New Approach to Gene Network Modeling
The article is devoted to the mathematical modeling of artificial genetic networks. A phenomenological model of the simplest genetic network called repressilator is considered. This network contains three elements unidirectionally coupled into a ring. More specifically, the first of them inhibits th...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2019-09-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/1230 |
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| _version_ | 1849338885878841344 |
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| author | Sergey D. Glyzin Andgey Yu. Kolesov Nikolay Kh. Rozov |
| author_facet | Sergey D. Glyzin Andgey Yu. Kolesov Nikolay Kh. Rozov |
| author_sort | Sergey D. Glyzin |
| collection | DOAJ |
| description | The article is devoted to the mathematical modeling of artificial genetic networks. A phenomenological model of the simplest genetic network called repressilator is considered. This network contains three elements unidirectionally coupled into a ring. More specifically, the first of them inhibits the synthesis of the second, the second inhibits the synthesis of the third, and the third, which closes the cycle, inhibits the synthesis of the first one. The interaction of the protein concentrations and of mRNA (message RNA) concentration is surprisingly similar to the interaction of six ecological populations — three predators and three preys. This allows us to propose a new phenomenological model, which is represented by a system of unidirectionally coupled ordinary differential equations. We study the existence and stability problem of a relaxation periodic solution that is invariant with respect to cyclic permutations of coordinates. To find the asymptotics of this solution, a special relay system is constructed. It is proved in the paper that the periodic solution of the relay system gives the asymptotic approximation of the orbitally asymptotically stable relaxation cycle of the problem under consideration. |
| format | Article |
| id | doaj-art-fdbafd0f292341f5a6ead123ca4a06ce |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2019-09-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-fdbafd0f292341f5a6ead123ca4a06ce2025-08-20T03:44:17ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172019-09-0126336540410.18255/1818-1015-2019-3-365-404916New Approach to Gene Network ModelingSergey D. Glyzin0Andgey Yu. Kolesov1Nikolay Kh. Rozov2P.G. Demidov Yaroslavl State UniversityP.G. Demidov Yaroslavl State UniversityM.V. Lomonosov Moscow State UniversityThe article is devoted to the mathematical modeling of artificial genetic networks. A phenomenological model of the simplest genetic network called repressilator is considered. This network contains three elements unidirectionally coupled into a ring. More specifically, the first of them inhibits the synthesis of the second, the second inhibits the synthesis of the third, and the third, which closes the cycle, inhibits the synthesis of the first one. The interaction of the protein concentrations and of mRNA (message RNA) concentration is surprisingly similar to the interaction of six ecological populations — three predators and three preys. This allows us to propose a new phenomenological model, which is represented by a system of unidirectionally coupled ordinary differential equations. We study the existence and stability problem of a relaxation periodic solution that is invariant with respect to cyclic permutations of coordinates. To find the asymptotics of this solution, a special relay system is constructed. It is proved in the paper that the periodic solution of the relay system gives the asymptotic approximation of the orbitally asymptotically stable relaxation cycle of the problem under consideration.https://www.mais-journal.ru/jour/article/view/1230artificial gene networkrepressilatorself-symmetric cycleasymptoticsstability |
| spellingShingle | Sergey D. Glyzin Andgey Yu. Kolesov Nikolay Kh. Rozov New Approach to Gene Network Modeling Моделирование и анализ информационных систем artificial gene network repressilator self-symmetric cycle asymptotics stability |
| title | New Approach to Gene Network Modeling |
| title_full | New Approach to Gene Network Modeling |
| title_fullStr | New Approach to Gene Network Modeling |
| title_full_unstemmed | New Approach to Gene Network Modeling |
| title_short | New Approach to Gene Network Modeling |
| title_sort | new approach to gene network modeling |
| topic | artificial gene network repressilator self-symmetric cycle asymptotics stability |
| url | https://www.mais-journal.ru/jour/article/view/1230 |
| work_keys_str_mv | AT sergeydglyzin newapproachtogenenetworkmodeling AT andgeyyukolesov newapproachtogenenetworkmodeling AT nikolaykhrozov newapproachtogenenetworkmodeling |