Dynamics of Metal Partitioning at the Cell–Solution Interface: Implications for Toxicity Assessment under Growth-Inhibiting Conditions

Abstract

Metal toxicity toward microorganisms is usually evaluated by determining growth inhibition. To achieve a mechanistic interpretation of such toxic effects, the intricate coupling between cell growth kinetics and metal partitioning dynamics at the cell-solution interface over time must be considered on a quantitative level. A formalism is elaborated to evaluate cell-surface-bound, internalized, and extracellular metal fractions in the limit where metal uptake kinetics is controlled by internalization under noncomplexing medium conditions. Cell growth kinetics is tackled using the continuous logistic equation modified to include growth inhibition by metal accumulation to intracellular or cell surface sites. The theory further includes metal-proton competition for adsorption at cell-surface binding sites, as well as possible variation of cell size during exposure to metal ions. The formalism elucidates the dramatic impacts of initial cell concentration on metal bioavailability and toxicity over time, in agreement with reported algae bioassays. It further highlights that appropriate definition of toxicity endpoints requires careful inspection of the ratio between exposure time scale and time scale of metal depletion from bulk solution. The latter depends on metal internalization-excretion rate constants, microorganism growth, and the extent of metal adsorption on nonspecific, transporter, and growth inhibitory sites. As an application of the theory, Cd toxicity in the algae Pseudokirchneriella subcapitata is interpreted from constrained modeling of cell growth kinetics and of interfacial Cd-partitioning dynamics measured under various exposure conditions.