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Many bacteria actively bias their motility towards more favourable nutrient environments. In liquid, cells rotate their corkscrew-shaped flagella to swim, but in surface attached biofilms cells instead use grappling hook-like appendages called pili to pull themselves along. In both forms of motility, cells selectively alternate between relatively straight 'runs' and sharp reorientations to generate biased random walks up chemoattractant gradients. However, recent experiments suggest that swimming and biofilm cells employ fundamentally different strategies to generate chemotaxis: swimming cells typically suppress reorientations when moving up a chemoattractant gradient, whereas biofilm cells increase reorientations when moving down a chemoattractant gradient. The reason for this difference remains unknown. Here we develop a mathematical framework to understand how these different chemotactic strategies affect the distribution of cells at the population level. Current continuum models typically assume a weak bias in the reorientation rate and are not able to distinguish between these two strategies, so we derive a model for strong chemotaxis that resolves how both the drift and diffusive components depend on the underlying chemotactic strategy. We then test predictions from our continuum model against individual-based simulations and identify further refinements that allow our continuum model to resolve boundary effects. Our analyses reveal that the strategy employed by swimming cells yields a larger chemotactic drift, but the strategy used by biofilm cells allows them to more tightly aggregate where the chemoattractant is most abundant. This new modelling framework provides new quantitative insights into how the different chemical landscapes experienced by swimming and biofilm cells might select for divergent ways of generating chemotaxis., (© The Author(s) 2019. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.)

In still fluid, many phytoplankton swim in helical paths with an average upwards motion. A new mechanistic model for gravitactic algae subject to an intrinsic torque is developed here, based on Heterosigma akashiwo, which results in upwards helical trajectories in still fluid. The resultant upwards swimming speed is calculated as a function of the gravitactic and intrinsic torques. Helical swimmers have a reduced upwards speed in still fluid compared to cells which swim straight upwards. However a novel result is obtained when the effect of fluid shear is considered. For intermediate values of shear and intrinsic torque, a new stable equilibrium solution for swimming direction is obtained for helical swimmers. This results in positive upwards transport in vertical shear flow, in contrast to the stable equilibrium solution for straight swimmers which results in downwards transport in vertical shear flow. Furthermore, for strong intrinsic torque, when there is no longer a stable orientation equilibrium, we show that the average downwards transport of helical swimmers in vertical shear flow is greatly suppressed compared to straight swimmers. We hypothesise that helical swimming provides robustness for upwards transport in the presence of fluid shearing motions.

Sinking aggregates provide important nutrient-rich environments for marine bacteria. Quantifying the rate at which motile bacteria colonize such aggregations is important in understanding the microbial loop in the pelagic food web. In this paper, a simple analytical model is presented to predict the rate at which bacteria undergoing a random walk encounter a sinking aggregate. The model incorporates the flow field generated by the sinking aggregate, the swimming behavior of the bacteria, and the interaction of the flow with the swimming behavior. An expression for the encounter rate is computed in the limit of large Péclet number when the random walk can be approximated by a diffusion process. Comparison with an individual-based numerical simulation is also given.

The biased random walk undergone by chemotactic bacteria such as Escherichia coli will be influenced at the microscopic level by flow in the ambient medium. In this paper, we model swimming bacteria being advected and rotated by a simple shear flow. Under certain scaling assumptions, we obtain an advection-diffusion equation for cell density, when the chemotactic response is small, which shows a coupling between the rotation and chemotaxis. We also present an alternative method for calculating the chemotactic flux in an unbounded region which is valid for more general chemotactic responses.