Independent Control of the Static and Dynamic Components of the Chlamydomonas Flagellar Beat

Abstract

When the green alga Chlamydomonas reinhardtii swims, it uses the breaststroke beat of its two flagella to pull itself forward [1]. The flagellar waveform can be decomposed into a static component, corresponding to an asymmetric time-averaged shape, and a dynamic component, corresponding to the time-varying wave [2]. Extreme lightening conditions photoshock the cell, converting the breaststroke beat into a symmetric sperm-like beat, which causes a reversal of the direction of swimming [3]. Waveform conversion is achieved by a reduction in magnitude of the static component, whereas the dynamic component remains unchanged [2]. The coupling between static and dynamic components, however, is poorly understood, and it is not known whether the static component requires the dynamic component or whether it can exist independently. We used isolated and reactivated axonemes [4] to investigate the relation between the two beat components. We discovered that, when reactivated in the presence of low ATP concentrations, axonemes displayed the static beat component in absence of the dynamic component. Furthermore, we found that the amplitudes of the two components depend on ATP in qualitatively different ways. These results show that the decomposition into static and dynamic components is not just a mathematical concept but that the two components can independently control different aspects of cell motility: the static component controls swimming direction, whereas the dynamic component provides propulsion.

The biomechanical role of extra-axonemal structures in shaping the flagellar beat of Euglena

“…Figure 6 illustrates a critical example in which the previous intuitive reasoning effectively plays out. We consider a target bending of the kind U * 2 (s) = A 0 + A 1 sin(2πs/L)), a fair idealization of the asymmetric shapes of a Chlamydomonas-like flagellar beat [10]. We take φ p = −π/4 (larger than the Euglena value, to obtain clearer graphs).…”

The tailored sperm cell

“…Sperm steering requires an additional symmetry break to change direction. Two mechanisms have been proposed to break this symmetry: an average flagellar curvature (Elgeti et al 2010; Friedrich et al 2010; Geyer et al 2016) or a buckling instability (Bukatin et al 2015; Gadêlha et al 2010). In principle, both mechanisms involve bending of the flagellum into one preferential direction.…”

The single flagellum ofLeishmaniahas a fixed polarisation of its asymmetric beat

“…An asymmetric beat can arise when a flagellum has a large static curvature (underlying 'shape' of the 74 flagellum) in addition to the symmetric dynamic curvature (the propagating wave) (Eshel and 75 Brokaw, 1987;Geyer et al, 2016). In Chlamydomonas, several mutants are known which have a 76 more symmetric beat, including pf2 (Brokaw and Kamiya, 1987) and mbo2 (Segal et al, 1984).…”

“…In Chlamydomonas, several mutants are known which have a 76 more symmetric beat, including pf2 (Brokaw and Kamiya, 1987) and mbo2 (Segal et al, 1984). These 77 mutants have a greatly reduced static curvature (Geyer et al, 2016). However, no known mutants 78 invert the bend of this static component to invert the asymmetry of the beat.…”

“…In Chlamydomonas, regulation of the symmetric dynamic curvature of the flagellum to make a wave 298 propagate and the static curvature of the flagellum to introduce asymmetry are separable, and some 299 mutants (such as mbo2) cannot form a static curvature giving an aberrant symmetric waveform 300 (Brokaw and Kamiya, 1987;Geyer et al, 2016;Segal et al, 1984). In Leishmania, no mutants are yet 301 known which lose the asymmetry of their base-to-tip beat -deletions of the outer dynein arm-302 associated proteins dDC2 and LC4-like do promote asymmetric or symmetric beats respectively, but 303 these beats occur in their normal base-to-tip and tip-to-base propagation directions respectively 304 (Edwards et al, 2018).…”