出现的三维精子运动：Kirchhoff杆模型中钙动力学和优选曲率的耦合
Emergent three-dimensional sperm motility: Coupling calcium dynamics and preferred curvature in a Kirchhoff rod model
摘要：
沿着精子鞭毛的钙浓度的变化调节精子运动和超活化，其特征在于鞭毛弯曲幅度增加和跳动不对称，使精子能够到达并穿透卵子。鞭毛内钙离子增加的信号传导途径已经建立。然而，钙如何调节鞭毛弯曲的确切机制仍在研究中。我们扩展了我们以前的平面鞭毛弯曲模型，通过开发一个流体-结构相互作用模型，耦合的三维运动的鞭毛在一个粘性的，牛顿流体与不断变化的钙浓度。鞭毛被建模为基尔霍夫杆：具有优选曲率和扭曲的弹性杆。钙动力学表示为一个一维的反应扩散模型上的移动域，鞭毛的中心线。这两个模型耦合假设的精子鞭毛的首选曲率和扭曲取决于当地的钙浓度。为了研究钙对精子活力的影响，我们比较了三种情况下鞭毛弯曲幅度和游泳速度的模型结果：平面，螺旋（螺旋在两个方向上的振幅相等），和准平面（螺旋在一个方向上的振幅小）。我们观察到，对于相同的参数，平面游泳者更快，更清楚地观察到一个转弯运动时，钙耦合占模型。在鞭毛弯曲耦合到钙浓度的情况下，我们观察到紧急的轨迹，可以被描述为一个次摆线的准平面和螺旋弯曲。
英文摘要：
Changes in calcium concentration along the sperm flagellum regulate sperm motility and hyperactivation, characterized by an increased flagellar bend amplitude and beat asymmetry, enabling the sperm to reach and penetrate the ovum (egg). The signaling pathways by which calcium increases within the flagellum are well established. However, the exact mechanisms of how calcium regulates flagellar bending are still under investigation. We extend our previous model of planar flagellar bending by developing a fluid-structure interaction model that couples the three-dimensional motion of the flagellum in a viscous, Newtonian fluid with the evolving calcium concentration. The flagellum is modeled as a Kirchhoff rod: an elastic rod with preferred curvature and twist. The calcium dynamics are represented as a one-dimensional reaction-diffusion model on a moving domain, the centerline of the flagellum. The two models are coupled assuming that the preferred curvature and twist of the sperm flagellum depend on the local calcium concentration. To investigate the effect of calcium on sperm motility, we compare model results of flagellar bend amplitude and swimming speed for three cases: planar, helical (spiral with equal amplitude in both directions), and quasi-planar (spiral with small amplitude in one direction). We observe that for the same parameters, the planar swimmer is faster and a turning motion is more clearly observed when calcium coupling is accounted for in the model. In the case of flagellar bending coupled to the calcium concentration, we observe emergent trajectories that can be characterized as a hypotrochoid for both quasi-planar and helical bending.
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