Cilia and flagella are thin, active, beam-like structures that extend from cells and beat rhythmically to move fluid or propel the cell. "How do cilia and flagella beat" remains one of the most important unsolved questions in science. Cilia are found in the human body, on cells that line the airways and fluid-filled passages in the brain. Flagella share the same structure as cilia, and are found on swimming cells, such as sperm. From an engineering perspective, cilia and flagella are tiny machines that independently and automatically produce wave-like motion. The components of these machines have previously been identified, but how these components work together to produce waves, without external control, remains mysterious. This award supports fundamental research into mechanisms that produce rhythmic motions at the microscopic scale. Researchers from engineering, biology, and imaging will work together to identify and characterize key changes in behavior, such as the initiation of beating, or the transition from forward swimming to backward swimming. Leveraging a summer research program for students from under-represented groups, this interdisciplinary project will provide training and research experience at the intersection of biology and engineering, for graduate and undergraduate students from diverse backgrounds.
Methods from dynamical systems and nonlinear mechanics can elucidate the mechanism of flagellar beating. Mathematical models of flagella are explicit quantitative statements of mechanistic hypotheses. A given model predicts specific bifurcations and transitions in behavior in response to changes in internal or environmental parameters. The PIs plan to pursue three experimental aims using the model organism Chlamydomonas reinhardtii. In each case observations will be compared to model predictions: (1) Characterize bifurcations from static equilibrium (paralyzed flagella) to oscillatory motion; (2) Characterize transitions from asymmetric waveform (forward swimming) to symmetric waveforms (backward swimming); (3) Measure internal mechanical deformations associated with these responses. The PIs will model flagella with one-dimensional partial differential equations (1D-PDEs), and analyze the stability of these PDEs using efficient and powerful methods developed with prior NSF support. High-speed video microscopy and image analysis will be used to characterize flagella motion, and optical and acoustic trapping will be exploited to measure mechanical properties. The ability of focused ion beam scanning electron microscopy (FIB-SEM) to visualize the deformation of the flagellar "skeleton" (the axoneme) will be explored. Focusing on bifurcations and transitions, the PIs can rigorously test the hypotheses, and firmly establish the basis of flagellar oscillations.
