Figure 1.

A comparison between mammalian sperm and the naive axonemal flagellum. Reprinted from [2,3] with permission from Elsevier. (a) A mammalian flagellum, depicting the additional reinforcing structures (red shading) and cross-sections of the mid-piece, characterized by the presence of nine outer dense fibres exterior to the axoneme and a fibrous sheath (yellow shading); all reinforcing fibres gradually taper along the flagellum, ending prior to the distal tip of the sperm. (b) Wave-compression and symmetry-breaking buckling instabilities in a high-viscosity methylcellulose solution for sea urchin sperm, which possess a flagellum without accessory structures of length approximately 42 μm; reproduced/adapted with permission from [11]. (c) Human spermatozoa, with reinforcing accessory structures on a flagellum of length approximately 50 μm, swimming in a similar highly viscous methylcellulose solution, which highlights a suppression of buckling instabilities; reproduced with permission (licence no. 4543770361396) from [10]. (d) Modelling predictions for the non-dimensional absolute compression, as a function of time t and arclength s for a naive flagellum undergoing buckling instability in high-viscosity medium [12]. The predicted transition can cause high curvatures and asymmetric waveforms, inducing circular swimming paths, depicted in (e), with a smaller circular radius for spermatozoa with larger heads. Note that (d) shows that high elastohydrodynamic internal compression is predicted at regions where the ultra-structural components are larger in mammalian flagella (black arrows in (d)). Plots (d,e), have been adapted from the simulations in [10]. (Online version in colour.)