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1 1 «. XXI (... ),, 2006, ( )... petoukhov@hotmail.com, ( ),..,,,.,,,.. Genbank : «,?,,.,,,.» [, 1999,. 14]..,..,,,.., -, (, ),.,,,,.,
2 2,.,.,..,.,..,,..,,.,,,.,,,..,,, (. 1): ( ), ( ), (G), (U) ( ( )). ( ). -G A-U,.. 1. :
3 3 - ( ), - G ( )..,, N, O.., (, )., ( ),. 20.,, ,.., ( ). 4 3 = 64., 20., 64 20,,, -. n, ( ) 3n,, 3n (. 2).,, P (n), ( ) (, n, ).,. (n) n,, :,,. (n) n-,,, U, G. n-,, (n) (n-1) ( ). (n) n, ( ). (n),
4 4 n-,., CC CA AC AA 1 10 CU C AU A = (2) = G 0 U G, = 01 UC UA G C 00 UU U G CCC CCA CAC CAA ACC ACA AAC AAA 110 CCU CCG CAU CAG ACU ACG AAU AAG 101 CUC CUA CGC CGA AUC AUA AGC AGA P (3) = 100 CUU CUG CGU CGG AUU AUG AGU AGG 011 UCC UCA UAC UAA GCC GCA GAC GAA 010 UCU UCG UAU UAG GCU GCG GAU GAG 001 UUC UUA UGC UGA GUC GUA GGC GGA 000 UUU UUG UGU UGG GUU GUG GGU GGG. 2. (n) n = 1, 2, 3 /, 2001/.,, G, U.,, [, 2001; Petoukhov, 1999, 2001a]., U, G. ( ), U 1, G 0. ( ) -, ( ): 1,,, - 0 ( ).. 2.,., AU 101 (, ), 110 (, ).. G U G G A G G
5 5 (3) 64. [Wittmann, 1961],.,. (n)... ( C=G=3, A=U=2),. P (n).,, G P (3) 3 3 2=18. (n) (.17.1): (1) = ; (2) = ; (3) = (n), (C=G=3, A=U=2). (n). (n) 5 n, 10 n., (3) 125, 1000., 3/2,,., , 18, 12, 8,. (n) = (1+50.5)/2 = 1,618, (n) MULT = ( (n) MULT ) 1/2, (.17.2)., (. [, 2004, 2006; Petoukhov, 2001, 2005]). (P ) 1/2 = = = -1-1 ; (P (2) ) 1/2 = = (2) = (3) = =( (3) ) 1/2 = (P (n) ) 1/2 = (n) ; -
6 6, : -,,,. ( ).,.,,.,,.,,, ( - ).,,,.. [, 2004; Petoukhov, 2005]... (n)... ( C=G=3, A=U=2),. P (n).,, G P (3) 3 3 2=18. (n)., (3) (.3): (3) = (3), (C=G=3, A=U=2).... (n),.., (n) 5 n, 10 n., (3) 125, (3) 5 12.
7 7., (n),,, (,.).. : -,,,.,. = ( )/2 = 1, 618, (n) (n) (n) : = ( (n) ) 2. (3) (. 4). 64, 1 3, ( - ): +1-1 ; +3-3.,,. (n), (n),. (n) (.. 2) : = G =, A = U = -1., G P (3) -1 =. (3) = ( (3) ) 1/2 = (3) = (P (3) ) 1/2,. (n) ( ) 1/2.,. : P = ; (P ) 1/2 = = = -1-1 ; (P (2) ) 1/2 = = (2) = (P (n) ) 1/2 = (n),. - : ( -1 ), P,
![8 (C=G=3, A=U=2). :,,.,, -1 ( -1 ).. -.,.,,,, [Petoukhov, 2001a].. -, [Petoukhov, 2001a, 2003;, 2004]. ( (3) ) 1/2 = (3).](/docs-images/57/40237608/images/8-0.png ": +1-1 ; +3-3,. +3-3,., -1,, «69» (. 6)., +1, «69».. 6. -1 (, ) +1 ( ),,,, ( 64 ). (3) -.,,., ( (3) ) 2 = (3) 8, 12, 18 27.,,,. -,.")
8 8 (C=G=3, A=U=2). :,,.,, -1 ( -1 ).. -.,.,,,, [Petoukhov, 2001a].. -, [Petoukhov, 2001a, 2003;, 2004]. ( (3) ) 1/2 = (3). : +1-1 ; +3-3,. +3-3,., -1,, «69» (. 6)., +1, «69» (, ) +1 ( ),,,, ( 64 ). (3) -.,,., ( (3) ) 2 = (3) 8, 12, ,,,. -,.
9 9,, (. 7). X(a, b, c, d) * Y(k, m, p, q) = Z(r, g, v, z) ( ),,,,,.., -,.,.,,,,.,, (n)? (n) (n) n = 2, 3, 4,,,,..
10 10,,,, [Petoukhov, 2003].., ( )., (3) «96». : «69», «96».,,, : [sh x ch x ; ch x sh x] ((,,, Matlab)., [, 2004 ].,, -, [, 1999]. (2 2). i = (-1) 1/2, : i = Arch(1/(2* )) / arccos (1/(2* )) ; i = Arch[cos(0,4* )] / (0,4* ), (1) Arch arc os., «-» [, 2003,. 255],.. (. 2),,.,,.,,, (. 9). P i ( i ) =G=3, A=U=2 (P i ) (n), (P ) (n).,. 9. -,,,, ( i ). (P i ) (n). 0 -i C -ia 3-2i - ( -1 )i i 0 ; P i = iu G ; P i = 2i 3 ; (P i ) 1/2 = i = ( -1 )i 3 - i - i i ( -3 )i
11 11 i i -1 - i -( -3 )i - -1 i i -1 -( -3 )i - i - -1 ( i ) ) (3) = - -1 i i 3 ( -3 )i i i ( -3 )i 3 - i - i i ( -3 )i -1 i i - -1 ( -3 )i i -1 i i -( -3 )i i - -1 i i P i. =G=3, A=U=2 (P i ), ( i ). i.. ( ) (. ).,. [Cook, 1914]. -,, : 1/3*[ -1 ; - -1 ] = [cos sin ; -sin cos ] ( ) : = ( 10/3 ) * asin( /2) ; = 10 * arcsin[1/(2* )] (2),, i,, ( ).,,.,.., ( ), (. [, 1981]).,,, (3), 64?. (3) -.,,,., 64
12 12 20,,.,, (3) [, 2001] ,. (3) (2 2),. NN-. 16 NN- 8.,. 10, NN-,.. NN-,,, ( - ). NN- P (3)., - - :,,.,,. 1-2, 3-4, 5-6, CCC Pro CCU Pro CUC Leu CUU Leu CCA Pro 62 CCG Pro 54 CUA Leu 46 CUG Leu 38 CAC His 61 CAU His 53 CGC Arg 45 CGU Arg 37 CAA Gln 60 CAG Gln 52 CGA Arg 44 CGG Arg 36 ACC Thr 59 ACU Thr 51 AUC Ile 43 AUU Ile 35 ACA Thr 58 ACG Thr 50 AUA Met 42 AUG Met 34 AAC Asn 57 AAU Asn 49 AGC Ser 41 AGU Ser 33 AAA Lys 56 AAG Lys 48 AGA Stop 40 AGG Stop UCC Ser 31 UCA Ser 30 UAC Tyr 29 UAA Stop 28 GCC Ala 27 GCA Ala 26 GAC Asp 25 GAA Glu UCU Ser 23 UCG Ser 22 UAU Tyr 21 UAG Stop 20 GCU Ala 19 GCG Ala 18 GAU Asp 17 GAG Glu UUC Phe 15 UUA Leu 14 UGC Cys 13 UGA Trp 12 GUC Val 11 GUA Val 10 GGC Gly 9 GGA Gly UUU UUG UGU UGG GUU GUG GGU GGG
13 13 Phe 7 Leu 6 Cys 5 Trp 4 Val 3 Val 2 Gly 1 Gly (3) /, 2001, /. 20 Pro, His, Gln. - stop. (2 2), NN-,,, NN (3), (3), , «National Center for Biotechnology Information ( )»: , 1 8., Thr,.. 4, ) The Vertebrate Mitochondrial Code ) The Standard Code ) The Mold, Protozoan, and Coelenterate Mitochondrial Code and the Mycoplasma /Spiroplasma Code ) The Invertebrate Mitochondrial Code ) The Echinoderm Mitochondrial Code ) The Euplotid Nuclear Code ) The Bacterial and Plant Plastid Code ) The Ascidian Mitochondrial Code ) The Flatworm Mitochondrial Code ) Blepharisma Nuclear Code
14 14 11) Chlorophycean Mitochondrial Code ) Trematode Mitochondrial Code ) Scenedesmus obliquus mitochondrial Code ) Thraustochytrium Mitochondrial Code ) The Alternative Yeast Nuclear Code ) The Yeast Mitochondrial Code ) The Ciliate, Dasycladacean and Hexamita Nuclear Code ( /, 2001/). ( 1 3) ( 4 8).,.,,.,.,,. 17,.,, 20 - ( 1 3) ( 4 8) [, 2004; Petoukhov, 2001] : - 20 : 12 ( 1 3), 8 ( 4 8). :, 11:9 13:7. 12:8 (, 20),.,., NN- P (3). NN- (. 10) Ala, Arg, Gly, Leu, Pro, Ser, Thr, Val, Asn, Asp, Cys, Gln, Glu, His, Ile, Lys, Met, Phe, Trp, Tyr NN , 2: - -, ( ).,
15 15,,,. UAG, Leu Gln,. 2 -,,, ( ), ( - )., 17,. : -,.,,,., ( - ).. 1: : 1, 2, 3, 4, 6, 8-24 (, 5 7; 17 0,88 %). :, 12 ( 24) [Petoukhov, 2001b].,, ,,, 24., «-»,,,. 24,.,,. 24 [Petoukhov, 2001b;, 2004]: ( ) 24-.
16 16.,,. (?) (),. [Petoukhov, 2001b;, 2004]. -,..? (),,. -,, 1:3 2:2 4:0 1:2:1. «-» [, 2004, ].. ( ),,,.. «?»,. ( ) - 1:3,,. :. ( ),.. - 4: : «( ).,, 3+1,,.,, -,» ( [, 1998,. 202]). : «-,.,. - ( ),» [,. 201].
17 17 -, 3:1.,, G, U ( ), ( ). - 3:1., N- G- 17, , N-,, - NN- 3:1. NN- -, - 1:3 2:2 4:0 1:2: NN- 1:1:1:1., NN-, -..,,, - (1:3 2:2 4:0 1:2:1),,. - ( ) ([, 2004, ])..,,. -,,. -,. (. [, 2004, ]) ( ),?, - 1:3?., 51 ( - ATG - 52 = 4 13): - - (21, ): 1GGC 2ATC 3GTT 4GAA 5CAG 6TGT 7TGC 8ACT 9TCT 10ATC 11TGC 12TCT 13CTT 14TAC 15CAG 16CTT 17GAG 18AAC 19TAC 20TGT 21AAC ;
18 (30, ): 1TTC 2GTC 3AAT 4CAG 5CAC 6CTT 7TGT 8GGT 9TCT 10CAC 11CTC 12GTT 13GAA 14GCT 15TTG 16TAC 17CTT 18GTT 19TGC 20GGT 21GAA 22CGT 23GGT 24TTC 25T TC 26TAC 27ACT 28CCT 29AAG 30ACT G- 38 A-, C- U- ( - ATG 39 ), 1:3. - EG13077 Escherichia: ATG-GTT-CAG-AAG-CCC-CTC-ATT-AAG-CAG-GGA-TAT-TCA-CTG-GCA-GAG-GAA-ATA-GCC-AAC- AGC-GTC-AGT-CAC-GGC-ATT-GGG-TTG-GTG-TTT-GGT-ATC-GTT-GGG-CTG-GTG-TTG-CTA-CTG- GTT-CAG-GCG-GTG-GAT-CTT-AAT-GCC-AGC-GCC-ACA-GCG-ATA-ACC-AGC-TAC-AGC-CTC-TAT- GGC-GGC-AGT-ATG-ATC-CTG-CTG-TTC-CTC-GCT-TCG-ACG-CTC-TAT-CAC-GCC-ATT-CCT-CAT-CAA- CGG-GCA-AAA-ATG-TGG-CTG-AAG-AAA-TTT-GAC-CAT-TGC-GCT-ATT-TAC-CTG-TTG-ATT-GCC- GGA-ACC-TAC-ACG-CCG-TTT-TTG-CTG-GTG-GGG-CTG-GAT-TCT-CCG-TTA-GCG-CGC-GGG-TTG- ATG-ATT-GTT-ATC-TGG-AGC-CTG-GCA-TTG-CTG-GGT-ATT-CTG-TTT-AAA-CTG-ACC-ATC-GCG-CAC- CGA-TTC-AAA-ATT-TTA-TCT-CTG-GTG-ACC-TAT-CTG-GCG-ATG-GGC-TGG-CTG-TCG-CTG-GTG-GTA- ATT-TAT-GAA-ATG-GCA-GTT-AAG-CTC-GCG-GCG-GGC-AGC-GTT-ACC-TTA-CTG-GCG-GTA-GGC- GGC-GTG-GTT-TAT-CG-CTC-GGG-GTG-ATT-TTC-TAC-GTC-TGC-AAA-CGC-ATT-CCA-TAC-AAC-CAT- GCC-ATC-TGG-CAC-GGC-TTC-GTG-CTC-GGC-GGT-AGT-GTG-TGC-CAC-TTT-CTG-GCG-ATC-TAT- TTG-TAT-ATT-GGG-CAG-GCG-TAA ( ) 165 (50 -, 69 -, 46 G- ) 55:165=1:3.,, - N- 1:3. -.,. -,,. 20?. : 20, 8 12 [Petoukhov, 2001b; 2004a].,, : ?,,. - - : 8 = = , , ,,.?., ,
19 19 -,., «-» , , «-», «-» ( ), «-» ( ) (. /, 2004; Petoukhov, 2004c/)., 20, -., (8=4 2 12=4 3) ,,,,,. ( ).. 10, N-., N-. (. [, 2004, ]). 8 = Pro, Arg (C- ) Lys, Met (A- ) Phe, Tyr (U- ) Ala, Gly (G- ) = Gln, His, Leu (C- ) Asn, Ile, Thr (A- ) Cys, Trp, Ser (U- ) Asp, Glu,Val (G- ) ( ) , N-...,,.,.
20 20. (., [,, 1989,. 61]).,.,,, (P i ) (n) ( i ) (n) (. 9),..,.,,.., -,, -.,..,.,.., [, 2003,. 753]. (3) (. 2), 4 64, -., (, G, A, U),., ( ) - ;, [, 2001]. : C=U=1, A=G=0 ( ); = =1, U=G=0 ( ); C=G=1, A=U=0 ( ). n- (n)., CGA 100; 101; 110. (n), n, n. (n) - (n) 1, (n) 2, (n) 3, (2) - (2) 1, (2) 2, (2) 3. CC CA AC AA
21 21 CU CG AU AG UC UA GC GA ; ; ; UU UG GU GG (2) - (2) 1, (2) 2, (2) 3. - (n),,,. - (n) 1, (n) 2, (n) 3.,. - (N) ( N N- ). (3n) 3n-,,...,, (n), ( ),,.,,,. (3n) (3),.,,, , : «, 3000,.,., » [G. Stent, 1969,.64].,,,.,,,., « -,,» [, 1998,.92].
22 22,., : «, » [F.Jacob, 1974].,..,, ( 1) ( 0). (. 14, ). ( 11 ) ( 10 ) ( 01 ) ( 00 ) ( ) 64 - ( ). 64, - [, 1997;, 1993;, 1994;, 2001] ,, (,,,..) [, 1997,. 101].,., (3) [, 2001]., (3). 2 (.. ),,, -,. 14,.,,,,.
23 23,.. 2 3,, [, 1994,. 15]. [, 2001,. 61] (3) (A=G=9, C=U=T=6).,, 144, 168, 168, 192, 168, 192, 192, 216.,, [, 2003, ]. 8 12,, « , » [, 1994, ]. 6, 7, 8 9 [, 1997,. 22, 522]., : 6 ( 6 ), N 7, 8, NH 2 9 [, 2001].,, [, 2001]. -, [, 2002]. 1:., (n) (.. 2) (C=G=3, A=U=2),, (n). 4, 5. (3)., =1, 2, 3. (. 15) (3) : 1),, :, CGA 1 C, 2 G, 3 A; 2) : =G=3, A=U= ; ;
24 B B B ; ; : B 1, B 2, B 3, (3), C=G=3, A= U =2. :, = ( /2 )/2 = 1, 618 = (B ) , = 1, 2, 3, : -1 (.. 15, = -1 ). 4 = 2.,, [, 2003]..,,, 1 2 = 2 3 = 1 3, 10., :. (n) (n). (n) 2 n -, ( ) (n)., 1 (, -1 ) 2 ( -1, ),, = [3 2; 2 3]..,,..,.,,,.,,,
25 25.,,,., ,.,, 6 9., ( -, ( -,, nova.edu/mst/issb)...,..,.,..,.,.,.. : , ,., ,,, 1998, ,, ,, 2002, ,, 1993, ,, ,, 1994, ,.... -,. 223, 2, , , ,, (... ),.,, , 1999, /...., 2001, «,,»,, 2003, ,. 15,, :..,.., 3-,, 2004a, b, 30., (, 4, 2004.).
26 c, 30., (, 8, 2004 ) , ITI, 2003, 261 c ,,, 2003, , 1997, Cook T.A. The curves of life. - L.: Constable and Co, 1914, 490 p. 22. He M., Petoukhov S., Ricci P. Genetic Code, Hamming Distance and Stochastic Matrices. Bulletin for Mathematical biology, 2004 ( ) 23. Jacob F. Le modele linguistique en biologie. - Critique, Mars 1974, tome XXX, 322, p Petoukhov S.V. Genetic Code and the Ancient Chinese Book of Changes. - Symmetry: Culture & Science, vol. 10, 3-4, 1999, Petoukhov S.V. Genetic Codes I: Binary sub-alphabets, bi-symmetric matrices and golden section.- Symmetry in Genetic Information, ed. Petoukhov S.V., special issue of the journal Symmetry: Culture and Science, Budapest, 2001a: Internat. Symmetry Foundation, Petoukhov S.V. Genetic Codes II: Numeric Rules of Degeneracy and a Chronocyclic Theory. - Symmetry in Genetic Information, ed. Petoukhov S.V., ISBN , special double issue of the journal Symmetry: Culture and Science, Budapest, 2001b: International Symmetry Foundation, Petoukhov S.V. The Biperiodic Table and Attributive Conception of Genetic Code. A Problem of Unification Bases of Biological Languages. In: Proceedings of The 2003 International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, session Bioinformatics 2003, Las Vegas, June 23-26, Petoukhov S.V. Attributive conception of genetic code, its bi-periodic tables and a problem of unification bases of biological languages.- Symmetry: Culture and Science, 2003, # 1-4, p Stent G.S. The Coming of the Golden Age. - N-Y, The Natural History Press, Wittmann H.G. Ansatze zur Entschlusselung des genetishen Codes. Die Naturwissenschaften, 1961, B.48, 24, S. 55
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