Dynamics of metal uptake by charged soft biointerphases: impacts of depletion, internalisation, adsorption and excretion†
A comprehensive theory is elaborated for the dynamics of metal ion uptake by charged spherical microorganisms. The formalism integrates the interplay over time between bulk metal depletion, metal adsorption, metal excretion (efflux) and transport of metals by conductive diffusion toward the metal-consuming biomembrane. The model further involves the basic physicochemical features of the microbial interphase in terms of size, distribution of electrostatic charges and thickness of peripheral soft surface appendage. A generalization of the Best equation is proposed and leads to the expression of the time-dependent concentration of metal ions at the active membrane surface as a function of bulk metal concentration. Combination of this equation with the metal conservation condition over the sample volume allows a full evaluation of bulk metal depletion kinetics and the accompanying time-dependent uptake and excretion fluxes as a function of metal–microorganism electrostatic interaction, microbe concentration and relevant biophysicochemical features of the interphase. Practically tractable expressions are derived in the limit where the Biotic Ligand Model (BLM) is obeyed and in situations where conductive diffusion transport of metals significantly determines the rate of biouptake. In particular, the plateau value reached at sufficiently long times by bulk metal concentration is rigorously expressed in terms of the key parameters pertaining to the adsorption process and to the kinetics of metal uptake and excretion. The theory extends and unifies previous approximate models where the impacts of extracellular metal transport and/or metal efflux on the overall rate of uptake were ignored.