The role of body rotation in bacterial flagellar bundling

In bacterial chemotaxis, E. coli cells drift up chemical gradients by a series of runs and tumbles. Runs are periods of directed swimming, and tumbles are abrupt changes in swimming direction. Near the beginning of each run, the rotating helical flagellar filaments which propel the cell form a bundle. Using resistive-force theory, we show that the counter-rotation of the cell body necessary for torque balance is sufficient to wrap the filaments into a bundle, even in the absence of the swirling flows produced by each individual filament

Twirling Elastica: Kinks, Viscous Drag, and Torsional Stress

Biological filaments such as DNA or bacterial flagella are typically curved in their natural states. To elucidate the interplay of viscous drag, twisting, and bending in the overdamped dynamics of such filaments, we compute the steady-state torsional stress and shape of a rotating rod with a kink. Drag deforms the rod, ultimately extending or folding it depending on the kink angle. For certain kink angles and kink locations, both states are possible at high rotation rates. The agreement between our macroscopic experiments and the theory is good, with no adjustable parameters.Comment: 4 pages, 4 figure

Film support and the challenge of ‘sustainability’: on wing design, wax and feathers, and bolts from the blue

In recognition of the importance of film in generating both economic and cultural value, the UK Labour government set up a new agency – the United Kingdom Film Council (UKFC) – in 2000 with a remit to build a sustainable film industry. But, reflecting a plethora of differing expectations in relation to the purposes behind public support for film, the UKFC's agenda shifted and broadened over the organisation's lifetime (2000–11). Apparently unconvinced by the UKFC's achievements, the Coalition government which came to power in May 2010 announced the Council's abolition and reassigned its responsibilities as part of a general cost-cutting strategy. Based on original empirical research, this article examines how the UKFC's sense of strategic direction was determined, how and why the balance of objectives it pursued changed over time and what these shifts tell us about the nature of film policy and the challenges facing bodies that are charged with enacting it in the twenty-first century

Predictors of recurrence and reoperation for prosthetic valve endocarditis after valve replacement surgery for native valve endocarditis

ObjectiveSurgical treatment of native valve endocarditis remains challenging, especially in cases with paravalvular destruction. Basic principles include complete debridement and reconstruction. This study is designed to evaluate the outcomes of surgical reconstruction of complex annular endocarditis using standard techniques and materials, including autologous and bovine pericardium.MethodsFrom 1975 to 2000, 358 cases (357 patients, mean age 49 ± 16 years, range 18–88 years) of native valve endocarditis were surgically managed. Bioprosthetic valves were implanted in 189 cases, and mechanical prostheses were implanted in 169 cases. A total of 78 cases of paravalvular destruction were identified: 62 annular abscesses, 8 fistulas, and 8 combined abscesses/fistulas. These were managed with 46 pericardial patches and 32 isolated suture reconstructions after radical debridement and prosthetic valve replacement.ResultsThe overall early mortality was 8.4% (n = 30). The mortality with paravalvular destruction was 17.9%, and the mortality with simple leaflet infection was 5.7% (P = .001). The unadjusted survival at 20 years was 26.4% ± 4.9% for bioprosthetic valves and 56.5% ± 8.1% for mechanical prostheses (P = .007). The freedom from recurrent prosthetic valve endocarditis was 78.9% ± 4.4% at 15 years. The freedom from reoperation for recurrent prosthetic valve endocarditis was 85.8% ± 4.2% at 15 years. The freedom from reoperation after reconstruction for paravalvular destruction was 88.2% ± 6.9% at 15 years. The freedom from mortality for recurrent prosthetic valve endocarditis was 92.7% ± 3.4% at 15 years. The independent predictors of reoperation were age (hazard ratio 0.930, P = .005) and intravenous drug use/human immunodeficiency virus plus surgical technique (hazard ratio 12.8, P = .003 for patch reconstruction plus valve and hazard ratio 3.6, P = .038 for valve replacement only). Prosthesis type was not predictive when separated from intravenous drug use/human immunodeficiency virus (hazard ratio 3.268, P = .088).ConclusionParavalvular destruction is associated with a higher operative mortality. Native valve endocarditis can be managed with reasonable long-term survival and low rates of reinfection with radical debridement and pericardial reconstruction with bioprostheses and mechanical prostheses. The type of prosthesis implanted does not influence long-term outcome. Patients with a history of intravenous drug use and human immunodeficiency virus are at increased risk for recurrent infection and reoperation

Twirling and Whirling: Viscous Dynamics of Rotating Elastica

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by a novel pair of coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two dynamical regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.Comment: To be published in Physical Review Letter

A Unifying Theory of Biological Function

A new theory that naturalizes biological function is explained and compared with earlier etiological and causal role theories. Etiological theories explain functions from how they are caused over their evolutionary history. Causal role theories analyze how functional mechanisms serve the current capacities of their containing system. The new proposal unifies the key notions of both kinds of theories, but goes beyond them by explaining how functions in an organism can exist as factors with autonomous causal efficacy. The goal-directedness and normativity of functions exist in this strict sense as well. The theory depends on an internal physiological or neural process that mimics an organism’s fitness, and modulates the organism’s variability accordingly. The structure of the internal process can be subdivided into subprocesses that monitor specific functions in an organism. The theory matches well with each intuition on a previously published list of intuited ideas about biological functions, including intuitions that have posed difficulties for other theories

Swimming in circles: Motion of bacteria near solid boundaries

Near a solid boundary, E. coli swims in clockwise circular motion. We provide a hydrodynamic model for this behavior. We show that circular trajectories are natural consequences of force-free and torque-free swimming, and the hydrodynamic interactions with the boundary, which also leads to a hydrodynamic trapping of the cells close to the surface. We compare the results of the model with experimental data and obtain reasonable agreement. In particular, we show that the radius of curvature of the trajectory increases with the length of the bacterium body.Comment: Also available at http://people.deas.harvard.edu/~lauga

The optimal elastic flagellum

Motile eukaryotic cells propel themselves in viscous fluids by passing waves of bending deformation down their flagella. An infinitely long flagellum achieves a hydrodynamically optimal low-Reynolds number locomotion when the angle between its local tangent and the swimming direction remains constant along its length. Optimal flagella therefore adopt the shape of a helix in three dimensions (smooth) and that of a sawtooth in two dimensions (non-smooth). Physically, biological organisms (or engineered micro-swimmers) must expend internal energy in order to produce the waves of deformation responsible for the motion. Here we propose a physically-motivated derivation of the optimal flagellum shape. We determine analytically and numerically the shape of the flagellar wave which leads to the fastest swimming while minimizing an appropriately-defined energetic expenditure. Our novel approach is to define an energy which includes not only the work against the surrounding fluid, but also (1) the energy stored elastically in the bending of the flagellum, (2) the energy stored elastically in the internal sliding of the polymeric filaments which are responsible for the generation of the bending waves (microtubules), and (3) the viscous dissipation due to the presence of an internal fluid. This approach regularizes the optimal sawtooth shape for two-dimensional deformation at the expense of a small loss in hydrodynamic efficiency. The optimal waveforms of finite-size flagella are shown to depend upon a competition between rotational motions and bending costs, and we observe a surprising bias towards half-integer wave-numbers. Their final hydrodynamic efficiencies are above 6%, significantly larger than those of swimming cells, therefore indicating available room for further biological tuning

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated

Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area