Simple models of the chemical field around swimming plankton

International audienceThe chemical field around swimming plankton depends on the swimming style and speed of the organism and the processes affecting uptake or exudation of chemicals by the organism. Here we present a simple model for the flow field around a neutrally buoyant self-propelled organism at low Reynolds number, and numerically calculate the chemical field around the organism. We show how the concentration field close to the organism and the mass transfer rates vary with swimming speed and style for Dirichlet (diffusion limited transport) boundary conditions. We calculate how the length of the chemical wake, defined as being the distance at which the chemical field drops to 10% of the surface concentration of the organism when stationary, varies with swimming speed and style for both Dirichlet and Neumann (production limited) boundary conditions. For Dirichlet boundary conditions, the length of the chemical wake increases with increasing swimming speed, and the self-propelled organism displays a significantly longer wake than the towed-body model. For the Neumann boundary conditions the converse is true; because swimming enhances the transport of the chemical away from the organism, the surface concentration of chemical is reduced and thus the wake length is reduced

The trapping in high-shear regions of slender bacteria undergoing chemotaxis in a channel

Recently published experimental observations of slender bacteria swimming in channel flow demonstrate that the bacteria become trapped in regions of high shear, leading to reduced concentrations near the channel's centreline. However, the commonly-used, advection-diffusion equation, formulated in macroscopic space variables and originally derived for unbounded homogeneous shear flow, predicts that the bacteria concentration is uniform across the channel in the absence of chemotactic bias. In this paper, we instead use a Smoluchowski equation to describe the probability distribution of the bacteria, in macroscopic (physical) and microscopic (orientation) space variables. We demonstrate that the Smoluchowski equation is able to predict the trapping phenomena and compare the full numerical solution of the Smoluchowski equation with the experimental results when there is no chemotactic bias and also in the presence of a uniform cross-channel chemotactic gradient. Moreover, a simple analytic approximation for the equilibrium distribution provides an excellent approximate solution for slender bacteria, suggesting that the dominant effect on equilibrium behaviour is flow-induced modification of the bacteria's swimming direction. A continuum framework is thus provided to explain how the equilibrium distribution of slender chemotactic bacteria is altered in the presence of spatially varying shear flow. In particular we demonstrate that whilst advection is an appropriate description of transport due to the mean swimming velocity, the random reorientation mechanism of the bacteria cannot be simply modelled as diffusion in physical space

Transport of helical gyrotactic swimmers in channels

We develop a mechanistic model that describes the transport of gyrotactic cells with propulsive force and propulsive torque that are not parallel. In sufficiently weak shear this yields helical swimming trajectories, whereas in stronger shear cells can attain a stable equilibrium orientation. We obtain the stable equilibrium solution for cell orientation as a function of the shear strength and determine the feasibility region for equilibrium solutions. We compute numerically the trajectories of cells in two dimensional vertical channel flow where the shear is non-uniform. Depending on the parameter values, we show that helical swimmers may display classical gyrotactic focussing towards the centre of the channel or can display a new phenomenon of focussing away from the centre of the channel. This result can be explained by consideration of the equilibrium solution for cell orientation. In this study we consider only dilute suspensions where there is no feedback from cell swimming on the hydrodynamics, and both cell-wall and cell-cell interactions are neglected

A model of strongly biased chemotaxis reveals the trade-offs of different bacterial migration strategies

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

When do shape changers swim upstream?

Using a multiple-scale analysis, Walker et al. (J. Fluid Mech., vol. 944, 2022, R2) obtain the long-time behaviour of a shape-changing swimmer in a Poiseuille flow. They show that the behaviour falls into one of three categories: endless tumbling at increasing distance from the midline of the flow; preserved initial behaviour of the swimmer; or convergence to upstream rheotaxis, where the swimmer is situated at the midline of the flow. Furthermore, a single swimmer-dependent constant is identified that determines which of the three behaviours is realised.</jats:p

Reaching Families through Social Media: Training Extension Professionals to Implement Technology in Their Work

Cooperative Extension professionals have a long tradition of helping improve the lives of the families they serve by sharing research-based information. More than ever, families are getting their information online, creating a need for Extension professionals to deliver content via technology. This article describes a training designed to teach Extension professionals ways to increase their reach to families through the use of technology in their work. Extension professionals attended an 8-hour, face-to-face training in which they completed a pre, post, and follow-up survey. Results from the training indicated that this training was effective in changing attitudes about the usefulness of technology and increasing their use of social media to reach families

Diffusion about the mean drift location in a biased random walk

Random walks are used to model movement in a wide variety of contexts: from the movement of cells undergoing chemotaxis to the migration of animals. In a two- dimensional biased random walk, the diffusion about the mean drift position is entirely dependent on the moments of the angular distribution used to determine the movement direction at each step. Here we consider biased random walks using several different angular distributions and derive expressions for the diffusion coefficients in each direction based on either a fixed or variable movement speed, and we use these to generate a probability density function for the long-time spatial distribution. we demonstrate how diffusion is typically anisotropic around the mean drift position and illustrate these theoretical results using computer simulations. we relate these results to earlier studies of swimming microorganisms and explain how the results can be generalized to other types of animal movement. © 2010 by the Ecological Society of America

Sedimentation of elongated non-motile prolate spheroids in homogenous isotropic turbulence

Phytoplankton are the foundation of aquatic food webs. Through photosynthesis, phytoplankton draw down CO2 at magnitudes equivalent to forests and other terrestrial plants and convert it to organic material that is then consumed by other organisms of phytoplankton in higher trophic levels. Mechanisms that affect local concentrations and velocities are of primary significance to many encounter-based processes in the plankton including prey-predator interactions, fertilization and aggregate formation. We report results from simulations of sinking phytoplankton, considered as elongated spheroids, in homogenous isotropic turbulence to answer the question of whether trajectories and velocities of sinking phytoplankton are altered by turbulence. We show in particular that settling spheroids with physical characteristics similar to those of diatoms weakly cluster and preferentially sample regions of down-welling flow, corresponding to an increase of the mean settling speed with respect to the mean settling speed in quiescent fluid. We explain how different parameters can affect the settling speed and what underlying mechanisms might be involved. Interestingly, we observe that the increase in the aspect ratio of the prolate spheroids can affect the clustering and the average settling speed of particles by two mechanisms: first is the effect of aspect ratio on the rotation rate of the particles, which saturates faster than the second mechanism of increasing drag anisotropy