Non-covalent interactions (NCIs) play critical roles in supramolecular chemistries; however, they are difficult to measure. Currently, reliable computational methods are being pursued to meet this challenge, but the accuracy of calculations based on low levels of theory is not satisfactory and calculations based on high levels of theory are often too costly. Accordingly, to reduce the cost and increase the accuracy of low-level theoretical calculations to describe NCIs, an efficient approach is proposed to correct NCI calculations based on the benchmark databases S22, S66 and X40 (Hobza in Acc Chem Rev 45: 663–672, 2012; Řezáč et al. in J Chem Theory Comput 8:4285, 2012). A novel type of NCI correction is presented for density functional theory (DFT) methods. In this approach, the general regression neural network machine learning method is used to perform the correction for DFT methods on the basis of DFT calculations. Various DFT methods, including M06-2X, B3LYP, B3LYP-D3, PBE, PBE-D3 and ωB97XD, with two small basis sets (i.e., 6-31G* and 6-31+G*) were investigated. Moreover, the conductor-like polarizable continuum model with two types of solvents (i.e., water and pentylamine, which mimics a protein environment with ε = 4.2) were considered in the DFT calculations. With the correction, the root mean square errors of all DFT calculations were improved by at least 70 %. Relative to CCSD(T)/CBS benchmark values (used as experimental NCI values because of its high accuracy), the mean absolute error of the best result was 0.33 kcal/mol, which is comparable to high-level ab initio methods or DFT methods with fairly large basis sets. Notably, this level of accuracy is achieved within a fraction of the time required by other methods. For all of the correction models based on various DFT approaches, the validation parameters according to OECD principles (i.e., the correlation coefficient R 2, the predictive squared correlation coefficient q 2 and $$q_{cv}^{2}$$ from cross-validation) were >0.92, which suggests that the correction model has good stability, robustness and predictive power. The correction can be added following DFT calculations. With the obtained molecular descriptors, the NCIs produced by DFT methods can be improved to achieve high-level accuracy. Moreover, only one parameter is introduced into the correction model, which makes it easily applicable. Overall, this work demonstrates that the correction model may be an alternative to the traditional means of correcting for NCIs.

Epitope prediction based on random peptide library screening has become a focus as a promising method in immunoinformatics research. Some novel software and web-based servers have been proposed in recent years and have succeeded in given test cases. However, since the number of available mimotopes with the relevant structure of template-target complex is limited, a systematic evaluation of these methods is still absent. In this study, a new benchmark dataset was defined. Using this benchmark dataset and a representative dataset, five examples of the most popular epitope prediction software products which are based on random peptide library screening have been evaluated. Using the benchmark dataset, in no method did performance exceed a 0.42 precision and 0.37 sensitivity, and the MCC scores suggest that the epitope prediction results of these software programs are greater than random prediction about 0.09–0.13; while using the representative dataset, most of the values of these performance measures are slightly improved, but the overall performance is still not satisfactory. Many test cases in the benchmark dataset cannot be applied to these pieces of software due to software limitations. Moreover chances are that these software products are overfitted to the small dataset and will fail in other cases. Therefore finding the correlation between mimotopes and genuine epitope residues is still far from resolved and much larger dataset for mimotope-based epitope prediction is desirable.

We propose a generalized regression neural network (GRNN) approach based on grey relational analysis (GRA) and principal component analysis (PCA) (GP-GRNN) to improve the accuracy of density functional theory (DFT) calculation for homolysis bond dissociation energies (BDE) of Y-NO bond. As a demonstration, this combined quantum chemistry calculation with the GP-GRNN approach has been applied to evaluate the homolysis BDE of 92 Y-NO organic molecules. The results show that the full-descriptor GRNN without GRA and PCA (F-GRNN) and with GRA (G-GRNN) approaches reduce the root-mean-square (RMS) of the calculated homolysis BDE of 92 organic molecules from 5.31 to 0.49 and 0.39 kcal mol⁻¹ for the B3LYP/6-31G (d) calculation. Then the newly developed GP-GRNN approach further reduces the RMS to 0.31 kcal mol⁻¹. Thus, the GP-GRNN correction on top of B3LYP/6-31G (d) can improve the accuracy of calculating the homolysis BDE in quantum chemistry and can predict homolysis BDE which cannot be obtained experimentally.

A representative dataset is crucial to build a robust and generalized machine learning model, especially for small databases. Correlation is not usually considered in distance‐based set partition methods; therefore, distant yet correlated samples might be incorrectly assigned. An improved sample subset partition method based on joint hybrid correlation and diversity x‐y distances (HSPXY) is proposed in the framework of the sample set partition based on joint x‐y distances (SPXY). Therein, a hybrid distance consisting of both cosine angle distance and Euclidean distance in variable spaces cooperates the correlation of samples in the distance‐based set partition method. To compare with some existing partition methods, partial least squares (PLS) regression models are built on four set partition methods, random sampling (RS), Kennard‐Stone (KS), SPXY, and HSPXY. Upon the applications on small chemical databases, the proposed HSPXY algorithm‐based models achieved smaller root mean square errors and better coefficients of determination than other tested set partition methods, which indicates the training set is well represented. This suggests the proposed algorithm provides a new option to obtain a representative calibration set. Sample subset partition is widely considered in machine learning modeling. An improved sample subset partition method based on a hybrid correlation and diversity x‐y distance (HSPXY) is proposed in the framework of SPXY. Cosine angle distance and Euclidean distance in variable spaces are used to represent the correlation and diversity of samples, respectively. To explore the effectiveness of HSPXY, PLS models are built on four set partition methods, RS, KS, SPXY, and HSPXY. The models based on the proposed HSPXY algorithm carried the overall best result among all regression models, which suggests the proposed algorithm may be taken as an alternative to other existing data partition methods.