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Fuzzy system model for gene expression

机译:基因表达的模糊系统模型

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Background The theoretical information of a gene is contained in cell’s genetic materials, namely, DNA, mRNA and proteins. In the synthesis of functional gene products, this information can be expressed in mathematical way. Aim In this paper, a fuzzy approach is used to analyse of the behaviour of a gene expression in a cell. The main aim of the present study is to unravel the complexity of gene expression and develop the mathematical model which can be used for better insight of functional gene products. Subjects and methods The model for gene expression is obtained in terms of the system of fuzzy differential equations assuming that the transcription and translation processes are taking place in the cell. The Michaelis–Menten’s mechanism is incorporated in the model. Results The analytic solution for crisp case as well as for fuzzy case is carried out. The sensitivity analysis is also performed and it is observed that the model is highly stable. Conclusion The model for gene expression is obtained in terms of system of differential equations involving fuzzy initial values using geometric approach. The numerical results have been obtained for TJK16 strain of E.coli. The semi temporal concentrations profile of DNA, mRNA and protein are obtained and sensitivity analysis has been performed to study the variation in concentrations of DNA, mRNA and protein with respect to variation in transcription and translation rates.
机译:背景技术基因的理论信息包含在细胞的遗传物质中,即DNA,mRNA和蛋白质。在功能基因产物的合成中,该信息可以数学方式表示。目的在本文中,模糊方法用于分析细胞中基因表达的行为。本研究的主要目的是阐明基因表达的复杂性,并开发可用于更好地了解功能基因产物的数学模型。主题和方法假设转录和翻译过程在细胞中进行,则根据模糊微分方程组获得基因表达模型。该模型中包含了Michaelis–Menten的机制。结果对脆性情况和模糊情况进行了解析。还进行了敏感性分析,并且观察到该模型是高度稳定的。结论使用几何方法,根据涉及模糊初始值的微分方程组,获得了基因表达模型。对于大肠杆菌的TJK16菌株已经获得了数值结果。获得了DNA,mRNA和蛋白质的半时间浓度曲线,并进行了敏感性分析,以研究DNA,mRNA和蛋白质的浓度相对于转录和翻译速率的变化。

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