纖毛不對稱運動的模擬

Simulated the Asymmetric Motion of Cilium

高德祐(Der-you Kao)

指導教授 ： 陳培亮

國立中央大學/理學院/物理學系/碩士(2006年)

摘要

纖毛運動包含了兩種划動，一個是提供推進力的有效划動，另一個是讓纖毛回復到原位的恢復划動。根據生物學家的觀察，驅使纖毛作出這兩種划動的機制是相同的，但卻造就出兩種運動模式，這就是這本論文中我們所要探究的問題。

我們用兩根有彈性但長度不變的棍子，以虎克彈簧連接(為了讓棍子的間距不會有太大變化)，再加上兩組驅使棍子滑動的力量，以對稱的結構進而模擬纖毛的不對稱運動。從模擬的結果中發現，當驅動力夠大時，只需要驅動其中一組讓棍子滑動的力量，使其作用在不同的位置，就可以觀察到兩個種類的划動。

關鍵字

模擬 ； 纖毛運動

並列摘要

Cilia are rod-like structures. They always occur in large numbers on cell surface. The primary function of a cilium is to generate fluid flow in a preferred direction. Therefore, a cilium could be used for locomotion and transportation. The bending of a cilium is caused by ATP-driven dyneins, arranged symmetrically in cilium, but they result an asymmetric beating motion.

There are two phases in the ciliary beating. One is for propelling and it is called the effective stroke. The other is for restoring the cilium to initial state and called the recovery stroke. In previous models, two groups of dyneins are proposed to drive the effective stroke and the recovery stroke respectively. They introduce asymmetric mechanism for triggering dyneins in their models. In this thesis, we show that the two strokes can be driven by dyneins in only one group and without asymmetric mechanism to trigger dyneins.

In our simulation, the cilium is modeled by two nonstretching elastic rods, connected by nexin links and drivn by triggered dyneins. The Hookean spring describe a nexin link and it lies on the local normal direction to maintain the diameter of cilium. Dyneins have two inclinations. One bends the cilium upward and the other bends the cilium downward.

Before simulating the dynamics of cilium, we investigate the steady state of cilium first. Under a small triggered force, no matter where dyneins are, the cilium responds positive curvature, and its form is similar to the effective stroke. Under a large triggered force, two different kinds of respondence are observed. When triggered dyneins are in the first half of the cilium, the cilium responds positive curvature. Its form is still similar to the effective stroke. The interesting behavior appears when triggered dyneins are in the last half of the cilium. The negative curvature occurs near the basal end, and this corresponds the recovery stroke. So, both effective and recovery strokes occur when dyneins are triggered with a large force.

The effective and recovery strokes occur in steady state when the magnitude of dynein force is large. This indicates that a complete beating cycle may be obtained with a successive variation in the locations of triggered dyneins. In the simulation, only one inclination of dyneins are triggered, and triggered dyneins propagate from the basal end to the tip of cilium. When a triggered dynein reaches the tip end, it will emerge from the basal end at the next propagating step. When the magnitude of dynein force is small, the continuous effective strokes are observed, and only beats in a small range. As the dynein force increasing, the beating range of cilium increases, and most importantly, a recovery stroke very similar to that observed in experiments is obtained.

並列關鍵字

simulation ； ciliary motion

參考文獻

3.Satir P. (1965), J. Cell Biol., 26, 805-834.

4.Sale W. S., and Satir P. (1977), Proc. Natl. Acad. Sci. U.S.A., 74, 2045-2049.

5.Warner F. D., and Mitchell D. R. (1978), J. Cell Biol., 76, 261-277.

6.Minoura I., Yagi T., and Kamiya R. (1999), Cell Struct. Funct., 24, 27-33.

9.Lindemann C. B. (1993), J. Theor. Biol., 168, 175-189.