一个Tessellation的成长:鱼骨模式的发展的几何规则
Binru Yang1,2, David Knötel3, Jana Ciecierska-Holmes1,2,4
1Max Planck Institute of Colloids and Interfaces, Potsdam Science Park, Am Mühlenberg 1 OT Golm, 14476, Potsdam, Germany.
Advanced science (Weinheim, Baden-Wurttemberg, Germany)
|November 7, 2024
概括
鱼和鱼骨扩张,同时通过更大的矿化 (tesserae) 的更快增长保持连续覆盖. 这种生物适应骨生长,挑战了简单的数学模型.
科学领域:
- 发展生物学 发展生物学
- 生物矿物化 生物矿物化
- 数学生物学 数学生物学
背景情况:
- 鱼和鱼骨是由软骨制成的,并被矿物化所覆盖,称为tesseras.
- 骨扩张对保持连续的形覆盖面构成了挑战.
研究的目的:
- 为了研究如何模块化模式适应鱼的骨生长.
- 分析底层的数学和生物机制,以分析图形的排列和生长.
主要方法:
- 微型计算机断层扫描 (microCT) 扫描正在生长的鱼下.
- 定制的视觉数据分析,以检查图形图案和形态.
- 在骨发育过程中分析形分布和生长速度.
主要成果:
- 尽管部长度增加了两倍,但部数量仍然保持不变.
- 特塞拉分布是自我相似的,由六边形,五边形和七边形主导.
- 较大的体呈现出更快的生长速度以适应骨扩张,偏离了均生长假设.
结论:
- 鱼和鱼的骨扩张是通过特塞拉的差异增长来适应的,而不是通过改变它们的数量.
- 观察到的模块化图案接近多面体规则,但显示了欧勒定律的缺陷.
- 局部调节的 tesserae 增长,可能由机械张力和细胞反应驱动,保持全球系统的复杂性.
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