Computational Cell Biomechanics Team, RIKEN, 2-1 Hirosawa, Saitama, Japan.
Biomech Model Mechanobiol. 2011 Jul;10(4):495-503. doi: 10.1007/s10237-010-0250-6. Epub 2010 Aug 19.
Membrane protrusion is a mechanochemical process of active membrane deformation driven by actin polymerization. Previously, Brownian ratchet (BR) was modeled on the basis of the underlying molecular mechanism. However, because the BR requires a priori load that cannot be determined without information of the cell shape, it cannot be effective in studies in which resultant shapes are to be solved. Other cellular-scale models describing the protrusion have also been suggested for modeling a whole cell; however, these models were not developed on the basis of coarse-grained physics representing the underlying molecular mechanism. Therefore, to express the membrane protrusion on the cellular scale, we propose a novel mathematical model, the coarse-grained BR (CBR), which is derived on the basis of nonequilibrium thermodynamics theory. The CBR can reproduce the BR within the limit of the quasistatic process of membrane protrusion and can estimate the protrusion velocity consistently with an effective elastic constant that represents the state of the energy of the membrane. Finally, to demonstrate the applicability of the CBR, we attempt to perform a cellular-scale simulation of migrating keratocyte in which the proposed CBR is used for the membrane protrusion model on the cellular scale. The results show that the experimentally observed shapes of the leading edge are well reproduced by the simulation. In addition, The trend of dependences of the protrusion velocity on the curvature of the leading edge, the temperature, and the substrate stiffness also agreed with the other experimental results. Thus, the CBR can be considered an appropriate cellular-scale model to express the membrane protrusion on the basis of its underlying molecular mechanism.
膜突是由肌动蛋白聚合驱动的主动膜变形的力化学过程。先前，基于潜在的分子机制，对布朗棘轮（BR）进行了建模。然而，由于 BR 需要先验负载，而没有细胞形状的信息就无法确定，因此在需要解决最终形状的研究中，它无法有效使用。其他描述突起的细胞尺度模型也被提出用于对整个细胞进行建模；然而，这些模型不是基于代表潜在分子机制的粗粒物理来开发的。因此，为了在细胞尺度上表达膜突，我们提出了一种新的数学模型，即粗粒 BR（CBR），它是基于非平衡热力学理论推导出来的。CBR 可以在膜突的准静态过程的限制内再现 BR，并使用代表膜能量状态的有效弹性常数一致地估计突进度。最后，为了证明 CBR 的适用性，我们尝试对迁移的角膜细胞进行细胞尺度的模拟，在该模拟中，将提出的 CBR 用于细胞尺度的膜突模型。结果表明，模拟很好地再现了实验观察到的前缘形状。此外，突进度对前缘曲率、温度和基质刚度的依赖性的趋势也与其他实验结果一致。因此，CBR 可以被认为是一种合适的细胞尺度模型，它可以基于其潜在的分子机制来表达膜突。
