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基于Delta-Notch信号通路的大肠边界形成改进分数阶模型分析

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

作者信息

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

机构信息

Shenzhen Key Laboratory of Tissue Engineering, Shenzhen Laboratory of Digital Orthopedic Engineering, Shenzhen Second People's Hospital, The First Hospital Affiliated to Shenzhen University, Health Science Center, Shenzhen, 518035 P.R. China.

Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518035 P.R. China.

出版信息

Adv Differ Equ. 2020;2020(1):377. doi: 10.1186/s13662-020-02836-1. Epub 2020 Jul 23.

DOI:10.1186/s13662-020-02836-1
PMID:32834816
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7376541/
Abstract

In this paper, an improved fractional-order model of boundary formation in the 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.

摘要

本文首次提出了一种改进的依赖Delta-Notch信号通路的大肠边界形成分数阶模型。研究了解的唯一性、非负性和有界性。在双细胞模型中，存在两个平衡点（Delta无表达和Delta正常表达）。证明了两种情况下的局部渐近稳定性。稳定性分析表明，分数阶微分方程模型的阶数会显著影响双细胞模型中的平衡点。给出了数值模拟以说明这些结论。接下来，计算了模型参数的敏感性，计算结果表明不同参数具有不同的敏感性。通过数值模拟验证了双细胞模型和60细胞模型中最敏感和最不敏感的参数。此外，我们通过模拟将分数阶模型与整数阶模型进行比较，结果表明阶数会显著影响动力学和表型。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/817f95f75468/13662_2020_2836_Fig13_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/817f95f75468/13662_2020_2836_Fig13_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/125527914610/13662_2020_2836_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/2d5674d9ecdc/13662_2020_2836_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/eac8d9c360fa/13662_2020_2836_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/ec7a89ebc2a3/13662_2020_2836_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/d398351f9edf/13662_2020_2836_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/fc466d32f976/13662_2020_2836_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/17a46470903b/13662_2020_2836_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/8392dad83577/13662_2020_2836_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/529cde7c8c3c/13662_2020_2836_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/a937bbf4dfd1/13662_2020_2836_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/efe8382bc28b/13662_2020_2836_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/09b666f6a4a3/13662_2020_2836_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4496/7376541/817f95f75468/13662_2020_2836_Fig13_HTML.jpg

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