Unstable oscillations and wave propagation in flagella

Flagella are active, beam-like, sub-cellular organelles that use wavelike oscillations to propel the cell. The mechanisms underlying the coordinated beating of flagella remain incompletely understood despite the fundamental importance of these organelles. The axoneme (the cytoskeletal structure of flagella) consists of microtubule doublets connected by passive and active elements. The motor protein dynein is known to drive active bending, but dynein activity must be regulated to generate oscillatory, propulsive waveforms. Mathematical models of flagella motion generate quantitative predictions that can be analyzed to test hypotheses concerning dynein regulation. Here we investigate the emergence of unstable modes in a mathematical model of flagella motion with feedback from inter-doublet separation (the "geometric clutch" or GC model). The unstable modes predicted by the model may be used to critically evaluate the underlying hypothesis. The least stable mode of the GC model exhibits switching at the base and robust base-to-tip propagation.