Spill Fabian, Andasari Vivi, Mak Michael, Kamm Roger D, Zaman Muhammad H
Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston MA 02215, USA. Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.
Phys Biol. 2016 Jun 25;13(3):036008. doi: 10.1088/1478-3975/13/3/036008.
During cell migration, cells become polarized, change their shape, and move in response to various internal and external cues. Cell polarization is defined through the spatio-temporal organization of molecules such as PI3K or small GTPases, and is determined by intracellular signaling networks. It results in directional forces through actin polymerization and myosin contractions. Many existing mathematical models of cell polarization are formulated in terms of reaction-diffusion systems of interacting molecules, and are often defined in one or two spatial dimensions. In this paper, we introduce a 3D reaction-diffusion model of interacting molecules in a single cell, and find that cell geometry has an important role affecting the capability of a cell to polarize, or change polarization when an external signal changes direction. Our results suggest a geometrical argument why more roundish cells can repolarize more effectively than cells which are elongated along the direction of the original stimulus, and thus enable roundish cells to turn faster, as has been observed in experiments. On the other hand, elongated cells preferentially polarize along their main axis even when a gradient stimulus appears from another direction. Furthermore, our 3D model can accurately capture the effect of binding and unbinding of important regulators of cell polarization to and from the cell membrane. This spatial separation of membrane and cytosol, not possible to capture in 1D or 2D models, leads to marked differences of our model from comparable lower-dimensional models.
在细胞迁移过程中，细胞会发生极化，改变其形状，并根据各种内部和外部线索移动。细胞极化是通过诸如PI3K或小GTP酶等分子的时空组织来定义的，并由细胞内信号网络决定。它通过肌动蛋白聚合和肌球蛋白收缩产生定向力。许多现有的细胞极化数学模型是根据相互作用分子的反应扩散系统来制定的，并且通常在一个或两个空间维度中定义。在本文中，我们引入了一个单细胞中相互作用分子的三维反应扩散模型，并发现细胞几何形状在影响细胞极化能力或当外部信号改变方向时改变极化方面具有重要作用。我们的结果提出了一个几何学观点，即为什么更圆的细胞比沿原始刺激方向拉长的细胞能够更有效地重新极化，从而使圆细胞能够更快地转向，这正如实验中所观察到的那样。另一方面，即使当梯度刺激从另一个方向出现时，细长细胞也优先沿其主轴极化。此外，我们的三维模型可以准确地捕捉细胞极化重要调节因子与细胞膜结合和解离的影响。这种膜和细胞质的空间分离在一维或二维模型中无法捕捉到，导致我们的模型与类似的低维模型存在显著差异。
