCCAACACACCAAA... ( = 1/2 = 1/2), A C . ( ..), . , C,


, .. C. AC- TG-, ...ACCACCCAACAAACACCA... ...TGGTGGGTTGTTTGTGGT... , , AG- TC- ...AGGAGGGAAGAAAGAGGA... ...TCCTCCCTTCTTTCTCCT... AT- TA- ...ATTATTTAATAAATATTA... ...TAATAAATTATTTATAAT... GC- CG- ...GCCGCCCGGCGGGCGCCG... ...CGGCGGGCCGCCCGCGGC... ­ (), . . - [2], , , [3], I tt ­ K/ a2 zz + V sin = - t + F0, (1)

­ , I ­ , K/ ­ , - , ­ , V ­ , , 90є, ­ , F0 ­ , . (1) , C I, K/ V


I() tt ­ K() a2 zz + V() sin = - t + F0.

(2)

(2), [4] ,

k(z, t; ) = 4 arctg{exp[() (z - k(t; C) t)/d()]};
k(t; C) ­ , () = {1 - [k(t;)/(C0())] } d() ­ d() = [K/() a2/V()]1/2.
2 -1/2 / 2

(3) ; C0() = [K () a )/I()]1/2, (4)

, [3, 7], E0() = 8 [K/() V()]1/2; H(z, t; ) = 4 () V()/ch2{exp[() (z - k(t) t)/d()]}; (5) (6)

C (C) F0 I (C) exp - 0 0 (C) - 0 I (C) 4 V (C) k (t ; C) = F I (C) 0 exp - 1 + 0 (C) - 0 I 4 V (C) C0 (C)

C (C) F0 t+ 0 4 F t+ 0 (C) 4

I (C) V (C) I (C) V (C)
2

(7)



0 ­ . (6) - (9) . , I, K/ V [6]. AC- I() = I + IC C; K/() = K/ + K/C C; V() = V + VC C. I IC ­ , ; K/ K/C ­ , - , C ; V VC ­ , , ( , ) 900. . , , (4) [5]. , , 1. , , AC- AG- , . TG- TC-. , , , AT . (8)


, AT- GC-. . [5].
1. , dTGII dAGI dTCII dATI dTAII) dGCI) dCGII dACI (е) (е) (е) (е) (е) (е) (е) (е)

0 0.25 0.50 0.75 1

28.58 30.42 32.13 33.82 35.44

28.57 29.56 30.87 32.76 35.46

28.57 29.95 31.48 33.30 35.44

28.58 29.94 31.49 33.37 35.46

35.46 35.40 35.45 35.40 35.44

35.44 35.40 35.45 35.40 35.46

28.58 28.57 28.57 28.57 28.57

28.57 28.57 28.57 28.57 28.58

. 1. ) AC- TG , ) AG- TC-, ) AT- TA-, ) GC- CG-

, , (5), [5]. , . 1, , 0 1 , AC-, 142.55 в10-20 () 174.28 в10-20 (), , TG-,


209.73 в10-20 () 119.30 в10-20 (). (crossing point), CAI crit (= CTIIcrit). CAI crit, AC. CAIcrit, TC ­. AT- TA- (. 1), GC- CG- (. 1d). , , AC- TG- . , , (6) [5] . 2. , . 2 2, (h). , (. 1), . , AC- (. 2), .
2. , hTG hAG hTC hAT hTA hGC hCG hAC в1020 в10-20 в10-20 в10-20 в10-20 в10-20 в10-20 в10-20 () () () () () () () ()

0 0.25 0.50 0.75 1

8.48 8.48 8.44 8.40 8.36

12.48 11.38 9.12 7.80 5.72

12.48 12.06 10.44 9.91 8.36

8.48 8.22 7.12 6.75 5.72

5.72 6.28 7.04 8.14 8.36

8.36 8.14 7.04 6.28 5.72

8.48 8.93 10.48 12.10 12.48

12.48 12.10 10.48 8.93 8.48

, (7), [5] = 4.25 в 10-34 ( ) F0 = 3.3 в 10-23 (). . 3.


) (AC)

) (TG)

) (AG)

) (TC)

) (AT)

) (TA)

) (CG) ) (GC) . 2. (H (z, t; )) , ) AC-, ) TG, ) AG-, ) TC-, ) AT-, ) TA-, ) GC- ) CG. , CI 1, ; CI = 0,75 ­ ; CI = 0,50 ­ ; CI = 0,25 ­ ; CI = 0 ­ . k = 189 /


a) (AC)

) (TG)

) (AG)

) (TC)

) (AT)

) (TA)

) (GC)

. 3. , ) AC-, ) TG, ) AG-, ) TC-, ) AT-, ) TA-, ) GC- ) CG. , CI 0, ; CI = 0,25 ­ ; CI = 0,50 ­ ; CI = 0,75 ­ ; CI = 1 ­ . 0 = 189 /; = 4.25 в 10-34 ( ), and F0 = 3.3 в 10-23 ()

) (CG)


, F0 Fcrit , Fcrit = (400/C0)[V(C)/I(C)]1/2 0 = [1 - (0/C0)2]1/2 [15]. F0 > Fcrit, , F0 < Fcrit, , F0 = Fcrit, . Fcrit, , 3 , . 3 . 3, . 3, . 3 , , AT- TA- F0 > Fcrit, GC- CG- - F0 < Fcrit. , . 3, . 3, . 3 . 3 F0 Fcrit CI = 0,5.
3. , Fcrit в FTGcrit в FGcrit в FTcrit в FTcrit в 10-23 10-23 10-23 10-23 10-23 () () () () () FTAcrit в 10-23 () FGcrit в 10-23 () FGcrit в 10-23 ()

0 0.25 0.50 0.75 1

3.93 3.37 3.28 3.04 2.87

3.37 3.34 3.31 3.12 2.97

3.37 3.31 3.25 3.07 2.87

3.93 3.45 3.28 3.10 2.97

2.97 2.92 2.93 2.81 2.87

2.87 2.81 2.93 2.92 2.97

3.93 3.61 3.65 3.52 3.37

3.93 3.61 3.65 3.52 3.37

. , . , ­ -, . : , , , . , . , , , , , .
( 08-04-00197).

1. Yagil, G. DNA tracts composed of only two bases concentrate in gene promoters // Genomics. 2006. V. 87. P. 591­597. 2. Englander, S.W., Kallenbach, N.R., Heeger, A.J., Krumhansl, J.A. and Litwin, A. Nature of the open state in long polynucleotide double helices: possibility of soliton excitations // Proc. Natl. Acad. Sci. 1980. V. 77. P. 7222-7226.


3. , .. , .. // . 2007. . 52, . 237-243. 4. McLaughlin, D.W. and Scott, A.C. Perturbation analysis of fluxon dynamics // Phys. Rev. A. 1978. V.18. P. 1652-1680. 5. , .., , .., , .. , .. - - // 2005. . 50. . 450-455. 6. Dominguez ­ Adame, F., Sanchez, A. and Kivshar, Yu.S. Soliton pinning by long range order in aperiodic systems // Phys. Rev. E. 1995. V. 52. P. 2183 ­ 2186. 7. , .. , .. , // X- "" "- "" ­ " 2007. . 42-44.

NONLINEAR DYNAMICS OF BINARY POLYNUCLEOTIDE CHAINS Yakushevich L. V. Krasnobava L. A.

Peculiarities of dynamics of nonlinear conformational distortions (kinks) are investigated. We worked out a method allowing to introduce linear dependence of sine-Gordon equation coefficients on the concentration of bases. Main dynamical characteristics of kinks, such as their dimension, energy, density of energy and velocity of their movement in binary polynucleotide chains with different composition, are calculated