在一个低维基因调节网络中,切换,多个时间尺度和几何膨胀
Samuel Jelbart1, Kristian Uldall Kristiansen2, Peter Szmolyan3
1School of Computer and Mathematical Sciences, The University of Adelaide, Ingkarni Wardli, Frome Road, Adelaide, 5005, South Australia, Australia. sam.jelbart@adelaide.edu.au.
Journal of mathematical biology
|December 29, 2025
概括
本研究使用单一扰动方法探索基因调节网络 (GRNs) 的缩小模型. 这些发现强调了参数大小对于准确的GRN动态和模型减少有效性的重要性.
科学领域:
- 系统生物学 系统生物学
- 计算生物学 计算生物学
- 数学生物学 数学生物学
背景情况:
- 基因调节网络 (GRN) 模型通常涉及多个小参数的普通微分方程 (ODEs).
- 这些参数与时间尺度的分离和"切换"行为有关,接近非平滑的极限.
- 标准的减速方法,如准稳定状态减速 (QSSR),利用时间尺度的分离,但可能会错过关键的动态.
研究的目的:
- 为了研究QSSR和GRN模型的片式平滑近似之间的相互作用.
- 使用奇点扰动理论和Fenichel的定理,严格缩小一个4D GRN模型.
- 分析较高阶项对减少GRN模型的定性动态的影响.
主要方法:
- 制定一个4D GRN模型作为一个在膨胀空间上的光滑的奇异扰动系统.
- 应用Fenichel的无坐标定理用于严格的系统缩小.
- 对缩小的二维系统的分析,包括其来自QSSR的扰动,以及分叉的识别.
主要成果:
- 确定了一个参数区域,允许在异常扰乱的GRN中统一处理切换行为.
- 实现了将4D GRN严格减少到2D系统,这是QSSR的扰动.
- 在缩小系统中发现了一个霍夫分叉,在QSSR中缺席,由于更高阶术语的影响.
结论:
- 小参数的相对大小对GRNs中QSS减值的有效性具有关键影响.
- 高阶术语,在QSSR中经常被忽视,可以在GRN动态中引入显著的定性变化.
- 开发的方法适用于更高维度的GRN模型,提供更强大的分析框架.
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