Long, Coiled, Actuated: Complex Flagella Moving Through Heterogeneous Fluid Environments

通过成像技术、计算方法、微流体装置和材料科学的进步，对自然微生物和机器人微生物如何通过鞭毛的跳动在流体中推动自己的研究取得了很大的成功。然而，在生物系统中，波浪状鞭毛很少自由跳动，但可能在靠近（或穿过）被动弹性结构（如嵌入流体环境中的粘膜链或管状管道壁）的地方跳动。该项目将研究微生物在带有悬浮聚合物网络的液体中的运动，其中聚合物细丝之间的间隙与生物体的大小相当。该研究与哺乳动物精子-卵子穿透和螺旋体通过粘膜组织的运动有关。该项目还将研究昆虫精子通过雌性生殖道狭窄的精子储存器官的旅程。这些系统需要新的数学模型和计算方法的发展，这些数学模型和计算方法不仅要超越精子鞭毛的简单表示，还要允许对离散粘弹性网络进行重塑，并捕获限制结构的几何形状。该项目包括通过参与研究培养一名博士后研究员、研究生和本科生。嵌入粘性流体中的柔顺粘弹性网络的力学，以及在受限环境中运动的长纤维的运动性，构成了弹性流体动力学的丰富系统。该项目将利用正则化Stokeslets方法及其最近的扩展。该方法将通过推导球内正则流的核进一步推进。通过选择离散网络而不是非牛顿流体的连续描述，可以很容易地表示异质环境。例如，可以研究生物体首先穿透粘弹性网络（如哺乳动物受精）所需的能量，以及当它穿过这些区域时，它的形态是如何演变的。特别是，莱姆病螺旋体在通过这种粘弹性网络迁移时的能量学将被研究。此外，昆虫精子在雌性生殖道内运动的动力学将被建模。它们的极端长度和它们在有限空间内移动的能力给数学和计算带来了挑战。该项目将利用最近的研究进展，对背景流中长而灵活的纤维的形状变形和屈曲进行建模，并结合对驱动鞭毛的建模，来研究这个系统。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The study of how natural and robotic microorganisms propel themselves in a fluid through the beating of flagella has enjoyed much success through advances in imaging technologies, computational methods, microfluidic devices, and materials science. However, in biological systems, rarely does an undulating flagellum beat freely, but may beat in close proximity to (or through) passive elastic structures such as mucosal strands embedded in the fluid environment or walls of tubular ducts. This project will investigate the motility of microorganisms through fluids with suspended polymeric networks where the gaps between polymer filaments are comparable to the size of the organism. The study is relevant to mammalian sperm-egg penetration and spirochete motility through mucosal tissues. The project will also investigate the journey of insect sperm through narrow sperm storage organs in the female reproductive tract. These systems require the development of novel mathematical models and computational methods that move beyond simple representations of sperm flagella, that allow remodeling of discrete viscoelastic networks, and that capture the geometry of confining structures. The project includes training of a postdoctoral researcher, graduate students, and undergraduates through involvement in the research. The mechanics of a compliant, viscoelastic network embedded in a viscous fluid and the motility of long, actuated fibers moving in confined environments present rich systems in elastohydrodyamics. The project will leverage the method of regularized Stokeslets and recent extensions of it. This methodology will be further advanced through deriving kernels for regularized flow inside a sphere. By choosing a discrete network rather than a continuum description of a non-Newtonian fluid, a heterogeneous environment is easily represented. For instance, the power required for an organism to first penetrate the viscoelastic network (as in mammalian fertilization) and how its form evolves as it moves through these regions can be studied. In particular, the energetics of the Lyme disease spirochete as it migrates through such a viscoelastic network will be investigated. In addition, the dynamics of insect sperm motility in the female reproductive tract will be modeled. Their extreme length and their ability to move into confined spaces present mathematical and computational challenges. The project will use recent advances in modeling the shape deformations and buckling of long, flexible fibers in background flows, coupled with modeling of actuated flagella, to investigate this system.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.