Emergence of Synchronized Beating during the Regrowth of Eukaryotic Flagella

Abstract

A fundamental issue in the biology of eukaryotic flagella is the origin of synchronized beating observed in tissues and organisms containing multiple flagella. Recent studies of the biflagellate unicellular alga Chlamydomonas reinhardtii provided the first evidence that the interflagellar coupling responsible for synchronization is of hydrodynamic origin. To investigate this mechanism in detail, we study here synchronization in Chlamydomonas as its flagella slowly regrow after mechanically induced self-scission. The duration of synchronized intervals is found to be strongly dependent on flagellar length. Analysis within a stochastic model of coupled phase oscillators is used to extract the length dependence of the interflagellar coupling and the intrinsic beat frequencies of the two flagella. Physical and biological considerations that may explain these results are proposed. DOI: 10.1103/PhysRevLett.107.148103 PACS numbers: 87.16.Qp, 05.45.Xt, 47.63.Àb, 87.18.Tt From unicellular organisms as small as a few microns to the largest vertebrates on Earth, we find groups of beating flagella or cilia that exhibit striking spatiotemporal organization. This may take the form of precise frequency and phase locking, as frequently found in the swimming of green algae [1], or beating with long-wavelength phase modulations known as metachronal waves, seen in ciliates such as Paramecium [2] and in our own respiratory systems. The remarkable similarity in the underlying molecular structure of flagella across the whole eukaryotic world leads naturally to the hypothesis that a similarly universal mechanism might be responsible for synchronization. Although this mechanism is poorly understood, one appealing hypothesis is that it results from hydrodynamic interactions between flagella.The role of hydrodynamics in synchronization has been the subject of intense theoretical investigation in the half century since the seminal work of Taylor [3] showed that phase synchronization of nearby undulating sheets minimizes viscous dissipation. Although minimizing dissipation is not a general principle from which to derive dynamics, a growing body of work has identified requirements for synchronization within minimal models involving systems of rotating spheres or helices [4][5][6]. It is now known that oscillators with more than one degree of freedom or those with suitable internal forcing can be synchronized by hydrodynamics [6,7]. Various levels of coordination are also found with more realistic models of flagella [8], which rely necessarily on simplified internal driving of the filaments. Nevertheless, these complex models yield important clues to the generation and regulation of flagellar motion [9].Experimental progress has lagged behind that of theory, due in large part to the challenge of finding a sufficiently simple model system that can be studied under an appropriately broad set of experimental conditions. But recent work [10] on Chlamydomonas reinhardtii (CR, Fig. 1), a biflagellate green alga well developed as a model to stud...

Hydrodynamics Versus Intracellular Coupling in the Synchronization of Eukaryotic Flagella

“…Flagella have often been suggested to synchronize due to interflagellar hydrodynamic interactions. This view has been supported by several theoretical studies [3,4,12,13] and recent experiments [14,15]. Recently, another view has emerged, suggesting that the cell rocking motion causes synchronization by creating synchrony-restoring hydrodynamic drag on the flagella [16,17].…”

Active Phase and Amplitude Fluctuations of Flagellar Beating

“…Analysis of phase-slips allowed a previous, indirect estimate of flagellar phase fluctuations, corresponding to Q≈25 for the quality factor of individual flagella [10]. A latter study indicated a length-dependence of Q, with corresponding Q ranging from ≈70−120 for length increasing from 6µm to 12µm [33]. Interestingly, flagellar synchronization in Chlamydomonas seems to operate just below a tolerable level of noise: Consider the approximate dynamics of the phase difference δ between two identical, coupled oscillators,δ = −λ/T sin δ + ζ, where ζ is Gaussian white noise with ζ(t)ζ(t ) = 4Dδ(t−t ) [10,34].…”

Bimodal rheotactic behavior reflects flagellar beat asymmetry in human sperm cells

“…A similar mechanism was recently discovered in the biflagellate eukaryote Chlamydomonas reinhardtii (18). This unicellular green alga actively redirects its swimming motion through occasional desynchronization of its two cilia (19), although it is still debated whether this effect is of mechanical (20) or hydrodynamic (21,22) origin. Experiments (23) show that the alga's reorientation dynamics can lead to localization in shear flow (24,25), with potentially profound implications in marine ecology.…”