From the volcano effect to banding: a minimal model for bacterial behavioral transitions near chemoattractant sources

Sharp chemoattractant (CA) gradient variations near food sources may give rise to dramatic behavioral changes of bacteria neighboring these sources. For instance, marine bacteria exhibiting run-reverse motility are known to form distinct bands around patches (large sources) of chemoattractant such as nutrient-soaked beads while run-and-tumble bacteria have been predicted to exhibit a 'volcano effect' (spherical shell-shaped density) around a small (point) source of food. Here we provide the first minimal model of banding for run-reverse bacteria and show that, while banding and the volcano effect may appear superficially similar, they are different physical effects manifested under different source emission rate (and thus effective source size). More specifically, while the volcano effect is known to arise around point sources from a bacterium's temporal differentiation of signal (and corresponding finite integration time), this effect alone is insufficient to account for banding around larger patches as bacteria would otherwise cluster around the patch without forming bands at some fixed radial distance. In particular, our model demonstrates that banding emerges from the interplay of run-reverse motility and saturation of the bacterium's chemoreceptors to CA molecules and our model furthermore predicts that run-reverse bacteria susceptible to banding behavior should also exhibit a volcano effect around sources with smaller emission rates

Inferring models of bacterial dynamics toward point sources

Experiments have shown that bacteria can be sensitive to small variations in chemoattractant (CA) concentrations. Motivated by these findings, our focus here is on a regime rarely studied in experiments: bacteria tracking point CA sources (such as food patches or even prey). In tracking point sources, the CA detected by bacteria may show very large spatiotemporal fluctuations which vary with distance from the source. We present a general statistical model to describe how bacteria locate point sources of food on the basis of stochastic event detection, rather than CA gradient information. We show how all model parameters can be directly inferred from single cell tracking data even in the limit of high detection noise. Once parameterized, our model recapitulates bacterial behavior around point sources such as the "volcano effect". In addition, while the search by bacteria for point sources such as prey may appear random, our model identifies key statistical signatures of a targeted search for a point source given any arbitrary source configuration

A novel method to accurately locate and count large numbers of steps by photobleaching

Photobleaching event counting is a single-molecule fluorescence technique that is increasingly being used to determine the stoichiometry of protein and RNA complexes composed of many subunits in vivo as well as in vitro. By tagging protein or RNA subunits with fluorophores, activating them, and subsequently observing as the fluorophores photobleach, one obtains information on the number of subunits in a complex. The noise properties in a photobleaching time trace depend on the number of active fluorescent subunits. Thus, as fluorophores stochastically photobleach, noise properties of the time trace change stochastically, and these varying noise properties have created a challenge in identifying photobleaching steps in a time trace. Although photobleaching steps are often detected by eye, this method only works for high individual fluorophore emission signal-to-noise ratios and small numbers of fluorophores. With filtering methods or currently available algorithms, it is possible to reliably identify photobleaching steps for up to 20-30 fluorophores and signal-to-noise ratios down to ∼1. Here we present a new Bayesian method of counting steps in photobleaching time traces that takes into account stochastic noise variation in addition to complications such as overlapping photobleaching events that may arise from fluorophore interactions, as well as on-off blinking. Our method is capable of detecting ≥50 photobleaching steps even for signal-to-noise ratios as low as 0.1, can find up to ≥500 steps for more favorable noise profiles, and is computationally inexpensive

Statistical signatures of a targeted search by bacteria

Chemoattractant gradients are rarely well-controlled in nature and recent attention has turned to bacterial chemotaxis toward typical bacterial food sources such as food patches or even bacterial prey. In environments with localized food sources reminiscent of a bacterium's natural habitat, striking phenomena—such as the volcano effect or banding—have been predicted or expected to emerge from chemotactic models. However, in practice, from limited bacterial trajectory data it is difficult to distinguish targeted searches from an untargeted search strategy for food sources. Here we use a theoretical model to identify statistical signatures of a targeted search toward point food sources, such as prey. Our model is constructed on the basis that bacteria use temporal comparisons to bias their random walk, exhibit finite memory and are subject to random (Brownian) motion as well as signaling noise. The advantage with using a stochastic model-based approach is that a stochastic model may be parametrized from individual stochastic bacterial trajectories but may then be used to generate a very large number of simulated trajectories to explore average behaviors obtained from stochastic search strategies. For example, our model predicts that a bacterium's diffusion coefficient increases as it approaches the point source and that, in the presence of multiple sources, bacteria may take substantially longer to locate their first source giving the impression of an untargeted search strategy

Counting Photobleach Steps and the Dynamics of Bacterial Predators

poster abstractPhotobleach (PB) counting is used to enumerate proteins by monitoring how the light intensity in some regions decreases by quanta as individual fluorophores photobleach. While it is straightforward in theory, PB counting is often difficult because fluorescence traces are noisy. In this work, we quantify the sources of noise that arise during photobleach counting to construct a principled likelihood function of observing the data given a model. Noise in the signal could arise from background fluorescence, variable fluorophore emission, and fluorophore blinking. In addition, in a completely different direction, we explore the role of hydrodynamic interactions on the dynamics of bacterial predators. Our study shows that Bdellovibrio (BV) - a model predatory bacterium - is susceptible to self-generated hydrodynamic forces. Near surfaces and defects, these hydrodynamic interactions co-localize BV with its prey, and this may enhance BV’s hunting efficiency

Hydrodynamic Hunters

The Gram-negative Bdellovibrio bacteriovorus (BV) is a model bacterial predator that hunts other bacteria and may serve as a living antibiotic. Despite over 50 years since its discovery, it is suggested that BV probably collides into its prey at random. It remains unclear to what degree, if any, BV uses chemical cues to target its prey. The targeted search problem by the predator for its prey in three dimensions is a difficult problem: it requires the predator to sensitively detect prey and forecast its mobile prey’s future position on the basis of previously detected signal. Here instead we find that rather than chemically detecting prey, hydrodynamics forces BV into regions high in prey density, thereby improving its odds of a chance collision with prey and ultimately reducing BV’s search space for prey. We do so by showing that BV’s dynamics are strongly influenced by self-generated hydrodynamic flow fields forcing BV onto surfaces and, for large enough defects on surfaces, forcing BV in orbital motion around these defects. Key experimental controls and calculations recapitulate the hydrodynamic origin of these behaviors. While BV’s prey (Escherichia coli) are too small to trap BV in hydrodynamic orbit, the prey are also susceptible to their own hydrodynamic fields, substantially confining them to surfaces and defects where mobile predator and prey density is now dramatically enhanced. Colocalization, driven by hydrodynamics, ultimately reduces BV’s search space for prey from three to two dimensions (on surfaces) even down to a single dimension (around defects). We conclude that BV’s search for individual prey remains random, as suggested in the literature, but confined, however—by generic hydrodynamic forces—to reduced dimensionality

Efficiency improvements in a dichroic dye-doped liquid crystal Fresnel lens

A dichroic dye-doped liquid crystal Fresnel lens was fabricated and investigated to observe the combination of phase and amplitude modulation based focusing. An anthraquinone dichroic dye was doped into a liquid crystal host, which when in the Fresnel lens configuration generates a Fresnel zone plate with alternating “transparent” and “opaque” zones. The zones were induced by using photo-alignment of a light-sensitive alignment layer to generate the alternating pattern. The voltage dependency of efficiency for the dye doped and pure liquid crystal Fresnel devices were investigated. Incorporation of dyes into the device yielded a significant 4 % improvement in relative efficiency in the lens, giving a maximum of 37 % achieved in the device, much closer to the theoretical 41 % limit when compared with the non dye doped device. The input polarization dependence of efficiency was also investigated, showing very small fluctuations (±1.5 %), allowing further insight into the effect of fabrication method on these liquid crystal Fresnel devices