# Exploration of Computational Approaches to Predict the Toxicity of Chemical Mixtures

^{*}

## Abstract

**:**

## 1. Introduction

- (a)
- toxicity data vary with different combinations of the same chemicals in a mixture;
- (b)
- form of exposure;
- (c)
- identification of each chemicals in a specific mixture is also difficult due to the presence of very small quantities; and
- (d)
- complex interactions among chemicals.

## 2. Why Exploration of Toxicity of Chemical Mixtures is Important?

_{50}), some times even below its individual, no observed effect concentration (NOEC). The problem is that these compounds can still alter substantially the toxic effect of the chemical which share the majority of the mixture concentration. Thus, toxicity checking of just this major component may not show the real toxicity value for the final mixture [11,12].

## 3. Hypothesis for a Mixture’s Toxicity Exploration and Data for Computational Modeling

- (i)
- If chemicals in a mixture showed same mechanism of action for a specific response and act on same site of action, then there are chances of dilution of the response. This method is known as concentration addition (CA).
- (ii)
- If chemicals in mixtures act on different sites of action with dissimilar modes of action (MOA), this may disclose statistically independent responses without interaction. This method is known as independent action (IA).
- (iii)
- If chemicals are interactive in nature, then they may show synergistic or antagonistic effects.

#### 3.1. Determination of Dosage Response Curves for All Chemicals in a Mixture

#### 3.2. Determining the Effect of the Chemical Mixture

#### 3.3. Modeling with Identified Hypothesis

#### 3.3.1. Concentration Addition (CA)

_{1}and C

_{2}are the specific concentrations of the compounds 1 and 2 creating the mixture, which results in an effect y, and EC

_{y}

_{1}and EC

_{y}

_{2}signifying the corresponding effect concentrations of the solo compounds 1 and 2 that alone would generate the same response y as the mixture. The combined effect or sum of c

_{1}and c

_{2}is y. Interestingly, the sum of Equation (1) is always equal to 1 for the CA modeling.

#### 3.3.2. Independent Action (IA)

_{A}is the effect of compound A at that definite concentration and e

_{B}is the same for chemical B. The equation can be expanded from binary mixtures to mixtures of more components.

#### 3.3.3. Synergistic and Antagonistic Actions

#### 3.3.4. Generalized Concentration Addition (GCA) Models

_{50A}is the EC

_{50}value of A and similar for chemical B, etc.

## 4. Importance of Computational Approaches to Determine the Toxicity of Chemical Mixtures

- (1.)
- To stop the unethical use of animal cruelty in the name of animal modeling. The application and acceptance of in silico approaches can decrease the use of animals in toxicity testing.
- (2.)
- Using in silico models from existing chemical mixtures, one can assess/predict the toxicity of untested and/or new different combinations of chemical mixtures for a specific species or systems if they fall under the applicability domain (AD).
- (3.)
- Regulatory agencies like United States Environmental Protection Agency (US EPA), European Union regulations like the Registration, Evaluation, Authorization and Restriction of Chemicals (REACH), and Health Canada consider and depend on in silico methods for toxicity and risk assessment followed by decision making.
- (4.)
- In silico methods are reliable tools to analyse the quantity of risk followed by methods to manage it.
- (5.)
- Without any doubt, in silico tools are cost- and time-effective compared to in vivo and in vitro methods.
- (6.)
- A reliable source of methods to fill gaps in mixture toxicity data as the majority of mixtures have no toxicity data at all.

## 5. Types of Computational Approach for a Mixture’s Toxicity Prediction

- (1)
- Methods are easy to implement and interpret.
- (2)
- Help to determine how compounds should be transformed to decrease their toxicity.
- (3)
- Capable of categorizing the structure of likely metabolites.

- (1)
- The presence or absence of SAs does not offer understanding of the biological pathways of toxicity.
- (2)
- If all SAs are not identified properly, the method can increase false negatives.

## 6. Successful Application of Computational Modeling for Predicting a Mixture’s Toxicity

_{50}of the mixtures and composition of binary mixtures. Agreement between the calculated and measured toxicity data can be expressed with the correlation value of 0.936 for 22 datapoints. Authors explained that the molar ratio R is the most suitable descriptor of the mixture composition that can be determined experimentally. They developed a mathematical equation with polynomial function describing the dependence of EC

_{50}on R that was demonstrated to be beneficial for the presented study. The molar ratio, R, was computed as shown by Equation (5):

_{A}and x

_{B}are corresponding molar concentrations of binary mixture components A and B. The most appropriate polynomial is suggested in the form:

_{j}and EC

_{50j}are the molar ratios of the j

^{th}binary mixture and normalized values of the acute toxicity. The constants a, (n = I - 5) are regression coefficients calculated as shown above.

- Daphnia EC
_{20}QSAR:$$E{C}_{20}\text{}={10}^{-0.532\times log\text{}{K}_{ow}+2.975}\text{\hspace{1em}}(\mu mol/L)$$ - Mesocosm NOEC QSAR:$$E{C}_{20}\text{}={10}^{-0.740\times log\text{}{K}_{ow}+3.22}\text{\hspace{1em}}(\mu mol/L)$$

^{2}= 0.95, s = 0.16 (split 1); N = 39, R

^{2}= 0.93, s = 0.19 (split 2); N = 37, R

^{2}= 0.92, s = 0.22 (split 3); N = 33, R

^{2}= 0.94, s = 0.20 (split 4); N = 36, R

^{2}= 0.89, s = 0.24 (split 5); N = 39, R

^{2}= 0.94, s = 0.18 (split 6). Based on mechanistic interpretation, authors concluded that the presence of bromine, chlorine and oxygen is the promoter of toxicity enhancement. By contrast, the nitrogen helped in decreasing the studied toxicity.

_{i}the concentration of the i

^{th}component in the mixture, EC

_{x,i}is the concentration of the i

^{th}component that provokes x% effect when applied singly, and n is the number of mixture components. Again, the IA model can be mathematically expressed as the following:

_{mix}) and c

_{mix}are total effect of the mixture and the total concentration, respectively, and E(c

_{i}) is the effect of the i

^{th}component with the concentration of c

_{i}in the mixture.

^{2}= 0.869 and Q

^{2}

_{LOO}= 0.864 for the training set, and R

^{2}= 0.853 and Q

^{2}

_{ext}= 0.825 for the test set. The RBFNN model gave the statistical parameters R

^{2}= 0.925 and Q

^{2}

_{LOO}= 0.924 for the training set, and R

^{2}= 0.896 and Q

^{2}

_{ext}= 0.890 for the external test set. The statistical results are very acceptable and the residuals between experimental and predicted toxicity for the majority of the mixtures are within the 5% range. Based on the presented result, the author found out that MLR can predict the mixture toxicity more precisely than the RBFNN model.

^{2}= 0.94, Q

^{2}

_{LOO}= 0.91) and external (R

^{2}

_{pred}= 0.78) validation parameters. The three modeled descriptors identified by GA are RDF035m (specifies the probability distribution of finding an atom in a spherical volume of radius R), HATSs (designates leverage-weighted total autocorrelation index/weighted by intrinsic state), and H-047 (defines that H

^{a}is attached to C

^{1}(sp3)/C

^{0}(sp2), where ‘a’ signifies the formal oxidation number). The obtained model presented more precise additive, antagonistic and synergistic toxicities of mixtures compared with traditional CA and IA models. Thus, the QSAR model may be employed to predict the non-additive and additive toxicities of mixtures.

_{17}–EC

_{19}(aliphatic fraction 17 to 19). The aliphatic compounds with mid-chain length were identified as a vital indicator of acute toxicity to soil organisms like earthworms. Additionally, this fraction combined with small aromatic compounds showed more bioavailability with the highest toxicity potential (for example: phenanthrene and acenaphtene). Authors suggested that the toxicity of mixtures may not be correctly predicted using classical regression analysis rather than multiple factors (combined effects)-based analysis accounts for correct prediction. The implication of ML models could advance the understanding of rate-limiting processes disturbing the spontaneously accessible fraction of pollutants in soil followed by a contribution to the mitigation of potential risks. The study strengthens the idea that the bioavailability of multiple metals and hydrocarbons drives the soil toxicity and ML models can be a fast and economic option to monitor multi-contaminated sites.

## 7. Future Avenues of Chemical Mixture Toxicity Research

- (a)
- Mixture assessment should use low doses, for example up to the no-observed-adverse-effect level (NOAEL);
- (b)
- There is no ultimate or universal method, and one needs to develop new or modified approaches from case to case to address the complex issue of mixture, noting that old-style animal-based toxicology practices are insufficient for such a multifaceted issue;
- (c)
- Collaborative efforts between experimentalist and computational communities are must to address majority of issues and challenges related to mixture toxicity;
- (d)
- A variant of the Hausdorff measure, called Hausdorff-like similarity (Hs), can be useful in modeling a complex system like mixtures [45]. To quantify the similarity degree between two systems, it is not suitable to account only for mutual or dissimilar features, but all the features of the systems have to be measured in the assessment. Hausdorff formula are capable of equally weighing both the existence of common/comparable elements. To measure the diversity relationship between the two sets X and Y, the Hausdorff formula can be defined as follows:$$dHau{s}_{XY}=max\left\{\begin{array}{c}sup\\ x\in X\end{array}\left[\begin{array}{c}inf\\ y\in Y\end{array}\left({d}_{xy}\right)\right],\begin{array}{c}sup\\ y\in Y\end{array}\left[\begin{array}{c}inf\\ x\in X\end{array}\left({d}_{yx}\right)\right]\right\}$$$$sHau{s}_{XY}=min\left\{\begin{array}{c}sup\\ x\in X\end{array}\left[\begin{array}{c}inf\\ y\in Y\end{array}\left({s}_{xy}\right)\right],\begin{array}{c}sup\\ y\in Y\end{array}\left[\begin{array}{c}inf\\ x\in X\end{array}\left({s}_{yx}\right)\right]\right\}$$

_{xy}and s

_{yx}are any pair-wise similarity measures between the p-dimensional elements x and y of the sets X and Y, respectively. The terms under the numerator signify the maximum similarity between the individual element for both sets; n

_{X}and n

_{Y}are the number of elements for both sets.

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The reasons behind the implication of computational approaches for a mixture’s toxicity prediction.

**Figure 6.**Strategy behind the integrated fuzzy concentration addition-independent action model (INFCIM).

**Table 1.**Classification of quantitative structure-activity relationship (QSAR) analysis based on dimension.

Dimension | Description | Representative Example of Descriptors or Computational Method | Reference |
---|---|---|---|

0D | Chemical formula derived descriptors | Constitutional indices (Molecular Weight (MW), sum of properties etc.), molecular property descriptors, count descriptors (count of bond, atom, non-hydrogen atom etc.) | [25] |

1D | Descriptors are derived using the representation of various sub-structural molecular fragments | Fingerprints, count of fragments, H-Bond acceptor/donor, Crippen AlogP98, PSA, SMARTS etc. | [25] |

2D | Descriptors are obtained from the graph theoretical representation of molecules including various structural and/or physicochemical property indices | Topological descriptors, eigenvalue-based descriptors, connectivity indices, descriptors containing topological and electronic information. | [25] |

3D | These independent variables encode various spatial as well as geometrical information of compounds and are derived using 3D representation of structure. Such parameters basically portray static representation of a ligand. | WHIM descriptors, MoRSE descriptors, Jurs parameters, GETAWAY descriptors, quantum-chemical descriptors, atomic coordinates, size, steric, surface and volume descriptors. Techniques e.g., Comparative Molecular Field Analysis (CoMFA), Comparative molecular similarity index analysis (CoMSIA) etc. | [25,26] |

4D | Depict multiple representation of the ligand molecule using various configurations, orientation, and protonation state representation. | Volsurf, GRID, Raptor etc. derived descriptors. | [27] |

5D | Descriptors consider the induced fit parameters and aim to establish a ligand-based virtual or pseudo receptor model. | Flexible-protein docking. | [28] |

6D | These are derived using the representation of various solvation circumstances along with the information obtained from 5D-descriptors. | Quasar. | [29] |

7D | Such analysis comprises real receptor or target-based receptor model data. | − | [30] |

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Kar, S.; Leszczynski, J.
Exploration of Computational Approaches to Predict the Toxicity of Chemical Mixtures. *Toxics* **2019**, *7*, 15.
https://doi.org/10.3390/toxics7010015

**AMA Style**

Kar S, Leszczynski J.
Exploration of Computational Approaches to Predict the Toxicity of Chemical Mixtures. *Toxics*. 2019; 7(1):15.
https://doi.org/10.3390/toxics7010015

**Chicago/Turabian Style**

Kar, Supratik, and Jerzy Leszczynski.
2019. "Exploration of Computational Approaches to Predict the Toxicity of Chemical Mixtures" *Toxics* 7, no. 1: 15.
https://doi.org/10.3390/toxics7010015