||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.
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