Feeding Rates in Sessile versus Motile Ciliates are Hydrodynamically Equivalent

Reviewer #1 (Public Review):

Summary:

The manuscript studies nutrient intake rates for stationary and motile microorganisms to assess the effectiveness of swim vs. stay strategies. This work provides valuable insights on how the different strategies perform in the context of a simplified mathematical model that couples hydrodynamics to nutrient advection and diffusion. The swim and stay strategies are shown to yield similar nutrient flux under a range of conditions.

Strengths:

Strengths of the work include (i) the model prediction in Fig. 3 of nutrient flux applied to a range of microorganisms including an entire clade that are known to use different feeding strategies and (ii) a study of the interaction between cilia and absorption coverage showing the robustness of their predictions provided these regions have sufficient overlap.

Weaknesses: To improve the work, the authors should further expand their discussion of the following points:

(1) The authors comment that a number of species alternate between sessile and motile behavior. It would be helpful to discuss what is known about what causes switching between these modes and whether this provides insights regarding the advantages of the different behaviors.

(2) An encounter zone of R=1.1a appears be used throughout the manuscript, but I could not find a biological justification for this particular value. This results appear to be quite sensitive to this choice, as shown in Supplement Fig. 3(B). In the Discussion, it is mentioned that using a much larger exclusion zone leads to significantly different nutrient flux, and it is implied that such a large exclusion zone is not biologically plausible, but this was not explained sufficiently.

(3) In schematic of the in Fig. 2(B) it was unclear if the encounter zone in the envelope model is defined analogously to the Stokeslet model or if a different formulation is used.

(4) The force balance argument should be clarified. Equation (3) of the supplement gives the force-velocity relation in the motile case. Since equation (4), which the authors state is the net force in the sessile case, seems to involve the same expression, would it not follow from U=0 in the sessile case that one would simply obtain quiescent flow with Fcilia=0?

Reviewer #2 (Public Review):

Summary:

The authors have collected a significant amount of data from the literature on the flow regimes associated with microorganisms whose propulsion is achieved through the action of cilia or flagella, with particular interest in the competition between sessile and motile lifestyles. They then use several distinct hydrodynamic models for the cilia-driven flows to quantify the nutrient uptake and clearance rate, reported as a function of the Peclet number. Among the interesting conclusions the authors draw concerns the question of whether, for certain ciliates, there is a clear difference in nutrient uptake rates in the sessile versus motile forms. The authors show that this is not the case, thereby suggesting that the evolutionary pressure associated with such a difference is not present. The analysis also includes numerical calculations of the uptake rate for spherical swimmers in the regime of large Peclet numbers, where the authors note an enhancement due to advection-generated thinning of the solutal boundary layer around the organism.

Strengths:

In addressing the whole range of organism sizes and Peclet numbers the authors have achieved an important broad perspective on the problem of nutrient uptake of ciliates, with implications for understanding evolutionary driving forces toward particular lifestyles (e.g. sessile versus motile).

Weaknesses:

The authors appear to be unaware of rather similar calculations that were done some years ago in the context of Volvox, in which the issue of the boundary layer size and nutrient uptake enhancement were clearly recognized [M.B. Short, et al., Flows Driven by Flagella of Multicellular Organisms Enhance Long-Range Molecular Transport, PNAS 103, 8315-8319 (2006)]. This reference also introduced the model of a fixed shear stress at the surface of the sphere as a representation of the action of the cilia, which may be more realistic than the squirmer-type boundary condition, although the two lead to similar large-Pe scalings.

The findings reported in Figure 4, that the uptake rate is robust to variations in cilia coverage and absorption fraction, are similar in spirit to an observation made recently in the context of the somatic cell neighbourhood areas in Vovox [Day, et al., eLife 11, e72707 (2022)]. There, it was found that while there is a broad distribution of those areas, and hence of the coarse-grained tangential flagellar force acting on the fluid, the propulsion speed is rather insensitive to those variations.