Chemical models for the lethality curves of toxic metal ions

Several equilibrium models are presented for the calculation of the lethality curves due to toxic metal ions. In the first, a generalized Langmuir model is used to examine the occupancy of linear arrays of 1, 2, ..., 6 interacting adsorption sites on a macromolecular species. This model permits one to take into account cooperative or anticooperative interaction of occupied adjacent sites. In the second model, a variety of nonlinear distributions of interacting sites (in triangular, square, tetrahedral, and octahedral array) are analyzed, and the corresponding adsorption isotherms are calculated. The third model treated, the Ising model, represents a linear infinite array of sites with nearest-neighbor interactions. The fourth and fifth models examined are the Bragg-Williams model and the quasi-chemical model, both of which permit approximate treatment of infinite arrays of adsorption sites having arbitrary numbers of interacting nearest neighbors. These models are then combined with the assumption that the differential distribution of mortality is a known function of the fraction of sites occupied by the toxic metal ion to generate lethality curves. Results are computed for the special case in which the differential mortality distribution is Gaussian, and it is shown that all of the models are capable of generating lethality curves of the sort found experimentally when plots are made of percentage lethality versus log dosage. The models can also be used for situations in which toxic effects other than lethality arise from the interaction of a toxic molecule or ion with more than one site on a linear macromolecule or for reactions involving certain other arrays of specified configuration.