A chemomechanical model of sperm locomotion reveals two modes of swimming

Abstract

The propulsion of mammalian spermatozoa during reproduction relies on the spontaneous periodic oscillation of their flagella. These oscillations are driven internally by the coordinated action of ATP-powered dynein motors that exert active sliding forces between microtubule doublets, resulting in bending waves that propagate along the flagellum and enable locomotion of the cell through the viscous medium. In this work, we present a chemomechanical model of a freely swimming spermatozoon that uses a sliding-control model of the flagellar axoneme capturing the coupling of motor kinetics with elastic deformations and accounts for the effect of non-local hydrodynamic interactions between the sperm head and flagellum. Nonlinear simulations of the model equations are shown to produce realistic beating patterns and swimming trajectories, which we analyze as a function of sperm number and motor activity. Our results demonstrate that the swimming velocity does not vary monotonically with dynein activity, but instead displays two local maxima corresponding to distinct modes of swimming, each characterized by qualitatively different waveforms and trajectories.

Elastohydrodynamic mechanisms govern beat pattern transitions in eukaryotic flagella

“…This work extends their findings to the emergence of three-dimensional asymmetrical beating without internal asymmetries. Our results also confirm findings there and elsewhere 18 that nonlinear effects become important at parameters that induce high flagellar curvatures. Rode et al .…”

“…This work extends their findings to the emergence of threedimensional asymmetrical beating without internal asymmetries. Our results also confirm findings there and elsewhere 18 that nonlinear effects become important at parameters that induce high flagellar curvatures. Rode et al 22 and Ling et al 47 showed that mechanical instabilities can lead to transitions between planar and three-dimensional beating for different types of internal driving patterns.…”

“…We have shown that the variety of beating patterns due to changes in the ambient medium viscosity can be systematically predicted with a single model. This work is in line with recent work that has underscored the importance of mechanical instabilities in understanding the shapes and dynamics of cilia and flagella 13,14,16,18,22,24,[47][48][49][50][51][52] .…”

“…Planar beating is also observed when sperm swim in fluids of viscosity above around 20 mPa s. 4,5 How does one explain these transitions observed in beating patterns? The travelling waveforms generated in the filaments could depend on the biochemical regulation of dynein motor activity, which in turn may modify the mechanism behind the oscillatory instability in the axoneme [11][12][13][14][15][16][17][18] or could modify the amplitude, wavelength and wave speed of the emergent travelling wave [19][20][21][22][23][24] . It would therefore seem that the variety in flagellar waveforms is largely due to internal differences in the dynein forcing.…”

The reaction-diffusion basis of animated patterns in eukaryotic flagella

“…5b does not change appreciably with the inclusion of non-local hydrodynamics through slender-body theory, as was reported recently in Ref. [58]. The wavelength of beating patterns in the decoupling region is approximately equal to the length of the flagellum L and this is observed in Chlamydomonas (see Fig.…”