Mathematical embryology: the fluid mechanics of nodal cilia
Mathematical embryology: the fluid mechanics of nodal cilia
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DOI：
10.1007/s10665-010-9383-y
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发表时间：
2011-07-01
影响因子：
1.3
通讯作者：
Blake, J. R.
中科院分区：
文献类型：
--
作者：
Smith, D. J.;Smith, A. A.;Blake, J. R.
左右对称性破缺对脊椎动物胚胎发育至关重要;在许多物种中，这个过程始于纤毛驱动的“节点”结构中的流动。初级'旋转'纤毛，向后倾斜，向左运输含形态发生素的囊泡，开始左右不对称的发展。最近的理论模型的基础上的点力stokeslet和点扭矩rotlet奇点，解释如何旋转和表面倾斜产生定向流进行审查。图像奇异性系统执行无滑移条件的分析表明，倾斜旋转如何产生远场的“应力波”定向流，以及如何在这方面的时间相关的点力和时间无关的点扭矩模型是等效的。相关的细长体理论分析进行审查，这种方法使高效和准确的三维随时间变化的流，时间依赖性是必不可少的预测功能的流，如混沌平流，随后已被实验确定的模拟。一个新的模型，节点流利用正则化stokeslet方法开发，以模拟覆盖Reichert的膜的效果。封闭域内的速度场和粒子路径的计算和比较与以前的“膜无”模型预测的流量剖面。计算证实，膜的存在下产生的流动逆转在上部区域，但没有连续区域的反向流动接近上皮。在膜模型中，应力波远场不再明显，这是由于腔的深度与纤毛长度的大小相似。模拟预测，囊泡释放在一个纤毛长度的上皮细胞通常被运送到左边通过一个'loopy漂移'的议案，有时涉及高度不可预测的迂回周围纤毛。纤毛顶端上方释放的颗粒预计不会到达节点的最边缘，而是通过逆流返回到右侧。流向纤毛阵列右侧和左侧的流量非常小，这表明颗粒有效运输到淋巴结末端需要纤毛一直分布到边缘。除了靠近淋巴结后缘的区域外，靠近上皮细胞处没有连续的淋巴结血流层。未来的工作将涉及调查的问题，如节点和纤毛分布的精确形状和平流和扩散对形态发生的影响，从而更充分地解释流体力学在这一重要的发展过程中的作用。
Left-right symmetry breaking is critical to vertebrate embryonic development; in many species this process begins with cilia-driven flow in a structure termed the 'node'. Primary 'whirling' cilia, tilted towards the posterior, transport morphogen-containing vesicles towards the left, initiating left-right asymmetric development. Recent theoretical models based on the point-force stokeslet and point-torque rotlet singularities, explaining how rotation and surface-tilt produce directional flow are reviewed. Analysis of image-singularity systems enforcing the no-slip condition shows how tilted rotation produces a far-field 'stresslet' directional flow, and how time-dependent point-force and time-independent point-torque models are in this respect equivalent. Associated slender-body-theory analysis is reviewed; this approach enables efficient and accurate simulation of three-dimensional time-dependent flow, time-dependence being essential in predicting features of the flow such as chaotic advection, which have subsequently been determined experimentally. A new model for the nodal flow utilising the regularized stokeslet method is developed, to model the effect of the overlying Reichert's membrane. Velocity fields and particle paths within the enclosed domain are computed and compared with the flow profiles predicted by previous 'membrane-less' models. Computations confirm that the presence of the membrane produces flow-reversal in the upper region, but no continuous region of reverse flow close to the epithelium. The stresslet far-field is no longer evident in the membrane model, due to the depth of the cavity being of similar magnitude to the cilium length. Simulations predict that vesicles released within one cilium length of the epithelium are generally transported to the left via a 'loopy drift' motion, sometimes involving highly unpredictable detours around leftward cilia. Particles released just above the cilia tips were not predicted to reach to the extreme edges of the node, but rather are returned to the right by the counterflow. Flow to the right and left of the cilia array is of very small magnitude, suggesting that effective transport of particles to the extremities of the node requires cilia to be distributed all the way to the edges. There is no continuous layer of rightward flow close to the epithelium, except for a region close to the posterior edge of the node. Future work will involve investigating issues such as the precise shape of the node and cilia distribution and the effect of advection and diffusion on morphogens, hence explaining more fully the role of fluid mechanics in this vital developmental process.