New models for the time dependent toxicity of individual and combined toxicants

Equations for estimating binary mixture toxicity: 3-methyl-2-butanone with a series of electrophiles

Mixture toxicity was determined for 32 binary combinations. One chemical was the non-reactive, non-polar narcotic 3-methyl-2-butanone (always chemical A) and the other was a potentially reactive electrophile (chemical B). Bioluminescence inhibition in Allovibrio fischeri was measured at 15-, 30-, and 45-minutes of exposure for A, B, and the mixture (MX). Concentration-response curves (CRCs) were developed for each chemical and used to develop predicted CRCs for the concentration addition (CA) and independent action (IA) mixture toxicity models. Also, MX CRCs were generated and compared with model predictions using the 45-minute data. Classification of observed mixture toxicity used three specific criteria: 1) predicted IA EC50 vs. CA EC50 values at 45-minutes, 2) consistency of 45-minute MX CRC fit to IA, CA, or otherwise at three effect levels (EC25, EC50 and EC75), and 3) the known/suspected mechanism of toxicity for chemical B. Mixture toxicity was then classified into one of seven groupings. As a result of the predicted IA EC50 being more toxic than the predicted CA EC50, IA represented the greater toxic hazard. For this reason, non-sham MXs having toxicity consistent with CA were classified as being "coincident" with CA rather than mechanistically-consistent with CA. Multiple linear regression analyses were performed to develop equations that can be used to estimate the toxicity of other 3M2B-containing binary mixtures. These equations were developed from the data for both IA and CA, at each exposure duration and effect level. Each equation had a coefficient of determination (r2) above 0.950 and a variance inflation factor <1.2. This approach can potentially reduce the need for mixture testing and is amenable to other model systems and to assays that evaluate toxicity at low effect levels.

Setting safer exposure limits for toxic substance combinations

Toxic stimuli (stressors) exposure limits are typically based on single toxic stimuli experiments, but are presently used for both toxic stimuli in isolation and in combination with other toxic stimuli (simultaneous co-exposure or exposures separated in time). In the combination case, typically less of each constituent of the combination is required to cause damage compared to the amount determined from single stressor experiments. Thus, exposure limits based on single toxic stimulus experiments are inadequate for setting limits for stressor combinations. This article presents a recommended simplified approach to improving regulatory exposure limits for toxic stimuli combinations, and a more expansive and expensive alternative to the recommended simplified approach. The recommended approach will partially compensate for the enhanced adverse effects of toxic stimuli combinations relative to adverse effects of toxic stimuli in isolation. The approach covers myriad categories of toxic stimuli reflective of real-life exposures due to lifestyle, iatrogenic, biotoxin, occupational/environmental, and psychosocial/socioeconomic conditions. The proposed approach 1) assumes that all potential toxic stimuli to which an individual might be exposed have the same mechanisms/modes of action on biological mechanisms, and are, thus, indistinguishable by the impacted organism; 2) normalizes the myriad stimuli by converting the doses of toxic stimuli exposures to the respective toxicity reference values (TRV) fractions; 3) sums all the TRVs fractions from these toxic stimuli exposures; and 4) divides all the single substance TRVs by the sum of fractions. While it is an additive approach conceptually, it differs from other additive approaches in the breadth of its inter-category coverage, in order to reflect true inter-category real-life simulation. The newly posited approach does not account for hormetic, antagonistic, or synergistic effects of toxic stimuli in combination. It does not adjust for 1) low-dose toxicants with adverse effects that have been under-reported, or 2) exposure limits like the Occupational Safety and Health Administration - Permissible Exposure Limits (OSHA PELs) that are orders of magnitude above levels shown by published single toxic stimuli studies to have caused adverse effects. Practical considerations for the application of this approach are presented.

Additive Dose Response Models: Defining Synergy

In synergy studies, one focuses on compound combinations that promise a synergistic or antagonistic effect. With the help of high-throughput techniques, a huge amount of compound combinations can be screened and filtered for suitable candidates for a more detailed analysis. Those promising candidates are chosen based on the deviance between a measured response and an expected non-interactive response. A non-interactive response is based on a principle of no interaction, such as Loewe Additivity or Bliss Independence. In a previous study, we introduced, an explicit formulation of the hitherto implicitly defined Loewe Additivity, the so-called Explicit Mean Equation. In the current study we show that this Explicit Mean Equation outperforms the original implicit formulation of Loewe Additivity and Bliss Independence when measuring synergy in terms of the deviance between measured and expected response, called the lack-of-fit. Further, we show that computing synergy as lack-of-fit outperforms a parametric approach. We show this on two datasets of compound combinations that are categorized into synergistic, non-interactive, and antagonistic.