Session T08: Biofluids: Cilia and Flagella I

Hydrodynamic performance of choanoflagellate cells with flexible flagella and microvilli

A unicellular choanoflagellate has an ovoid cell body and a single flagellum surrounded by a collar of microvilli.  By waving its flagellum, it swims and creates a water current that brings bacteria to its collar of microvilli.  Alternatively, a thecate cell is not free swimming, but attaches itself to a substrate by a stalk that can deform with flow. Some choanoflagellates, like C. flexa, form colonies that are able to rapidly change their shape due to contraction of the microvilli apparatus.   Detailed computational models of choanoflagellate hydrodynamics that capture body morphology typically assume rigid microvilli, rigid stalks, and prescribe the kinematics of the flagellum.  However, the flagellum, microvilli, and stalks are not rigid structures, but flexible filaments whose evolving shapes are coupled to their fluid environment.   We present a model that treats the flagellum and the microvilli as elastic Kirchhoff rods whose shapes are not pre-set, but emerge from the coupled system. In addition to understanding the effect of compliance of these structures on the swimming of a single organism, we will study the hydrodynamic interaction of two choanoflagellates and how the collars might affect this interaction.    

Hydrodynamic forces shape eukaryotic microswimmers

Eukaryotic swimming cells encompass spermatozoa, algae and protozoa that use flagella or cilia for locomotion in aqueous environments. Their flexible appendages induce propulsive forces which are balanced  by the viscous drag on the cells, thus leading to a directed swimming motion. We use our recently built database of cell motility (BOSO-Micro) and perform exploratory data analysis to address two questions of hydrodynamic optimality. We first examine the morphology of flexible flagella undergoing waving deformations and show that their amplitude-to-wavelength ratio is close to the one predicted theoretically to optimise the propulsion of active filaments. We then analyse ciliates, which achieve propulsion by the collective beating of short active cilia covering their surface. We show that the aspect ratios of ciliate cell bodies are close to the aspect ratio of an axisymmetric cell body predicted to minimise the viscous drag. Both results strongly suggest a crucial role played by hydrodynamic constraints, in particular viscous drag, in shaping eukaryotic swimming cells.   

Spherical choanocyte chamber of sponge achieves optimized pumping efficiency

Sponges, the basalmost members of the animal kingdom, exhibit a range of complex architectures in which microfluidic channels connect multitudes of spherical chambers lined with choanocytes, which are flagellated filter-feeding cells. Choanocyte chambers can possess scores or even hundreds of such cells, which drive complex flows entering through porous walls and exiting into the sponge channels. One of the mysteries of the choanocyte chamber is its spherical shape, as it seems inappropriate for inducing directional flow given that some choanocytes flagellate in the opposite direction of flow. To answer this question, we combined direct imaging of choanocyte chambers in living sponges with computational studies of many-flagellum models. Computationally, we found that the flagella beating against the flow play a role in raising the pressure inside the choanocyte chamber. As a result, the mechanical pumping efficiency, calculated from the pressure rise and flow rate, reaches a maximum at the small outlet opening angle. Moreover, a comparison between the experiments and numerical simulations revealed that the chamber diameter, flagellar wave number and the outlet opening angle of E. muelleri, as well as some other species are designed so as to maximize the mechanical pumping efficiency. These results imply that the morphogenesis of the choanocyte chamber is appropriate in terms of hydrodynamics. The findings are useful for understanding the physiology and body design of sponges.   

Seeing new depths: visualizing the three-dimensional flow field of a free-swimming alga

Insights into the locomotion of microswimmers and their interactions with environment rely on the detailed understanding of the structure of the flow they induce while swimming. While measurements of the projected two-dimensional flow around different microswimmers have been achieved as a milestone in experimental fluid mechanics in the past decade, mapping the full three-dimensional (3D) flow structures of microswimmers remains a challenging task. Here, we utilize high-speed holographic microscopy to measure the time-averaged and phase-specific 3D flow of a free-swimming Chlamydomonas reinhardtii, a premier model for swimming microorganisms. The flow field is obtained by tracking the 3D motion of micron-sized tracers at 500 fps over thousands of the flagellar beat cycles of algae. Our measurements reveal complex near-field flow structures, defying the common wisdom on the algal flow based on three Stokelets.  We further develop a modified three-sphere model of algae, which qualitatively captures the unusual time-averaged 3D flow structure. Our study sheds new light on algal swimming and demonstrates the potential of holographic microscopy in imaging complex flows induced by microorganisms in their natural habitats.   

Trade-offs in flagella propulsion, feeding and stealth

Flagellates are key components of aquatic microbial food webs. Their flagella propel the cell through the water and generate a feeding current from which bacterial prey is harvested. However, the activity of the flagella also disturbs the ambient water, thereby attracting the flagellate’s flow-sensing predators. Here we use computational fluid dynamics to explore the optimality and fluid dynamics of the diverse arrangements, beat patterns, and external morphologies of flagella found among free-living flagellates in light of the fundamental propulsion-foraging-predation-risk trade-off. We examine 5-μm-sized representative model organisms with different resource acquisition modes: autotrophs relying on photosynthesis and uptake of nutrient molecules, phagotrophs that feed on bacteria, and mixotrophs that employ both strategies. For all types, the transport of inorganic molecules is diffusion dominated, and the flagellum in autotrophic species therefore mainly serves propulsion purposes. Flagellates with a single, naked flagellum found among non-foraging swarmer stages have a waveform (less than one wave) that is optimized for swimming and stealth but inefficient for feeding. Flagellates with a hairy flagellum typically have many waves, which optimizes swimming and stealth but is suboptimal for foraging, leading to a design trade-off. However, when compared with naked flagella, the presence of hairs allows an efficient feeding current, making these primarily phagotrophic flagellates the most efficient and dominant bacterivores in the ocean. Autotrophic biflagellates have wave patterns optimized for both propulsion and foraging but conflicting weakly with stealth. Finally, the mixotrophic haptophytes are optimized for foraging, conflicting with both stealth and propulsion. This is largely due to the long haptonema that improves prey collection but at the cost of stealth and propulsion.    

Oscillatory phototaxis of Chlamydomonas reinhardtii

Biological microswimmers typically switch between positive and negative taxis under favorable and unfavorable environmental stimuli, respectively. However, it remains largely unclear how the cell transition between taxis of opposite signs. Here, we focus on investigating the transition between positive and negative phototaxis of Chlamydomonas reinhardtii. In particular, we observe that Chlamydomonas cells exhibit oscillatory phototaxis at an intermediate light intensity, where the cells oscillate between positive and negative phototaxis which occur at low and high light intensity, respectively. By experimentally tracking the Chlamydomonas cells at different phototaxis modes, we find that oscillatory phototaxis is mediated by tuning the phase relationship between the eyespot and the cell orientation as well as their flagellar beats. We develop a hydrodynamic model to capture how the cell tunes the phase relationship and how they respond to light stimuli. This study will lead to a general understanding on how swimming microorganisms transition between their positive and negative taxis behaviors.   

A macroscopic model for hydrodynamic interactions of bacterial flagellar bundles

Flagellated bacteria such as E. coli swim by rotating a helical rod-shaped propeller composed of a bundle of multiple flagella. Although the swimming of flagellated bacteria has been extensively studied, the collective dynamics of individual flagella in a bundle dictated by complex hydrodynamic, elasto-hydrodynamic and steric interactions at short distances of tens of nanometers remain elusive. Here, we experimentally investigate the hydrodynamic interactions between flagella by constructing a macroscopic scale model of a flagellar bundle. Specifically, we fabricate centimeter-scaled metal helical filaments and use high-viscosity silicone oil as our working fluid. Slow rotation of filaments in the oil at various controlled distances allow us to explore the effect of hydrodynamic coupling on the rotational dynamics of filaments at low Reynolds numbers. We further image the flow field around rotating helical filaments via PIV and compare our results with the predictions of slender-body theory. Our study reveals the hydrodynamic principles governing the collective dynamics of bacterial flagella and provides new insights into the locomotion of flagellated bacteria.