Wavy membranes and the growth rate of a planar chemical garden: Enhanced diffusion and bioenergetics

TL;DR

This study combines theory and experiments to show that wavy membranes enhance ion transport via fluctuations in a gel layer, significantly increasing effective diffusivity, which may have supported early bioenergetics.

Contribution

It introduces a model explaining how wavy, porous gel layers increase ion transport rates, with experimental validation in microfluidic setups.

Findings

Growth rate proportional to square root of time, indicating diffusive transport.

Enhanced ion transport due to velocity fluctuations in wavy gel layers.

Effective diffusivity about ten times higher than molecular diffusion.

Abstract

In order to model ion transport across protocell membranes in Hadean hydrothermal vents, we consider both theoretically and experimentally the planar growth of a precipitate membrane formed at the interface between two parallel fluid streams in a two-dimensional microfluidic reactor. The growth rate of the precipitate is found to be proportional to the square root of time, which is characteristic of diffusive transport. However, the dependence of the growth rate on the concentrations of hydroxide and metal ions is approximately linear and quadratic, respectively. We show that such a difference in ionic transport dynamics arises from the enhanced transport of metal ions across a thin gel layer present at the surface of the precipitate. The fluctuations in transverse velocity in this wavy porous gel layer allow an enhanced transport of the cation, so that the effective diffusivity is about an order of magnitude higher than that expected from molecular diffusion alone. Our theoretical predictions are in excellent agreement with our laboratory measurements of the growth of a manganese hydroxide membrane in a microfluidic channel, and this enhanced transport is thought to have been needed to account for the bioenergetics of the first single-celled organisms.