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Fuzzy system model for gene expression

Amit Sharma
Neeru Adlakha


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.

Keyword: Fuzzy Linear Differential equation model, DNA, mRNA, Protein, TJK16