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

通过成像技术、计算方法、微流控设备和材料科学的进步，研究自然和机器人微生物如何通过鞭毛在流体中推动自己的研究取得了很大成功。然而，在生物系统中，波动的鞭毛很少自由跳动，而是可能在接近(或穿过)被动弹性结构(如嵌入在流体环境中的粘膜股或管状导管的壁)时跳动。这个项目将研究微生物通过悬浮聚合物网络的流体的运动性，其中聚合物细丝之间的间隙与生物体的大小相当。这项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。该项目还将调查昆虫精子通过女性生殖道中狭窄的精子存储器官的旅程。这些系统需要开发新的数学模型和计算方法，这些模型和计算方法超越了精子鞭毛的简单表示，允许重建离散的粘弹性网络，并捕捉限制结构的几何形状。该项目包括通过参与研究培训博士后研究员、研究生和本科生。嵌入在粘性流体中的顺应性粘弹性网络的力学以及在受限环境中运动的长的、受激励的纤维的运动性为弹性流体动力学提供了丰富的系统。该项目将利用正规化的Stokelet方法及其最近的扩展。通过推导球体内正则流的核，这一方法将得到进一步的发展。通过选择离散网络而不是非牛顿流体的连续描述，可以很容易地表示非均质环境。例如，可以研究生物体首先穿透粘弹性网络所需的力量(如在哺乳动物受精过程中)，以及当有机体穿过这些区域时，其形式如何演变。特别是，莱姆病螺旋体通过这种粘弹性网络迁移时的能量学将被研究。此外，还将模拟昆虫精子在雌性生殖道中的运动动力学。它们的极端长度和进入受限空间的能力带来了数学和计算方面的挑战。该项目将使用背景流中长而灵活的纤维的形状变形和屈曲建模的最新进展，以及驱动鞭毛的建模来研究这一系统。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.