Collaborative Research: Computational Models of Cilia and Flagella in a Brinkman Fluid

活动的纤毛和鞭毛是动态的、有弹性的生物结构，表现出有节奏的运动。通过协调跳动，肺部和呼吸道中的纤毛有助于清除呼吸道中潜在的有害颗粒和粘液。纤毛运动受损可导致严重的呼吸道感染。这种损害可能是由体液环境改变引起的，这是囊性纤维化的一个特征，由纤毛本身的缺陷引起，如原发性纤毛运动障碍，或由其他呼吸系统疾病引起。类似地，只有当卵子的鞭毛能够推动卵子前进时，精子才能到达卵子并使其受精；运动能力受损会导致不育。纤毛和精子的跳动高度依赖于流体环境，流体环境包含纤维、蛋白质网络以及化学信号。了解弹性结构和异质液体之间的这种关系对于开发吸入药物和药物、新的避孕药以及帮助由于精子活力降低而导致的不育症的给药策略至关重要。该项目将专注于开发新的计算模型和数值方法来解释这些液体中的纤维和蛋白质网络，以推断纤毛和精子的活体行为。最近的实验表明，i)当浸泡在含有大蛋白质网络的液体中时，精子-鞭毛的波形会发生变化，同时鞭毛的钙浓度也会改变，ii)之前认为的围绕呼吸道纤毛的“水”液体实际上包含了一个大蛋白质网络，或称“刷子”。本项目将专注于识别精子鞭毛和呼吸道纤毛的紧急波形，当考虑到非平面弯曲和内部鞭毛生物化学时。纤毛和鞭毛将被模拟为浸泡在布林克曼方程所支配的流体中的细长、有弹性的结构。正则化框架和基本解将被用来推导各种约束几何的新的数值方法。新的数值方法将在计算上高效，并为在高性能计算系统上使用而开发。这项研究将确定调节精子向卵子前进的因素，探索纤毛和精子的各种波形，并调查纤毛周围液体中的“刷子”如何影响液体中的粒子运输。

Motile cilia and flagella are dynamic, elastic, biological structures that exhibit rhythmic motion. Through coordinated beating, cilia in the lung and respiratory tract help to clear the airway of potentially harmful particles and mucus. Impaired cilia motion can result in serious respiratory infection. This impairment can be caused by an altered fluid environment, a characteristic of cystic fibrosis, by defects in the cilia themselves as with primary ciliary dyskinesia, or by other respiratory diseases. Similarly, a sperm is only able to reach and fertilize an egg if its flagellum can propel it forward; impaired motility results in infertility. Cilia and sperm beating is highly dependent on the fluid environment, which contains fibrous, protein networks as well as chemical signals. Understanding this relationship between elastic structure and heterogeneous fluid is vital for development of delivery strategies for inhaled drugs and medicines, new contraceptives, and aiding in infertility due to reduced sperm motility. This project will focus on the development of new computational models and numerical methods that account for these fibrous, protein networks within the fluid to infer in vivo behavior of cilia and sperm.Recent experiments have shown that i) sperm-flagella waveforms are altered when immersed in fluids containing networks of large proteins and also with flagellar calcium concentration, ii) the previously-considered `watery' fluid surrounding airway cilia actually contains a network of large proteins, or, 'brush'. This project will focus on identifying emergent waveforms of sperm flagella and airway cilia when nonplanar bending and internal flagellar biochemistry are taken into account. Cilia and flagella will be modeled as slender, elastic, structures immersed in a fluid governed by the Brinkman equation. A regularized framework and fundamental solutions will be used to derive new numerical methods for various confined geometries. The new numerical methods will be computationally-efficient and developed for use on high-performance computing systems. This research will identify factors that modulate sperm progression towards the egg, explore various waveforms of cilia and sperm, and investigate how a 'brush' in the fluid surrounding cilia might affect transport of particles within that fluid.