Fig. 5: Optimal designs explain the diversity of cilia arrangements in sessile and swimming ciliates.
From: Flow physics of nutrient transport drives functional design of ciliates
A, B Solid yellow lines are local optima at each Af from Fig. 4. Pareto fronts that maximize \({{\mathcal{J}}}=(\alpha {{\rm{Sh}}}+(1-\alpha ){{\rm{U}}})\) for swimming cells (purple solid line) and \({{\mathcal{J}}}=(\alpha {{\rm{Sh}}}-(1-\alpha )F)\) for sessile cells (blue solid line). Here, we normalized Sh, U and F to each lie in the range from 0 to 1, and for each value of α ∈ [0, 1], we computed the corresponding optimal cell design (Ac, Af) to obtain the Pareto front as α increases from 0 to 1. We surveyed 31 motile (purple and red) and sessile (blue and green) ciliates, listed by their genus (Supplementary Tables S.3 and S.4). Empirical measurements are mapped onto the design space (Ac, Af): sessile ciliates cluster in one region of the morphospace, characterized by a ciliary crown surrounding the feeding apparatus, while motile ciliates exhibit two types of cell morphologies, one similar to the sessile ciliates and one that maximizes cilia coverage over the entire cell surface. C All surveyed ciliates lie in a region of the morphospace where the model predicts a feeding rate Q of over 104 body volumes per hour, consistent with experimental measurements (Supplementary Table S.5) (contour lines of Q and optimal designs taken from Fig. 4 (A, B). D Likewise, all surveyed ciliates correspond to over twofold increase in nutrient uptake compared to diffusion alone at Pe = 100; (contour lines of Sh and optimal designs taken from Fig. 4C, D. Superimposing optimal solutions, including the Pareto fronts, show remarkable consistency between optimal model predictions and surveyed ciliates.
