Dynamics of metal uptake by charged biointerphases: bioavailability and bulk depletion.

A theory is proposed for the dynamics of metal uptake by a spherical microorganism whose peripheral structure consists of a charged bioactive surface surrounded by a soft (ion-permeable) charged layer. The formalism explicitly considers the concomitant steady-state conductive diffusion transport of metals from bulk medium to the bioactive surface and the kinetics of intracellular metal internalisation described by a Michaelis-Menten mechanism. The spatial distribution of metals at the microorganism/solution interphase is derived from an explicit solution of the Nernst-Planck equation with differentiated metal diffusion coefficients inside and outside the microorganism soft surface layer. The metal concentration profile involves the interphasial electrostatic potential distribution governed by the Poisson-Boltzmann equation accounting for the dielectric permittivity gradient across the soft layer/solution interface. The resulting metal uptake flux is rationalized in terms of dimensionless metal-biosurface affinity and the ratio between limiting uptake flux and limiting conductive diffusion flux. Both parameters depend on background electrolyte concentration, microorganism soft surface composition and geometry via their connection to a Boltzmann surface term and a factor expressing the electrostatically-driven retardation or acceleration of metal diffusion. Illustrations demonstrate how metal transport dynamics impacts biouptake depending on electrolyte concentration and on the key bio-physico-chemical properties of the biointerphase. The mathematical framework is then applied to practical situations where a swarm of charged microorganisms deplete metals under steady-state transport conditions. Several depletion kinetic regimes are evaluated as a function of medium salinity and microorganism electrostatic features. Expressions of their characteristic timescales are derived and analogies with equivalent electrochemical circuits are formulated.