Development of New Methods for the (Q)SAR Applicability Domain Assessment: Using Structural Information in a Statistical Study of the Errors in Prediction

The main aim of (Q)SAR is to build models to evaluate and predict properties of molecules, such as biological and environmental effects, and physicochemical properties. These models are built using available experimental data, whose quality and quantity heavily affect their capability of obtaining reliable predictions for new chemicals. A dataset can be viewed as a "sampling" of the whole chemical space, if a sample is too small and / or too homogeneous, the model will inevitably have limitations in the type of chemicals it can predict. From the point of view of protecting the human health and the environment, it is preferable that a model is able to predict even a small number of chemicals, but with the highest possible reliability. The "coverage" issue can be overcome by integrating results from different models. In this perspective the importance of clearly defining the model's applicability domain is crucial to identify which model is most suitable for each chemical to assess. The definition of the applicability domain (AD) of (Q)SAR models is still an open research field. Several approaches have been proposed and implemented through years, including the use of structural features such as functional groups and atom-centered fragments. These features have also proven to be useful for an a priori definition of AD, making it independent from the specific algorithm chosen to develop the model. Within this study, the definition of (Q)SAR models' applicability domain has been investigated using structural features of different complexity: thresholds for chemical composition and molecular weight, chemical classes related to commonly well and badly predicted molecules, and statistically-extracted structural fragments to model the error in prediction. In the case studies considered, these approaches improved the AD definition provided by the model developers, supporting their integration within the definition of the models' applicability domain

Software: QSAR for Anticancer Agents

CORrelations And Logic (CORAL at http://www.insili co.eu/coral) is freeware aimed at establishing a quantitative structure -property ⁄ activity relationships (QSPR ⁄ QSAR). Simplified molecular input line entry system (SMILES) is used to represent the molecular structure. In fact, symbols in SMILES nomenclatures are indicators of the presence of defined molecular fragments. By means of the calculation with Monte Carlo optimization of the so called correlation weights (contributions) for the above-mentioned molecular fragments, one can define optimal SMILES-based descriptors, which are correlated with an endpoint for the training set. The predictability of these descriptors for an external validation set can be estimated. A collection of SMILES-based models of anticancer activity of 1,4-dihydro-4-oxo-1-(2-thiazolyl)-1,8-naphthyridines for different splits into training and validation set which are calculated with the CORAL are examined and discussed. Good performance has been obtained for three splits: the r 2 ranged between 0.778 and 0.829 for the subtraining set, between 0.828 and 0.933 for the calibration set, and between 0.807 and 0.931 for the validation set. There are a number of systems for the establishing of the quantitative structure -property ⁄ activity relationships (QSPR ⁄ QSAR) based on different collections of molecular descriptors (1-4). The use of large databases, especially databases that are available via the Internet, is typical in modern natural sciences. The majority of the Internet databases oriented on molecular properties are based on the representation of the molecular structure by simplified molecular input line entry system (SMILES) (5-8). Thus, the development of molecular descriptors that are calculated directly from SMILES is an attractive scenario of the QSPR ⁄ QSAR researches. The CORrelations And Logic (CORAL) software is an attempt to develop the standardized SMILES-based optimal descriptors. The aim of the present publication is the demonstration of the ability of the CORAL freeware to be a tool for the QSAR modelling. The numerical data on the anticancer activity for 1,4-dihydro-4-oxo-1-(2-thiazolyl)-1,8-naphthyridines (9) is used to demonstrate this freeware in practice. Most popular 'classic' approach of QSAR modelling can be formulated as the following: (i) definition of a model with compounds of the training set; and (ii) checking of the model with compounds of an external validation set. One can formulate a few questions related to the optimization of this approach. For instance, how the statistical quality of the model will be modified in case of another split into the training and validation sets? How to avoid the overtraining (i.e., how avoid the situation when a good model for the training set becomes a poor model for external substances)? How one can estimate the probability of obtaining a satisfactory and reliable model? Algorithms that are used in the CORAL can give some solutions for the above-mentioned problems from a probabilistic point of view. In fact, CORAL is a producer of random models, which are calculated by the Monte Carlo method. A random model can be a reasonable predictor for an endpoint, if the statistical quality of this model (for both the training and validation set) can be reproduced in a sequence of attempts to build this model. Obeying to this logic, we have examined three different splits in a cascade of attempts to build the models for the anticancer activity. In addition to the above-mentioned classic scheme, one can use the balance of correlations that is available in the CORAL. The basic idea of the balance of correlations is the split of the training set into sub-training and calibration set. The preliminary check of the model is the function of the calibration set. This preliminary check helps to avoid the overtraining. As further step to improve the predictability, the balance of correlations with ideal slopes has been examined. Slopes of the cluster at the plot of experimental versus calculated values of the endpoint on the subtraining and calibration set are ideal if their values are as equivalent as possible. Thus, the discussion of the CORAL as a tool for QSPR ⁄ QSAR analyses is the aim of the present work, considering the specific case study of anticancer activity. Method Data The concentration of the agent to reduce cell viability by 50%, against Murine P388 Leukemia IC 50 (9) is the biological activit