Self-buckling of undulating flagella: an elastohydrodynamic mechanism for double waves in spermatozoa
The relatively long flagella of spermatozoa from insects, birds, and octopuses display double waves, characterized by two superimposed helical waves. The prevalance of these highly organized waveforms across diverse taxa and distinct flagellar architectures hints at shared underlying physics, motivating a model of the flagellum as an elastic filament immersed in a viscous fluid, actively driven…
Spermatozoa, the flagellated reproductive cells, display a striking phenomenon known as double waves. These complex wave patterns, composed of two intertwined helical waves, are observed across various species ranging from insects to octopuses. Despite the diverse nature of these organisms and their unique flagellar structures, the presence of these organized waves suggests a common underlying physics.
To understand this intriguing behavior, scientists have treated the flagellum as an elastic filament immersed in a viscous fluid, driven by internal bending moment waves. Simulations of a fixed filament have demonstrated that it can buckle under its own activity, transitioning into whirling and flapping states. An analysis of the elastohydrodynamic equations, using a multiple-scales approach, reveals how nonlinear interactions between fast undulations can generate an effective compression, driving the buckling process.
When this model is extended to a swimming spermatozoon, it produces the same double wave pattern. Parameter estimates across different species indicate that most observed double waves fall within the regime where buckling is permitted. This finding supports the self-buckling mechanism as a generic physical explanation for the occurrence of double waves in spermatozoa.
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