Emergent Lag Phase in Flux-Regulation Models of Bacterial Growth.

Lag phase is observed in bacterial growth during a sudden change in conditions: growth is inhibited whilst cells adapt to the environment. Bi-phasic, or diauxic growth is commonly exhibited by many species. In the presence of two sugars, cells initially grow by consuming the preferred sugar then undergo a lag phase before resuming growth on the second. Biomass increase is characterised by a diauxic growth curve: exponential growth followed by a period of no growth before a second exponential growth. Recent literature lacks a complete dynamic description, artificially modelling lag phase and employing non-physical representations of precursor pools. Here, we formulate a rational mechanistic model based on flux-regulation/proteome partitioning with a finite precursor pool that reveals core mechanisms in a compact form. Unlike earlier systems, the characteristic dynamics emerge as part of the solution, including the lag phase. Focussing on growth of Escherichia coli on a glucose-lactose mixture we show results accurately reproduce experiments. We show that for a single strain of E. coli, diauxic growth leads to optimised biomass yields. However, intriguingly, for two competing strains diauxic growth is not always the best strategy. Our description can be generalised to model multiple different microorganisms and investigate competition between species/strains.

Simultaneous two-color imaging in digital holographic microscopy.

We demonstrate the use of two-color digital holographic microscopy (DHM) for imaging microbiological subjects. The use of two wavelengths significantly reduces artifacts present in the reconstructed data, allowing us to image weakly-scattering objects in close proximity to strongly-scattering objects. We demonstrate this by reconstructing the shape of the flagellum of a unicellular eukaryotic parasite Leishmania mexicana in close proximity to a more strongly-scattering cell body. Our approach also yields a reduction of approximately one third in the axial position uncertainty when tracking the motion of swimming cells at low magnification, which we demonstrate with a sample of Escherichia coli bacteria mixed with polystyrene beads. The two-wavelength system that we describe introduces minimal additional complexity into the optical system, and provides significant benefits.

Pulse Generation in the Quorum Machinery of Pseudomonas aeruginosa.

Pseudomonas aeruginosa is a Gram-negative bacterium that is responsible for a wide range of infections in humans. Colonies employ quorum sensing (QS) to coordinate gene expression, including for virulence factors, swarming motility and complex social traits. The QS signalling system of P. aeruginosa is known to involve multiple control components, notably the las, rhl and pqs systems. In this paper, we examine the las system and, in particular, the repressive interaction of rsaL, an embedded small regulative protein, employing recent biochemical information to aid model construction. Using analytic methods, we show how this feature can give rise to excitable pulse generation in this subsystem with important downstream consequences for rhamnolipid production. We adopt a symmetric competitive inhibition to capture the binding in the lasI-rsaL intergenic region and show our results are not dependent on the exact choice of this functional form. Furthermore, we examine the coupling of lasR to the rhl system, the impact of the predicted capacity for pulse generation and the biophysical consequences of this behaviour. We hypothesize that the interaction between the las and rhl systems may provide a quorum memory to enable cells to trigger rhamnolipid production only when they are at the edge of an established aggregation.

Bugs on a Slippery Plane : Understanding the Motility of Microbial Pathogens with Mathematical Modelling.

Many pathogenic microorganisms live in close association with surfaces, typically in thin films that either arise naturally or that they themselves create. In response to this constrained environment, the cells adjust their behaviour and morphology, invoking communication channels and inducing physical phenomena that allow for rapid colonization of biomedically relevant surfaces or the promotion of virulence factors. Thus, it is very important to measure and theoretically understand the key mechanisms for the apparent advantage obtained from swimming in thin films. We discuss experimental measurements of flows around a peritrichously flagellated bacterium constrained in a thin film, derive a simplified mathematical theory and Green's functions for flows in a thin film with general slip boundary conditions, and establish connections between theoretical and experimental results. This article aims to highlight the importance of mathematics as a tool to unlock qualitative mechanisms associated with experimental observations in the medical and biological sciences.

Differential dynamic microscopy: a high-throughput method for characterizing the motility of microorganisms.

We present a fast, high-throughput method for characterizing the motility of microorganisms in three dimensions based on standard imaging microscopy. Instead of tracking individual cells, we analyze the spatiotemporal fluctuations of the intensity in the sample from time-lapse images and obtain the intermediate scattering function of the system. We demonstrate our method on two different types of microorganisms: the bacterium Escherichia coli (both smooth swimming and wild type) and the biflagellate alga Chlamydomonas reinhardtii. We validate the methodology using computer simulations and particle tracking. From the intermediate scattering function, we are able to extract the swimming speed distribution, fraction of motile cells, and diffusivity for E. coli, and the swimming speed distribution, and amplitude and frequency of the oscillatory dynamics for C. reinhardtii. In both cases, the motility parameters were averaged over ∼10(4) cells and obtained in a few minutes.

The orientation of swimming biflagellates in shear flows.

Biflagellated algae swim in mean directions that are governed by their environments. For example, many algae can swim upward on average (gravitaxis) and toward downwelling fluid (gyrotaxis) via a variety of mechanisms. Accumulations of cells within the fluid can induce hydrodynamic instabilities leading to patterns and flow, termed bioconvection, which may be of particular relevance to algal bioreactors and plankton dynamics. Furthermore, knowledge of the behavior of an individual swimming cell subject to imposed flow is prerequisite to a full understanding of the scaled-up bulk behavior and population dynamics of cells in oceans and lakes; swimming behavior and patchiness will impact opportunities for interactions, which are at the heart of population models. Hence, better estimates of population level parameters necessitate a detailed understanding of cell swimming bias. Using the method of regularized Stokeslets, numerical computations are developed to investigate the swimming behavior of and fluid flow around gyrotactic prolate spheroidal biflagellates with five distinct flagellar beats. In particular, we explore cell reorientation mechanisms associated with bottom-heaviness and sedimentation and find that they are commensurate and complementary. Furthermore, using an experimentally measured flagellar beat for Chlamydomonas reinhardtii, we reveal that the effective cell eccentricity of the swimming cell is much smaller than for the inanimate body alone, suggesting that the cells may be modeled satisfactorily as self-propelled spheres. Finally, we propose a method to estimate the effective cell eccentricity of any biflagellate when flagellar beat images are obtained haphazardly.

A tale of three taxes: photo-gyro-gravitactic bioconvection.

The term bioconvection encapsulates the intricate patterns in concentration, due to hydrodynamic instabilities, that may arise in suspensions of non-neutrally buoyant, biased swimming microorganisms. The directional bias may be due to light (phototaxis), gravity (gravitaxis), a combination of viscous and gravitational torques (gyrotaxis) or other taxes. The aim of this study is to quantify experimentally the wavelength of the initial pattern to form from an initially well-mixed suspension of unicellular, swimming green algae as a function of concentration and illumination. As this is the first such study, it is necessary to develop a robust and meticulous methodology to achieve this end. The phototactic, gyrotactic and gravitactic alga Chlamydomonas augustae was employed, with various red or white light intensities from above or below, as the three not altogether separable taxes were probed. Whilst bioconvection was found to be unresponsive to changes in red light, intriguing trends were found for pattern wavelength as a function of white light intensity, depending critically on the orientation of the illumination. These trends are explored to help unravel the mechanisms. Furthermore, comparisons are made with theoretical predictions of initial wavelengths from a recent model of photo-gyrotaxis, encouragingly revealing good qualitative agreement.

Microbial mutualism at a distance: The role of geometry in diffusive exchanges.

The exchange of diffusive metabolites is known to control the spatial patterns formed by microbial populations, as revealed by recent studies in the laboratory. However, the matrices used, such as agarose pads, lack the structured geometry of many natural microbial habitats, including in the soil or on the surfaces of plants or animals. Here we address the important question of how such geometry may control diffusive exchanges and microbial interaction. We model mathematically mutualistic interactions within a minimal unit of structure: two growing reservoirs linked by a diffusive channel through which metabolites are exchanged. The model is applied to study a synthetic mutualism, experimentally parametrized on a model algal-bacterial co-culture. Analytical and numerical solutions of the model predict conditions for the successful establishment of remote mutualisms, and how this depends, often counterintuitively, on diffusion geometry. We connect our findings to understanding complex behavior in synthetic and naturally occurring microbial communities.

Dispersion of swimming algae in laminar and turbulent channel flows: consequences for photobioreactors.

Shear flow significantly affects the transport of swimming algae in suspension. For example, viscous and gravitational torques bias bottom-heavy cells to swim towards regions of downwelling fluid (gyrotaxis). It is necessary to understand how such biases affect algal dispersion in natural and industrial flows, especially in view of growing interest in algal photobioreactors. Motivated by this, we here study the dispersion of gyrotactic algae in laminar and turbulent channel flows using direct numerical simulation (DNS) and a previously published analytical swimming dispersion theory. Time-resolved dispersion measures are evaluated as functions of the Péclet and Reynolds numbers in upwelling and downwelling flows. For laminar flows, DNS results are compared with theory using competing descriptions of biased swimming cells in shear flow. Excellent agreement is found for predictions that employ generalized Taylor dispersion. The results highlight peculiarities of gyrotactic swimmer dispersion relative to passive tracers. In laminar downwelling flow the cell distribution drifts in excess of the mean flow, increasing in magnitude with Péclet number. The cell effective axial diffusivity increases and decreases with Péclet number (for tracers it merely increases). In turbulent flows, gyrotactic effects are weaker, but discernable and manifested as non-zero drift. These results should have a significant impact on photobioreactor design.

Persistence of cluster synchronization under the influence of advection.

We present a study on the emergence of spatial structure in plankton dynamics under the influence of stirring and mixing. A distribution of plankton is represented as a lattice of nonidentical, interacting, oscillatory plankton populations. Each population evolves according to (i) the internal biological dynamics represented by an NPZ model with population-specific phytoplankton growth rate, (ii) sub-grid-cell stirring and mixing parameterized by a nearest-neighbor coupling, and (iii) explicit advection resulting from a constant horizontal shear. Using the methods of synchronization theory, the emergent spatial structure of the simulation is investigated as a function of the coupling strength and rate of advection. Previous work using similar methods has neglected the effects of explicit stirring (i.e., at scales larger than the grid cell), leaving as an open question the relevance of the work to real marine systems. Here, we show that persistent spatial structure emerges for a range of coupling strengths for all realistic levels of surface ocean shear. Spatially, this corresponds to the formation of temporally evolving clusters of local synchronization. Increasing shear alters the spatial characteristics of this clustering by stretching and narrowing patches of synchronized dynamics. These patches are not stretched into stripes of synchronized abundance aligned with the flow, as may be expected, but instead lie at an angle to the flow. This study shows that advection does not diminish the relevance of conclusions from previous studies of spatial structure in plankton simulations. In fact, the inclusion of advection adds characteristic filamental structure, as observed in real-world plankton distributions. The results also show that the ability of coupled oscillators to synchronize depends strongly on the spatial arrangement of oscillator natural frequencies; under the influence of advection, therefore, the impact of the coupling strength on the emergent spatial structure of a biophysical simulation is time-dependent.

Unexpected bipolar flagellar arrangements and long-range flows driven by bacteria near solid boundaries.

Experiments and mathematical modeling show that complex flows driven by unexpected flagellar arrangements are induced when peritrichously flagellated bacteria are confined in a thin layer of fluid, between asymmetric boundaries. The flagella apparently form a dynamic bipolar assembly rather than the single bundle characteristic of free swimming bacteria, and the resulting flow is observed to circulate around the cell body. It ranges over several cell diameters, in contrast to the small extent of the flows surrounding free swimmers. Results also suggest that flagellar bundles on bacteria that lie flat on a solid substrate have an effective rotation rate slower than "free" flagella. This discovery extends our knowledge of the dynamic geometry of bacteria and their flagella, and reveals new mechanisms for motility-associated molecular transport and intercellular communication.