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Your search keyword '"Delta-Notch signaling pathway"' showing total 3 results
Start Over Descriptor "Delta-Notch signaling pathway" Journal advances in difference equations
3 results on '"Delta-Notch signaling pathway"'

1. Analysis of an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway

Author

Deshun Sun, Lingyun Lu, Fei Liu, Li Duan, Daping Wang, and Jianyi Xiong

Subjects
Delta-Notch signaling pathway, Fractional-order differential equations, Local stability analysis, Sensitive analysis, Mathematics, QA1-939
Abstract

Abstract In this paper, an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway is proposed for the first time. The uniqueness, nonnegativity, and boundedness of solutions are studied. In a two cells model, there are two equilibriums (no-expression of Delta and normal expression of Delta). Local asymptotic stability is proved for both cases. Stability analysis shows that the orders of the fractional-order differential equation model can significantly affect the equilibriums in the two cells model. Numerical simulations are presented to illustrate the conclusions. Next, the sensitivity of model parameters is calculated, and the calculation results show that different parameters have different sensitivities. The most and least sensitive parameters in the two cells model and the 60 cells model are verified by numerical simulations. What is more, we compare the fractional-order model with the integer-order model by simulations, and the results show that the orders can significantly affect the dynamic and the phenotypes.

Published
2020
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2. Analysis of an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway.

Author

Sun, Deshun, Lu, Lingyun, Liu, Fei, Duan, Li, Wang, Daping, and Xiong, Jianyi

Subjects
LARGE intestine, DROSOPHILA, DIFFERENTIAL equations, COMPUTER simulation, LAUNCH vehicles (Astronautics)
Abstract

In this paper, an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway is proposed for the first time. The uniqueness, nonnegativity, and boundedness of solutions are studied. In a two cells model, there are two equilibriums (no-expression of Delta and normal expression of Delta). Local asymptotic stability is proved for both cases. Stability analysis shows that the orders of the fractional-order differential equation model can significantly affect the equilibriums in the two cells model. Numerical simulations are presented to illustrate the conclusions. Next, the sensitivity of model parameters is calculated, and the calculation results show that different parameters have different sensitivities. The most and least sensitive parameters in the two cells model and the 60 cells model are verified by numerical simulations. What is more, we compare the fractional-order model with the integer-order model by simulations, and the results show that the orders can significantly affect the dynamic and the phenotypes. [ABSTRACT FROM AUTHOR]

Published
2020
Full Text
View/download PDF

3. Analysis of an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway

Author

Lingyun Lu, Fei Liu, Daping Wang, Li Duan, Deshun Sun, and Xiong Jianyi

Subjects
Local stability analysis, Algebra and Number Theory, Partial differential equation, Fractional-order differential equations, Differential equation, lcsh:Mathematics, Applied Mathematics, Research, 010102 general mathematics, Expression (computer science), lcsh:QA1-939, Delta-Notch signaling pathway, 01 natural sciences, Stability (probability), 010101 applied mathematics, Sensitive analysis, Exponential stability, Ordinary differential equation, Applied mathematics, Uniqueness, Sensitivity (control systems), 0101 mathematics, Analysis, Mathematics
Abstract

In this paper, an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway is proposed for the first time. The uniqueness, nonnegativity, and boundedness of solutions are studied. In a two cells model, there are two equilibriums (no-expression of Delta and normal expression of Delta). Local asymptotic stability is proved for both cases. Stability analysis shows that the orders of the fractional-order differential equation model can significantly affect the equilibriums in the two cells model. Numerical simulations are presented to illustrate the conclusions. Next, the sensitivity of model parameters is calculated, and the calculation results show that different parameters have different sensitivities. The most and least sensitive parameters in the two cells model and the 60 cells model are verified by numerical simulations. What is more, we compare the fractional-order model with the integer-order model by simulations, and the results show that the orders can significantly affect the dynamic and the phenotypes.

Published
2020

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