Predicting Mixture Effects over Time with Toxicokinetic–Toxicodynamic Models (GUTS): Assumptions, Experimental Testing, and Predictive Power

Abstract

Current methods to assess the impact of chemical mixtures on organisms ignore the temporal dimension. The General Unified Threshold model for Survival (GUTS) provides a framework for deriving toxicokinetic–toxicodynamic (TKTD) models, which account for effects of toxicant exposure on survival in time. Starting from the classic assumptions of independent action and concentration addition, we derive equations for the GUTS reduced (GUTS-RED) model corresponding to these mixture toxicity concepts and go on to demonstrate their application. Using experimental binary mixture studies with Enchytraeus crypticus and previously published data for Daphnia magna and Apis mellifera , we assessed the predictive power of the extended GUTS-RED framework for mixture assessment. The extended models accurately predicted the mixture effect. The GUTS parameters on single exposure data, mixture model calibration, and predictive power analyses on mixture exposure data offer novel diagnostic tools to inform on the chemical mode of action, specifically whether a similar or dissimilar form of damage is caused by mixture components. Finally, observed deviations from model predictions can identify interactions, e.g., synergism or antagonism, between chemicals in the mixture, which are not accounted for by the models. TKTD models, such as GUTS-RED, thus offer a framework to implement new mechanistic knowledge in mixture hazard assessments.

BeeGUTS—A Toxicokinetic–Toxicodynamic Model for the Interpretation and Integration of Acute and Chronic Honey Bee Tests

“…In the first case the survival probabilities for each compound to which a bee is exposed can be multiplied to obtain the combined effect of the total exposure (Baas et al, 2007). In the second case, the scaled damage can be added, and the survival probability can then be calculated for the combined effect of the total exposure (Bart et al, 2021).…”

“…Therefore, they allow for a much more realistic evaluation of effects under field-realistic conditions with time-variable exposures. Effects can be calculated for oral and contact exposure separately and later combined by adding their scaled damage and, as such, treating them as a simultaneous exposure to two compounds acting on an identical target (Bart et al, 2021).…”

Predicting Combined Effects of Chemical Stressors: Population‐Level Effects of Organic Chemical Mixtures with a Dynamic Energy Budget Individual‐Based Model

“…They also included mixture toxicity data at the apical level in their assessment, which were not used in the present study. Bart et al (2021) argued that low effect concentrations are important to derive the applicable mixture toxicity mode. This is true for their implementation (with the hockey stick approach) because low effect levels under the damage threshold will not produce toxic effects under IA.…”

“…The number of published studies on mechanistic effect models for mixture toxicity is limited (Bart et al, 2021; Cedergreen et al, 2017; Jager et al, 2010), and the focus is mainly on individual‐level assessment. Only recently have applications of mixture toxicity in mechanistic population models been published (Hansul et al, 2021; Vlaeminck et al, 2021).…”

“…Our study went further and included lethal effects while also extrapolating them to the population level. Bart et al (2021) have developed a mixture toxicity approach for GUTS-RED, building on the theory suggested by Jager and Ashauer (2018). They specifically tested the applicability of DA and IA for both the SD and the IT (IA) approaches in GUTS-RED, hence only testing effects on apical survival (i.e., mortality after 21 days).…”