Feeding of sessile ciliates in uniform and nonuniform nutrient concentrations*

Aquatic eukaryotic microorganisms use strategies such as swimming, sinking, or generating flow currents to increase their feeding rate. While many studies analyze nutrient uptake of swimming and sinking cells, less is known about how well sessile cells can compete in feeding compared to motile cells. Based on Blake's envelope model, we represent a sessile ciliated cell by a fixed sphere with a slip surface velocity representing the ciliary motion. We solve analytically for the cilia-generated flow field, then investigate the advection-diffusion behavior of a concentration of surrounding nutrients via numerical and asymptotic analysis. Starting from uniform background concentration of nutrients, we find that sessile ciliated cells can outperform, in terms of nutrient uptake, cells that use buoyancy-driven sinking, but they are no match to cells that use the same ciliary activity for self-propulsion. Importantly, we show that, in non-uniform background concentration, sessile ciliates can enhance their feeding to transcend the limitation they face in uniform concentration by generating flow currents from regions of higher concentration towards the cell.