Prediction of noninteractive mixture toxicity of organic compounds based on a fuzzy set method

Reflected generalized concentration addition and Bayesian hierarchical models to improve chemical mixture prediction

Environmental toxicants overwhelmingly occur together as mixtures. The variety of possible chemical interactions makes it difficult to predict the danger of the mixture. In this work, we propose the novel Reflected Generalized Concentration Addition (RGCA), a piece-wise, geometric technique for sigmoidal dose-responsed inverse functions that extends the use of generalized concentration addition (GCA) for 3+ parameter models. Since experimental tests of all relevant mixtures is costly and intractable, we rely only on the individual chemical dose responses. Additionally, RGCA enhances the classical two-step model for the cumulative effects of mixtures, which assumes a combination of GCA and independent action (IA). We explore how various clustering methods can dramatically improve predictions. We compare our technique to the IA, CA, and GCA models and show in a simulation study that the two-step approach performs well under a variety of true models. We then apply our method to a challenging data set of individual chemical and mixture responses where the target is an androgen receptor (Tox21 AR-luc). Our results show significantly improved predictions for larger mixtures. Our work complements ongoing efforts to predict environmental exposure to various chemicals and offers a starting point for combining different exposure predictions to quantify a total risk to health.

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Artificial Neural Networks (ANNs) are transforming how we understand chemical mixtures, providing an expressive view of the chemical space and multiscale processes. Their hybridization with physical knowledge can bridge the gap between predictivity and understanding of the underlying processes. This overview explores recent progress in ANNs, particularly their potential in the 'recomposition' of chemical mixtures. Graph-based representations reveal patterns among mixture components, and deep learning models excel in capturing complexity and symmetries when compared to traditional Quantitative Structure-Property Relationship models. Key components, such as Hamiltonian networks and convolution operations, play a central role in representing multiscale mixtures. The integration of ANNs with Chemical Reaction Networks and Physics-Informed Neural Networks for inverse chemical kinetic problems is also examined. The combination of sensors with ANNs shows promise in optical and biomimetic applications. A common ground is identified in the context of statistical physics, where ANN-based methods iteratively adapt their models by blending their initial states with training data. The concept of mixture recomposition unveils a reciprocal inspiration between ANNs and reactive mixtures, highlighting learning behaviors influenced by the training environment.

Environmental health and risk assessment metrics with special mention to biotransfer, bioaccumulation and biomagnification of environmental pollutants

The environment pollutants, which are landed up in environment because of human activities like urbanization, mining and industrializations, affects human health, plants and animals. The living organisms present in environment are constantly affected by the toxic pollutants through direct contact or bioaccumulation of chemicals from the environment. The toxic and hazardous pollutants are easily transferred to different environmental matrices like land, air and water bodies such as surface and ground waters. This comprehensive review deeply discusses the routes and causes of different environmental pollutants along with their toxicity, impact, occurrences and fate in the environment. Environment health and risk assessment tools that are used to evaluate the harmfulness, exposure of living organisms to pollutants and the amount of pollutant accumulated are explained with help of bio-kinetic models. Biotransfer, toxicity factor, biomagnification and bioaccumulation of different pollutants in the air, water and marine ecosystems are critically addressed. Thus, the presented survey would be collection of correlations those addresses the factors involved in assessing the environmental health and risk impacts of distinct environmental pollutants.

Effects of long-term and low-concentration exposures of benzene and formaldehyde on mortality of Drosophila melanogaster

Single-chemical thresholds cannot comprehensively evaluate the risk of chemical mixture exposure in indoor air. Moreover, a large number of researches have focused on short-term and high-concentration co-exposure scenarios related to different species, based on diverse endpoints, which hampers the application and improvement of existing risk evaluation models of chemical mixture exposures. More importantly, current risk evaluation models are not user-friendly for construction practitioners who do not have sufficient toxicological knowledge. Therefore, in this study, an inhalation experiment system and a hazard index (HI) were developed to investigate the risks associated with low-concentration and long-term inhalation exposure scenarios of formaldehyde and benzene, individually and combined, based on Drosophila melanogaster mortality. The results showed that the system exhibited good reproducibility in providing stable exposure concentrations during D. melanogaster life cycle. Furthermore, in a range of experimental concentrations, the interaction between formaldehyde and benzene was additive or synergistic, which was concentration- and ratio-dependent. This study is of great significance in harmonising and providing toxicity data under long-term and low-concentration exposure scenarios, which is beneficial for establishing a new user-friendly risk evaluation model for indoor chemical mixture exposures. It should be noted that the proposed HI value could indicate the hazard degrees of long-term inhalation exposures of formaldehyde and benzene, individually and combined, to D. melanogaster. However, the applicability of this index requires further experiments to evaluate the exposure risks of other volatile organic compounds (VOCs) to D. melanogaster.

Computational Modeling of Mixture Toxicity

Environmental pollution has become an inevitable problem and a relevant global issue of the twenty-first century. The fast industrial growth has caused the production and release of various chemical species and multicomponent mixtures to the environment which affect the entire living world adversely. Various industrial regulatory agencies are working in this domain to regulate the production of chemical entities, proper release of chemical wastes, and the risk assessment of the industrial and hazardous chemicals; however, they mostly rely upon the single chemical risk assessment instead of considering the toxicity of multicomponent mixtures. In this era of chemical advances, single chemical exposure is a myth. The entire living world is always being exposed to the environmental chemical mixtures but the scarcity of toxicity data of chemical mixtures is a serious concern. The nature of toxicity of mixtures is entirely different and complex from the individual chemicals because of the interactions (synergism/antagonism) among the mixture components. Various regulatory authorities and the scientific world have come up with a handful of methodologies and guidelines for evaluating the harmful effects of the multicomponent mixtures, though there is no such significant, standard, and reliable approach for the toxicity evaluation of chemical mixtures and their management across diverse fields. Toxicity experimentations on laboratory animals are troublesome, time-consuming, costly, and unethical. Thus, to reduce the animal experimentations, the scientific communities, regulatory agencies, and the industries are now depending upon the already proven computational alternatives. The computational approaches are capable of predicting toxicities, prioritizing chemicals, and their risk assessment. Besides these, the in silico methods are cost-effective, less time-consuming, and easy to understand. It has been found out that most of the in silico toxicity predictions are on single chemicals and till date there are very few computational studies available for chemical mixtures in the scientific literature. Therefore, the current chapter illustrates the importance of determination of toxicity of mixtures, the conventional methods for toxicity evaluation of chemical mixtures, and the role of in silico methods to assess the toxicity, followed by the types of various computational methods used for such purpose. Additionally, few successful applications of computational tools in toxicity prediction of mixtures have been discussed in detail. At the end of this chapter, we have discussed some future perspectives toward the role and applications of in silico techniques for toxicity prediction of mixtures.

New methods of top-to-down mixture toxicity prediction: A case study of eliminating of the effects of cosolvent from binary mixtures

At present, the toxicity prediction of mixtures mainly focuses on the concentration addition (CA) and independent action (IA) based on individual toxicants to predict the toxicity of multicomponent mixtures. This process of predicting the toxicity of multicomponent mixtures based on single substances or low component mixtures is called down-to-top method in this study. However, due to the particularity of some toxicants, we have to use the top-to-down idea to obtain or eliminate the toxicity of some components from mixtures. For example, the toxicity of toxicants is obtained from the toxicity of a mixture with, especially toxic, cosolvent added. In the study, two top-to-down methods, the inverse CA (ICA) and inverse IA (IIA) models, were proposed to eliminate the effects of a certain component from multicomponent mixtures. Furthermore, taking the eight binary mixtures consisting of different shapes of cosolvents (isopropyl alcohol (IPA) having hormesis and dimethyl sulfoxide (DMSO)) and toxicants (two ionic liquids and two pesticides) as an example, combined with the interaction evaluated by CA and IA model, the influence of different shapes of components on top-to-down toxicity prediction was explored. The results showed that cosolvent IPA having hormesis may cause unpredictable effects, even at low concentrations, and should be used with caution. For DMSO, most of the toxicant's toxicity obtained by ICA and IIA models were almost in accordance with those observed experimentally, which showed that ICA and IIA could effectively eliminate the effects of cosolvent, even if toxic cosolvent, from the mixture. Ultimately, a frame of cosolvent use and toxicity correction for the hydrophobic toxicant were suggested based on the top-to-down toxicity prediction method. The proposed methods improve the existing framework of mixture toxicity prediction and provide a new idea for mixture toxicity evaluation and risk assessment.

Study of the joint action of multi-component mixtures based on parameter σ2(k∙ECx) characterizing the shape difference of concentration-response curves

A previous study has revealed that the parameter k∙EC_x, characterizing the shape of concentration-response curves (CRCs), could predict the combined toxicity of binary mixtures. This study further explored the predictability of multi-component mixtures. Eleven component mixtures were designed using the uniform design ray, and the acute toxicity of the eleven environmental pollutants and their mixtures to Vibrio fischeri was determined using microplate toxicity analysis. We used independent action (IA) and the effect residual ratio (ERR_x) models to evaluate the combined toxicity of multi-component mixtures and ascertain the functional relationship between σ²_(k∙ECx), a parameter characterizing the CRC morphological difference of multi-component mixtures, and combined toxicity. The variance σ²_(k∙ECx) of each component characteristic parameter of multi-component mixtures gradually increased in the concentration range, and the relationship between σ²_(k∙ECx) and ERR_x was consistent with the exponential function. The literature verification showed that this rule is generally applicable to the acute toxicity of multi-component mixtures to luminescent bacteria. The exponential function showed the variation rule of the joint action of multi-component mixtures. In the present study, the joint toxicity of multi-component mixtures can be predicted from single toxicity and small amount of multiple toxicity, circumventing complex multi-component toxicity experiments.

Prediction of the joint action of binary mixtures based on characteristic parameter k∙ECx from concentration-response curves

The evaluation of joint toxicity of mixtures is an important topic in toxicology. Previous studies have found that the parameter k∙EC_x of concentration response curves (CRCs) can be used to assess the applicability of concentration addition model (CA). This study further assesses the predictability of k∙EC_x on the joint toxicity evaluation. The toxicities of the twelve environmental pollutants, as well as those of binary mixtures with an equivalent-effect concentration ratio, to Vibrio fischeri were determined by using the microplate toxicity analysis. The toxicity evaluation of mixtures was conducted by CA and independent action model (IA). The relationship between the joint toxicity (measured by the relative model deviation ratio (rMDR)) and the k∙EC_x was studied. The results shows that the k∙EC_x could reflect the shape of CRCs in the whole concentration range. According to the IA and CA, 65% of the mixtures produce strong antagonistic or synergistic effect due to the significant difference of k∙EC_x. The percentage of the relative difference of k∙EC_x of components and the rMDR_x can be fitted by an exponential function. Different types of interactions could be described using this function. It is suggested that the joint toxicity of binary mixtures can be assessed with the parameter k∙EC_x, which can quickly get very important data when planning experiments, but also reduce the number of experiments.

Toxicity of binary mixtures of pesticides and pharmaceuticals toward Vibrio fischeri: Assessment by quantitative structure-activity relationships

Pollutants in real aquatic systems commonly occur as chemical mixtures. Yet, the corresponding risk assessment is still mostly based on information on single-pollutant toxicity, accepting the assumption that pollutant mixtures exhibit additive toxicity effect which is often not the case. Therefore, it is still better to use the experimental approach. Unfortunately, experimental determination of toxicity for each mixture is practically unfeasible. In this study, quantitative structure-activity relationship (QSAR) models for the prediction of toxicity of binary mixtures towards bioluminescent bacteria Vibrio fischeri were developed at three toxicity levels (EC₁₀, EC₃₀ and EC₅₀). For model development, experimentally determined toxicity values of 14 pollutants (pharmaceuticals and pesticides) were correlated with their structural features, applying multiple linear regression together with genetic algorithm. Statistical analysis, internal validation and external validation of the models were carried out. The toxicity is accurately predicted by all three models. EC₃₀ and EC₅₀ values are mostly influenced by geometrical distances between nitrogen and sulfur atoms. Furthermore, the simultaneous presence of oxygen and chlorine atoms in mixture can induce the increase in toxicity. At lower effect levels (EC₁₀), nitrogen atom bonded to different groups has the highest impact on mixture toxicity. Thus, the analysis of the descriptors involved in the developed models can give insight into toxic mechanisms of the binary systems.

BNNmix: A new approach for predicting the mixture toxicity of multiple components based on the back-propagation neural network

The chemical mixtures in various environmental media not only have concentration diversity but also mixture-ratio diversity. It is impossible to experimentally determine the toxicities of all mixtures; therefore, it is necessary to develop effective methods based on models to predict mixture toxicity. In this study, a new approach (BNNmix) based on the back-propagation neural network (BPNN) was developed and used to predict the toxicities of seven-component mixtures (consisting of two substituted phenols, two pesticides, two ionic liquids, and one heavy metal) on Caenorhabditis elegans. We found that the combined toxicities of various mixtures used in the experiments were neither global concentration-additive nor global response-additive, which implied that it was impossible to accurately predict the toxicities of such mixtures by using common models such as concentration addition (CA) and response addition (independent action, IA). Using the BNNmix approach to estimate or predict the toxicities of the mixtures under test, it was found that the predictive toxicities of various mixtures with different mixture ratios and concentrations were almost in accordance with those observed experimentally. Unlike the CA and IA models, the BNNmix approach can predict not only the toxicities of mixtures having toxicological interactions but also those with global concentration or response additivities.

Mathematical Modeling Approaches for Assessing the Joint Toxicity of Chemical Mixtures Based on Luminescent Bacteria: A Systematic Review

Developments in industrial applications inevitably accelerate the discharge of enormous substances into the environment, whereas multi-component mixtures commonly cause joint toxicity which is distinct from the simple sum of independent effect. Thus, ecotoxicological assessment, by luminescent bioassays has recently brought increasing attention to overcome the environmental risks. Based on the above viewpoint, this review included a brief introduction to the occurrence and characteristics of toxic bioassay based on the luminescent bacteria. In order to assess the environmental risk of mixtures, a series of models for the prediction of the joint effect of multi-component mixtures have been summarized and discussed in-depth. Among them, Quantitative Structure-Activity Relationship (QSAR) method which was widely applied in silico has been described in detail. Furthermore, the reported potential mechanisms of joint toxicity on the luminescent bacteria were also overviewed, including the Trojan-horse type mechanism, funnel hypothesis, and fishing hypothesis. The future perspectives toward the development and application of toxicity assessment based on luminescent bacteria were proposed.

Pesticides, cosmetics, drugs: identical and opposite influences of various molecular features as measures of endpoints similarity and dissimilarity

The similarity is an important category in natural sciences. A measure of similarity for a group of various biochemical endpoints is suggested. The list of examined endpoints contains (1) toxicity of pesticides towards rainbow trout; (2) human skin sensitization; (3) mutagenicity; (4) toxicity of psychotropic drugs; and (5) anti HIV activity. Further applying and evolution of the suggested approach is discussed. In particular, the conception of the similarity (dissimilarity) of endpoints can play the role of a "useful bridge" between quantitative structure property/activity relationships (QSPRs/QSARs) and read-across technique.

Human health risk assessment of antibiotics in binary mixtures for finished drinking water

The present study developed a new step-wise approach to estimate the potential human health risk of antibiotics in binary mixture for drinking water samples for two different sub-populations. Monte Carlo simulation based uncertainty analysis was performed to reduce uncertainty in risk assessment. Human health risk assessment studies were carried out using the acceptable daily intake (ADIs) for exposures of individual antibiotics considering point of departure (POD) and uncertainty factors (UFs). The estimated ADI values were used to estimate the predicted no effect concentrations (PNECs), at or below which no adverse human health effects are anticipated. Hazard quotient (HQ) in risk assessment was calculated as a ratio of environmental concentrations (ECs) and PNECs (EC/PNEC). The study showed that the average HQs values of individual antibiotics in adult and children were found below the acceptable limit, demonstrating no possible human health risk for both the subgroups. HI_interaction values of antibiotics in binary mixture was calculated using HQ values of antibiotics. The study observed that the estimated HI_interaction values of antibiotics in binary mixture was found to be less than 1 for both the sub populations, indicating no potential adverse effects on human health. Concentration of antibiotics was the primary contributor (>65%) to the overall variance in the uncertainty estimates for HQs of individual antibiotics in drinking water for adult and children. The co-occurrence of antibiotics in binary mixture for drinking water samples doesn't possess any possible risk on human health for the studied population.

Exploration of Computational Approaches to Predict the Toxicity of Chemical Mixtures

Industrial advances have led to generation of multi-component chemicals, materials and pharmaceuticals which are directly or indirectly affecting the environment. Although toxicity data are available for individual chemicals, generally there is no toxicity data of chemical mixtures. Most importantly, the nature of toxicity of these studied mixtures is completely different to the single components, which makes the toxicity evaluation of mixtures more critical and challenging. Interactions of individual chemicals in a mixture can result in multifaceted and considerable deviations in the apparent properties of its ingredients. It results in synergistic or antagonistic effects as opposed to the ideal case of additive behavior i.e., concentration addition (CA) and independent action (IA). The CA and IA are leading models for the assessment of joint activity supported by pharmacology literature. Animal models for toxicity testing are time- and money-consuming as well as unethical. Thus, computational approaches are already proven efficient alternatives for assessing the toxicity of chemicals by regulatory authorities followed by industries. In silico methods are capable of predicting toxicity, prioritizing chemicals, identifying risk and assessing, followed by managing, the risk. In many cases, the mechanism behind the toxicity from species to species can be understood by in silico methods. Until today most of the computational approaches have been employed for single chemical's toxicity. Thus, only a handful of works in the literature and methods are available for a mixture's toxicity prediction employing computational or in silico approaches. Therefore, the present review explains the importance of evaluation of a mixture's toxicity, the role of computational approaches to assess the toxicity, followed by types of in silico methods. Additionally, successful application of in silico tools in a mixture's toxicity predictions is explained in detail. Finally, future avenues towards the role and application of computational approaches in a mixture's toxicity are discussed.

Linear regression model for predicting interactive mixture toxicity of pesticide and ionic liquid

The nature of most environmental contaminants comes from chemical mixtures rather than from individual chemicals. Most of the existed mixture models are only valid for non-interactive mixture toxicity. Therefore, we built two simple linear regression-based concentration addition (LCA) and independent action (LIA) models that aim to predict the combined toxicities of the interactive mixture. The LCA model was built between the negative log-transformation of experimental and expected effect concentrations of concentration addition (CA), while the LIA model was developed between the negative log-transformation of experimental and expected effect concentrations of independent action (IA). Twenty-four mixtures of pesticide and ionic liquid were used to evaluate the predictive abilities of LCA and LIA models. The models correlated well with the observed responses of the 24 binary mixtures. The values of the coefficient of determination (R (2)) and leave-one-out (LOO) cross-validated correlation coefficient (Q(2)) for LCA and LIA models are larger than 0.99, which indicates high predictive powers of the models. The results showed that the developed LCA and LIA models allow for accurately predicting the mixture toxicities of synergism, additive effect, and antagonism. The proposed LCA and LIA models may serve as a useful tool in ecotoxicological assessment.

Characteristics of concentration-inhibition curves of individual chemicals and applicability of the concentration addition model for mixture toxicity prediction

The concentration addition (CA) model has been widely applied to predict mixture toxicity. However, its applicability is difficult to evaluate due to the complexity of interactions among substances. Considering that the concentration-response curve (CRC) of each component of the mixture is closely related to the prediction of mixture toxicity, mathematical treatments were used to derive a characteristic index kECx (k was the slope of the tangent line of a CRC at concentration ECx). The implication is that the CA model would be applicable for predicting the mixture toxicity only when chemical components have similar kECx in the whole or part of the concentration range. For five selected chemicals whose toxicity was detected using luminescent bacteria, sodium dodecyl benzene sulfonate (SDBS) showed much higher kECx values than the others and its existence in the binary mixtures brought about overestimation of the mixture toxicity with the CA model. The higher the mass ratio of SDBS in a multi-mixture was, the more the toxicity prediction deviated from measurements. By applying the method proposed in this study to analyze some published data, it is confirmed that some components having significantly different kECx values from the other components could explain the large deviation of the mixture toxicity predicted by the CA model.

State of the art in the application of QSAR techniques for predicting mixture toxicity in environmental risk assessment

The focus of regulatory chemical risk assessment has been mainly placed on single chemicals rather than mixtures. However, living organisms and the environment might be exposed to mixtures of chemicals. Many scientific studies have revealed that mixture toxicity can arise from the combined effects of components present at levels below their individual no-effect concentrations. Predictive approaches will be essential for estimating mixture toxicity, as the number of possible mixtures is extremely large. Although predictive models are virtually indispensable for estimating mixture toxicity for both scientific and regulatory purposes, risk assessors encounter substantial difficulties in using conventional models, mainly due to the lack of information on the modes of toxic action of the mixture constituents. Alternative models that use different information instead of the modes of action thus need to be developed. The objective of this study is to investigate the state of the art in predictive models based on quantitative structure-activity relationship techniques for estimating the toxicity of mixture components, and to identify future challenges hindering more reliable mixture risk assessment for environmental risk assessment. Alternative models need to be developed not only to overcome the limitations of conventional models, but also to improve their performance.

A new approach to radial basis function approximation and its application to QSAR

We describe a novel approach to RBF approximation, which combines two new elements: (1) linear radial basis functions and (2) weighting the model by each descriptor's contribution. Linear radial basis functions allow one to achieve more accurate predictions for diverse data sets. Taking into account the contribution of each descriptor produces more accurate similarity values used for model development. The method was validated on 14 public data sets comprising nine physicochemical properties and five toxicity endpoints. We also compared the new method with five different QSAR methods implemented in the EPA T.E.S.T. program. Our approach, implemented in the program GUSAR, showed a reasonable accuracy of prediction and high coverage for all external test sets, providing more accurate prediction results than the comparison methods and even the consensus of these methods. Using our new method, we have created models for physicochemical and toxicity endpoints, which we have made freely available in the form of an online service at http://cactus.nci.nih.gov/chemical/apps/cap.

Predicting synergistic toxicity of heavy metals and ionic liquids on photobacterium Q67

Results from three mathematical approaches to predict the toxicity of uniform design mixtures of four heavy metals (HMs) including Cd(II), Ni(II), Cu(II), and Zn(II) and six ionic liquids (ILs) were compared to the observed toxicity of these mixtures on Vibrio qinghaiensis sp.-Q67. Single toxicity analysis indicated that the ILs had greater toxicity than the HMs. Combined toxicities of HMs and ILs were found to be synergistic. The combined toxicities were underestimated by concentration addition (CA) and independent action (IA) models. However, the mixture toxicities were effectively predicted by the integrated CA with IA based on multiple linear regression model (ICIM). We propose that ICIM model can serve as a useful tool for predicting the toxicity of interactive mixtures.

Evaluation of the ecotoxicity of pollutants with bioluminescent microorganisms

This chapter deals with the use of bioluminescent microorganisms in environmental monitoring, particularly in the assessment of the ecotoxicity of pollutants. Toxicity bioassays based on bioluminescent microorganisms are an interesting complement to classical toxicity assays, providing easiness of use, rapid response, mass production, and cost effectiveness. A description of the characteristics and main environmental applications in ecotoxicity testing of naturally bioluminescent microorganisms, covering bacteria and eukaryotes such as fungi and dinoglagellates, is reported in this chapter. The main features and applications of a wide variety of recombinant bioluminescent microorganisms, both prokaryotic and eukaryotic, are also summarized and critically considered. Quantitative structure-activity relationship models and hormesis are two important concepts in ecotoxicology; bioluminescent microorganisms have played a pivotal role in their development. As pollutants usually occur in complex mixtures in the environment, the use of both natural and recombinant bioluminescent microorganisms to assess mixture toxicity has been discussed. The main information has been summarized in tables, allowing quick consultation of the variety of luminescent organisms, bioluminescence gene systems, commercially available bioluminescent tests, environmental applications, and relevant references.

QSAR with quantum topological molecular similarity indices: toxicity of aromatic aldehydes to Tetrahymena pyriformis

Extensive production and utilization of aromatic aldehydes and their derivatives without proper certification is alarming with regard to environmental safety. This concern motivated our construction of predictive quantitative structure-activity relationship (QSAR) models for the toxicity of aldehydes to the ecologically important species Tetrahymena pyriformis. Quantum topological molecular similarity (QTMS) descriptors, along with the lipid-water partition coefficient (log K(o/w)), were used as predictor variables. The QTMS descriptors were calculated at different levels of theory including AM1, HF/3-21G(d), HF/6-31G(d), B3LYP/6-31 + G(d,p), B3LYP/6-311 + G(2d,p) and MP2/6-311+G(2d,p). The data set of 77 aromatic aldehydes was divided into a training set (n = 58) and a test (n = 19) set, and 58 models were developed using partial least squares (PLS) and genetic partial least squares (G/PLS). We evaluated the overall predictive capacity of the models based on leave-one-out predictions for the training set compounds and model derived predictions for the test set compounds. For both PLS and G/PLS, the models built at the HF/6-31G(d) level show better predictivity (based on overall prediction) than the models developed at any of the other five levels. Further validation was also performed utilizing (process and model) randomization tests. We show that improved predictive QSAR models for aldehydic toxicity to Tetrahymena pyriformis can be generated using QTMS descriptors along with log K(o/w).

Combined photobacterium toxicity of herbicide mixtures containing one insecticide

To test whether the dose-addition (DA) model can predict the combined toxicity of the mixtures of herbicides that coexisted with insecticide(s), we selected five herbicides (simetryn, prometon, bromacil, velpar, and diquat) and one organophosphorus insecticide (dichlorvos) as the test components. The inhibition toxicities of the six pesticides as well as those of their mixtures to Vibrio qinghaiensis sp.-Q67 were determined by using the microplate toxicity test procedure. The dose-response curves (DRCs) between the observed inhibition toxicities and the doses of the pesticides or the mixtures were modeled by using the nonlinear least square fitting. It was shown that all dose-response relationships were effectively described by the Weibull function. To fully explore the combined toxicities of mixtures including various concentration compositions, we designed three equivalent-effect concentration ratio (EECR) mixtures and six uniform design concentration ratio (UDCR) mixtures. The combined toxicity of a mixture is identified by inspecting whether the DRC predicted by the dose addition (DA) or independent action (IA) locates in the 95% confidence interval of the DRC of the mixture. Furthermore, the possible reason for the three mixtures to depart from the DA action was the very high concentration ratio of diquat in the mixtures.

Integrated fuzzy concentration addition-independent action (IFCA-IA) model outperforms two-stage prediction (TSP) for predicting mixture toxicity

Mixture toxicities were determined for 12 industrial organic chemicals bearing four different modes of toxic action (MOAs) to Vibrio fischeri, to compare the predictability of the integrated fuzzy concentration addition-independent action (IFCA-IA) model and the two-stage prediction (TSP) model. Three mixtures were designed: The first and second mixtures were based on the ratios of each component at the 1% and 50% effect concentrations (EC(1) and EC(50)), respectively; and the third mixture contained an equimolar ratio of individual components. For the EC(1), EC(50) and equimolar ratio, prediction errors from the IFCA-IA model at the 50% experimental mixture effects were 0.3%, 6% and 0.6%, respectively; while for the TSP model, the corresponding errors were 2.8%, 19% and 24%, respectively. Thus, the IFCA-IA model performed better than the TSP model. The IFCA-IA model calculated two weight coefficients from the molecular structural descriptors, which weigh the relation between concentration addition (CA) and independent action (IA) through the fuzzy membership functions. Thus, MOAs are not pre-requisites for mixture toxicity prediction by the IFCA-IA approach, implying the practicability of this method in toxicity assessment of mixtures.

A novel logic-based approach for quantitative toxicology prediction

There is a pressing need for accurate in silico methods to predict the toxicity of molecules that are being introduced into the environment or are being developed into new pharmaceuticals. Predictive toxicology is in the realm of structure activity relationships (SAR), and many approaches have been used to derive such SAR. Previous work has shown that inductive logic programming (ILP) is a powerful approach that circumvents several major difficulties, such as molecular superposition, faced by some other SAR methods. The ILP approach reasons with chemical substructures within a relational framework and yields chemically understandable rules. Here, we report a general new approach, support vector inductive logic programming (SVILP), which extends the essentially qualitative ILP-based SAR to quantitative modeling. First, ILP is used to learn rules, the predictions of which are then used within a novel kernel to derive a support-vector generalization model. For a highly heterogeneous dataset of 576 molecules with known fathead minnow fish toxicity, the cross-validated correlation coefficients (R2CV) from a chemical descriptor method (CHEM) and SVILP are 0.52 and 0.66, respectively. The ILP, CHEM, and SVILP approaches correctly predict 55, 58, and 73%, respectively, of toxic molecules. In a set of 165 unseen molecules, the R2 values from the commercial software TOPKAT and SVILP are 0.26 and 0.57, respectively. In all calculations, SVILP showed significant improvements in comparison with the other methods. The SVILP approach has a major advantage in that it uses ILP automatically and consistently to derive rules, mostly novel, describing fragments that are toxicity alerts. The SVILP is a general machine-learning approach and has the potential of tackling many problems relevant to chemoinformatics including in silico drug design.

QSAR approach for mixture toxicity prediction using independent latent descriptors and fuzzy membership functions

The principle of using a singe model to predict the toxicity of mixtures of chemicals based on the characterisation of the degrees of similarity and dissimilarity of the constituent chemicals using descriptors has been demonstrated in a previous work. The current study introduces a feature extraction technique, independent component analysis, to the method to remove the correlations and dependencies between descriptors and reduce the dimension prior to similarity and dissimilarity calculations. In addition, a goal attainment multi-objective optimisation technique is used for the determination of the fuzzy membership function parameters. For three mixtures, which include a new mixture and two previously studied mixtures that all inhibit reproduction (via different mechanisms of action) in green freshwater algae scenedesmus vacuolatus, the approach showed better or equivalent prediction performance than either concentration addition or independent action models. Unlike QSARs for pure compounds that require large collections of data, the new approach for mixtures only requires one mixture at a particular composition to determine the necessary fuzzy membership function parameter values. These values can then be used to predict the toxicity of the mixture at any other compositions. This could potentially lead to a reduction in the frequency of bioassay tests. Use of the fuzzy membership functions and parameter values obtained for one mixture when used to predict the toxicity of a completely different mixture is also tested and it is found that the approach also gives prediction results with good accuracy.