Current methods for the prediction of mixture toxicity have shown to be valid for mixtures that conform to some assumptions that were ideally formulated for mixtures comprising constituents exhibiting either completely similar or dissimilar mechanisms of action. Approaches are needed that predict the toxicity of mixtures representative of real environmental occurrences i.e., those comprising constituents of mixed similar and dissimilar compounds and therefore are more complex. In this paper such a methodology is proposed which uses molecular descriptors and fuzzy set theory to characterize the degree of similarity and dissimilarity of mixture constituents, integrates the concentration addition and independent action models, and therefore is called INFCIM (INtegrated Fuzzy Concentration addition--Independent action Model). INFCIM is tested in two case studies using toxicity data of four mixtures, and its performance is compared against those of both concentration addition and independent action models. Mixture 1 consists of 18 s-triazines acting on green freshwater algae scenedemus vacuolatus. Mixture 2 comprises 16 acting constituents tested on scenedemus vacuolatus. Both mixtures inhibit reproduction in the biological assays. There are 10 quinolone compounds in mixture 3 and 16 phenol derivative compounds in mixture 4 all causing long-term inhibition of bioluminescence in the marine bacterium Vibrio fischeri. It was shown that INFCIM performed comparably or better than the best performing existing model in the original studies for all the mixtures tested.
Automatic induction of decision trees and production rules from data to develop structure-activity models for toxicity prediction has recently received much attention, and the majority of methodologies reported in the literature are based upon recursive partitioning employing greedy searches to choose the best splitting attribute and value at each node. These approaches can be successful; however, the greedy search will necessarily miss regions of the search space. Recent literature has demonstrated the applicability of genetic programming to decision tree induction to overcome this problem. This paper presents a variant of this novel approach, using fewer mutation options and a simpler fitness function, demonstrating its utility in inducing decision trees for ecotoxicity data, via a case study of two data sets giving improved accuracy and generalization ability over a popular decision tree inducer.
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.
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