Nonlinear biotic ligand model for assessing alleviation effects of Ca, Mg, and K on Cd toxicity to soybean roots

Developing a nonlinear biotic ligand model (BLM) that considers the geometrical constraints for binding of different cations on biotic ligands will provide more reliable details about the hypothetical mechanism governing the alleviation of cadmium (Cd) toxicity by coexistent cations. Soybean seedlings under Cd stress produced by various activities of coexistent cations such as calcium (Ca²⁺), magnesium (Mg²⁺), and potassium (K⁺) were hydroponically assayed for Cd toxicity to soybean roots. The Cd²⁺ activity resulting in 50% reduction of root elongation (RE), EA ₅₀, was used for assessing the Cd toxicity to the soybean seedling. Increasing Ca²⁺, Mg²⁺, and K⁺ activities resulted in a significant alleviation of Cd toxicity to soybean roots. This alleviation was markedly higher with increasing Ca²⁺ and K⁺ levels than with increasing Mg²⁺ level. In addition, EA ₅₀ increased in nonlinear positive relationships with Ca²⁺ and Mg²⁺. The real data obtained from the soybean assay were thus used to develop the nonlinear BLM for Cd rhizotoxicity. Two parameters, competition equivalent and stability constant, indicated the profiles of the geometrical constraint and affinity of Ca²⁺, Mg²⁺, and K⁺ binding on the soybean root surface to alleviate Cd toxicity. Compared with the traditional linear BLM, the nonlinear BLM provided more precise predictions of relative root elongation (RRE) and EA ₅₀. Therefore, adopting the nonlinear BLM approach will successfully improve the monitoring and assessment of heavy metal toxicity to terrestrial plants.