Prediction of the transition temperature of bent-core liquid crystals using fuzzy “digital thermometer” model based on artificial neural networks

Abstract

A dataset containing transition temperature values for 243 bent-core liquid crystal (LC) compounds was used to develop quantitative structure–property relationship (QSPR) models using only 2D molecular descriptors and general regression neural network (GRNN). Beside a standard analogue GRNN model, another GRNN model with fuzzy digital response was created with the aim to estimate the prediction error for each compound. Two approaches for the selection of most relevant subset of descriptors, namely the partial mutual information (PMI) and self-organizing maps combined with chi square ranking, were also compared. The best results were obtained using analogue GRNN model based on PMI selected subset ($R^2=0$.91), with the mean absolute error (MAE) lower in comparison with previously published corresponding QSPR models. The digital PMI-GRNN model enabled distinction between high and low accurate predictions, i.e. ones with absolute error higher than mean absolute error (MAE) and others with absolute error $\le$ MAE, with the accuracy of 81%.

Introduction

Quantitative structure–property/activity relationship (QSPR/QSAR) models for the prediction of physical properties and biological activities of organic compounds from their molecular structures have been a focus of great attention for a long time (Mu et al., 2007). In recent years, artificial neural networks (ANNs) have opened a new avenue for developing empirical models useful for predicting the performance of the process outside the experimental domain (Olea, 2007). A literature review indicate that QSPR modeling based on ANNs has grown dramatically, suggesting the importance of applications of ANN in molecular modeling (Katritzky et al., 2010). ANNs are useful tools in QSPR studies because a given structure–property relationship is often nonlinear (Yao et al., 2004).

The QSPR models are very important in the field of liquid crystals, since small structural modifications of liquid crystal (LC) molecules can drastically influence their transition temperature. Therefore, the design of molecular structure with desired LC phase temperature, based only on empirical rules, is a very complex task. The QSPR methodology has been successfully applied to predict various physical and chemical properties of LCs Al-Fahemi (2014), Antanasijević et al. (2016a), Gong et al. (2008), Johnson and Jurs (1999), which possess unique physicochemical properties and have wide application in a variety of fields Bahadur (1994), Vicari (2016). Nowadays, bent-core LCs are the most attractive type of these materials due to their promising applications Eremin and Jákli (2013), Takezoe and Takanishi (2006), and their transition temperatures have been the subject of recent QSPR studies Antanasijević et al. (2016b), Antanasijević et al. (2016c). In those studies, the QSPR models with good predictive ability (R² $\ge$ 0.90) based on decision trees, multivariate adaptive regression splines and group method of data handling (GMDH-type) neural network have been proposed for the prediction of five-ring bent-core LCs transition temperatures.

In this study, the transition temperature of bent-core LCs was predicted using general regression neural network (GRNN) with the aim to develop a more accurate model that will allow the estimation of prediction error for each compound. For this purpose, the ANN model with digital output neurons, previously proposed for the transition temperatures of smectic LC compounds by Schroder et al. (1996), has been adapted using fuzzy logic. Since a large number of molecular descriptors can be calculated for each compound, two model-free methods that can take into account both linear and nonlinear relationships, namely the partial mutual information (PMI) and self-organizing maps (SOM) combined with chi square ranking, were applied prior to the model development for the selection of the most relevant subset.