Nutrient uptake in a suspension of squirmers

Abstract

Nutrient uptake is one of the most important factors in cell growth. Despite the biological importance, little is known about the effect of cell-cell hydrodynamic interactions on nutrient uptake in a suspension of swimming micro-organisms. In this study, we numerically investigate the nutrient uptake in an infinite suspension of squirmers. In the dilute limit, our results are in good agreement with a previous study by Magar et al. (Q. J. Mech. Appl. Maths, vol. 56, 2003, pp. 65-91). When we increased the volume fraction of squirmers, the nutrient uptake of individual cells was enhanced by the hydrodynamic interactions. The average nutrient concentration in the suspension decayed exponentially as a function of time, and the relaxation time could be scaled using the Sherwood number, the Péclet number and the volume fraction of cells. We propose a fitting function for the Sherwood number, which is useful in predicting nutrient uptake in the non-dilute regime. Furthermore, we analyse the swimming energy consumed by individual cells. The results indicate that both the energetic cost and the nutrient uptake increased as the volume fraction of cells was increased, and that the uptake per unit energy was not significantly affected by the volume fraction. These findings are important in understanding the mass transport and metabolism of swimming micro-organisms in nature and for industrial applications.

Swimming mediated by ciliary beating: comparison with a squirmer model

“…Squirming enhanced uptake compared to that of a rigid sphere moving at the same speed. Ishikawa et al (2016) extended the analysis to squirmer suspensions; nutrient uptake increased in a quadratic manner to volume fractions of up to 30 %. The squirmer model has also been used to study bioconvection in suspensions of upswimming cells, which generate gravitational instability (Kessler 1986;Ishikawa, Locsei & Pedley 2008;Evans et al 2011), and to explore the coherent structures of non-gravitational active swimmers (Simha & Ramaswamy 2002;Saintillan & Shelley 2008).…”

Universal entrainment mechanism controls contact times with motile cells

“…For swimming microorganisms, many interactions hinge on close contact. These include fundamental processes like nutrient uptake [24][25][26][27][28][29][30][31]; viral and fungal infection of microorganisms of ecological and commercial importance [32][33][34], eukaryotic fertilisation [35]; and grazing, which happens on natural preys [30,[36][37][38] as well as marine microplastics [39,40], and is recently being discovered as a fundamental behaviour in many strains of motile green algae until recently regarded as exclusive phototrophs [34,41,42]. With the exception of complex feeding currents in ciliates like Vorticella [43,44] or Paramecium [45,46], the window of opportunity for these microbial interactions to take place will depend on a finite contact time T .…”

Simulation of the nodal flow of mutant embryos with a small number of cilia: comparison of mechanosensing and vesicle transport hypotheses

“…Particle motion was then determined by the advection velocity calculated using equation (2.1) and diffusion due to Brownian motion. In the same manner as described previously [31], the positions of particles, x p , were updated by ${\mathit{x}}^{\mathrm{p}}false(t+\mathrm{normal\Delta }tfalse)={\mathit{x}}^{\mathrm{p}}false(tfalse)+{\int }_t^{t+\mathrm{normal\Delta }t}{\mathit{v}}^{\mathrm{p}}false(t^{\prime }false)\hspace{0.17em}\mathrm{d}{t}^{\prime }+{\mathit{r}}^{B}false(\mathrm{normal\Delta }tfalse),$where r B is the displacement due to Brownian motion, the variance of which is determined by the Péclet number. To discuss flow-dominant particle transportation, we used a Pe of a  = 1 μm, throughout this study.…”