We use two datasets: KIBA dataset (Tang et al., 2014) and Davis dataset (Davis et al., 2011) (The data sets can obtain from Supplementary Material), as shown in Table 1. KIBA (Tang et al., 2014) was used as a benchmark dataset to evaluate the algorithm model. The Davis dataset (Davis et al., 2011) is lysed selectively using the kinase protein family and associated inhibitors for the dissofarence constant (K_d) value, including the affinity of 442 proteins and 68 drugs. We calculate (_pK_d) value (as shown in formula 1) regarding the Davis data set use literature processing method to show.

It can be seen from Table 1 that the number of true interrelationships in the KIBA dataset is about three times that of the statistical interrelationship. KIBA values are calculated based on combinations of different information sources such as IC50, K_i, and K_d. We used a filtered version of the KIBA data set, where each protein and ligand has ten interactions at least (He et al., 2017).

The graphs of the drugs are constructed by using the GraphDTA (Nguyen and Venkatesh, 2019) method. It reflects interactions of internal atom for each SMILES compound. RDkit, open source chemical informatics package (G, 2013), is used to calculate the feature vectors of atom and adjacent atomic connection of drugs. The nodes of the graph represent the features of the drug's atoms, and the bonding bonds between the atoms are represented by the edges. The features vectors of the drug atomic are made up of five characteristics: atomic class, atomic rank, the total number of hydrogen atoms, implied value of atoms, and the existence or absence of aromatic groups. The atomic rank is the sum of the number of the bond between the current atom and neighboring atoms and the number of hydrogen atoms. The edge of graph represents the connection relation of adjacent atoms. The overall process is shown in Figure 1.

A novel model that combining graph convolutional neural networks and convolutional neural networks are designed to regressively predict DTA. The multi-layers graph convolutional neural network is used to obtain the hidden relationships of drug graphs. The hidden relationships of the polypeptide frequency of word frequency are obtained through the convolutional neural network calculation. The output results of the two networks are combined as the input of fully connected layers. The complete process is shown in Figure 2.

We use the improved four types of graph convolutional neural networks by GraphDTA to discover potential relationships for the graph structure of drug features, which are GCN (Kipf and Welling, 2017), GAT (Veličković et al., 2018), GIN (Xu et al., 2019), GAT-GCN (Nguyen and Venkatesh, 2019). The linear connected layer that the inputs are results of graph convolutional neural networks maps to a 128-dimensional features vectors, which is consistent with the size of feature vectors for protein.

The GCN model is originally proposed by Kipf and Welling (2017) as a graph structure learner for semi-supervised classification. In order to meet the requirements of regression in our work, three graph convolutional units are made that include a GCN layer and a ReLU activation layer. The number of output channels is 78, 156, 312, respectively. And a fully connected layer of 1,024 neurons is created, the results are mapped to a 128-dimensional features vector in the output layer.

Graph Isomorphism Network (GIN) is an improved algorithm based on GCN. Injective aggregation updates the parameters and performs the feature vector mapping to obtain better model performance. The network model of the five-layer GIN layer is designed, and each GIN layer consists of two linear calculations with an output size of 32. The input and output layers are mapped into 128-dimensional features vectors.

Graph Attention Network (GAT) is different from the GCN model, the difference is that it calculates the corresponding hidden information for each node and introduces an attention mechanism when computing its neighboring nodes. The network model is designed using two GAT layers. In the first layer, the number of output channel is 78, and the number of attention nodes is 10. In the second layer, the number of output channel is 128, and the number of attention nodes is 1. The results are input to the output layer, which map to a 128-dimensional features vector.

Based on the GAT and GCN models, GAT- CCN integrates the advantages of the two models in series to obtain better model performance. The output channel of the GAT layer is 78, the number of attention nodes is 10. And the output channel of the GCN layer is 780. And a fully connected layer of 1,500 neurons is created, results are mapped to a 128-dimensional features vector in the output layer.

Convolutional neural network is used to obtain hidden relationships in vector of protein features. A 1D convolutional neural network is designed by analyzing the characteristic structure of protein word frequency and polypeptide frequency. The model contains a convolution kernel that the size is 32. The result of the convolution calculation is input to the fully connected layer for mapping to 256 neurons, keeping the size of the drug, and protein consistent.

We concatenate the feature vectors of proteins from convolutional neural networks and the feature vectors of drugs from graph convolutional neural networks. And they are input to two fully connected layers with 512 and 128 neutrons, respectively. And set the batch size to 512 and the learning rate to 0.00005.

In this work, the datasets are divided into two parts: training set and test set. That is, 80% of data instances are used for training, and 20% are for testing the models. The performances of our model are comprehensively compared by several experiment using evaluation metrics such as Concordance Index (CI), Mean Squared Error (MSE), as well as Pearson correlation coefficient. The evaluation indicators are consistent with WideDTA and GraphDTA. the performance of the predicted models of output continuous values is evaluated by CI, the formula is as follows.

where b_x is the prediction value for the larger affinity δ_x, b_y is the prediction value for the smaller affinity δ_y. Z is the normalization constant, h(m) is the step function, and as shown in the following formula:

MSE is often used for the difference between the predicted value and the actual value vector, and it's an important index for evaluating regression models, the formula is as follows.

where n is the number of data in the data set of KIBA or Davis, and other parameters have the same meaning as above.

Pearson correlation coefficient evaluates the difference of the affinity between the true value and the predicted value, the formula is as follows.

where cov indicates the co-variance, p is predicted values, y is original values, σ represents the standard deviation.

In this study, we introduced polypeptide frequency of word frequency that was a novel way of protein feature extraction. The peptide frequency includes several methods. For every protein sequence, we calculated the word frequency characteristics and frequency of single peptide, dipeptides, as well as tripeptides. And different graph convolutional network models were designed to predict drug-target binding affinity. The results of comparative experiment are shown in Table 2.

When the protein sequence is represented by the word frequency dipeptide frequency and the GAT_GCN model, the model is the best predictor for 3 evaluation metrics yielding a CI of 0.901, a MSE of 0.126, and a Pearson of 0.893 in KIBA data set, and yielding a CI of 0.895, a MSE of 0.220 and a Pearson of 0.701 in Davis data set. When word frequency dipeptide frequency was used to represent protein sequences, compared with the second best GCN model, the CI and Pearson of GAT_GCN model in KIBA data set are increased by 0.03 and 0.029, respectively, and the MSE value decreases by 0.01. Compared with GAT and GIN models, the CI values of GAT_GCN model are 0.033 and 0.020 higher, the MSE values are reduced by 0.050 and 0.022, and Pearson values are increased by 0.020 and 0.037, respectively. In the Davis data set, the CI value of GAT_GCN model is same with GAT model as the next-highest model, the MSE value is reduced by 0.011, and Pearson is increased by 0.003. The CI value of the GAT_GCN model is 0.005 higher than the GCN and 0.002 higher than GIN. The MSE values are decreased by 0.003 and 0.005, and the Pearson values are increased by 0.004 and 0.006, respectively. So, the GAT_GCN model has the best performance in these four models.

When the GAT_GCN model is used as a graph calculator, compared with the word frequency single peptide frequency and the word frequency tripeptide frequency, the CI values of word frequency dipeptide frequency in the KIBA dataset are higher by 0.103 and 0.049, the MSE values are reduced by 0.498 and 0.065, respectively. In the Davis data, CI values are 0.251 and 0.003 higher, the MSE values are decreased by 0.578 and 0.004, and Pearson values are increased by 0.195 and 0.054, respectively. The word frequency dipeptide frequency characteristics can also obtain the optimal index when combined with GIT, GAT, GCN models in the KIBA and Davis data sets, indicating that the word frequency dipeptide frequency characteristics have the best performance index compared to other characteristics.

We also compared the differences in dipeptide frequencies with or without word frequency characteristics. The results are shown in Table 3 and Figure 3.

After adding the word frequency characteristics based on the dipeptide frequency, the MSE decreased by 0.022 and the CI and Pearson increased by 0.009 and 0.033 in the KIBA data set, and MSE decreased by 0.019 and the CI and Pearson increased by 0.018 and 0.009 in Davis data set. This shows that the dipeptide frequency of word frequency is more conducive to the prediction of the classifier than the dipeptide frequency, and has better represented ability for protein sequences.

Through the analysis of comparative experiments, we found that the model was obtained the best performance metrics when dipeptide frequency of word frequency be used to represent protein sequences. For every protein, we calculated the mean and variance in the Davis and KIBA datasets, respectively. The results are shown in Figure 4.

In the Davis dataset and the KIBA dataset, the distribution of score are basically same. The single peptide frequency of word frequency features scores are mainly concentrated between 0.20 and 0.61, and the variances are mainly concentrated between 0.007 and 0.220. Although there is a high features scores and large variance, the features have too high differences in the vectors of feature. And the number of features is only 25 dimensions, which contributes less to the spatially specific division of the model. Although the tripeptide frequency of word frequency features have a huge number of 15,625 dimensions, the scores are mainly distributed below 0.018, and the variances are mainly distributed below 0.003. The features have small differences between data, and there are a lot of features with value of 0. The scores of dipeptide frequency of word frequency characteristic mainly have a distribution range between 0 and 0.14, and the variances have a main distribution range between 0 and 0.0149, which has a good score and data difference.

Compared with the dipeptide frequency of word frequency, the score of dipeptide frequency are mainly distributed below 0.17, and the variances are mainly distributed between 0 and 0.021. Although it has a good score, the difference is high in vectors of feature, as same as the word frequency single peptide frequency. In order to discover the difference between the frequency characteristics of dipeptide and word frequency dipeptide, we draw a histogram of the frequency distribution of the two and perform overlapping processing, the results are shown in Figure 5.

After adding the word frequency characteristics, the number of dipeptide frequency of word frequency features is less than that of the dipeptide frequency in the score intervals [0.025, 0.175] and [0.250, 0.300]. And the number of dipeptide frequency of word frequency features is more than that of dipeptide frequency features in the score intervals [0, 0.025] and [0.175, 0.250]. Dipeptide frequency features distribution is at [0, 0.35], and the dipeptide frequency of word frequency features distribution is at [0, 0.45], and the interval range is greater and more continuous. It shows that the frequency characteristics of words can play a role in reducing non-significant features and improving score difference.

The protein dipeptide frequency of word frequency is composed of 625-dimensional features. The Variable Importance Measures (VIM) is used to analyze the contribution of each feature. In bioinformatics, Random Forest (RF) is a commonly used classification and regression model (Belgiu et al., 2016). And its unique advantage is to calculate VIM (Rawi et al., 2018), compared with other machine learning algorithms such as support vector machine (SVM). We used the RF model containing 10,000 decision trees to obtain the VIM score of features in the dipeptide frequency of word frequency, as shown in Figure 6. Features of non-zero VIM score have 199 dimensions, indicating that there's much noise in the vectors of features. The 27-dimensional features what a contribution >0.5% are listed in Figure 7. The top five dipeptide frequency of word frequency features are PE (20.1%), WT (6.6%), AA (4.4%), EB (3.9%), and VV (3.2%). This shows that PE (the combination of proline and glutamic acid) is significantly related to the affinity prediction, which is about three times of the second highest WT (the combination of tryptophan and threonine) and much larger than other combinations.

The predictor of our work was compared with state-of-the-art methods what DeepDTA, WideDTA, and GraphDTA by using an independent test set in Davis and KIBA. The results are shown in Table 4.

Our method outperformed state-of-the-art methods with two main quality metrics as CI and MSE in Davis and KIBA. Compared with the DeepDTA and WipeDTA models, our model reduced the MSE by 0.068 and 0.041, which increased the CI by 0.048 and 0.026, respectively in the KIBA dataset. And MSE decreased by 0.061 and 0.062, CI increased by 0.021 and 0.013, respectively, in the Davis data set. It shows that the graph neural network model with input as the graph structure of the drug can obtained better performance. Our method outperformed the GraphDTA model using the same graph convolutional neural network, the MSE decreased by 5% (0.007) and the CI increased by 0.01 in the KIBA data set, the MSE decreased by 4% (0.009) and the CI increased by 0.006 in the Davis data set. It shown that the dipeptide frequency of word frequency has better ability to express targeted proteins and can obtain better prediction models than 1D coding.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.