Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session H31: Biological Fluid Dynamics: Locomotion Flagella |
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Chair: Henry Fu, University of Utah Room: 613 |
Monday, November 25, 2019 8:00AM - 8:13AM |
H31.00001: Geometry and Hydrodynamics of Flagellar Bundles Maria Tatulea-Codrean, Eric Lauga Most motile bacteria exploit chirality in order to break the symmetry of low Reynolds number flows and generate propulsion. Spirochaetes have developed corkscrew-shaped bodies, while bacteria with simpler bodies can assemble and actuate helical flagellar filaments. In the case of multi-flagellated species, the bacterium can bundle and unbundle its flagellar filaments in order to swim in a straight line or change direction, respectively. This process is central to their “run-and-tumble” mobility. The hydrodynamic benefit of having multiple filaments, however, is associated with an increasing risk of tangling within the bundle. At one extreme, we know that straight flagellar filaments could not intertwine, but neither could they propel the cell forward in a viscous fluid. Similarly, one filament could never tangle on its own, but neither could it generate a propulsive force as large as a bundle of flagellar filaments. In this talk, we will present some recent theoretical results about the role that flagellar geometry and number play in the robustness of forming a tangle-free bundle and the hydrodynamic efficiency thereof. [Preview Abstract] |
Monday, November 25, 2019 8:13AM - 8:26AM |
H31.00002: Synchronization modes of active microfilaments Yi Man, Eva Kanso Biological filaments are rarely found in isolation. Eukaryotic flagella beat in synchrony, an array of cilia generate the phase-locking metachronal wave. Experimental and computational studies provide a body of evidence that active filaments can synchronize through hydrodynamic coupling only. Previous theoretical models mostly address interactions in a far-field regime, where the interfilamentous distance $h$ is much larger than the filament length $L$. Here, we employ a simple active filament model and combine it with an asymptotic result of hydrodynamic interactions in a more biologically-relevant regime where $h/L\ll 1$. By varying the activity and coupling strength, we find three synchronization modes: in-phase, anti-phase, and a new mode which we refer to as \textit{asymmetric synchronization}. We map the basins of attraction of these modes and find bistable in-phase and anti-phase synchronization when the coupling is strong. Furthermore, we present a thorough Floquet-type stability analysis to show the evolution of the phase difference between two filaments. The Floquet analysis proves the existence of the new mode of \textit{asymmetric synchronization}, and it reveals a time scale it takes to reach the synchronized equilibria. [Preview Abstract] |
Monday, November 25, 2019 8:26AM - 8:39AM |
H31.00003: How do colonial micro-algae swim towards light? Helene De Maleprade, Frederic Moisy, Takuji Ishikawa, Raymond E. Goldstein Microscopic algae are commonly found in mud, puddles or lakes, and show great diversity in structural complexity. One of the simplest algae encountered is the unicellular `Chlamydomonas', exhibiting two flagella whose beating enables them to swim in a breast stroke. One also finds `Gonium pectorale', a colony made of 16 Chlamydomonas-like cells arranged in two concentric squares, with all flagella on one side of the plate. These colonies are among the first multicellular algae and their study offers an insight into the evolution from unicellular to coherent multicellular behaviour. Algae, like plants, get energy from photosynthesis: Gonium colonies take advantage of their motility to swim towards light, efficiently reorienting within a couple of seconds. However, the mechanism of this phototactic behaviour is not yet understood: how do all 16 cells individually produce a coherent collective response? How are the flagella modulated to create an asymmetry in the swimming pattern, and how does that lead to reorientation? We experimentally investigate the phototaxis of Gonium, analysing their reorientation trajectory towards light. We compare those results to an analytical model and numerical simulations, describing with high precision the reorientation process. [Preview Abstract] |
Monday, November 25, 2019 8:39AM - 8:52AM |
H31.00004: Bending Stiffness and Critical Forces for Polymorphic Transformations of Salmonella Flagella Measured in a Microfluidic Channel Hossein Moghimifam, Jamel Ali, Mehdi Jabbarzadeh, MinJun Kim, Henry C Fu Bacterial flagella have been shown to reversibly switch between different polymorphic forms under external forces. We present experiments on \textit{Salmonella} flagella tethered to the surface of a microfluidic channel that measure the flagellar bending stiffness and the critical force required to transform between coiled and normal forms. The near-wall shear flow exerts forces on the flagella and elastically stretches them, and when strong enough triggers polymorphic transformations. We developed a method to reconstruct the 3D geometry of a bacterial flagellum from fluorescent microscopy images with sub-pixel accuracy. The flagellar geometry is specified as a helix with pitch, radius, and axis direction that vary along its length. The expected image of the geometry is generated using point spread function. For each flow rate, we find the best-fit flagellar geometry by minimizing the pixel-to-pixel intensity difference between the generated and the microscopic image using a genetic algorithm. From the geometry of the flagellum and the known flow in the microchannel, we determined the forces on the flagellum using a boundary element method and found the critical force that caused the transformation. We also use a Kirchoff rod model to find the bending stiffness of the flagellum. [Preview Abstract] |
Monday, November 25, 2019 8:52AM - 9:05AM |
H31.00005: Time-dependent hook flexibilities in run-reverse-flick motility. Mehdi Jabbarzadeh, Henry C. Fu The deformation of the hook and flagellum affects bacterial motility in run-reverse-flick motility of single-flagellated bacteria. Previously, we have modeled the initiation of a flick, in which the flagellum makes a large off-axis motion, by an efficient linear spring model with a rigid cell body and flagellum while neglecting hydrodynamic interactions between the cell body and flagellum. However, a complete flick event involves bending of both the hook and flagellum as well as a time-varying hook stiffness. Here, we study the dynamic bending of the hook and flagellar filament during run-reverse and flick motility of single flagellated bacteria. We develop an accurate and more efficient numerical approach to model the dynamics of free-swimming bacteria that includes flexibility of both the hook and flagellum. Using numerical models, we are able to constrain the time dependent flexibility of the hook during run-reverse-flick motility. We compare results from rigid body simulations to the flexible flagellar filaments. Finally, we simulate complete flick events, investigating the buckling angle and reorientations of the swimming cells due to time dependent hook stiffness. [Preview Abstract] |
Monday, November 25, 2019 9:05AM - 9:18AM |
H31.00006: Hook flexibility and body trajectories of swimming microorganisms Zonghao Zou, Wilson Lough, Saverio Spagnolie The flexibility of the hook connecting the bacterial flagellum to the cell body, and an associated buckling instability, is believed to play an important role in microorganism locomotion. We consider a simplified model for the flagellum-cell dynamics and solve analytically for the flagellum orientation and cell trajectories through space. To better understand how hook flexibility affects the swimming pathway, we consider a sequence of problems, from fixed flagellar orientation, to specified orientation, to free, flexible motion dictated by force and torque balance. Exact helical trajectories yield to nearly-helical and then more complex paths. Other geometrical features are also explored, including baseline flagellum orientation. Numerical simulations reveal the regions of accuracy of our analytical predictions. [Preview Abstract] |
Monday, November 25, 2019 9:18AM - 9:31AM |
H31.00007: ABSTRACT WITHDRAWN |
Monday, November 25, 2019 9:31AM - 9:44AM |
H31.00008: Estimation of Internal Power Distribution in Sperm Flagella from Measurements of Beat Patterns Ashwin Nandagiri, Avinash Gaikwad, David Potter, Julio Soria, Moira O’Bryan, Sameer Jadhav, Ranganathan Prabhakar Sperm flagella are internally-driven flexible filaments that display complex beating patterns. We estimate energetics of the internal driving from measurements of beat patterns. A large number of beat cycles (~40) of mouse sperm tethered at their heads are recorded using high-speed, high-resolution microscopy. Flagellar centrelines are digitally extracted using image processing techniques. Proper Orthogonal Decomposition (POD) is used to represent the beat cycle data in a compact form and obtain an average representative beat cycle. The Kirchhoff theory for inextensible, elastic, rods is adapted to account for internal driving and combined with the Resistive Force Theory for hydrodynamic forces to compute the spatiotemporal power distribution of the internal forces exerted by protein motors in the sperm axoneme. Representative beat patterns and internal power distributions are computed for a large number of sperm samples from mutant mice deficient in a family of proteins that regulate calcium ion flux in the flagellum. Clear differences in beat patterns are observed which are found to be correlated with the active power distribution. [Preview Abstract] |
Monday, November 25, 2019 9:44AM - 9:57AM |
H31.00009: Stokeslets in the clinic: biological fluid dynamics applied to human sperm motility David Smith, Meurig Gallagher, Gemma Cupples, Cara Neal, Atticus Hall-McNair, Jackson Kirkman-Brown The motility of the male gamete has been central to the development of the theory of very low Reynolds number fluid mechanics, exemplified by Gray \& Hancock's classical work in the 1950s on sea urchin spermatozoa. This presentation will focus on translating recent research in biological fluid dynamics back to biology to provide new methods to analyse human sperm motility with the level of scale and automation necessary for the clinical context. Key areas of focus are: (1) automated capture of the flagellar movement from digital images (the FAST software package) and dimensionality reduction of the large datasets, (2) robust, simple and efficient fluid mechanical methods (the NEAREST software package), (3) elastohydrodynamics modelling of the active beating of the flagellum and energetic demands of motility, (4) statistical represention and summary of data from cell populations, and across patients. [Preview Abstract] |
Monday, November 25, 2019 9:57AM - 10:10AM |
H31.00010: Effect of external shear flow on sperm motility Manish Kumar, Arezoo Ardekani The presence of background flow affects the sperm trajectory and hence the success rate of the fertilization. We have studied the effect of unbounded simple shear flow and Poiseuille flow on the sperm trajectory. The sperm moves on an elliptical trajectory in the reference frame advecting with the local background flow in the simple shear flow and the length of the major-axis of this elliptical trajectory decreases with the shear rate. In the presence of Poiseuille flow, the sperm moves downstream or upstream depending on the flow strength. The sperm also moves toward the centerline in a Poiseuille flow. The cross-stream migration velocity of sperm decreases as the transverse distance of the sperm from the centerline decreases in the close vicinity of the centerline, while it increases far away from the centerline. We use sperm number, a dimensionless number representing the ratio of viscous force to elastic force, to study the effect of flagellar flexibility on the sperm trajectory. The length of the major axis of the elliptical trajectories increases with the sperm number in the simple shear flow and the cross-stream migration velocity of the sperm increases with the sperm number in a Poiseuille flow. [Preview Abstract] |
Monday, November 25, 2019 10:10AM - 10:23AM |
H31.00011: Finite Element Modeling of Microswimmers with Applications in Reproductive Biology Cara Neal, David Smith, Meurig Gallagher, Thomas Montenegro-Johnson The journey of human sperm to the egg is a complex and extremely important process. Sperm cells must navigate the intricate geometry of the fallopian tubes, generating active bending to swim through cervical mucus - a highly viscous, rheologically complex fluid. Many current models of sperm locomotion are computationally expensive, and most make the inaccurate assumption that the surrounding fluid is Newtonian. Here we develop a method capable of dealing with the non-linear equations associated with non-Newtonian fluids. This method uses a combination of a finite element technique and an elastohydrodynamic integral formulation (Hall-McNair et al. 2019) to model sperm cells with active flexible flagellum. This formulation provides an efficient way of modeling single or multiple cells, accounting for the hydrodynamic interactions between them. In particular, the finite element component is formulated in such a way that the solution can be calculated on a coarse mesh, for reduced computational costs compared to more commonly used body-fitted meshes. We study how the model can be made more biologically accurate through the inclusion of varying bending stiffness as well as a passive distal region of the flagellum, and the subsequent effect on swimming efficiency. [Preview Abstract] |
Monday, November 25, 2019 10:23AM - 10:36AM |
H31.00012: Interaction of spermatozoa with micro structured surfaces. Vasily Kantsler, Anton Bukatin, Enkeleida Lushi, Petr Denissenko Spermatozoa navigation plays crucial role in the process of mammalian fertilization. Mechanical interactions in the heterogonous environment of the fertility such as surface scattering and rheotaxis are the key mechanisms in determining the sperm journey towards the ovum. Here we report an experimental study of interaction mechanisms for single human sperm cells scattering off solid surface boundaries of different curvature. The investigation is based on measuring the trajectories of the cells near convex and concave surfaces with 30 -- 300 um radii of curvature in a microfluidic device. By analysing several thousands of cells' trajectories we built the residence time dependences, concentration profiles the scattering distributions as a function of the surface curvature. For the concave objects, we have identified the surface curvature corresponding to the minimum of the cell residence time within the concave cavity, while in the convex case, we define a critical curvature that traps the cells. The results enable us to design a new type of microfluidic devices for rapid selection of motile cells in-vitro. [Preview Abstract] |
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