A coupled bulk-surface model for cell polarisation
A coupled bulk-surface model for cell polarisation
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DOI：
10.1016/j.jtbi.2018.09.008
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发表时间：
2019-11-21
影响因子：
2
通讯作者：
Madzvamuse, A.
中科院分区：
文献类型：
--
作者：
Cusseddu, D.;Edelstein-Keshet, L.;Madzvamuse, A.
几种细胞活动，如定向细胞迁移，由复杂的生化反应网络协调，导致细胞的极化状态，其中细胞对称性被打破，导致细胞具有明确的前部和后部。最近的工作平衡生物复杂性与数学的易处理性导致了一个著名的最小模型的建议和制定细胞极化，被称为波钉扎模型。在这项研究中，我们提出了一个三维的概括这个数学框架，通过成熟的理论耦合体表面半线性偏微分方程，其中蛋白质区室化成为自然。我们展示了如何在表面上的局部扰动可以触发传播反应，最终停止在一个稳定的配置文件与散装组件的相互作用。我们通过渐近和局部扰动分析，其中的几何形状的作用进行了研究，描述了该模型的行为。体表面有限元方法被用来生成简单和复杂的几何形状，这证实了我们的分析，显示图案的形成，由于传播和钉扎动力学的数值模拟。我们的数学和计算框架的一般性允许研究更复杂的生化反应和生物力学特性与细胞极化在多维。(C)2018爱思唯尔有限公司版权所有。
Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which cellular symmetry is broken, causing the cell to have a well defined front and back. Recent work on balancing biological complexity with mathematical tractability resulted in the proposal and formulation of a famous minimal model for cell polarisation, known as the wave pinning model. In this study, we present a three-dimensional generalisation of this mathematical framework through the maturing theory of coupled bulk-surface semilinear partial differential equations in which protein compartmentalisation becomes natural. We show how a local perturbation over the surface can trigger propagating reactions, eventually stopped in a stable profile by the interplay with the bulk component. We describe the behavior of the model through asymptotic and local perturbation analysis, in which the role of the geometry is investigated. The bulk-surface finite element method is used to generate numerical simulations over simple and complex geometries, which confirm our analysis, showing pattern formation due to propagation and pinning dynamics. The generality of our mathematical and computational framework allows to study more complex biochemical reactions and biomechanical properties associated with cell polarisation in multi-dimensions. (C) 2018 Elsevier Ltd. All rights reserved.