对Hes1-mRNA相互作用的延迟反应扩散模型的稳定周期溶液
Mohammed Alanazi1, Majid Bani-Yaghoub1, Bi-Botti C Youan2
1Division of Computing, Analytics & Mathematics, School of Science and Engineering, University of Missouri-Kansas City, 5100 Rockhill Rd., Kansas City, Missouri 64110, USA.
Mathematical biosciences and engineering : MBE
|September 3, 2025
概括
这项研究引入了Hes1 (毛发和分裂1的增强剂) 基因表达的新数学模型,包括时间延迟和扩散. 该模型成功地产生了持续的Hes1振荡,这对于胚胎发生和细胞命运至关重要.
科学领域:
- 发育生物学
- 系统生物学
- 数学生物学
背景情况:
- Hes1 (分裂1的毛发和增强剂) 是一个关键的转录抑制剂,调节胚胎生成和细胞系特征.
- 在Hes1 mRNA和蛋白质中持续的振荡是生物学观察到的,但通常不会被现有的数学模型重现.
- 模型中的短暂波动限制了它们的生物忠实性和预测能力.
研究的目的:
- 为Hes1表达力学开发一个更具生物现实的数学框架.
- 研究时间延迟和空间扩散在产生持续的HES1振荡中的作用.
- 在Hes1表达中建立稳定,持久的振荡条件.
主要方法:
- 制定了一个具有离散时间延迟的反应扩散 (RD) 系统来建模Hes1的时空动态.
- 对延迟诱导的Hopf分叉进行分析,以确定稳定周期溶液的条件.
- 数字模拟以验证理论预测并评估参数的灵敏度.
主要成果:
- 提出的 RD 模型具有时间延迟和扩散,成功产生持续的 Hes1 振荡.
- 确定了延迟和扩散系数的明确标准,以确保持续的振荡模式.
- 数字模拟证实了在生物可信的参数下振荡的稳定性和持续性.
结论:
- 将时间延迟和扩散纳入数学模型对于准确地表示HES1持续振荡至关重要.
- 开发的RD框架提供了对Hes1基因调节动态的更准确的表现.
- 这种模型提高了我们对发育过程中振荡基因表达的机制的理解.
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