Modelling the adsorption of phospholipid vesicles to a silicon dioxide surface using Langmuir kinetics

The rate constants and equilibrium constant for the adsorption and desorption of lipid vesicles from a SiO2 surface have been determined.

Large-scale mRNA translation and the intricate effects of competition for the finite pool of ribosomes

We present a new theoretical framework for large-scale mRNA translation using a network of models called the ribosome flow model with Langmuir kinetics (RFMLK), interconnected via a pool of free ribosomes. The input to each RFMLK depends on the pool density, and it affects the initiation rate and the internal ribosome entry rates at each site along each RFMLK. Ribosomes that detach from an RFMLK due to termination or premature drop-off are fed back into the pool. We prove that the network always converges to a steady-state, and study its sensitivity to variations in the parameters. For example, we show that if the drop-off rate at some site in some RFMLK is increased then the pool density increases and consequently the steady-state production rate in all the other RFMLKs increases. Surprisingly, we also show that modifying a parameter of a certain RFMLK can lead to arbitrary effects on the densities along the modified RFMLK, depending on the parameters in the entire network. We conclude that the competition for shared resources generates an indirect and intricate web of mutual effects between the mRNA molecules, that must be accounted for in any analysis of translation.

Adsorption of fluoride by porous adsorbents: Estimating pore diffusion coefficients from batch kinetic data

A simple method is presented for extracting pore diffusion coefficients from batch adsorption kinetic data. The method employs the classic Langmuir kinetics model which is characterized by a single rate coefficient. An analytical solution in the form of a simple algebraic equation is available for this rate model. Fitting the algebraic equation to batch kinetic data to determine the rate coefficient is straightforward and can be conveniently accomplished using standard spreadsheet programs. The resultant rate coefficient can be converted to the pertinent pore diffusion coefficient via a separate algebraic expression. The proposed modeling approach provides accurate fits of experimental kinetic data taken from the literature and yields acceptable errors in the best estimates for pore diffusion coefficients. Specific examples discussed are the adsorption of fluoride by bone char and laterite adsorbents.

On the possibility of spontaneous chemomechanical oscillations in adsorptive porous media

We derive general conditions for the emergence of sustained chemomechanical oscillations from a non-oscillatory adsorption/desorption reaction in a gas/solid porous medium. The oscillations arise from the nonlinear response of the solid matrix to the loading of the adsorbed species. More particularly, we prove that, in order for oscillations to occur, adsorption of the gas must in general cause a swelling of the solid matrix. We also investigate the prototypical case of Langmuir kinetics both numerically and analytically. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.