Douglas R. Brumley

Flagellar synchronization through direct hydrodynamic interactions

Flows generated by ensembles of flagella are crucial to development, motility and sensing, but the mechanisms behind this striking coordination remain unclear. We present novel experiments in which two micropipette-held somatic cells of Volvox carteri, with distinct intrinsic beating frequencies, are studied by high-speed imaging as a function of their separation and orientation. Analysis of time series shows that the interflagellar coupling, constrained by lack of connections between cells to be hydrodynamical, exhibits a spatial dependence consistent with theory. At close spacings it produces robust synchrony for thousands of beats, while at increasing separations synchrony is degraded by stochastic processes. Manipulation of the relative flagellar orientation reveals in-phase and antiphase states, consistent with dynamical theories. Flagellar tracking with exquisite precision reveals waveform changes that result from hydrodynamic coupling. This study proves unequivocally that flagella coupled solely through a fluid can achieve robust synchrony despite differences in their intrinsic properties. DOI: http://dx.doi.org/10.7554/eLife.02750.001

Oscillation of cylinders of rectangular cross section immersed in fluid

The ability to calculate flows generated by oscillating cylinders immersed in fluid is a cornerstone in micro- and nanodevice development. In this article, we present a detailed theoretical analysis of the hydrodynamic load experienced by an oscillating rigid cylinder, of arbitrary rectangular cross section, that is immersed in an unbounded viscous fluid. We also consider the formal limit of inviscid flow for which exact analytical and asymptotic solutions are derived. Due to its practical importance in application to the atomic force microscope and nanoelectromechanical systems, we conduct a detailed assessment of the dependence of this load on the cylinder thickness-to-width ratio. We also assess the validity and accuracy of the widely used infinitely-thin blade approximation. For thin rectangular cylinders of finite thickness, this approximation is found to be excellent for out-of-plane motion, whereas for in-plane oscillations it can exhibit significant error. A database of accurate numerical results for the hydrodynamic load as a function of the thickness-to-width ratio and normalized frequency is also presented, which is expected to be of value in practical application and numerical benchmarking.

Live from under the lens: exploring microbial motility with dynamic imaging and microfluidics

Motility is one of the most dynamic features of the microbial world. The ability to swim or crawl frequently governs how microorganisms interact with their physical and chemical environments, and underpins a myriad of microbial processes. The ability to resolve temporal dynamics through time-lapse video microscopy and the precise control of the physicochemical microenvironment afforded by microfluidics offer powerful new opportunities to study the many motility adaptations of microorganisms and thereby further our understanding of their ecology. In this Review, we outline recent insights into the motility strategies of microorganisms brought about by these techniques, including the hydrodynamic signature of microorganisms, their locomotion mechanics, chemotaxis, their motility near and on surfaces, swimming in moving fluids and motility in dense microbial suspensions.

Squirmers with swirl: a model for Volvox swimming

Colonies of the green alga Volvox are spheres that swim through the beating of pairs of flagella on their surface somatic cells. The somatic cells themselves are mounted rigidly in a polymeric extracellular matrix, fixing the orientation of the flagella so that they beat approximately in a meridional plane, with axis of symmetry in the swimming direction, but with a roughly azimuthal offset which results in the eponymous rotation of the colonies about a body-fixed axis. Experiments on colonies of Volvox carteri held stationary on a micropipette show that the beating pattern takes the form of a symplectic metachronal wave (Brumley et al. Phys. Rev. Lett., vol. 109, 2012, 268102). Here we extend the Lighthill/Blake axisymmetric, Stokes-flow model of a free-swimming spherical squirmer (Lighthill Commun. Pure Appl. Maths, vol. 5, 1952, pp. 109–118; Blake J. Fluid Mech., vol. 46, 1971b, pp. 199–208) to include azimuthal swirl. The measured kinematics of the metachronal wave for 60 different colonies are used to calculate the coefficients in the eigenfunction expansions and hence predict the mean swimming speeds and rotation rates, proportional to the square of the beating amplitude, as functions of colony radius. As a test of the squirmer model, the results are compared with measurements (Drescher et al. Phys. Rev. Lett., vol. 102, 2009, 168101) of the mean swimming speeds and angular velocities of a different set of 220 colonies, also given as functions of colony radius. The predicted variation with radius is qualitatively correct, but the model underestimates both the mean swimming speed and the mean angular velocity unless the amplitude of the flagellar beat is taken to be larger than previously thought. The reasons for this discrepancy are discussed.

Physical limits on bacterial navigation in dynamic environments

Many chemotactic bacteria inhabit environments in which chemicals appear as localized pulses and evolve by processes such as diffusion and mixing. We show that, in such environments, physical limits on the accuracy of temporal gradient sensing govern when and where bacteria can accurately measure the cues they use to navigate. Chemical pulses are surrounded by a predictable dynamic region, outside which bacterial cells cannot resolve gradients above noise. The outer boundary of this region initially expands in proportion to the square root of time before rapidly contracting. Our analysis also reveals how chemokinesis—the increase in swimming speed many bacteria exhibit when absolute chemical concentration exceeds a threshold—may serve to enhance chemotactic accuracy and sensitivity when the chemical landscape is dynamic. More generally, our framework provides a rigorous method for partitioning bacteria into populations that are ‘near’ and ‘far’ from chemical hotspots in complex, rapidly evolving environments such as those that dominate aquatic ecosystems.

Flagella, flexibility and flow: Physical processes in microbial ecology

How microorganisms interact with their environment and with their conspecifics depends strongly on their mechanical properties, on the hydrodynamic signatures they generate while swimming and on fluid flows in their environment. The rich fluid-structure interaction between flagella – the appendages microorganisms use for propulsion – and the surrounding flow, has broad reaching effects for both eukaryotic and prokaryotic microorganisms. Here, we discuss selected recent advances in our understanding of the physical ecology of microorganisms, which have hinged on the ability to directly interrogate the movement of individual cells and their swimming appendages, in precisely controlled fluid environments, and to image them at appropriately fast timescales. We review how a flagellar buckling instability can unexpectedly serve a fundamental function in the motility of bacteria, we elucidate the role of hydrodynamics and flexibility in the emergent properties of groups of eukaryotic flagella, and we show how fluid flows characteristic of microbial habitats can strongly bias the migration and spatial distribution of bacteria. The topics covered here are illustrative of the potential inherent in the adoption of experimental methods and conceptual frameworks from physics in understanding the lives of microorganisms.

Natural search algorithms as a bridge between organisms, evolution, and ecology.

The ability to navigate is a hallmark of living systems, from single cells to higher animals. Searching for targets, such as food or mates in particular, is one of the fundamental navigational tasks many organisms must execute to survive and reproduce. Here, we argue that a recent surge of studies of the proximate mechanisms that underlie search behavior offers a new opportunity to integrate the biophysics and neuroscience of sensory systems with ecological and evolutionary processes, closing a feedback loop that promises exciting new avenues of scientific exploration at the frontier of systems biology.

Transitions in synchronization states of model cilia through basal-connection coupling

Despite evidence for a hydrodynamic origin of flagellar synchronization between different eukaryotic cells, recent experiments have shown that in single multi-flagellated organisms, coordination hinges instead on direct basal body connections. The mechanism by which these connections lead to coordination, however, is currently not understood. Here, we focus on the model biflagellate Chlamydomonas reinhardtii, and propose a minimal model for the synchronization of its two flagella as a result of both hydrodynamic and direct mechanical coupling. A spectrum of different types of coordination can be selected, depending on small changes in the stiffness of intracellular couplings. These include prolonged in-phase and anti-phase synchronization, as well as a range of multi-stable states induced by spontaneous symmetry breaking of the system. Linking synchrony to intracellular stiffness could lead to the use of flagellar dynamics as a probe for the mechanical state of the cell.

Correction to ‘Physical limits on bacterial navigation in dynamic environments’

[ J. R. Soc. Interface 13 , 20150844 (2016; Published online 13 January 2016) ([doi:10.1098/rsif.2015.0844][2])][2] The authors wish to correct a typographical error in the definition of the coefficient, α , just beneath equation (3.3). It should read as follows:![Formula][2] []: /lookup/

Erratum: “Oscillation of cylinders of rectangular cross section immersed in fluid” [Phys. Fluids 22, 052001 (2010)]

in fluid” †Phys. Fluids 22, 052001 „2010...‡ Douglas R. Brumley, Michelle Willcox, and John E. Sader Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia Received 9 August 2010; accepted 9 August 2010; published online 13 September 2010 doi:10.1063/1.3487694 Numerical values in Table I a of Ref. 1 for the inviscid solution → with aspect ratios A 1 should read as follows. These corrections do not affect the discussion and conclusions, and all other results are unchanged.