涌现的三维精子运动:耦合钙动力学和Kirchhoff棒模型中的首选曲率。

IF 0.8 4区 数学 Q4 BIOLOGY Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-12-04 DOI:10.1093/imammb/dqy015
Lucia Carichino, Sarah D Olson
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引用次数: 13

摘要

沿着精子鞭毛的钙浓度的变化调节精子的运动和过度激活,其特征是鞭毛弯曲幅度的增加和跳动的不对称,使精子能够到达并穿透卵子。钙在鞭毛内增加的信号通路已经建立。然而,钙如何调节鞭毛弯曲的确切机制仍在研究中。我们扩展了先前的平面鞭毛弯曲模型,开发了一种流体-结构相互作用模型,该模型将鞭毛在粘性牛顿流体中的三维运动与钙浓度的变化耦合在一起。鞭毛被建模为基尔霍夫杆:一种具有首选曲率和捻度的弹性杆。钙动力学被表示为一个一维的反应-扩散模型在一个移动的领域,鞭毛。这两个模型是耦合的,假设精子鞭毛的首选曲率和扭曲取决于局部钙浓度。为了研究钙对精子运动的影响,我们比较了平面、螺旋和准平面三种情况下鞭毛弯曲幅度和游动速度的模型结果:平面、螺旋和准平面(一个方向上的小幅度螺旋)。我们观察到,在相同的参数下,当模型中考虑钙偶联时,平面游动速度更快,并且更清楚地观察到转弯运动。在鞭毛弯曲与钙浓度耦合的情况下,我们观察到出现的轨迹可以被描述为准平面和螺旋弯曲的下锥体。
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Emergent three-dimensional sperm motility: coupling calcium dynamics and preferred curvature in a Kirchhoff rod model.

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 signalling 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 3D motion of the flagellum in a viscous Newtonian fluid with the evolving calcium concentration. The flagellum is modelled as a Kirchhoff rod: an elastic rod with preferred curvature and twist. The calcium dynamics are represented as a 1D reaction-diffusion model on a moving domain, 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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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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