ON METACHRONISM IN CILIARY SYSTEMS - A MODEL DESCRIBING THE DEPENDENCE OF THE METACHRONAL WAVE PROPERTIES ON THE INTRINSIC CILIARY PARAMETERS
ON METACHRONISM IN CILIARY SYSTEMS - A MODEL DESCRIBING THE DEPENDENCE OF THE METACHRONAL WAVE PROPERTIES ON THE INTRINSIC CILIARY PARAMETERS
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DOI：
10.1002/cm.970160304
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发表时间：
1990-01-01
影响因子：
--
通讯作者：
PRIEL, Z
中科院分区：
文献类型：
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作者：
GHEBER, L;PRIEL, Z
提出了一个数学模型来解释依赖的方向和长度的异时波的参数，其特征在于纤毛拍，纤毛的尺寸，和几何形状的纤毛表面上的安排。异时波被分解成两个相互垂直的分量，这两个分量被选择成使得其中一个的方向在有效冲程的方向上。这两个分量的大小通过使用相邻纤毛之间的延迟时间的概念来确定。然后计算作为睫状体参数的函数的异时波的属性。与本模型得到的结果预测，波的传播方向是强烈依赖于类型的异时性的有效中风的方向和极化的时间和空间的纤毛拍。发现异时波长取决于四个参数：纤毛长度，恢复中风期间由纤毛尖端投射在细胞表面上的弧的角度，纤毛跳动的不对称程度，以及暂停所占据的周期的部分。异时波长也被发现是只有弱依赖于纤毛频率。在这一阶段，存在相对较少的实验信息，充分表征异时性的睫状系统。即使只有部分信息存在，该模型允许，预测，在一定范围内，波的传播方向。它还提出了一个可能的机制，在环境条件的变化对波的方向和波长的影响。在充分信息确实存在的几种情况下，实验结果和模型的预测之间有很好的一致性，根据这个模型，这将是值得投入更多的精力来测量纤毛跳动的时间作为空间极化和纤毛之间的延迟时间。
A mathematical model is proposed to explain the dependence of the direction and the length of the metachronal wave on parameters that characterize the ciliary beat, the dimensions of the cilia, and the geometry of their arrangement on the ciliated surface. The metachronal wave is decomposed into two mutually perpendicular components, which are chosen in such a way that the direction of one of them is in the direction of the effective stroke. The magnitudes of the two components are determined by using the concept of the time of delay between adjacent cilia. The properties of the metachronal wave are then calculated as a function of the ciliary parameters. The results obtained with the present model predict that the direction of the wave propagation is strongly dependent on the type of metachronism in the direction of the effective stroke and the polarization in time and in space of the ciliary beat. The metachronal wavelength is found to depend on four parameters: the ciliary length, the angle of the arc projected on the cell surface by the ciliary tip during the recovery stroke, the degree of asymmetry of ciliary beat, and the portion of the cycle occupied by the pause. The metachronal wavelength is also found to be only weakly dependent on the ciliary frequency. At this stage there exists relatively little experimental information with which to characterize fully the metachronal properties of ciliary systems. Even when only partial information exists, the model allows, prediction, to within a certain range, of the direction of the wave propagation. It also suggests a possible mechanism for the influence of changes in environmental conditions on wave direction and wavelength. In several cases in which full information does exist, good agreement between the experimental findings and the predictions of the model is found. According to this model it will be worthwhile to invest more effort in measuring the time as space polarization of cilary beating and the times of delay between cilia.