Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session LQ: Biolocomotion VII: Micro-Swimming III |
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Chair: Silas Alben, Georgia Institute of Technology Room: Long Beach Convention Center 203B |
Monday, November 22, 2010 3:35PM - 3:48PM |
LQ.00001: Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration? H. Gadelha, E. Gaffney, D. Smith, J. Kirkman-Brown Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. While the mechanics of flagellum-fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear. In this talk, we study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape - no signalling or asymmetric forces are required. We conclude that non-linear models are essential in understanding the flagellar waveform in migratory human sperm. [Preview Abstract] |
Monday, November 22, 2010 3:48PM - 4:01PM |
LQ.00002: Nature's Helical Propeller Saverio Spagnolie, Eric Lauga Many microorganisms propel themselves through fluids by passing either planar waves (typically eukaryotes) or helical waves (typically prokaryotes) along a filamentous flagellum. Both from a biological and an engineering perspective, it is of great interest to understand the role of the waveform shape in determining an organism's locomotive kinematics, as well as its hydrodynamic efficiency. In this talk we consider the specific issue of locomotion optimization for bacterial swimming, and we investigate the agreement between experimentally measured biological data on the swimming of E. coli and Salmonella, and optimization results from accurate numerical computations of the viscous flow fields around rotating bacterial flagella. [Preview Abstract] |
Monday, November 22, 2010 4:01PM - 4:14PM |
LQ.00003: Flagellar propulsion near walls Arthur Evans, Eric Lauga Confinement and wall effects are known to affect the kinematics and propulsive characteristics of swimming microorganisms. When a solid body is dragged through a viscous fluid at constant velocity, the presence of a wall increases fluid drag, and thus the net force required to maintain speed has to increase. In contrast, recent optical trapping experiments have revealed that the propulsive force generated by human spermatozoa is decreased by the presence of boundaries. Here we use simple models to analytically elucidate the propulsive effects of a solid boundary on passively actuated filaments and model eukaryotic flagella. We show that in some cases, the increase in fluid friction induced by the wall can lead to a change in the waveform expressed by the flagella which results in a decrease of their propulsive force near a no-slip wall. [Preview Abstract] |
Monday, November 22, 2010 4:14PM - 4:27PM |
LQ.00004: Hydrodynamics of insect spermatozoa On Shun Pak, Eric Lauga Microorganism motility plays important roles in many biological processes including reproduction. Many microorganisms propel themselves by propagating traveling waves along their flagella. Depending on the species, propagation of planar waves (e.g. \textit{Ceratium}) and helical waves (e.g. \textit{Trichomonas}) were observed in eukaryotic flagellar motion, and hydrodynamic models for both were proposed in the past. However, the motility of insect spermatozoa remains largely unexplored. An interesting morphological feature of such cells, first observed in $\textit{Tenebrio molitor}$ and $\textit{Bacillus rossius}$, is the double helical deformation pattern along the flagella, which is characterized by the presence of two superimposed helical flagellar waves (one with a large amplitude and low frequency, and the other with a small amplitude and high frequency). Here we present the first hydrodynamic investigation of the locomotion of insect spermatozoa. The swimming kinematics, trajectories and hydrodynamic efficiency of the swimmer are computed based on the prescribed double helical deformation pattern. We then compare our theoretical predictions with experimental measurements, and explore the dependence of the swimming performance on the geometric and dynamical parameters. [Preview Abstract] |
Monday, November 22, 2010 4:27PM - 4:40PM |
LQ.00005: The dependence of the swimming efficiency of multi-flagellated bacteria on the geometric arrangement of flagella Nobuhiko Watari, Ronald Larson Multi-flagellated bacteria, such as \textit{Escherichia coli}, often have flagella attached at random locations to the cell body. To study the effect of the number of flagella and the geometric arrangement of them to the swimming efficiency, we develop a simulation method using a bead-spring model to account for the hydrodynamic and the mechanical interactions between multiple flagella and the cell body. First, a modeled bacterium is constructed using beads, which represent the hydrodynamic drag centers of the geometric elements of the bacterium. This modeled bacterium swims by rotating the flagella with constant torques at the bases of them. We have found that for modeled bacteria with two flagella, the swimming speed varies by 30\% depending on the position of the base of the flagellum along the cell body, which affects the tightness of the bundling. We have also found that overly rigid flagella can slow migration by inhibiting flagellar bundling, since bundling requires some adjustment in flagellar shape to compensate for helical phase miss-match produced by irregular flagellar positioning. In general, by changing the geometric arrangement and the number of flagella, our simulation enables us to determine the optimal designing of a flagellated micro-swimmer. [Preview Abstract] |
Monday, November 22, 2010 4:40PM - 4:53PM |
LQ.00006: ``Corkscrew'' vs. ``tank-treading'' propulsion of spirochetes. Alexander Leshansky, Oded Kenneth We consider the potential mechanism of spirochete propulsion driven by twirling of the outer cell surface coupled to counter-rotation of the helical body. We construct a proper slender body theory and use particle-based numerical approach allowing for modeling of locomotion in heterogeneous viscous environment. Depending on the helical pitch angle, two distinct propulsion gaits are identified: corkscrew-like locomotion, similar to propulsion powered by rotating helical flagellum, and surface tank-treading mode relying on hydrodynamic self-interaction of curved helical coils. The latter mechanism is closely related to the considered earlier propulsion of Purcell's toroidal swimmer (Kenneth and Leshansky, Phys. Fluids \textbf{20}, 063104, 2008). Significant augmentation of corkscrew propulsion gait in heterogeneous viscous medium anticipated from the numerical model is in accord with experimental observations of enhanced spirochete propulsion in polymer gels. [Preview Abstract] |
Monday, November 22, 2010 4:53PM - 5:06PM |
LQ.00007: Parametric Studies of Swimming Filaments at Low Reynolds Numbers Tristan Spoor, Stephan Koehler, Eric Willisson Swimming of microorganisms in viscous fluids is a complex problem involving many degrees of freedom. In order to gain insight on this problem we investigate a simple model for locomotion of a thin, finite-length undulating filament. By keeping the number of parameters minimal we are able to compare similarities for four waveforms; two different sinusoidal (Cartesian and curvature), sawtooth, and square strategies. Beyond the domain of straight motion a number of turning strategies are also considered. These strategies are evaluated and in the case of the straight swimmers, although the differences between the strategies in terms of greatest speed are substantial, the differences in terms of greatest efficiency are small. [Preview Abstract] |
Monday, November 22, 2010 5:06PM - 5:19PM |
LQ.00008: Dynamics of flagellar bundling Pieter Janssen, Michael Graham Flagella are long thin appendages of microscopic organisms used for propulsion in low-Reynolds environments. For \emph{E. coli} the flagella are driven by a molecular motor, which rotates the flagella in a counter-clockwise motion (CCM). When in a forward swimming motion, all flagella bundle up. If a motor reverses rotation direction, the flagella unbundle and the cell makes a tumbling motion. When all motors turn in the same CC direction again, the flagella bundle up, and forward swimming continues. To investigate the bundling, we consider two flexible helices next to each other, as well as several flagella attached to a spherical body. Each helix is modeled as several prolate spheroids connected at the tips by springs. For hydrodynamic interactions, we consider the flagella to made up of point forces, while the finite size of the body is incorporated via Fax\'{e}n's laws. We show that synchronization occurs quickly relative to the bundling process. For flagella next to each other, the initial deflection is generated by rotlet interactions generated by the rotating helices. At longer times, simulations show the flagella only wrap once around each other, but only for flagella that are closer than about 4 helix radii. Finally, we show a run-and-tumble motion of the body with attached flagella. [Preview Abstract] |
Monday, November 22, 2010 5:19PM - 5:32PM |
LQ.00009: An Integrative Model of Hyperactivated Sperm Motility Sarah Olson, Susan Suarez, Lisa Fauci Calcium (Ca2+) dynamics in mammalian sperm are directly linked to motility. These dynamics depend on diffusion, nonlinear fluxes, Ca2+ channels specific to the sperm flagellum, and other signaling molecules. The goal of this work is to couple Ca2+ dynamics to a mechanical model of a motile sperm within a viscous, incompressible fluid. An immersed boundary formulation of regularized Stokeslets is used to investigate the hydrodynamics and emergent waveforms and velocities. We will present recent progress on elements of this integrative model. [Preview Abstract] |
Monday, November 22, 2010 5:32PM - 5:45PM |
LQ.00010: Elastic symmetry-breaking in synchronizing cells Gwynn Elfring, Eric Lauga Swimming microorganisms such as spermatozoa have been observed to synchronize their flagella when swimming in close proximity. We showed recently that this can arise passively in part due to an asymmetry in the flagellar waveforms of the cells. Using a simple two dimensional model we investigate here the role of fluid body interactions and flagella elasticity as a source of asymmetry, and whether or not flexibility is sufficient to induce synchronization. [Preview Abstract] |
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