The datasets used in this experiment come from the literature (Leyi et al., 2018). The samples in this dataset were also collected from literature (Tyagi et al., 2013; Atul et al., 2015). Among them, the positive samples are anti-cancer peptides that have been confirmed by physical experiments, and the negative samples are selected from anti-microbial peptides that have no anti-cancer activity. The training dataset ACPs500 consists of 250 anti-cancer peptides and 250 non-anti-cancer peptides. The test dataset ACPs164 consists of 82 positive samples and 82 non-anticancer peptide samples. All of the samples are filtered by CD-HIT (Ying et al., 2010) to filter out redundant sequences with a similarity higher than 90% so that the sequences in the training dataset and the test dataset are different. Two other data sets, neuropeptides and antifungal peptides, were also used in this paper. The details of the dataset are shown in Table 1.

This chapter details the ACP-MCAM model structural frame used to predict the anticancer peptides.

The architecture of the ACP-MCAM model is shown in Figure 1. It consists of five modules, 1) an embedding layer, 2) a Multi-kernel CNN layer, 3) the position embedding layer, 4) the encoder layer, and 5) the task output layer. In module 1), the embedding layer first processes the input anticancer peptide sequence and converts each amino acid of the anticancer peptide sequence into a low dimensional dense vector as the embedding vector representation of amino acid nodes. No matter where the amino acid appears in the sequence, the same type of amino acid uniquely corresponds to the same vector. 2) In the multi-kernel CNN layer, this paper uses convolution neural network (CNN) technology to encode the amino acid nodes of anticancer peptide sequence by using the context information and different semantic information of specific amino acids in the anticancer peptide sequence. We perform a two-dimensional convolution operation with padding on the output of the embedding layer to ensure that the dimensions of the input and output are the same. The kernel can take odd numbers such as 1, 3, and 5, connect them in the last dimension, and then do a linear transformation. 3) The position embedding layer encodes the position information of the amino acids in the anti-cancer peptide sequence. It is a vector containing the position embedding information of the amino acid sequence. 4) The encoding layer is the core of the model, and the input feature matrix is the output of the position embedding layer and the multi-kernel CNN layer. The encoder layer includes multiple encoder blocks. Each encoder block is based on a multi-head attention mechanism and a fully connected neural network. The feed forward part of each encoder block ensures that the input and output sizes of each encoder block are consistent. The sequential stacking of multiple coding layers makes the representation of anticancer peptide sequences more effective. In module 4), the encoder layer is used to capture the context of each remaining embedding vector at different positions, so that the remaining embedding has different feature vectors according to the context, and learning the discriminative features of ACP. Finally, module 5) is the last part of the model, called the task output layer, which is composed of a fully connected neural network and a nonlinear activation function. It converts the representation of ACPs into the probability distribution of the classes for prediction. Please note that the penultimate neural network in the task output layer is specifically designed for feature visualization. These five modules are described in detail below.

The following evaluation indicators were used to evaluate our model. Including recall, precision, accuracy (ACC), Matthew correlation coefficient (MCC), and the area under the ROC curve (AUC) (Balachandran et al., 2018; Leyi et al., 2020; Mehedi et al., 2020). The specific formula is as follows: { S e n s i t i v e = Re c a l l = T P T P + F N = T P P × 100 % S p e c i f i c i t y = T N T N + F P = T N N × 100 % Pr e c i s i o n = T P T P + F P × 100 % A c c u r a c y =   T P + T N T P + T N + F P + F N = T P + T N P + N × 100 %   M C C = T P × T N − F P × F N ( T P + F N ) ( T P + F P ) ( T N + F N ) ( T N + F P ) × 100 %               F 1 = 2 × p r e c i s i o n × r e c a l l p r e c i s i o n + r e c a l l T P R = T P T P + F N × 100 % F P R = F P F P + F P × 100 % C o r r e c t   i n d e x = ( T P R + 1 − F P R ) / 2 (6)

Among them, true positive (TP) and false negative (FN) represent the number of true anticancer peptides that are predicted correctly and incorrectly. True negative (TN) and false positive (FP) represent the number of non-anticancer peptides that are predicted correctly and incorrectly. Accuracy is the percentage of correctly classified samples in all samples. The sensitivity (SE) and specificity (SP) index measure the predictive ability of predictors for positive and negative samples, respectively. Precision represents the prediction success rate of positive samples. The recall represents the proportion of predicting positive samples in all true positive samples. The F1 score is the coordinated average value of accuracy and recall. The higher the selected value, the better the performance of the model. The other two indicators, AUC and MCC measure the overall performance of the predictor. AUC sorts all samples obtained from model evaluation by score. By calculating the area enclosed by the ROC curve, the AUC value can be obtained.

To verify the predictive performance of anticancer peptide ACP-MCAM, we compared it with several existing models, including iACP(Chen et al., 2016), ACPred-FL (Leyi et al., 2018), PEPred-Suite (Leyi et al., 2019), ACPred-Fuse (Rao et al., 2020), AntiCP_ACC (Vijayakumar and Ptv, 2015), AntiCP_DC(Vijayakumar and Ptv, 2015) and Hajisharifi’s(Hajisharifi et al., 2014). The cross validation results are shown in Table 2.

As shown in Table 2, we can see that the performance of our proposed method ACP-MCAM on all indicators (SE, SP, Accuracy, MCC, and AUC) is significantly better than other predictors, reaching 85.6, 95.2, 90.4, 81.3, and 91.9%, respectively. SE, SP, Accuracy, and MCC are 8.4, 7.8, 8, and 16.1%, which is higher than other predictors.

In order to verify the superiority of the proposed ACP-MCAM model, we used an independent test dataset to compare its performance with several existing predictions. As shown in Table 3, we can see that the performance of our proposed method ACP-MCAM on all indicators is significantly better than other predictors. SE、SP、ACC、MCC和AUC have reached 85.4, 96.3, 90.9, 82.2 and 94.8%, respectively. Especially SE, MCC, and AUC are 13.4, 50.2, and 8% higher than other predictors. In general, independent test results confirm that our prediction method performs better than other prediction methods, and can better distinguish true anti-cancer peptides from non-anti-cancer peptides.

Several important parameters may affect the performance of our models, such as the learning rate and the kernel of multi-kernel CNN. Learning rate is an important parameter of deep learning. Through the adjustment of learning rate, we can see whether the objective function can quickly converge to the minimum value and fall into the local optimal value. An appropriate learning rate can make the objective function converge to the optimal value quickly.

In this section, we will perform a sensitivity analysis on these parameters. In our model, the number of training epochs is set to 50. The output dimension is 64. We train our model by modifying the learning rate. Table 4 shows that as the learning rate changes, the performance first gradually increases and then decreases. If the learning rate is equal to 2e-4, three of the five main evaluation indexes are the best. Accuracy, AUC, and F1-score are the highest. The model has achieved the best performance.

Since the CNN kernel represents several amino acids on an anti-cancer peptide sequence sharing the same parameters during the process of convolution. Therefore, the different combination of kernels means that the sequence of the anticancer peptide is affected by different combinations of several amino acids. Modifying the combination of the kernels may improve the effect of the model. Therefore, the combination of the kernel is also a very important parameter. As shown in Table 5, when the combination of kernels = (Li et al., 2006; Plumb et al., 2019; Song et al., 2020), the model achieved the best effect. Four of the five main evaluation indexes are the best. Accuracy, precision, AUC, and F1-score are the highest. This means that when using multi-kernel CNN to extract features from the model, selecting 1, 3, and 5 amino acid combinations for convolution calculation, and then combining these three features to obtain the best model effect. Our model adopts the combination of one, three, and five amino acids, which is better than considering all the amino acid sequences or just considering the properties of a single amino acid. This is the excellence of the CNN model.

We compared our model to the ACP164 data set for ablation experiments. It can be seen that the experiment is mainly to compare three models: the embedding attention model, CNN attention model, and Multi-kernel CNN attention model. From Table 6 and Figure 3, we can observe the performance comparison of three different embedding methods. In general, the performance of multi-kernel CNN is better than that of all existing methods on the ACP dataset, indicating that Multi-kernel CNN’s embedding method is more powerful than models based on other embedding features.

Figure 3 is a more intuitive comparison between the several embedding methods of our model, including the ROC curve and precision-recall (PR) curve. From Figure 3, we can see that in both the ROC curve and PR curve, the embedding method of the embedding_multi_cnn can achieve the best effect of the model. Note that the experimental results in this section only reflect the performance of the model on the ACP data set, and it is difficult to avoid certain deviations. Therefore, we evaluate the performance of this model through experiments on other peptide datasets (NPs and AFP). The dataset is shown in Table 1. NPs1400 was used as the training set, NPs350 was used as the test set; AFPs2336 was used as the training set, and AFPs582 was used as the test set to verify the model.

The results in Table 6 show that Multi-kernel CNN performs best on the ACP dataset and AFPs dataset, especially in ACC and AUC. On the NPs data set, CNN has the best feature extraction effect. Therefore, it can be inferred that on the NPs data set, every three consecutive amino acids were regarded as an amino acid group for classification prediction to achieve the best effect.

Principal Component Analysis (PCA) (Smith, 2002) is a common linear dimensionality reduction method, while t-distributed Stochastic Neighbor Embedding (TSNE) (Laurens and Hinton, 2008) is a non-linear dimensionality reduction method. Due to different principles and mechanisms, TSNE runs slower, while PCA is relatively fast. PCA transforms a set of potentially correlated variables into a set of linearly uncorrelated variables through orthogonal transformation, and the transformed set of variables is called principal components. The idea of PCA is to map n-dimensional features to k-dimensions (k < n), which are brand new orthogonal features. In this paper, k is equal to 2. The basic idea of TSNE is that similar data points in high-dimensional space map to similar distances in low-dimensional space. The attribute information retained by TSNE is more representative and can relatively reflect the differences between samples. To visually verify the effectiveness of the ACP-MCAM model and improve the interpretability of the model, this paper uses principal component analysis (PCA) and t-distributed stochastic neighborhood embedding (TSNE) to learn the high-dimensionality of ACP sequences at different stages. The high-dimensional feature representation vectors of anticancer peptide sequences at different stages are reduced to a two-dimensional plane for easy visualization, and the results are shown in Figure 4.

The figure shows that in the ACP dataset, the positive examples (represented by train:1 and purple dots) and negative examples (represented by train:0 and blue dots) in the training dataset are mixed in the initial stage because they are initialized randomly. The same is in the test dataset (positive examples are represented by test:0 and red dots, and negative examples are represented by test:1 and blue dots), which indicates that the model has no distinguishing ability before training. As the training epoch number increases, positive and negative samples are gradually separated from the sample points. We can observe that in the training dataset and the test dataset, the embedding vectors of the ACP samples almost belong to the same cluster, and after training, the positive and negative examples have similar distributions, which indicates that the model has indeed learned feature of the positive and negative samples. This shows that the model in this paper can learn the common features and distinguishing features of positive and negative cases.

In addition, there are many ACPs in the negative cluster, but few non-ACPs in the positive cluster, which explains the reason why the performance of SP is better than SE to some extent. We speculate that those ACPs predicted to be negative samples have characteristics that our method cannot capture. Therefore, the unique physical and chemical properties of these indistinguishable samples should be further studied in the future.