Nonlinear amplitude dynamics in flagellar beating

Abstract

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive crosslinkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatiotemporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

References in corpus (9)

• The hydrodynamics of swimming microorganisms
• Tug-of-war as a cooperative mechanism for bidirectional cargo transport by molecular motors
• Spontaneous Oscillations of Collective Molecular Motors
• Physical Aspects of Axonemal Beating and Swimming
• Self-organized Beating and Swimming of Internally Driven Filaments
• Active phase and amplitude fluctuations of flagellar beating
• Beating patterns of filaments in viscoelastic fluids
• Nonlinear Dynamics of Cilia and Flagella
• Shape mode analysis exposes movement patterns in biology: flagella and flatworms as case studies

Cited by in corpus (10)

• A multiscale biophysical model gives quantized metachronal waves in a lattice of cilia
• Run stop shock, run shock run: Spontaneous and stimulated gait-switching in a unicellular octoflagellate
• Hydrodynamic synchronization of spontaneously beating filaments
• The reaction-diffusion basis of animated patterns in eukaryotic flagella
• Efficient Implementation of Elastohydrodynamics via Integral Operators
• Internal friction controls active ciliary oscillations near the instability threshold
• A Minimal Model of the Hydrodynamical Coupling of Flagella on a Spherical Body with application to Volvox
• The 3D coarse-graining formulation of interacting elastohydrodynamic filaments and multi-body microhydrodynamics
• Role of activity and dissipation in achieving precise beating in cilia: Insights from the rower model
• The asymptotic coarse-graining formulation of slender-rods, bio-filaments and flagella