一种基于细胞生物力学和椭圆拟合的植物细胞分裂算法。
A plant cell division algorithm based on cell biomechanics and ellipse-fitting.
作者信息
Abera Metadel K, Verboven Pieter, Defraeye Thijs, Fanta Solomon Workneh, Hertog Maarten L A T M, Carmeliet Jan, Nicolai Bart M
出版信息
Ann Bot. 2014 Sep;114(4):605-17. doi: 10.1093/aob/mcu078.
BACKGROUND AND AIMS
The importance of cell division models in cellular pattern studies has been acknowledged since the 19th century. Most of the available models developed to date are limited to symmetric cell division with isotropic growth. Often, the actual growth of the cell wall is either not considered or is updated intermittently on a separate time scale to the mechanics. This study presents a generic algorithm that accounts for both symmetrically and asymmetrically dividing cells with isotropic and anisotropic growth. Actual growth of the cell wall is simulated simultaneously with the mechanics.
METHODS
The cell is considered as a closed, thin-walled structure, maintained in tension by turgor pressure. The cell walls are represented as linear elastic elements that obey Hooke's law. Cell expansion is induced by turgor pressure acting on the yielding cell-wall material. A system of differential equations for the positions and velocities of the cell vertices as well as for the actual growth of the cell wall is established. Readiness to divide is determined based on cell size. An ellipse-fitting algorithm is used to determine the position and orientation of the dividing wall. The cell vertices, walls and cell connectivity are then updated and cell expansion resumes. Comparisons are made with experimental data from the literature.
KEY RESULTS
The generic plant cell division algorithm has been implemented successfully. It can handle both symmetrically and asymmetrically dividing cells coupled with isotropic and anisotropic growth modes. Development of the algorithm highlighted the importance of ellipse-fitting to produce randomness (biological variability) even in symmetrically dividing cells. Unlike previous models, a differential equation is formulated for the resting length of the cell wall to simulate actual biological growth and is solved simultaneously with the position and velocity of the vertices.
CONCLUSIONS
The algorithm presented can produce different tissues varying in topological and geometrical properties. This flexibility to produce different tissue types gives the model great potential for use in investigations of plant cell division and growth in silico.
背景与目的
自19世纪以来，细胞分裂模型在细胞模式研究中的重要性已得到认可。迄今为止开发的大多数现有模型仅限于具有各向同性生长的对称细胞分裂。通常，细胞壁的实际生长要么未被考虑，要么在与力学不同的时间尺度上间歇性更新。本研究提出了一种通用算法，该算法考虑了具有各向同性和各向异性生长的对称和不对称分裂细胞。细胞壁的实际生长与力学同时进行模拟。
方法
将细胞视为一个封闭的薄壁结构，通过膨压保持张力。细胞壁表示为服从胡克定律的线性弹性元件。细胞膨胀由作用于可屈服细胞壁材料的膨压引起。建立了一个关于细胞顶点位置和速度以及细胞壁实际生长的微分方程组。根据细胞大小确定分裂准备状态。使用椭圆拟合算法确定分裂壁的位置和方向。然后更新细胞顶点、壁和细胞连通性，细胞膨胀恢复。与文献中的实验数据进行比较。
关键结果
通用植物细胞分裂算法已成功实现。它可以处理与各向同性和各向异性生长模式相结合的对称和不对称分裂细胞。该算法的开发突出了椭圆拟合在产生随机性（生物变异性）方面的重要性，即使在对称分裂的细胞中也是如此。与以前的模型不同，为细胞壁的静止长度建立了一个微分方程，以模拟实际的生物生长，并与顶点的位置和速度同时求解。
结论
所提出的算法可以产生拓扑和几何性质不同的组织。这种产生不同组织类型的灵活性使该模型在植物细胞分裂和生长的计算机模拟研究中具有巨大的应用潜力。
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