2.1 Dataset preparation & pre-processing
Protein-peptide complexes were prepared from LEADS-PEP (11), PeptiDB (6), and PepPro (12), consisting of 212 complexes (Supp. Mat. 1). A similar number of protein-protein complexes, i.e., 212 protein complexes (Supp. Mat. 2), were taken from the Vreven et al. (2015) protein-protein benchmark dataset (13). The dataset of 212 protein complexes for non-interacting proteins was taken from Das and Chakrabarti (14), which is curated from the Negatome database (15, 16) based on PatchDock docking scores. A total of 583 sequence- and physicochemical-based features were calculated using open-source Python scripts of Pfeature (17) for 636 PDBs, which consist of 212 entries each of protein-protein, protein-peptide, and non-interacting protein complexes. The normalised features we calculated were pre-processed for better and more accurate prediction of protein and peptide interactions. Additionally, another dataset of 73 descriptors comprising structural, geometrical, and physicochemical features more relevant to protein-protein interactions was calculated from 2P2I Inspector v2.0 (18, 19) and was also used for PPI and PPepI classification. Furthermore, nine interface-characterising descriptors were also segregated. The details of all the 73 descriptors are provided in Supp. Mat. 3. 2P2I Inspector v2.0 is embedded with SURFNET to calculate geometrical features and with VMD and PyMOL to calculate structural and physiochemical features.
2.2 Feature Selection and Feature Ranking
To reduce the number of features, including the most important ones, 56 out of 583 features were selected by using the correlation-based feature selection (CFS) attribute evaluater method (20, 21) and the best-first search method (22, 23) from the calculated feature dataset. The CFS method measures the significance of attributes on the basis of their predictive ability and their degree of redundancy. It uses a correlation-based heuristic to evaluate the worth of features. The algorithm is simple, fast to execute, and extends easily to discrete and continuous class problems by applying suitable correlation measures. The subsets having less inter-correlation but highly correlated to the target class were preferred. We used bidirectional direction and chose the search termination number as 5 in the Best First search method. We performed different ranking methods like correlation attribute ranker, gain ratio ranker (24), infogain ranker (25), relief ranker (26), oneR ranker, and symmetrical ranker (27) to know the significance of all 56 features. The consensus ranking was calculated from all six methods (discussion about the significant features in the following section). Rankings of all six methods for 56 features and overall ranking are given in Supplement Mat. 4.
2.3 Supervised Machine Learning
We used different classification methods of supervised machine learning (28–31) available in the Java-based WEKA platform (32–33) on three different feature sets (Sets 1–3).
Set-1 consists of the 56 selected features described in Section 2. 2 out of the total 583 features were calculated, and the following methods were used: Bayes Net, Random Forest, AdaBoost, Logistic Regression, and ANN (Multi-layer Perceptron) to perform binary classification: PPI vs. PPepI, PPI vs. non-interacting PPI, and PPepI vs. non-interacting PPI. Ten-fold cross-validation was employed to train in all our methods; that is, the data was randomly divided into 10 parts (folds); each time, one fold was employed for the test, nine folds were used for training, and all 10-folds were used for calculating the overall performance of cross-validation.
Set-2 consists of 73 features calculated with 2P2I Inspector v2.0 (18, 19), and ML algorithms like Simple Logistic (34), Random Forest, AdaBoost, and ANN were used on the WEKA platform. Features are listed in Supp. Mat. 3. Attribute importance was computed using the Random Forest method and plotted in the graph shown in Fig. 4.
Set-3 consists of 9 features (out of 73) that are directly related to the interface properties of the PPI and PPepI complexes, and the same ML algorithms like Logistic, Simple Logistic, Random Forest, and AdaBoost were applied to the WEKA platform. The features are listed in Supp. Mat. 5. This was carried out separately to examine the difference in analysis, if any, between Set-2 and Set-3. The feature importance of the nine interface properties of the PPepI and PPI complexes was also computed and plotted as shown in Fig. 5.
2.3.1 Bayesian Network: Bayesian networks (Bayes Net, or BNs) (35), also referred to as belief networks or probabilistic causal networks, are an established framework for uncertainty management in artificial intelligence (AI). Bayesian networks are a special case of a wider class of statistical models called graphical models, which include networks with undirected edges (called Markov networks). Bayesian Network Classifiers has different search algorithms like K2, HillClimbing, RepeatedHillClimber, TAN (Tree Augmented Naïve Bayes), Tabu Search, Simulated Annealing, and Genetic Search and estimators like Baysian Net Estimator, BMA Estimator, Multinomial BMA Estimator, and Simple Estimator. We got good accuracy and performance values with the TAN Search algorithm and simple estimator. The TAN search algorithm is a one-dependence estimator (ODE) search algorithm (35) in which a tree is formed by calculating the maximum weight spanning tree using the well-known Chow and Liu algorithm. In this model, mutual information between two random variables is used to find the most correlated attributes.
2.3.2 Random Forest.
Ensemble methods of decision trees, such as bagging and boosting, combine several decision trees to generate improved predictive performance compared to employing a single decision tree. Random Forest (37, 38) is an augmentation of bagging where it takes one extra step. In addition to taking a random subset of data, it also takes a random selection of features rather than using all features to grow trees. We developed our Random Forest model with a seed value of 4, a maximum depth of unlimited, and a number of trees of 100, where it achieved its maximum accuracy and other performance measurements. We also computed attribute importance for the classification of PPepI and PPI (graphs for Set-1 to Set-3 are in Figs. 1, 4, and 5), and PPI and PPepI with non-interacting proteins and significant features were identified (Figs. 2 and 3).
2.3.3 Logistic regression and Simple Logistic Regression
Logistic regression (LR) (39, 40) and simple logistic regression (SLR) (34, 41) are probabilistic view types of classifications that compute the curvilinear relationship between the categorical dependent variable and one or more independent variables by calculating probabilities using a logistic function. The algorithm both in LR and SLR learns a coefficient for each input value, which is linearly combined into a regression function and transformed using a logistic (s-shaped) function. The LR in Weka is ridge logistic regression (maximum likelihood), whereas in simple logistic regression it is logit boost-based regression. We constructed our LR and SLR algorithms with default parameters.
2.3.4: AdaBoost
Adaptive Boosting (AdaBoost) (42, 43) is a boosting ensemble and meta-learning algorithm, formulated by Yeave Freud and Robert Scapire in 1996, that performs with decision trees. It combines weak classifiers and, while training, chooses the attributes that will increase the classifier's prediction ability. The advantage of AdaBoost is that it requires fewer input parameters and little or no prior knowledge of the weak learner. AdaBoost increases the weight of misclassified data points by learning from mistakes in the next iteration, and it is less vulnerable to overfitting. We built our models of AdaBoost with 10 number of iterations, 100 weight thresholds, Random Forest as the base classifier algorithm for Set 1 dataset, and LMT and Decision Stunt for Set 2 and Set 3 datasets, respectively.
2.3.5 Artificial Neural Network
Multi-Layer Perceptron (MLP) (44–46) uses a backpropagation algorithm to train instances, which repeatedly uses the weights to minimise the difference between desired and actual outputs and performs learning on a multilayer feed-forward neural network. We developed our models with two hidden layers having 29 neuron nodes in each layer for the classification of PPepI and PPI and for the prediction of PPepI interactions in the set 1 dataset. The hidden layer parameter ‘a’ of WEKA is used for the prediction of PPI interactions in set 1, and ‘o’ of WEKA is used for the PPepI and PPI classification of set 2 datasets. We built our models with parameters like learning rate as 0.3, momentum as 0.2, and epochs as 500 for all our ANN models. The sigmoid function was used as the activation function for all of the nodes, and it combines linear, curvilinear, and constant behaviour based on the input value.