National Institute for Mathematical Sciences, Daejeon, 34047, Republic of Korea.
Bull Math Biol. 2018 Mar;80(3):583-597. doi: 10.1007/s11538-018-0390-x. Epub 2018 Jan 17.
In this paper, a mathematical model of contractile ring-driven cytokinesis is presented by using both phase-field and immersed-boundary methods in a three-dimensional domain. It is one of the powerful hypotheses that cytokinesis happens driven by the contractile ring; however, there are only few mathematical models following the hypothesis, to the author's knowledge. I consider a hybrid method to model the phenomenon. First, a cell membrane is represented by a zero-contour of a phase-field implicitly because of its topological change. Otherwise, immersed-boundary particles represent a contractile ring explicitly based on the author's previous work. Here, the multi-component (or vector-valued) phase-field equation is considered to avoid the emerging of each cell membrane right after their divisions. Using a convex splitting scheme, the governing equation of the phase-field method has unique solvability. The numerical convergence of contractile ring to cell membrane is proved. Several numerical simulations are performed to validate the proposed model.
本文采用相场法和浸入边界法在三维域中建立了收缩环驱动胞质分裂的数学模型。这是胞质分裂由收缩环驱动的有力假设之一；然而，据作者所知，只有少数数学模型遵循这一假设。我考虑使用混合方法来模拟这一现象。首先，细胞膜通过相场的零轮廓来表示，因为细胞膜的拓扑发生了变化。否则，根据作者之前的工作，浸入边界粒子显式地表示收缩环。这里，多分量（或向量值）相场方程被用来避免在细胞分裂后立即出现每个细胞膜。使用凸分裂方案，相场方法的控制方程具有唯一的可解性。证明了收缩环到细胞膜的数值收敛性。进行了几个数值模拟来验证所提出的模型。
