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

Enhanced sedimentation of elongated plankton in simple flows

Negatively buoyant phytoplankton play an important role in the sequestration of CO_2 from the atmo-sphere and are fundamental to the health of the world’s fisheries. However, there is still much to discoveron transport mechanisms from the upper photosynthetic regions to the deep ocean. In contrast to intuitive expectations that mixing increases plankton residence time in light-rich regions, recent experimental and computational evidence suggests that turbulence can actually enhance sedimentation of negatively buoyant diatoms. Motivated by these studies we dissect the enhanced sedimentation mechanisms using the simplest possible two-dimensional flows, avoiding expensive computations and obfuscation. In particular, we find that in vertical shear, preferential flow alignment and aggregation in down-welling regions both increase sedimentation, whereas horizontal shear reduces the sedimentation due only to alignment. However the magnitude of the shear does not affect the sedimentation rate. In simple vertical Kolmogorov flow elongated particles also have an enhanced sedimentation speed as they spend more time in down-welling regions of the flow with vertically aligned orientation, an effect that increases with the magnitude of shear. An additional feature is identified in horizontal Kolomogorov flow, whereby the impact of shear-dependent sedimentation speed is to cause aggregation in regions of high-shear where the sedimentation speed is minimum. In cellular flow, there is an increase in mean sedimentation speed with aspect ratio and shear strength associated with aggregation in down-welling regions. Furthermore, spatially projected trajectories can intersect and give rise to chaotic dynamics, which is associated with a depletion of particles within so called retention zones

Inherent High Correlation of Individual Motility Enhances Population Dispersal in a Heterotrophic, Planktonic Protist

Quantitative linkages between individual organism movements and the resulting population distributions are fundamental to understanding a wide range of ecological processes, including rates of reproduction, consumption, and mortality, as well as the spread of diseases and invasions. Typically, quantitative data are collected on either movement behaviors or population distributions, rarely both. This study combines empirical observations and model simulations to gain a mechanistic understanding and predictive ability of the linkages between both individual movement behaviors and population distributions of a single-celled planktonic herbivore. In the laboratory, microscopic 3D movements and macroscopic population distributions were simultaneously quantified in a 1L tank, using automated video- and image-analysis routines. The vertical velocity component of cell movements was extracted from the empirical data and used to motivate a series of correlated random walk models that predicted population distributions. Validation of the model predictions with empirical data was essential to distinguish amongst a number of theoretically plausible model formulations. All model predictions captured the essence of the population redistribution (mean upward drift) but only models assuming long correlation times (minute), captured the variance in population distribution. Models assuming correlation times of 8 minutes predicted the least deviation from the empirical observations. Autocorrelation analysis of the empirical data failed to identify a de-correlation time in the up to 30-second-long swimming trajectories. These minute-scale estimates are considerably greater than previous estimates of second-scale correlation times. Considerable cell-to-cell variation and behavioral heterogeneity were critical to these results. Strongly correlated random walkers were predicted to have significantly greater dispersal distances and more rapid encounters with remote targets (e.g. resource patches, predators) than weakly correlated random walkers. The tendency to disperse rapidly in the absence of aggregative stimuli has important ramifications for the ecology and biogeography of planktonic organisms that perform this kind of random walk

The spatial distribution of gyrotactic swimming micro-organisms in laminar flow fields

We compare the results of two-dimensional, biased random walk models of individual swimming micro-organisms with advection–diffusion models for the whole population. In particular, we consider the influence of the local flow environment (gyrotaxis) on the resulting motion. In unidirectional flows, the results of the individual and population models are generally in good agreement, even in flows in which the cells can experience a range of shear environments, and both models successfully predict the phenomena of gravitactic focusing. Numerical results are also compared with asymptotic expressions for weak and strong shear. Discrepancies between the models arise in two cases: (i) when reflective boundary conditions change the orientation distribution in the random walk model from that predicted by the long-term asymptotics used to derive the advection–diffusion model; (ii) when the spatial and temporal scales are not large enough for the advection–diffusion model to apply. We also use a simple two-dimensional flow containing a variety of flow regimes to explore what happens when there are localized regions in which the generalized Taylor dispersion theory used in the derivation of the population model does not apply. For spherical cells, we find good agreement between the models outside the ‘break-down’ regions, but comparison of the results within these regions is complicated by the presence of nearby boundaries and their influence on the random walk model. In contrast, for rod-shaped cells which are reorientated by both vorticity and strain, we see qualitatively different spatial patterns between individual and advection–diffusion models even in the absence of gyrotaxis, because cells are advected between regions of differing rates of strain.</jats:p

Sedimentation of inertia-less prolate spheroids in homogenous isotropic turbulence with application to non-motile phytoplankton

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 planktonic organisms 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 downwelling 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

Tight control of hypoxia-inducible factor-α transient dynamics is essential for cell survival in hypoxia

Intracellular signaling involving hypoxia-inducible factor (HIF) controls the adaptive responses to hypoxia. There is a growing body of evidence demonstrating that intracellular signals encode temporal information. Thus, the dynamics of protein levels, as well as protein quantity and/or localization, impacts on cell fate. We hypothesized that such temporal encoding has a role in HIF signaling and cell fate decisions triggered by hypoxic conditions. Using live cell imaging in a controlled oxygen environment, we observed transient 3-h pulses of HIF-1α and -2α expression under continuous hypoxia. We postulated that the well described prolyl hydroxylase (PHD) oxygen sensors and HIF negative feedback regulators could be the origin of the pulsatile HIF dynamics. We used iterative mathematical modeling and experimental analysis to scrutinize which parameter of the PHD feedback could control HIF timing and we probed for the functional redundancy between the three main PHD proteins. We identified PHD2 as the main PHD responsible for HIF peak duration. We then demonstrated that this has important consequences, because the transient nature of the HIF pulse prevents cell death by avoiding transcription of p53-dependent pro-apoptotic genes. We have further shown the importance of considering HIF dynamics for coupling mathematical models by using a described HIF-p53 mathematical model. Our results indicate that the tight control of HIF transient dynamics has important functional consequences on the cross-talk with key signaling pathways controlling cell survival, which is likely to impact on HIF targeting strategies for hypoxia-associated diseases such as tumor progression and ischemia

Bioconvection

Bioconvection patterns are usually observed in the laboratory in shallow suspensions of randomly, but on average upwardly, swimming micro-organisms which are a little denser than water, but have also been found in situ in micropatches of zooplankton [Kils (1993), 1993. Bull. Mar. Sci. 53, 160–169]. The mechanism of upswimming differs between bottom-heavy algae and oxytactic bacteria. Rational continuum models have been formulated and analysed in each of these cases for low cell volume fraction. These will be described, as will new theoretical and experimental developments, including nonlinear analysis of the patterns, dispersion in shear flows, measurements of algal cell swimming behaviour, and new attempts to set up a model for more concentrated suspensions. The paper will review all work in this area since 1992, the year of the publication of the article "Hydrodynamic phenomena in suspensions of swimming micro-organisms" by Pedley and Kessler [1992b. Annu. Rev. Fluid Mech. 24, 313–358]