在球体上形成的图灵图案是强大的,可以去除一个洞
Johannes G Borgqvist1, Philip Gerlee2,3, Carl Lundholm4
1Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building Radcliffe Observatory Quarter (550) Woodstock Road, Oxford, Oxfordshire, OX2 6GG, UK. johannes.borgqvist@gmail.com.
Journal of mathematical biology
|January 31, 2024
概括
由Cdc42蛋白质扩散和反应驱动的起芽酵母细胞生长,尽管有芽痕,但仍然有效. 芽痕作为细胞膜上的洞的数学建模表明,模式形成是强大的,支持扩散驱动的不稳定性.
科学领域:
- 细胞生物学 细胞生物学
- 数学建模的数学建模
- 生物物理学的生物物理.
背景情况:
- 发芽酵母细胞分裂涉及蛋白质Cdc42,通过反应-扩散过程驱动芽的形成.
- 施纳肯伯格系统,一组部分微分方程,模拟这些过程,并以扩散驱动的模式形成而闻名.
- 累积的芽痕对这种模式形成机制的影响还不太清楚.
研究的目的:
- 为了研究酵母细胞膜上的芽痕如何影响由施纳肯伯格系统支配的模式形成.
- 以球形细胞表面上的几何修饰 (孔) 来建模芽痕.
- 在存在这些几何变化的情况下,分析扩散驱动模式形成的稳定性.
主要方法:
- 模拟芽痕作为球形细胞膜上的洞.
- 分析了洞大小对拉普拉斯-贝尔特拉米运算子光谱的影响.
- 用有限元法在一个有洞的球体上数量解决了施纳肯伯格系统.
主要成果:
- 理论预测和数值模拟表明,模式形成是强大的存在显著的芽痕大小.
- 拉普拉斯-贝尔特拉米运算子的光谱被证明会受到模拟孔的大小的影响.
- 尽管发生了几何学破坏,但Schnakenberg系统的模式形成能力在很大程度上被保留了下来.
结论:
- 这项研究支持这样一个假设:酵母菌中芽的形成是由扩散驱动的不稳定性驱动的.
- 芽酵母中的模式形成对芽痕引入的几何变化具有弹性.
- 数学建模为细胞形态发生的生物物理机制提供了宝贵的见解.
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