Flexural Rigidity and Shear Stiffness of Flagella

Abstract

Cilia are thin subcellular organelles that line airways and other passages and bend actively to propel fluid and foreign materials. The ciliary cytoskeleton (the axoneme) consists of nine outer microtubule doublets surrounding a central pair of singlet microtubules. Large bending deformations of the axoneme involve relative sliding of the outer doublets driven by the motor protein dyneins. The genetics and cell biology of the ciliary structure and function have been studied extensively, but the mechanics of the axoneme remain unclear. In this study, we used the unicellular alga Chlamydomonas reinhardtii as the model system for their flagellum replicates the highly conserved molecular structure of the ciliary axoneme. Piconewton forces were applied perpendicularly on the tip of a single flagellum (length L) through a microsphere trapped in optical tweezers. Dividing the force (P) by the corresponding deflection of the flagellar tip (δ) yields the flexural stiffness of the flagellum (K = P/δ), which was then used to calculate the apparent flexural rigidity (EI = KL3/3). The contributions of major structural components to passive mechanical properties were quantified by testing on flagella of specific mutations. The average apparent flexural rigidity of wild-type, pf-3 (without nexin links), and pf-13 flagella (without outer dynein arms) was about 2700 ± 1100, 1300 ± 550, and 650 ± 140 pN·μm2, respectively. In addition, the ratio of elastic shear stiffness (resistance to interdoublet sliding) to true flexural rigidity was estimated by the counterbend response in bent flagella manipulated with a glass microneedle. The quantitative understanding of axonemal mechanics will help illuminate the roles of certain genes and molecular structures in the normal and abnormal axoneme.