轴丝跳动和游动的物理方面
Physical Aspects of Axonemal Beating and Swimming
摘要：
我们讨论了由分子马达内部产生的力驱动的轴丝变形动力学的二维模型。我们的模型包括一个弹性纤维对连接的主动元素。我们推导了该系统在存在内力时的动力学方程。在小变形的限制下，微扰方法允许我们计算细丝形状和张力分布。我们证明了周期性的细丝运动可以通过弹性细丝和分子马达的自组织产生。振动运动和弯曲波的传播可以发生在一个初始的非运动状态通过一个不稳定称为霍普夫分叉。接近这种不稳定性，该系统的行为被证明是独立的轴丝和力产生机制的微观细节。然而，振荡频率依赖于分子马达的性质。我们计算的振荡频率在分叉点，并表明，一个大的频率范围是通过改变1和50 $μ$ m之间的轴丝长度访问。计算了鞭毛游动的速度，讨论了边界条件和外力对鞭毛轴丝振动的影响。
英文摘要：
We discuss a two-dimensional model for the dynamics of axonemal deformations driven by internally generated forces of molecular motors. Our model consists of an elastic filament pair connected by active elements. We derive the dynamic equations for this system in presence of internal forces. In the limit of small deformations, a perturbative approach allows us to calculate filament shapes and the tension profile. We demonstrate that periodic filament motion can be generated via a self-organization of elastic filaments and molecular motors. Oscillatory motion and the propagation of bending waves can occur for an initially non-moving state via an instability termed Hopf bifurcation. Close to this instability, the behavior of the system is shown to be independent of microscopic details of the axoneme and the force-generating mechanism. The oscillation frequency however does depend on properties of the molecular motors. We calculate the oscillation frequency at the bifurcation point and show that a large frequency range is accessible by varying the axonemal length between 1 and 50$μ$m. We calculate the velocity of swimming of a flagellum and discuss the effects of boundary conditions and externally applied forces on the axonemal oscillations.
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