Eukaryotes swim with coordinated flagellar (ciliary) beating and steer by fine-tuning the coordination. The model organism for studying flagellate motility, Chlamydomonas reinhardtii, employs synchronous, breaststroke-like flagellar beating to swim, and it modulates the beating amplitudes differentially to steer. This strategy hinges on both inherent flagellar asymmetries (e.g. different response to chemical messengers) and such asymmetries being effectively coordinated in the synchronous beating. In C. reinhardtii, the synchrony of beating is known to be supported by a mechanical connection between flagella; however, how flagellar asymmetries persist in the synchrony remains elusive. For example, it has been speculated for decades that one flagellum leads the beating, as its dynamic properties (i.e. frequency, waveform, etc.) appear to be copied by the other one. In this study, we combine experiments, computations, and modeling efforts to elucidate the roles played by each flagellum in synchronous beating. With a non-invasive technique to selectively load each flagellum, we show that the coordinated beating essentially only responds to load exerted on the cis flagellum; and that such asymmetry in response derives from a unilateral coupling between the two flagella. Our results highlight a distinct role for each flagellum in coordination and have implication for biflagellates’ tactic behaviors.@en

The swift deformations of flagella and cilia are crucial for locomotion and fluid transport on the micron scale. Most hydrodynamic models of flagellar and ciliary flows assume the zero Reynolds number limit and model the flow using Stokes equations. Recent work has demonstrated that this quasi-steady approximation breaks down at increasing distances from the cilia. Here, we use optical tweezer-based velocimetry to measure the flow velocity with high temporal accuracy, and to reconstruct the entire unsteady flow field around beating cilia. We report both the steady and the unsteady component of the ciliary flow and compare them with the solutions to both the Stokes and the Navier-Stokes equations. Our experimental measurements of the velocity and vorticity fields are in agreement with the numerical solution to the Navier-Stokes equations and show significant differences with the solution to the Stokes equations. We characterize the phase difference between the flow oscillations and the oscillations of the ciliary motion and evidence a significant anisotropic phase lag. We show that this phase lag presents the spatiotemporal characteristics of the unsteady Stokes equations and that the flow field around beating cilia is well represented by the fundamental solution to the unsteady Stokes equations: the oscillet.

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The flagella of Chlamydomonas reinhardtii possess fibrous ultrastructures of a nanometer-scale thickness known as mastigonemes. These structures have been widely hypothesized to enhance flagellar thrust; however, detailed hydrodynamic analysis supporting this claim is lacking. In this study, we present a comprehensive investigation into the hydrodynamic effects of mastigonemes using a genetically modified mutant lacking the fibrous structures. Through high-speed observations of freely swimming cells, we found the average and maximum swimming speeds to be unaffected by the presence of mastigonemes. In addition to swimming speeds, no significant difference was found for flagellar gait kinematics. After our observations of swimming kinematics, we present direct measurements of the hydrodynamic forces generated by flagella with and without mastigonemes. These measurements were conducted using optical tweezers, which enabled high temporal and spatial resolution of hydrodynamic forces. Through our measurements, we found no significant difference in propulsive flows due to the presence of mastigonemes. Direct comparison between measurements and fluid mechanical modeling revealed that swimming hydrodynamics were accurately captured without including mastigonemes on the modeled swimmer's flagella. Therefore, mastigonemes do not appear to increase the flagella's effective area while swimming, as previously thought. Our results refute the longstanding claim that mastigonemes enhance flagellar thrust in C. reinhardtii, and so, their function still remains enigmatic.

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The microscopicworld is surprisingly busywith swimming micro-organisms. In a droplet of pondwater, there can be tens of thousands of microbes. They are predators and preys, producers and consumers, and they formthe bottom levels of the ecology of our world. The swimming micro-organisms can be in general classified into prokaryotes and eukaryotes. Eukaryotes come later in evolution. They are higher organisms than the prokaryotes as they possess more complex cellular structures such as the nucleus and mitochondria. Motile eukaryotic micro-organisms all use an active hair-like structure for swimming, known as flagella or cilia. Although nuanced difference exists between flagella (cilia) of different species, their general internal structure and driving mechanisms are mostly the same. In some sense, they are one of the bestselling machines for locomotion on themicron scale. Although flagella are the first-ever documented organelles in cell biology, our understanding of them is still limited. For example, we have only begun to appreciate how the conformational change of single protein motors results in the waveformon the scale of a flagellum. Our understanding of the flow generated by even a single flagellum is rudimentary: resolving the temporal features of such flow field remains experimentally challenging. On a larger scale, how thousands of cilia interact with each other to facilitate fluid transport is still elusive: theoretical models and simulations are waiting for experimental verification. In this thesis, I explore different topics centering around flagellar/ciliary motility by employing novel experimental and numerical techniques, and hence advance our understanding. My experimental investigation starts by resolving the flow generated by the beating cilia of single cells. Due to the high beating frequency, high temporal resolution is required to map the time-varying flow field, which conventional tracer particle-based flow velocimetry techniques cannot provide. To tackle this challenge, I implemented an optical tweezers-based flow velocimetry (OTV) technique. In this technique, a bead is trapped and placed at a particular location by a focused laser beam. The local flow displaces the bead from the trapping center. This displacement, although small, can be accurately monitored by laser interferometry and converted into an electrical signal by photoelectric detectors. Essentially,we gain the desired accuracy and temporal resolution by exploiting the high resolution and large bandwidth of interferometric and electrical measurements. With this technique, I revealed that the ciliary flow deviates fundamentally fromhow it is often modeled by Stokes equations. More specifically, the flow’s amplitude decays faster spatially, and its phase shifts over distance. These discrepancies are resolved by adding a linear unsteady term to Stokes equations. Furthermore, I systematically characterized the ciliary flow field created by captured C. reinhardtii cells. The flow field in different directions and over the ciliary beating plane are measured experimentally, modelled numerically, and analyzed theoretically. Results displayed excellent agreement with each other, and altogether increased our knowledge in the ciliary flow. With the OTV measurements, I not only studied the basic hydrodynamics of ciliary flowbut also addressed a long-standing hypothesis regarding the function of a ciliary appendage. Many cilia have fibrous ultrastructures called mastigoneme. These fibrous appendages are believed to help cells swim faster by increasing the ciliary surface area. Our experiments, together with numerical studies, completely refute this hypothesis: such fibrous hairs do not show any hydrodynamic significance in C. reinhardtii. Instead, its absence in genetically modifiedmutants appeared to result in some behavioral changes, causing the cells to turn abruptly more often than usual. Therefore, I have re-opened the question about the function of the fibrous mastigonemes. Future investigation towards this direction is needed and is likely to lead to more exciting findings. Lastly, I attempted to bridge the physics of ciliary flowwith the biology of ciliary beating. I focused on the ciliary difference and investigated it by selectively loading each cilium of C. reinhardtii with external flows. The ciliary difference is critical for the steering of biflagellates (micro-organisms swimming with two flagella/cilia). I observed an unreported functional difference between the two cilia, as I found that the coupling between the two cilia is unilateral. One cilium serves as the coordinator of beating, and a cell is coupled to external hydrodynamic forces mostly through this coordinating cilium. Altogether, by introducing the OTV technique and incorporating different numerical methods, I was able to elucidate the ciliary flowin a time-resolvedway, updating the current understanding in these unsteady flows. The effectiveness of this methodology was demonstrated again by its application in studying the function of the fibrous ultrastructures. By further moving on to the biological aspect of ciliary beating, we found a new type of difference between the two cilia, which enriches our knowledge in inter-ciliary coupling. @en

Abstract: In the study of micro-scale biological flows, velocimetry methods based on passive tracers, such as micro-PIV and micro-PTV, are well established to characterize steady flows. However, these methods become inappropriate for measuring unsteady flows of small amplitude, because, on these scales, the motion of passive tracers cannot be distinguished from Brownian motion. In this study, we use optical tweezers (OTs) in combination with Kalman filtering, to measure unsteady microscopic flows with high temporal accuracy. This method is referred to as optical tweezers-based velocimetry (OTV). The OTV method measures the nanometric displacements of a trapped bead, and predicts the instantaneous velocity of the flow by employing a Kalman filter. We discuss the accuracy of OTV in measuring unsteady flows with 1.5–70 μ m s^{- 1} amplitudes and 10–90 Hz frequencies. We quantify how the bead size and the laser power affect the velocimetry accuracy, and specify the optimal choices for the bead size and laser power to measure different unsteady flows. OTV accurately measures unsteady flows with amplitudes as small as 3–6 μ m s^{- 1}. We compare the accuracy of OTV and micro-PTV, and characterize the flow regime for which OTV outperforms micro-PTV. We also demonstrate the robustness of OTV by measuring the unsteady flow created by the cilia of green alga Chlamydomonas reinhardtii, and comparing with numerical predictions based on Stokes equations. An open-source implementation of the OTV software in Matlab is available through the 4TU.Centre for Research Data. Graphic abstract: [Figure not available: see fulltext.].

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Stokes equations are commonly used to model the hydrodynamic flow around cilia on the micron scale. The validity of the zero Reynolds number approximation is investigated experimentally with a flow velocimetry approach based on optical tweezers, which allows the measurement of periodic flows with high spatial and temporal resolution. We find that beating cilia generate a flow, which fundamentally differs from the stokeslet field predicted by Stokes equations. In particular, the flow velocity spatially decays at a faster rate and is gradually phase delayed at increasing distances from the cilia. This indicates that the quasisteady approximation and use of Stokes equations for unsteady ciliary flow are not always justified and the finite timescale for vorticity diffusion cannot be neglected. Our results have significant implications in studies of synchronization and collective dynamics of microswimmers.

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