Session T05: Biological Fluid Dynamics: Locomotion, Cilia & Flagella

Imaging the 3D flow field of free-swimming Chlamydomonas reinhardtii with high-speed holographic microscopy

The flow induced by microswimmers provides invaluable insights in the mode of their locomotion, as well as their interactions with each other and surrounding environment. While the two-dimensional (2D) flow fields of single microswimmers have been well-characterized in previous experiments, obtaining reliable measurements on the three-dimensional (3D) flow field around a single microswimmer remains challenging due to experimental difficulties associated with the high-speed, high-resolution velocimetry of 3D flow. Here, we present a precise measurement of the time-averaged 3D flow induced by a motile, free-swimming microalga, Chlamydomonas reinhardtii, using high-speed holographic microscopy. The flow of the alga is obtained by tracking the motion of micron-sized tracers over thousands of its flagellar beating cycle. Our experiments capture the crucial details of the 3D flow field of microorganisms in their natural swimming mode and demonstrate the power of holographic microscopy in imaging complex flow fields with unprecedented spatiotemporal resolutions.   

Enhanced feeding of model ciliates in non-uniform concentration fields

Aquatic sessile microorganisms often use cilia to generate feeding currents. Existing studies

focus on feeding in uniform background concentrations. Although concentrations that are non-

uniform at length scales comparable to the organism are more common, little is known about

whether and how sessile organisms can generate flows that benefit from this non-uniformity. Here,

we consider a classic squirmer, based on Blake’s spherical envelope model, fixed in a non-uniform

background concentration, and we analyze the effects of the squirming motion on nutrients up-

take. The squirmer model emulates packed cilia as a continuous deformable surface for which an

analytical solution of the cilia-generated flow field exists as a Legendre expansion in terms of the

fundamental squirming modes. Using the analytical solution of the flow field in conjunction with

direct numerical simulation of the advection-diffusion equation, we solve for the steady and un-

steady concentration fields and compute nutrients uptake in uniform and non-uniform background

concentrations. The steady and unsteady results consistently show that the surface cilia motion,

dominantly putting energy into the squirming mode bringing flows from the direction of higher

concentration, enhances the feeding nutrients of the squirmer.   

Asymmetric driving forces and spatial heterogeneity enhance metachronal order in ciliary carpets

Ciliary carpets drive biological flows through the coordination of thousands of multiciliated cells, each containing hundreds of cilia. Despite progress in analyzing cilia coordination in certain models, general quantitative theories that can resolve both the multi-scale cilia coordination and flow patterns remain lacking. Combining numerics and theory based on the phased oscillator model of individual cilia, we systematically demonstrate how multi-scale disorder affects the long-term synchronization dynamics and resulting flow patterns in ciliary carpets. In particular, we show how individual cilium activity that leads to worse synchrony under uniformly covered tissues can surprisingly accelerate the formation of global metachronal order and outperform their counterparts when cilia coverage is reduced and tissue-level patchiness is introduced. Our findings are consistent with recent suggestion that spatial heterogeneity in cilia organization and tissue architecture enhance particle clearance, and go beyond these results to simultaneously probe the effect of spatial heterogeneity on cilia coordination and cilia-induced flows.   

Studying ctenophore maneuverability with reduced-order analytical modeling

Ctenophores are centimeter-scale zooplankton capable of performing complex maneuvers by metachronally coordinating eight rows of cilia-based paddles (ctenes) that circumscribe their bodies. We used high-speed videography to study the maneuverability of Bolinopsis vitrea. From the animal experiments, we have observed three potentially different turning mechanisms: sharp, wide, and reversal turn. During sharp turns, only the ctene rows on the outside of the turn are active. For wide turns, all ctene rows are active; however, the beat frequency varies between opposing pairs of ctene rows. During reversals, ctenophores perform sharp turns while transitioning from backward to forward swimming, which also slightly changes the body orientation. Despite these observations, we do not have a systematic understanding of how rowing coordination impacts maneuverability. To explore the role of ctene row coordination, we developed an analytical model of a ctenophore swimming freely in three dimensions. This model allows us to calculate the forces created by the ctenes under these three different turning scenarios. The results from both experimental observation and analytical modeling show that ctenophore propulsion is a prime candidate to inform future bioinspired aquatic vehicles.   

A multiscale biophysical model gives quantized metachronal waves in a lattice of cilia

Motile cilia are slender, hair-like cellular appendages that spontaneously oscillate under the action of internal molecular motors and are typically found in dense arrays. These active filaments coordinate their beating to generate metachronal waves that drive long-range fluid transport and locomotion. Until now, our understanding of their collective behavior largely comes from the study of minimal models that coarse-grain the relevant biophysics and the hydrodynamics of slender structures. Here we build on a detailed biophysical model to elucidate the emergence of metachronal waves on millimeter scales from nanometer-scale motor activity inside individual cilia. Our study of a 1D lattice of cilia in the presence of hydrodynamic and steric interactions reveals how metachronal waves are formed and maintained. We find that in homogeneous beds of cilia these interactions lead to multiple attracting states, all of which are characterized by an integer charge that is conserved. This even allows us to design initial conditions that lead to predictable emergent states. Finally, and very importantly, we show that in nonuniform ciliary tissues, boundaries and inhomogeneities provide a robust route to metachronal waves.    

Coordinated motion of active filaments on spherical surfaces

Active filaments (slender, self-deforming, and microscopic elastic bodies) are prevalent in biological settings with the prime examples being cilia and flagella.  For cilia in particular, which can appear in dense arrays, their resulting motions are coupled through the surrounding fluid, as well as through the surfaces to which they are attached.  In this talk, I will present numerical simulations exploring the coordinated motion of hundreds of active filaments and how it depends on the driving force, density of filaments, as well as the attached surface.  We find that when the surface is spherical, its topology introduces defects in the coordinated motion which alter filament motion, especially in their vicinity.  Further, when the sphere is not held fixed, its motion feeds back onto the filaments, leading to more profound changes in their motion and the emergence of a new coordinated state.   

An integrated chemomechanical model of sperm locomotion reveals two fundamental swimming modes

Mammalian sperm cells achieve locomotion by the spontaneous periodic oscillation of their flagellum. Dynein motors inside the flagellum consume energy from ATP to exert active sliding forces between microtubule doublets, thus creating bending waves along the flagellum and enabling the sperm cell to swim in a viscous medium. Using a sliding-control model of the axoneme that captures the coupling of motor kinetics with elastic deformations, we develop a chemomechanical model of a freely swimming sperm cell that accounts for the effect of non-local hydrodynamic interactions between the sperm head and flagellum. The model is shown to produce realistic beating patterns and swimming trajectories, which we analyze as a function of sperm number and motor activity. Remarkably, we find that the swimming velocity does not vary monotonically with motor activity, but instead displays two local maxima corresponding to distinct modes of swimming.   

Flow-Induced Deformations and Bending Stiffness of Tethered Salmonella Flagella

The mechanical properties of the bacterial flagellum are essential for understanding bacterial locomotion. We analyze an experiment where a Salmonella flagellum, attached to the bottom of a microfluidic channel, is stretched due to the hydrodynamic forces. We reconstruct the 3D geometry of the flagellum from microscopic images. Using the method of regularized Stokeslets, we determine hydrodynamic forces acting on the flagellum. Coupling the forces to a Kirchhoff rod model allows us to predict the deformed shape of the flagellum, taking as inputs the background flow, the undeformed geometry of the flagellum, and its bending stiffness. Previous studies suggest that flagella can take 12 different polymorphic forms, distinguished by the pitch and radius of their helical shapes. However, in absence of any flow, we observed flagella with a different pitch and radius not comparable to any known form. Furthermore, we found that if the undeformed shape is assumed to be that of a known polymorphic form, predicted deformed shapes are unlike those that are observed in the presence of flow. On the other hand, if the undeformed shape is assumed to be that observed in the absence of flow, bending stiffness of 2-2.5 pN.μm² predicts the observed deformed shapes.   

Macroscopic robophysical model of turning in biflagellate algae

Single-cell algae exhibit diverse behaviors and are capable of goal-directed motion. Of interest is phototaxis, a light-triggered response during which algae swim and turn their eyespot towards a light source. While the photoreceptor responsible for this behavior has been characterized, the mechanics behind this response remain unknown. In Chlamydomonas, studies suggest that phototactic turning is mediated by differential changes in the beating frequency and amplitude of the flagella (Witman, 1996). To study algae turning, we developed a macroscopic motor-driven robophysical model (two flagella, body length of 8 cm) that swims in a viscous fluid (glycerin, 1,100 cSt) to replicate low Reynolds number swimming. We varied the frequency of one flagella (trans) while maintaining the other constant (cis). We observed that turning rate depended on the phase of the cis flagellum. When the cis flagellum was in the recovery phase, the robot achieved a rotation from 23– 34 degrees per cycle (deg/cyc). When the cis flagellum was in the power phase, the robot achieved a rotation of 8 – 13 deg/cyc. The results suggest that turning is sensitive to flagellar coordination. Preliminary experiments suggest feedback control can be implemented in the robot to generate autonomous phototactic turning.   

Hydrodynamic effects of mastigonemes in Cryptophytes

Cryptophytes are aquatic unicellular eukaryotes that inhabit both marine and freshwater environments worldwide and whose photosynthetic forms may be responsible for a large part of primary carbon production. Cryptophytes have flattened, elliptical cells and swim using two flagella that are known to bear rigid mastigonemes, fibrous ultrastructures of a nanometer-scale thickness. It has been claimed that by affecting the drag of flagella, mastigonemes can affect swimming behavior — even reversing swimming direction, but the hydrodynamic effect of these filaments seems to be different for different species. In this study, we experimentally investigate flagellar kinematics and mastigoneme geometry on Chilomonas paramecium through high-speed imaging of freely swimming cells, and SEM and TEM imaging. We then numerically investigate the hydrodynamic effects of these mastigonemes using the method of regularized Stokeslets. Finally, we also study and simulate the kinematics of a singly flagellated protist, which we believe may be a haploid form of Chilomonas paramecium.    

Hydrodynamic interactions are key in thrust-generation of microswimmers with hairy flagella

The important role of flagellates in aquatic microbial food webs is mediated by their flagella that enable them to swim and generate a feeding current. The flagellum in most predatory flagellates is equipped with rigid hairs that reverse the direction of thrust compared to the thrust due to a smooth flagellum. Conventionally, such reversal has been attributed to drag anisotropy of individual hairs, neglecting their hydrodynamic interactions. Here, we show that hydrodynamic interactions are key to thrust-generation and reversal in hairy flagellates, making their hydrodynamics fundamentally different from the slender-body theory governing microswimmers with smooth flagella. Using computational fluid dynamics and model analysis, we demonstrate that long and not too closely spaced hairs and strongly curved flagellar waveforms are optimal for thrust-generation. Our results form a theoretical basis for understanding the diverse flagellar architectures and feeding modes found in predatory flagellates.   

Hydrodynamic interactions between bacterial flagellar filaments

Hydrodynamic interactions are essential in many biological flows, from the collective self-organisation of micro-swimmers to the coordination of cilia and flagella into well-defined swimming gaits. In this talk, we show how to use an asymptotic expansion to compute the extended resistance matrix of two hydrodynamically-coupled slender filaments, valid when the inter-filament distance is greater than the filament length [1]. Next, we demonstrate how this analytical theory can be applied to the case of helical filaments and, in conjunction with slender-body theory (SBT) simulations, lead to valuable insights on the hydrodynamic synchronization [2] and the propulsive capacity of multiple rotating bacterial flagella.