Fluid flow enhances the effectiveness of toxin export by aquatic microorganisms: a first-passage perspective on microvilli and the concentration boundary layer

TL;DR

This study models how fluid flow around aquatic microorganisms enhances toxin export efficiency, highlighting the role of microvilli and boundary layers in mass transport during embryo development.

Contribution

It introduces a first-passage model linking fluid dynamics to toxin export, emphasizing the impact of turbulence and boundary layers on microvilli function.

Findings

Fluid flow improves toxin export compared to diffusion alone.

A concentration boundary layer forms at high Péclet numbers.

Cell surface roughness and microvilli are functionally connected.

Abstract

A central challenge for organisms during development is determining a means to efficiently export toxic molecules from inside the developing embryo. For aquatic microorganisms, the strategies employed should be robust with respect to the variable ocean environment and limit the chances that exported toxins are reabsorbed. As a result, the problem of toxin export is closely related to the physics of mass transport in a fluid. In this paper we consider a model first-passage problem for the uptake of exported toxins by a spherical embryo. By considering how macroscale fluid turbulence manifests itself on the microscale of the embryo, we determine that fluid flow enhances the effectiveness of toxin export as compared to the case of diffusion-limited transport. In the regime of large P\'eclet number, a perturbative solution of the advection-diffusion equation reveals that a concentration boundary layer forms at the surface of the embryo. The model results suggest a functional role for cell surface roughness in the export process, with the thickness of the concentration boundary layer setting the length scale for cell membrane protrusions known as microvilli. We highlight connections between the model results and experiments on the development of sea urchin embryos.