## 4 Discussion
The synergism/antagonism (S/A) sub-module provides a broad indication of synergisms, while the dose ratio-dependent deviation (DR) and the dose level-dependent deviation (DL) sub-modules show a more complex pattern, moving from synergism to antagonism. DR has the most conservative score, yet it is very similar to DL. Specifically, in the case of DR, a negative \"_a_\" and a positive \"_b_\" indicate the presence of antagonism, where the toxicity of the mixture is primarily due to one component (either high Cd or high Zn). The DL sub-module suggests a shift from synergism to antagonism at toxic values higher than LC\({}_{50}\). It is noteworthy that the responses identified by the two systems (CA, IA, and their derived models) are not identical. However, it should be pointed out that they account for additivity in markedly different ways. In particular, CA tends to overestimate mixture toxicity, making it relatively simpler to highlight an antagonistic effect from its derived sub-modules. In the IA module, each sub-module explains a very similar amount of data variance, approximately 77%. Among these sub-modules, DL stands out as the best performer, significantly outperforming both IA and SA. The parameters of the DL sub-module, labelled as \"_a_\" and \"_b_,\" indicate synergism at low dose levels and antagonism at high doses. It is noteworthy that although the results of the CA and IA modules are not identical, their significant DL modules are similar in their predictions. In particular, they both indicate synergism at very low doses, such as the no observed adverse effect levels (NOAELs) for either Cd or Zn. This study represents a novel exploration, marking the first analysis of the MixTOX tool in the context of bimetallic mixtures involving Cd, Zn, and ZnO in the freshwater ciliate _E. adecitulatus_. The data analysis shows no substantial differences in the predictability of joint effects using CA and IA for the tested bimetallicsystem. Both models explain between 34% and 88% of the variance in the 1a-1b bimetallic mixture, and between 35% and 99% in the 1c-1d binary mixture. The MixTOX tool emerged as the superior and predominant method, demonstrating statistically significant deviations in bimetallic mixtures by incorporating additional parameters to tailor the dataset. For instance, with the exception of the Cd + Zn and Cd + ZnO mixtures, the inclusion of S/A, DR, and DL deviation parameters in the reference models results in a modest increase of less than 5% in the goodness of fit, as measured by R2. While CA and IA predictions are nearly identical in most cases, there are subtle differences. For instance, in the case of the Cd + Zn mixture, positive \"_a_\" values at 1 h and 24 h are observed in all deviation patterns of the CA module, except DL, while the opposite is true for the IA module. Conversely, in the case of Cd + ZnO, both modules give similar results at 1 h and 24 h. In general, the CA models explain the mixture toxicity of the 1a-1d mixtures based on free ion activity. For Cd + Zn mixtures, the CA model explains the variation, showing an increase from 34% to 72% at 24 h, while the IA model shows a decrease from 82% to 77% over the same period. For the bimetallic mixture of Cd + ZnO, the CA model shows an increase from 47% to 87%, while the IA module shows an increase from 35% to 86%. Notably, IA predictions are consistently lower than CA predictions, as exemplified by the mixture of Cd + ZnO at 1 h, where IA accounts for 35% of the model predictability compared to 47% for CA. The lower predictability of IA has been studied in various organisms, with particular emphasis on chemicals known to interact with xenobiotic metabolism [72; 73; 74]. We observed that the presence of one metal does not significantly affect the free ion activity of another metal in the mixed solution. Our results indicate that the joint toxicity effect of Cd, Zn, and ZnO, after different exposure times, is predominantly antagonistic at chronic levels, whereas it shows synergism at acute levels.