Escherichia coli bacteria use rotating helical flagella to swim. At this scale, viscous effects dominate inertia, and there are significant hydrodynamic interactions between nearby helices. These interactions cause the flagella to bundle during the "runs" of bacterial chemotaxis. Here we use slender-body theory to solve for the flow fields generated by rigid helices rotated by stationary motors. We determine how the hydrodynamic forces and torques depend on phase and phase difference, show that rigid helices driven at constant torque do not synchronize, and solve for the flows. We also use symmetry arguments based on kinematic reversibility to show that for two rigid helices rotating with zero phase difference, there is no time-averaged attractive or repulsive force between the helices.

Escherichia coli and other bacteria use rotating helical filaments to swim. Each cell typically has about four filaments, which bundle or disperse depending on the sense of motor rotation. To study the bundling process, we built a macroscopic scale model consisting of stepper motor-driven polymer helices in a tank filled with a highviscosity silicone oil. The Reynolds number, the ratio of viscous to elastic stresses, and the helix geometry of our experimental model approximately match the corresponding quantities of the full-scale E. coli cells. We analyze digital video images of the rotating helices to show that the initial rate of bundling is proportional to the motor frequency and is independent of the characteristic relaxation time of the filament. We also determine which combinations of helix handedness and sense of motor rotation lead to bundling. T he cells of Escherichia coli and Salmonella typhimurium have several helical propellers, or flagella, which they use to swim. Each flagellum consists of a rotary motor embedded in the cell wall, a short (50 nm) flexible hook that acts as a universal joint, and a helical filament Ϸ20 nm in diameter and Ϸ10 m long (1). The trajectory of an individual swimming cell consists of runs interrupted by tumbles. For most of a run, the motors turn counterclockwise when viewed from outside the cell, the filaments wrap into a tight bundle, and the cell swims along a roughly straight path. Near the end of a run, one or more of the motors reverses direction, the corresponding filaments come out of the bundle, and the cell moves erratically, or tumbles. The tumbling process is complex and involves polymorphic transitions of the filament first from the left-handed ''normal'' state to the right-handed ''semicoiled'' state, and then to the ''curly-1'' state (2). The first transition reorients the cell body. When the motors resume their counterclockwise rotation, the curly-1 filaments transform directly to the normal state and rejoin the bundle, and the cell resumes its initial speed (2).The chemotaxis strategy of E. coli is to decrease the likelihood of tumbling during runs that happen to carry the cell toward higher concentrations of chemoattractants. Thus, the formation and dispersal of the helical bundle is central to bacterial chemotaxis. Since the radius of the flagellar filament is well below optical wavelengths, and the motor rotation is relatively rapid (100 Hz), it is difficult to study the mechanics of the bundling process directly. Therefore, we built a macroscopic scale-model system consisting of flexible rotating helices in a very viscous fluid. By including the viscous fluid and properly accounting for the relative strengths of viscous and elastic stresses, our scale model builds on and extends the work of Macnab, who studied the geometry of rotating flexible helices in a bundle (3).Our article begins with a discussion of the material parameters of bacterial flagella and how we chose the parameters for the experimental model. The next section describes the geometry ...

BackgroundHypoxic niches in solid tumors harbor therapy-resistant cells. Hypoxia-activated prodrugs (HAPs) have been designed to overcome this resistance and, to date, have begun to show clinical efficacy. However, clinical HAPs activity could be improved. In this study, we sought to identify non-pharmacological methods to acutely exacerbate tumor hypoxia to increase TH-302 activity in pancreatic ductal adenocarcinoma (PDAC) tumor models.ResultsThree human PDAC cell lines with varying sensitivity to TH-302 (Hs766t > MiaPaCa-2 > SU.86.86) were used to establish PDAC xenograft models. PDAC cells were metabolically profiled in vitro and in vivo using the Seahorse XF system and hyperpolarized 13C pyruvate MRI, respectively, in addition to quantitative immunohistochemistry. The effect of exogenous pyruvate on tumor oxygenation was determined using electroparamagnetic resonance (EPR) oxygen imaging. Hs766t and MiaPaCa-2 cells exhibited a glycolytic phenotype in comparison to TH-302 resistant line SU.86.86. Supporting this observation is a higher lactate/pyruvate ratio in Hs766t and MiaPaCa xenografts as observed during hyperpolarized pyruvate MRI studies in vivo. Coincidentally, response to exogenous pyruvate both in vitro (Seahorse oxygen consumption) and in vivo (EPR oxygen imaging) was greatest in Hs766t and MiaPaCa models, possibly due to a higher mitochondrial reserve capacity. Changes in oxygen consumption and in vivo hypoxic status to pyruvate were limited in the SU.86.86 model. Combination therapy of pyruvate plus TH-302 in vivo significantly decreased tumor growth and increased survival in the MiaPaCa model and improved survival in Hs766t tumors.ConclusionsUsing metabolic profiling, functional imaging, and computational modeling, we show improved TH-302 activity by transiently increasing tumor hypoxia metabolically with exogenous pyruvate. Additionally, this work identified a set of biomarkers that may be used clinically to predict which tumors will be most responsive to pyruvate + TH-302 combination therapy. The results of this study support the concept that acute increases in tumor hypoxia can be beneficial for improving the clinical efficacy of HAPs and can positively impact the future treatment of PDAC and other cancers.Electronic supplementary materialThe online version of this article (doi:10.1186/s40170-014-0026-z) contains supplementary material, which is available to authorized users.