All posts by khalidjm@umich.edu

Flagellar mechanics at APS meeting (03/14/16)

Our work on the effect of a rigid boundary on the propulsion and instability of flagellar propulsion will be presented at American Physical Society (APS) March meeting to be held in Baltimore, MD. The presentation is scheduled for 1:27-1:39pm, March 14, 2016, in Baltimore Convention Center. Click here for details. More details on our research on flagellar mechanics can be found here.

March 14, 2016

Flagellar mechanics at APS meeting (11/24/15)

Our work on the effect of a rigid boundary on the propulsion and instability of flagellar propulsion was presented at American Physical Society (APS) Division of Fluid Dynamics (DFD) annual meeting to be held in Boston. The presentation is scheduled for 1:29-1:42pm, November 24, 2015, in Hynes Convention Center. Click here for details. More details on our research on flagellar mechanics can be found here.

November 24, 2015

Biolocomotion

Our research focuses on the mechanics of bacterial flagella. Bacteria propel themselves by rotating one or more helical slender structures, known as the flagella. The rotation generates a propulsive force that allows for the bacteria to locomote. At this length-scale, viscous forces overcome inertia, and the flow is at low Reynolds number.

Two primary challenges in modeling flagella include:

  • Experimentally systematic manipulation of micron-sized bacterial flagella is difficult, and often impossible
  • Numerically, coupling the hydrodynamics of the fluid with the structural mechanics of the flagella pose a challenging fluid-structure problem

To overcome these two challenges, we take a two pronged approach, and combine desktop model experiments and cutting-edge simulation tools from computer graphics.

Experiments: As an analog system for flagella, we consider custom fabricated flexible helical rods of ~20 cm length, and rotate them in a bath of glycerine, see the image below.  Our procedure allows us to systematically vary all the relevant parameters: material (Young’s modulus), geometry (rod radius, helix pitch, helix radius, length of rod), and fluid (viscosity). The setup is temperature controlled since it allows us to change the viscosity of the fluid medium.

FlagellaSetup

Figure: (a) Experimental apparatus: a helical rod (1), is rotated by a motor (2), inside a glycerin bath (3), that is enclosed by an external water tank (4) for temperature control. Two orthogonal video cameras (5,6) record the rod. (b) Schematic diagram of the rod.

NumericalSetupFlagellaSimulations: We performed numerical simulations where we combined Discrete Elastic Rods (DER) for an elastic description of the rod and Lighthill Slender Body Theory (LSBT) to model the hydrodynamics. DER describes a rod as a centerline parameterized by an arc-length parameter, s, and discretizes the line into a number of nodes. LSBT relates the velocity along the arc-length as a function of the viscous force applied by the fluid. Such a formulation accounts for the long-range hydrodynamic interaction between flows induced by distant parts of the rod. This is in contrast with Resistive Force Theories that use local drag coefficients, and can result in oversimplification.

Results: The flexibility of the flagellum interacts with the hydrodynamics to produce novel physical phenomena. Above a certain critical angular velocity, the hydrodynamic forces cause the rod to buckle (see video above). Our analysis shows that this buckling instability can potentially  happen in biologically relevant regime. We hypothesize that natural bacteria exploit this instability for physiological purposes, e.g. to change swimming direction. For more details, please refer to our publications below.

Publications

  1. Jawed, M. K., Reis, P., “Deformation of a soft helical filament in an axial flow at low Reynolds number” Soft Matter 12, 1898-1905 (2016)
  2. Jawed, M. K., Khouri, N., Da, F., Grinspun, E., Reis, P., “Propulsion and instability of flexible helical rod rotating in viscous fluidPhysical Review Letters 115:16, 168101 (2015)
    Press coverage: Physics Synopsis

Coauthors

Noor Khouri (MIT), Fang Da (Columbia), Eitan Grinspun (Columbia), Pedro Reis (MIT)

Image reused under Creative Commons Attribution-ShareAlike license.