Abstract
We propose and discuss a model for flagellar mechanics in Euglena gracilis. We show that the peculiar non-planar shapes of its beating flagellum, dubbed 'spinning lasso', arise from the mechanical interactions between two of its inner components, namely, the axoneme and the paraflagellar rod. The spontaneous shape of the axoneme and the resting shape of the paraflagellar rod are incompatible. Thus, the complex non-planar configurations of the coupled system emerge as the energetically optimal compromise between the two antagonistic components. The model is able to reproduce the experimentally observed flagellar beats and the characteristic geometric signature of spinning lasso, namely, traveling waves of torsion with alternating sign along the length of the flagellum.
Highlights
Flagella and cilia propel swimming eukaryotic cells and drive fluids on epithelial tissues of higher organisms (Alberts et al, 2015)
We have shown how the origin of the peculiar shapes of the euglenid flagellum can be explained by the mechanical interplay of two antagonistic flagellar components, the Ax and the paraflagellar’ rod (PFR)
Non-planarity in E. gracilis can arise because of a marked asymmetry in the Ax-bonding links-PFR complex in the euglenid flagellum, which is not found in kinetoplastids such as Leishmania (Gluenz et al, 2010) or Trypanosoma (Portman and Gull, 2010)
Summary
Flagella and cilia propel swimming eukaryotic cells and drive fluids on epithelial tissues of higher organisms (Alberts et al, 2015). The inner structure of the eukaryotic flagellum is an arrangement of microtubules (MTs) and accessory proteins called the axoneme (Ax). A highly conserved structure in evolution, the Ax typically consists of nine cylindrically arranged MT doublets cross-bridged by motor proteins of the dynein family. An internal central pair of MTs is connected by radial spokes to the nine peripheral doublets, determining the typical ’9+2’ axonemal structure. Motor proteins hydrolyze ATP to generate forces that induce doublet sliding. Due to mechanical constraints exerted by linking proteins (nexins) and the basal body, dynein-induced sliding of MTs translates into bending movements of the whole structure. Motor proteins are thought to self regulate their activity via mechanical feedback, generating the periodic beats of flagella, see, for example, Brokaw, 2009 and Lindemann and Lesich, 2010
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