Computing steady-state metal flux at microorganism and bioanalogical sensor interfaces in multiligand systems. A reaction layer approximation and its comparison with the rigorous solution

In complicated environmental or biological systems, the fluxes of chemical species at a consuming interface, like an organism or an analytical sensor, involve many coupled chemical and diffusion processes. Computation of such fluxes thus becomes difficult. The present paper describes an approximate approach, based on the so-called reaction layer concept, which enables one to obtain a simple analytical solution for the steady-state flux of a metal ion at a consuming interface, in the presence of many ligands, which are in excess with respect to the test metal ion. This model can be used for an unlimited number of ligands and complexes, without limit for the values of the association/dissociation rate constants or diffusion coefficients. This approximate solution is compared with a rigorous approach for the computation of the fluxes based on an extension of a previously published method (J. Galceran, J. Puy, J. Salvador, J. Cecília, F. Mas and J. L. Garcés, Phys. Chem. Chem. Phys., 2003, 5, 5091-5100). The comparison is performed for a very wide range of the key parameters: rate constants and diffusion coefficients, equilibrium constants and ligand concentrations. Their combined influence is studied in the whole domain of fully labile to non-labile complexes, via two combination parameters: the lability index, L, and the reaction layer thickness, mu. The results show that the approximate solution provides accurate results in most cases. However, for particular combinations of metal complexes with specific values of L or mu, significant differences between the approximate and rigorous solutions may occur. They are evaluated and discussed. These results are important for three reasons: (i) they enable the use of the approximate solution in a fully reliable manner, (ii) when present, the differences between approximate and rigorous solution are largely due to the coupling of chemical reactions, whose importance can thus be estimated, (iii) due to its simple mathematical expression, the individual contribution of each metal species to the overall flux can be computed.