(A) Phylogenetic tree showing microorganisms known to feature cilia that generate feeding currents in either sessile (blue) or free swimming (purple) states. The class of diatoms – non-motile cells that sink when experiencing nutrient limitation – is shown for comparison. (B) Flow fields around a sessile ciliate, swimming ciliate, and sinking diatom, in lab and body frame of references. Streamlines are shown in blue in lab frame (X, Y, Z).

Stokeslet and Envelope models of sessile and motile ciliates.

(A) Stokeslet model where ciliary activity is represented by a Stokeslet force Fcilia is located at a distance (L a)/a outside the spherical cell surface with no-slip surface velocity. (B)Envelope model where cilia activity is distributed over the entire cell surface with slip surface velocity. (C,D) Fluid streamlines (white) and nutrient concentration fields (colormap) in the sessile and swimming cases. Here, L/a = 2, a = 1 and Fcilia is chosen to generate a swimming speed U = 2/3 in the motile case to ensure consistency with the envelope model. (E) Nutrient uptake in sessile and motile Stokeslet-sphere model based on calculation of clearance rate Q of a fluid volume passing through an annular disk of radius R/a = 1.1 and Sherwood number Sh. In the latter, Pe is 100. (F) Nutrient uptake in sessile and motile envelope model based on calculation of Sherwood number Sh as a function of Pe. (G) Difference in clearance rate ΔQ = Qmotile Qsessile and Sherwood number ΔSh = ΔI/Idiffusion = Shmotile Shsessile in the Stokeslet-sphere model for L/a = 1.1 and L/a = 2 and in the envelope model. In both metrics, the difference is less than 20%: ΔQ is less than 20% the advective flux πR2U and ΔI is less than 20% of the corresponding diffusive uptake Idiffusion = 4πRDC∞. Shaded grey area denotes when the sessile strategy is advantageous.

Survey of size a and flow measurements U in sessile and swimming ciliates and sinking diatoms (Table S6). Size a is calculated using the volume-equivalent spherical radius (Fig. S7). Corresponding ranges of Pe numbers are based on the diffusivity of oxygen, D = 10−9 m2·s−1, live bacteria, D = 4 × 10−10, m2·s−1), and dead bacteria D = 2×10 m ·s .

Sherwood number versus Péclet number for the sinking (green) diatom and the swimming (purple) and sessile (blue) ciliates based on the envelope model. (A) Shifted Sherwood number (Sh - 1) versus Péclet number in the logarithmic scale for a range of Pe from 0 to 1000. Pe numbers associated with experimental observations of diatoms (square), swimming ciliates (triangle), and sessile ciliates (circle) are superimposed. Corresponding Sh numbers are calculated based on the mathematical model. Empty symbols are for oxygen diffusivity D = 1 10−9m2 s−1 and the solid symbols correspond to the diffusivity D = 4 10−10m2 s−1 of live bacteria [72]. (B-C) Asymptotic analysis (dashed lines) of Sherwood number in the large Péclet limit (B) and small Péclet limit (C).

Robustness to variations in cilia coverage and absorption fraction.

We considered a 50% cilia coverage and 50% absorption fraction located at back, middle, and front of the (A) sessile and (B) motile sphere. Concentration fields and Sherwood numbers with 100% cilia coverage and absorption area are shown in the top right corner. In all other cases, the Sh number is reported as a percentage of the full coverage/absorption case.