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Article information
2015 , Volume 20, ¹ 1, p.38-52
Kogai V.V., Khlebodarova T.M., Fadeev S.I., Likhoshvai V.A.
Complex dynamics in alternative mRNA splicing: mathematical model
Purpose. Development of computational methods for analyzing dynamic parameters of a set of two-dimensional differential equations with retarding arguments is proposed. The set describes the minimal genetic system of alternative splicing. This aim is motivated by the necessity of investigation for relationships between the structure-functional organization of gene networks and their dynamic properties. As the molecular processes occurring in gene networks are nonlinear and the networks contain regulatory loops, gene networks are dissipative systems capable of extremely intricate dynamic behavior. Alternative splicing (AS) is a widespread mechanism contributing to the functional diversity of proteins in higher eukaryotes. About 95 % of RNAs synthesized in a human body undergo AS; that is, AS is a component of nearly all gene networks. If AS results in the production of two isoforms of a transcription factor protein controlling the expression of its own gene via a feedback loop, such system naturally could generate conditions for formation of complex behavior. This study analyzes the dynamic properties of a model in which isoforms of a transcription factors are dimers performing opposite regulatory functions: one protein is an activator, and the other, repressor. Methodology. The approach to the numerical analysis for the dynamic properties of the model involves the reduction of the initial problem to a boundary problem with periodicity conditions for the set of ordinary differential equations whose structure is determined by retardation setting. The analysis is done by parameter continuation of the solution. Findings. Numerical analysis of the model solutions reveals a complex time variation of the concentrations of the activator and repressor isoforms. It manifests itself as multiple periodic solutions and period doubling according to the Feigenbaum scenario. Value. An oscillatory pattern of protein concentration values is demonstrated in the model with parameters falling in the physiological range of functioning of such systems in eukaryotes. Thus, they may occur in natural AS systems.
Keywords: modeling, genetic networks, transcription, alternative splicing, equations with delayed arguments, periodic solutions, flip bifurcation
Author(s):
Kogai Vladislav Vladimirovich
PhD.
Position: Senior Research Scientist
Office: Sobolev Institute of Mathematics of SB RAS
Address: 630090, Russia, Novosibirsk, Prospekt Academika Koptyga, 4
Phone Office: (383) 363-46-95
E-mail: kogai@math.nsc.ru
Khlebodarova Tamara Mikhailovna
Dr.
Position: Leading research officer
Office: Institute of Cytology and Genetics of Siberian Branch of Russian Academy of Sciences
Address: 630090, Russia, Novosibirsk, Prospekt Academika Lavrentyeva, 10
Phone Office: (383) 363-49-69
E-mail: tamara@bionet.nsc.ru
Fadeev Stanislav Ivanovich
Dr. , Professor
Position: General Scientist
Office: Sobolev Institute of Mathematics of SB RAS, Novosibirsk state university
Address: 630090, Russia, Novosibirsk, Prospekt Academika Koptyga, 4
Phone Office: (383) 329-76-80
E-mail: fadeev@math.nsc.ru
Likhoshvai Vitali Aleksandrovich
Dr.
Position: Leading research officer
Office: Institute of Cytology and Genetics of SB RAS
Address: 630090, Russia, Novosibirsk, Prospekt Academika Lavrentyeva, 10
Phone Office: (383)363-49-69
E-mail: likho@bionet.nsc.ru
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Bibliography link:
Kogai V.V., Khlebodarova T.M., Fadeev S.I., Likhoshvai V.A. Complex dynamics in alternative mRNA splicing: mathematical model // Computational technologies. 2015. V. 20. ¹ 1. P. 38-52
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