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Щербик В. В., Бучацкий Л. П. Группа альтернатив и явление сплайсинга.
01.06.2014, 14:50

Резюме
 Щербик В. В.1, Бучацький Л.П.2 Група альтернатив і явище сплайсингу.
Розглянуто основні діаграми інтронів при сплайсингу РНК і діаграма інтеіна при білковому сплайсингу за допомогою групи альтернатив – групи ISO(2). Показано, що для опису простих діаграм інтронів достатньо застосування внутрішнього автоморфізму групи ISO(2), тоді як для опису альтернативного сплайсингу більш ефективним є застосування комутаторів групи. Запропоновані різні варіанти опису альтернативного сплайсингу.
Ключові слова: сплайсинг РНК, білковий сплайсинг, група ISO (2).
Резюме
Щербик В. В., Бучацкий Л. П. Группа альтернатив и явление сплайсинга.
Рассмотрены основные диаграммы интронов при сплайсинге РНК и диаграмма интеина при белковом сплайсинге с помощью группы альтернатив – группы ISO(2). Показано, что для описания простых диаграмм интронов достаточно применения внутреннего автоморфизма группы ISO(2), тогда как для описания альтернативного сплайсинга более эффективным является использование коммутаторов группы. Предложены различные варианты описания альтернативного сплайсинга.
Ключевые слова: сплайсинг РНК, белковый сплайсинг, группа ISO(2).
Summary
Stcherbic V. V., Buchatsky L. P. Group of alternatives and splicing phenomenon.
Group of alternatives, ISO(2) group, was used to consider main intron diagrams at RNA splicing and intein diagram at protein splicing. Application of internal automorphism of group ISO(2) was shown to be sufficient for description of simple intron diagrams, whereas the use of group commutators was more effective for description of alternative splicing. Different variants are proposed to describe alternative splicing.
Key words: RNA splicing, protein splicing, group ISO(2).
Рецензент: д. біол.н., проф. В.К. Рибальченко

УДК 577.218

Киевский национальный университет имени Тараса Шевченко

Украина, 01601, г. Киев, ул. Владимирская, 64/13

Taras Shevchenko National University of Kyiv

64/13, Volodymyrska Street, City of Kyiv, Ukraine, 01601

1stcherbic_v@bigmir.net

2irido1@bigmir.net

RNA splicing and protein splicing belong to most important biochemical processes underlying the conservation and transformation of genetic information [1]. RNA splicing exhibits a mosaic of genes showing partial independence of RNA information from the primary gene sequence transcribed on DNA matrix.

 RNA splicing, in other words, cutting out of RNA fragments (introns) and ligation together of remained RNA pieces (exons), takes place after DNA transcription. There are two large groups of introns: group I introns with linear structure and group II introns forming lariat structures. Group I and II introns possess autocatalytic activity, that is, they are ribozymes. Group II introns in pre-mRNA are cut out by spliceosome. Group I intron splicing occurs in the presence of the external guanosine cofactor. Moreover, group I introns may function as nucleotidyl transferases and endoribonucleases. Cofactors are not required for cutting out group II introns; splicing initiation is carried out by internal adenine of intron. There is also alternative splicing, trans-splicing and tRNA-splicing. In addition to RNA splicing, there is protein splicing.

 Splicing biochemistry is most complicated [2]. To initiate splicing, specified 3'- and 5'-sequences must be available. Splicing is catalyzed by a large complex (spliceosome) composed of RNA and proteins. Spliceosome includes five small nuclear ribonucleoproteins (snRNPs) – U1, U2, U4, U5 and U6. RNA from content of snRNP interacts with intron and, possibly, takes part in catalysis. It takes place in splicing of introns that contain GU in 5'-site and AG in 3'-site of the splicing. Sometimes in the process of maturation, mRNA may go through alternative splicing, during which introns from the content of pre-mRNA are cut out in various alternative combinations with possible frequent cutting out of exons. Alternative splicing of pre-mRNA from one gene leads to the formation of many mRNAs and proteins coded by them.

 Enzyme conception changed when RNA self-splicing was discovered [3]: besides proteins, RNAs can also possess enzymatic activity. Yet more surprising is alternative splicing [4], when different protein molecules are produced from one gene. Alternative splicing is a characteristic feature of RNA processing in eucaryotes. Trans-splicing introns [5] sometimes looks as alternatives, when from a point of adenine site there may be observed RNA ramification.

 Functional differences between RNA and proteins became still less, when in 1990 T. Stevens group discovered the phenomenon of protein auto-splicing [6].

Group of alternatives

 Different types of splicing are characterized by high accuracy of the intron cutting out [7]. Alternative splicing, carried out by spliceosomes, resembles a deterministic chaos: on the one hand, the alternative has a probabilistic nature, but, on the other hand, it is characterised by the high accuracy of RNA splicing. One may supposed that the alternative is controlled by the symmetry of the splicing process – a continuous group.

 Classic representation of groups (functional) are extensively used in quantum mechanics [8]. Vectors of states are connected between themselves through the symmetry of groups. In quantum mechanics, measuring the result of a physical process nearly always strongly decreases the role of the state symmetry. However, in biological systems, enzymes are active molecules, which do not decrease but increase the role of the symmetry between states of a biochemical process. This leads to high accuracy of genetic information transformation, characteristic for the splicing phenomenon.

 Group of alternatives, well-known group ISO(2), cannot pretend to describe the splicing process but allows to interpret formally the intron structures. Apparently, the group ISO(2) cannot provide understanding of the GUAG rule for group II introns, as well as spliceosome existence. We also will keep of the explanation of pre-mRNA capping and polyadenylation. Besides, we want to emphasize at once that we will call the group ISO(2) representations substantiated further as alternative representations, so as they contain many non trivial vector interpretations.

 The group ISO(2) is a very simple group, which is related to the photon spin. It is a group of Euclidean plane shifts and rotations, which is well explored [9]. We use vector interpretation of the group ISO(2). Vectors of the group are fragments of RNA or protein. We use also parallel transfer of vectors at their summation.

 The group ISO(2) is a group of complex matrices of the second order, which have the following structure: where r exp ij is radius-vector of Euclidean plane; exp ia is phase factor of the same point after shift along the axis OX.

The group ISO(2) is Lie group. Generators of this group may be easily calculated; they satisfy commutator relations:

[a1, a2] = 0; [a2, a3] = a1; [a3, a1] = a2.

 In our reasoning, major role is taken to inner automorphisms of the group ISO(2), which are generated by the action of the group on itself with similarity transformation:

G(a0, r0, j0) ® G(a, r, j) G(a0, r0, j0) G(a, r, j)-1,

that is, three vectors are taken instead of one vector of the group ISO(2). Commutators of the group are also used.

 Equation of the alternative may be recorded as automorphism of the group ISO(2) in the form gs = gg0g-1, where

 Figure 1 shows diagrams of the group ISO(2) alternatives.

 Vectors of the direct alternative are linearly independent, when vectors of the inverse alternative are dependent on arrangement of the direct alternative vectors. At summation of alternative vectors into one vector, it is supposed that their reference point maintains immovable. Any vector orientation always may be changed through shifting the reference point of its phase by the angle 180º.

 

Intron diagrams . It is clear that one may obtain only linear intron of the group I when mechanically adding vectors of alternative into one vector. Therefore, parallel transfer of vectors and their mutual arrangement plays a key role in construction of intron diagrams.

 Figure 2 shows basic intron diagrams at splicing of RNA and proteins. Further, we describe each intron diagram in detail.

Alternative splicing. The use of the group ISO(2) automorphism for interpretation of alternative splicing is not effective because of strong mutual dependence of the vectors. Therefore, we will consider group vector transformation not on the basis of automorphism, but on the basis of inverse intron transformation, that is, embedding of introns into group commutators. Each intron is included between exones which inverse group elements are associated with intron.

 Let us consider the simplest case, when two introns or one intron are cut out from the initial RNA transcript (Figure 3).

Each cuting out intron is surrounded by two opposite exones in inverse order. On splicing diagrams (Figure 4), exon vectors remain in the reference point and intron vectors are forming lariat.

 Alternative splicing with partial cutting out of exon (Figure 5).

The group element is recorded in two versions, because two inverse elements of the group ISO(2) are sufficient to cut out one intron.

 Figure 6 shows diagrams of the reduced version of alternative splicing with partial cutting out of exon.

 Alternative splicing of RNA from virus SV40 (Figure 7). Here small T-antigen, equals to the sum of exon ex1 and intron in1, comes to an end inside intron (in1 + in2) [14], therefore additional fictious vector r5 must be introduced to build correctly the commutator.

 Figure 8 shows diagrams of alternative splicing of T-antigens of the virus SV40.

 

 In general, alternative diagrams of introns are present at alternative splicing. Here the group ISO(2) is no homogeneous. Besides, addition of exon vectors is carried out in succession, which is collinear to the exon succession in pre-mRNA, because the group ISO(2) do not suppose any ordering at vector summation.

Литература
1. Сингер М. Гены и геномы / M. Сингер, П. Берг. - Москва: Мир, 1998. - 391 с.
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3. Cech T.R. In vitro splicing of the ribosomal RNA precursor of Tetrahymena: involment of a guanosine nucleotide in the excision of the intervening sequence / T.R. Cech, A.G. Zaug, P.J. Grabowski // Cell – 1981. - Vol. 27. – P. 487–496.
4. McManus C.J. RNA structure and the mechanisms of alternative splicing / C.J. McManus, B.R. Gravely // Curr. Opin. Genet. Dev. – 2011. - Vol. 21. – P. 373–379.
5. Trans and cis splicing in trypanosamids: mechanism, factors and regulation / X. Liang, A. Haritan, S. Uliel, S. Michaeli // Eukar. Cell. – 2003. - Vol. 2. – P. 830–840.
6. Protein splicing converts the yeast TFP1 gene product to the 69-kD subunit of the vacuolar H(+)-adenosine triphosphatase / P.M. Kane, C.T. Yamashiro, D.F. Wolczyk [е.а.] // Science. – 1990. - Vol. 250. – P. 651–657.
7. Watson James D. Molecular biology of the gene. Chapter 13 / RNA Splicing / James D. Watson. -841 p.
8. Петрашень М.И. Применение теории групп в квантовой механике / М.И. Петрашень, Е.Д. Трифонов. - М.: Наука, 1967. - 308 с.
9. Виленкин Н.Я. Специальные функции и теория представлений групп / Н.Я. Виленкин. - М.: Наука, 1965. - 588 с.
10. Nielsen H. Group I introns. Moving in new directions / H. Nielsen, S.D. Johansen // RNA Biology. – 2009. - Vol. 6. – P. 375–383.
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12. Ralph D. Physical identification of branched intron side-products of splicing in Trypanosoma brucei / D. Ralph, J. Huang, L.H.T. Van der Ploeg // EMBO J. – 1988. - Vol. 7. – P. 2539–2545.
13. Clarke N.D. A proposed mechanism for self-splicing of proteins / N.D. Clarke // Proc. Natl. Acad. Sci. USA. – 1994. - Vol. 91. – P. 11084–11088.
14. Noble J.C.S. Alternative splicing of SV40 early pre-mRNA is determined by branch site selection / J.C.S. Noble, C. Prives, J.L. Manley // Genes & Dev. – 1988. - Vol. 2. – P. 1460–1475.

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