A model for African trypanosome cell motility and quantitative description of flagellar dynamics

Short Running Title: A model for trypanosome cell motility 2 Abstract: The eukaryotic flagellum is a complex and dynamic organelle that provides a cell with highly specialized functions. The flagellated protozoa are highly dependent on flagellar dynamics for environmental sensing, reproduction, cell morphology, and disease progression. Due to the functional diversity and structural nuances of the flagellum, comparing flagellar motion between different cell types is difficult and a quantitative description of the flagellar dynamics in each flagellated cell type is necessary. Although some aspects of flagellar motion have been measured in Chlamydomonas, Crithidia, Leishmania, T. cruzi, and T. brucei, neither a kinematic model of cell motility nor a quantitative description of flagellar dynamics in procyclic T. brucei has hitherto been reported. In this study, we used digital video microscopy to quantify the geometry of trypanosome flagellar waveforms and describe the dynamic properties of the waveforms. We determined the ranges of amplitude and wavelength in procyclic T. brucei and concluded trypanosome flagellar waveforms are dynamic conic functions (ellipses or hyperbolas). Using the experimental waveform parameters, we derived a novel hyperbolic solution to a nonlinear partial differential equation, which enables us to model trypanosome flagellar motion. By investigating the types of motion observed in each of four discrete regions of the cell, we propose a step-wise kinematic model of the coordination of flagellar movement and cell motility that results in the auger-like