The shape effect of flagella is more important than bottom-heaviness on passive gravitactic orientation in Chlamydomonas reinhardtii.

The way the unicellular, biflagellated, green alga Chlamydomonas orients upward has long been discussed in terms of both mechanics and physiology. In this study, we focus on the mechanics, i.e. the 'passive' mechanisms, of gravitaxis. To rotate the body upwards, cellular asymmetry is critical. Chlamydomonas can be depicted as a nearly spherical cell body with two anterior, symmetric flagella. The present study looks at the question of whether the existence of the flagella significantly affects torque generation in upward reorientation. The 'density asymmetry model' assumes that the cell is spherical and bottom-heavy and that the shape and weight of the flagella are negligible, while the 'shape asymmetry model' considers the shape of the flagella. Both our experimental and simulation results revealed a considerable contribution from shape asymmetry to the upward orientation of Chlamydomonas reinhardtii, which was several times larger than that of density asymmetry. From the experimental results, we also quantified the extent of bottom-heaviness, i.e. the distance between the centers of gravity and the figure when the cell body is assumed to be spherical. Our estimation was approximately 30 nm, only one-third of previous assumptions. These findings indicate the importance of the viscous drag of the flagella to the upward orientation, and thus negative gravitaxis, in Chlamydomonas.

Evidence for a self-organized compliant mechanism for the spontaneous steady beating of cilia.

Cilia or eukaryotic flagella are slender 200-nm-diameter organelles that move the immersing fluid relative to a cell and sense the environment. Their core structure is nine doublet microtubules (DMTs) arranged around a central-pair. When motile, thousands of tiny motors slide the DMTs relative to each other to facilitate traveling waves of bending along the cilium's length. These motors provide the energy to change the shape of the cilium and overcome the viscous forces of moving in the surrounding fluid. In planar beating, motors walk toward where the cilium is attached to the cell body. Traveling waves are initiated by motors bending the elastic cilium back and forth, a self-organized mechanical oscillator. We found remarkably that the energy in a wave is nearly constant over a wide range of (ATP) and medium viscosities and inter-doublet springs operate only in the central and not in the basal region. Since the energy in a wave does not depend on its rate of formation, the control mechanism is likely purely mechanical. Further the torque per length generated by the motors acting on the doublets is proportional to and nearly in phase with the microtubule sliding velocity with magnitude dependent on the medium. We determined the frequency-dependent elastic moduli and strain energies of beating cilia. Incorporation of these in an energy-based model explains the beating frequency, wavelength, limiting of the wave amplitude and the overall energy of the traveling wave. Our model describes the intricacies of the basal-wave initiation as well as the traveling wave.

Individual Flagellar Waveform Affects Collective Behavior of Chlamydomonas reinhardtii.

Bioconvection is a form of collective motion that occurs spontaneously in the suspension of swimming microorganisms. In a previous study, we quantitatively described the "pattern transition," a phase transition phenomenon that so far has exclusively been observed in bioconvection of the unicellular green alga Chlamydomonas. We suggested that the transition could be induced by changes in the balance between the gravitational and shear-induced torques, both of which act to determine the orientation of the organism in the shear flow. As both of the torques should be affected by the geometry of the Chlamydomonas cell, alteration in the flagellar waveform might change the extent of torque generation by altering overall geometry of the cell. Based on this working hypothesis, we examined bioconvection behavior of two flagellar mutants of Chlamydomonas reinhardtii, ida1 and oda2, making reference to the wild type. Flagella of ida1 beat with an abnormal waveform, while flagella of oda2 show a normal waveform but lower beat frequency. As a result, both mutants had swimming speed of less than 50% of the wild type. ida1 formed bioconvection patterns with smaller spacing than those of wild type and oda2. Two-axis view revealed the periodic movement of the settling blobs of ida1, while oda2 showed qualitatively similar behavior to that of wild type. Unexpectedly, ida1 showed stronger negative gravitaxis than did wild type, while oda2 showed relatively weak gravitaxis. These findings suggest that flagellar waveform, not swimming speed or beat frequency, strongly affect bioconvection behavior in C. reinhardtii.

Metachronal waves in the flagellar beating of Volvox and their hydrodynamic origin.

Groups of eukaryotic cilia and flagella are capable of coordinating their beating over large scales, routinely exhibiting collective dynamics in the form of metachronal waves. The origin of this behavior--possibly influenced by both mechanical interactions and direct biological regulation--is poorly understood, in large part due to a lack of quantitative experimental studies. Here we characterize in detail flagellar coordination on the surface of the multicellular alga Volvox carteri, an emerging model organism for flagellar dynamics. Our studies reveal for the first time that the average metachronal coordination observed is punctuated by periodic phase defects during which synchrony is partial and limited to specific groups of cells. A minimal model of hydrodynamically coupled oscillators can reproduce semi-quantitatively the characteristics of the average metachronal dynamics, and the emergence of defects. We systematically study the model's behaviour by assessing the effect of changing intrinsic rotor characteristics, including oscillator stiffness and the nature of their internal driving force, as well as their geometric properties and spatial arrangement. Our results suggest that metachronal coordination follows from deformations in the oscillators' limit cycles induced by hydrodynamic stresses, and that defects result from sufficiently steep local biases in the oscillators' intrinsic frequencies. Additionally, we find that random variations in the intrinsic rotor frequencies increase the robustness of the average properties of the emergent metachronal waves.

A Structural Basis for How Motile Cilia Beat.

The motile cilium is a mechanical wonder, a cellular nanomachine that produces a high-speed beat based on a cycle of bends that move along an axoneme made of 9+2 microtubules. The molecular motors, dyneins, power the ciliary beat. The dyneins are compacted into inner and outer dynein arms, whose activity is highly regulated to produce microtubule sliding and axonemal bending. The switch point hypothesis was developed long ago to account for how sliding in the presence of axonemal radial spoke-central pair interactions causes the ciliary beat. Since then, a new genetic, biochemical, and structural complexity has been discovered, in part, with Chlamydomonas mutants, with high-speed, high-resolution analysis of movement and with cryoelectron tomography. We stand poised on the brink of new discoveries relating to the molecular control of motility that extend and refine our understanding of the basic events underlying the switching of arm activity and of bend formation and propagation.