Assessment of toxicity using dehydrogenases activity and mathematical modeling

Dehydrogenase activity is frequently used to assess the general condition of microorganisms in soil and activated sludge. Many studies have investigated the inhibition of dehydrogenase activity by various compounds, including heavy metal ions. However, the time after which the measurements are carried out is often chosen arbitrarily. Thus, it can be difficult to estimate how the toxic effects of compounds vary during the reaction and when the maximum of the effect would be reached. Hence, the aim of this study was to create simple and useful mathematical model describing changes in dehydrogenase activity during exposure to substances that inactivate enzymes. Our model is based on the Lagergrens pseudo-first-order equation, the rate of chemical reactions, enzyme activity, and inactivation and was created to describe short-term changes in dehydrogenase activity. The main assumption of our model is that toxic substances cause irreversible inactivation of enzyme units. The model is able to predict the maximum direct toxic effect (MDTE) and the time to reach this maximum (T_MDTE). In order to validate our model, we present two examples: inactivation of dehydrogenase in microorganisms in soil and activated sludge. The model was applied successfully for cadmium and copper ions. Our results indicate that the predicted MDTE and T_MDTE are more appropriate than EC₅₀ and IC₅₀ for toxicity assessments, except for long exposure times.