Nutrient Transport in Concentration Gradients

TL;DR

This study models how sessile ciliates adjust their ciliary motion to optimize nutrient uptake in non-uniform, patchy environments, revealing that aligned ciliary motion enhances nutrient absorption over time, especially in concentration gradients.

Contribution

It introduces a model for ciliate feeding currents in non-uniform nutrient fields and identifies optimal ciliary strategies for nutrient uptake in patchy environments.

Findings

Aligned ciliary motion increases nutrient uptake over time.

Nutrient uptake scales with the square root of time and Péclet number.

Optimal ciliary activity varies with patchiness of nutrients.

Abstract

Sessile ciliates attach to substrates and generate feeding currents to capture passing particulates and dissolved nutrients. Optimal ciliary activity that maximizes nutrient flux at the cell surface while minimizing the rate of hydrodynamic energy dissipation is well characterized in uniform nutrient fields. However, it is unclear how ciliary motion should change when nutrients are non-uniform or patchy. To address this question, we modeled the sessile ciliate and feeding currents using the spherical envelope model, and used an unsteady advection-diffusion equation to describe the nutrient scalar field. In the absence of flows, we calculated the diffusive nutrient uptake analytically in linear nutrient gradients and found no advantage over uptake in uniform fields. With ciliary activity driving feeding currents, we used a spectral method to solve for the unsteady nutrient concentration. We found that, when the axis of symmetry of the ciliary motion is aligned with the nutrient gradient, nutrient uptake at the cell surface increases steadily over time, with highest uptake achieved by the treadmill ciliary motion which is optimal in uniform fields as well. The associated nutrient uptake in concentration gradients scales with the square root of the product of time and P\'eclet number. In patchy environments, optimal ciliary activity depends on the nature of the patchiness. Our findings highlight strategies that enable sessile ciliates to thrive in environments with fluctuating nutrient availability.