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

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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.