Bioaccumulation Dynamics of Metal Ions and Complexes by Aquatic Organisms: An Extended Best and Michaelis–Menten Framework for the Interplay between Chemodynamics, Bioavailability, and Biouptake Kinetics

Abstract

This study elaborates a theoretical framework to understand metal bioaccumulation beyond the limitations of the equilibrium-based Biotic Ligand Model (BLM). By integrating the dynamics of metal speciation in aquatic media with the kinetics of metal biouptake, the formalism predicts metal bioavailability under conditions where the BLM fails, such as high degrees of metal complexation, diffusion-limited metal uptake, and/or internalization of intact metal complexes. The theory accounts for the reactive transport of free metal ions and complexes, incorporating different uptake mechanisms by facilitated and passive diffusion. Extended Best expressions are derived for the flux of metal biouptake by coupling extracellular metal chemodynamics (intertwined diffusion and complexation) with Michaelis–Menten uptake kinetics. The approach provides a unified rationale for various bioaccumulation situations, including the uptake of lipophilic complexes, and the concomitant uptake of free and complexed metals through distinct or shared diffusion-facilitated pathways with competitive, noncompetitive, and/or uncompetitive inhibitions. Computational examples are detailed to illustrate the intricate interplay between metal species transport dynamics and biouptake kinetics for all bioaccumulation cases, particularly addressing how the metal internalization flux is impacted by the (bioavai)lability of metal complexes, whether or not they are internalized intact. The benefits of the formalism are further illustrated through an analysis of well-characterized experimental data on neodymium (Nd) uptake by Chlamydomonas reinhardtii in the absence/presence of well-defined organic ligands. This analysis not only derives key metal biouptake and bioaffinity parameters but also provides solid evidence of the BLM’s failure to describe the data. The quantitative interpretation of Nd bioaccumulation data leads to the identification of two potential uptake mechanisms, and a methodology to distinguish between them is discussed. Overall, this work establishes a more accurate and comprehensive theoretical foundation for predicting metal bioaccumulation in aquatic systems, thereby fundamentally challenging the common equilibrium-based perception of metal bioavailability.