The benchmark dataset used in this study is exactly the same as that in pLoc_bal-mHum [12]. It can be formulated as

S = S 1 ∪ S 2 ∪ ⋯ ∪ S u ∪ ⋯ ∪ S 13 ∪ S 14 (1)

where S 1 only contains the protein samples from the “Centrosome” location (cf. Table 1), S 2 only contains those from the “Cytoplasm” location, and so forth; ∪ denotes the symbol for “union” in the set theory [52]. The detailed sequences of these proteins and their accession numbers (or ID codes) are given in Supporting Information S1 that is also available at http://www.jci-bioinfo.cn/pLoc_bal-mHum/Supp1.pdf where none of proteins included has ≥25% sequence identity to any other in the same subset.

Now let us consider the 2^nd step of the 5-step rule [51]; i.e., how to formulate the biological sequence samples with an effective mathematical expression that can truly reflect their essential correlation with the target concerned. Given a protein sequence P, its most straightforward expression is

^aSee Eq. 4 for the definition of the metrics. ^bSee [12], where the reported metrics rates were obtained by the jackknife test on the benchmark dataset of Supporting Information S1 that contains experiment-confirmed proteins only. ^cThe proposed predictor; to assure that the test was performed on exactly the same experimental data as reported in [12] for pLoc_bal-mHum.

P = R 1 R 2 R 3 R 4 R 5 R 6 R 7 ⋯ R L (2)

where L denotes the protein’s length or the number of its constituent amino acid residues, R 1 is the 1^st residue, R 2 the 2^nd residue, R 3 the 3^rd residue, and so forth. Since all the existing machine-learning algorithms} can only handle vectors as elaborated in [3], one has to convert a protein sample from its sequential expression (Equation (2)) to a vector. But a vector defined in a discrete model might completely miss all the sequence-order or pattern information. To deal with this problem, the Pseudo Amino Acid Composition [53] or PseAAC [54]. Ever since then, the concept of “Pseudo Amino Acid Composition” or “PseAAC” has been widely used in nearly all the areas of computational proteomics with the aim to grasp various different sequence patterns that are essential to the targets investigated (see, e.g., [11,55-207]).

Because it has been widely and increasingly used, recently three powerful open access soft-wares, called “PseAAC-Builder” [87], “propy” [144], and “PseAAC-General” [114], were established: the former two are for generating various modes of special PseAAC [208]; while the 3rd one for those of general PseAAC [51], including not only all the special modes of feature vectors for proteins but also the higher level feature vectors such as “Functional Domain” mode, “Gene Ontology” mode, and “Sequential Evolution” or “PSSM” mode. Encouraged by the successes of using PseAAC to deal with protein/peptide sequences, its idea and approach were extended to PseKNC (Pseudo K-tuple Nucleotide Composition) to generate various feature vectors for DNA/RNA sequences [209] that have proved very successful as well [210-221]. According to the concept of general PseAAC [51], any protein sequence can be formulated as a PseAAC vector given by

P = [ Ψ 1 Ψ 2 ⋯ Ψ u ⋯ Ψ Ω ] T

P = [ Ψ 1 Ψ 2 ⋯ Ψ u ⋯ Ψ Ω ] T (3)

where T is a transpose operator, while the integer Ω is a parameter and its value as well as the components Ψ u ( u = 1 , 2 , ⋯ , Ω ) will depend on how to extract the desired information from the amino acid sequence of P, as elaborated in [12]. Thus, by following exactly the same procedures as described in the Section 2.2 of [12], each of the protein samples in the benchmark dataset can be uniquely defined as a 14-D numerical vector as given in columns 16-29 of Supporting Information S2, which can also be directly downloaded at http://www.jci-bioinfo.cn/pLoc_bal-mHum/Supp2.pdf.

In this study, a novel deep CNN-BiLSTM neural network (Figure 1) model included one convolution layer and one BiLSTM block is proposed to predict subcellular localization of multi-label human proteins. The strong point of this model is that it allows extracting the maximum amount of information from human protein features using CNN convolution layers. This output becomes the BiLSTM input, which allows keeping the dependency relationship between the features in both directions.

CNN is known for its ability to extract as many features as possible from the data. In our model, 14 human protein features are used as convolutional neural network input. Then, fourteen filters of sizes 2 with a stride of 1 are applied. This gives a 14 * 14 feature map. After each filter, a layer of MaxPooling1D is applied to update and reduce the size of the data and this gives a 7 * 14 feature map.

Then, the 7 * 14 feature map is concatenated to build the BiLSTM input, which applies a BiLSTM layer to filter the information, using its three gates. The output of this step is the input of the fully connected layer which consists of 3 hidden layer. It links each piece of input information with a piece of output information. Finally, we apply the sigmoid function as an activation function in order to transform the vector into probability to define the class of each output. The label of human protein was decided by the Probability value θ. If the output is greater than 0.5, the outcome was true; otherwise, false.

The new predictor developed via the above procedures is called “pLoc_Deep-mHum”, where “pLoc_Deep” stands for “predict subcellular localization by deep learning”, and “mHum” for “multi-label human proteins”.

The new predictor developed via the above procedures is called “pLoc_Deep-mHum”, where “pLoc_Deep” stands for “predict subcellular localization by deep learning”, and “mHum” for “multi-label human proteins”.

Different from the metrics used to measure the prediction quality of single-label systems, the metrics for the multi-label systems are much more complicated [222]. For the latter, two kinds of metrics are needed: one is the “global metrics” and the other is the “local metrics”.

Listed in Table 1 are the rates achieved by the current pLoc_Deep-mHum predictor via the cross validations on the same experiment-confirmed dataset as used in [22] according to the scores of “global metrics”. For facilitating comparison, listed there are also the corresponding results obtained by the pLoc_bal-mHum [12], the existing most powerful predictor for identifying the subcellular localization of human proteins with both single and multiple location sites. As shown in Table 1, the newly proposed predictor pLoc_Deep-mHum is remarkably superior to the existing state-of-the-art predictor pLoc_bal-mHum in all the five metrics. Particularly, it can be seen from the table that the absolute true rate achieved by the new predictor is over 81%, which is far beyond the reach of any other existing methods. This is because it is extremely difficult to enhance the absolute true rate of a prediction method for a multi-label system as clearly elucidated in [12]. Actually, to avoid embarrassment, many investigators even chose not to mention the metrics of absolute true rate in dealing with multi-label systems (see, e.g., [85,141,147]).

Moreover, to in-depth examine the prediction quality of the new predictor for the proteins in each of the subcellular locations concerned (cf. Table 2), we used a set of four “local metrics” to score its accuracy,

^aSee Table 1 and the relevant context for further explanation. ^bSee Eq.6 for the metrics definition.

which were derived in [223] based on the Chou’s symbols introduced for studying protein signal peptides [224] and that have ever since been widely concurred or justified (see, e.g., [209-217,223,225-274]).

Listed in Table 2 are the rates achieved by pLoc_Deep-mHum for the human proteins in each of 22 subcellular locations. As we can see from the table, nearly all the success rates achieved by the new predictor for the human proteins in each of the 22 subcellular locations are within the range of 90%-100%, which is once again far beyond the reach of any of its counterparts.

Meanwhile, as a byproduct, the present paper has also stimulated some very interesting or challenging papers (see, e.g., [275-280]).

In this paper, the CNN-BiLSTM neural network model is constructed through the Python language and Keras, and the model is trained through binary_crossentropy and Adam optimizers (lr = 0.001, beta_1 = 0.9, beta_2 = 0.999, epsilon = 10⁻⁸).

In order to improve the performance of the CNN-BiLSTM neural network model, based on the above parameter settings, the hyperparameters of the constructed CNN-BiLSTM model are adjusted. Through experimental analysis, we find that four parameters have a greater impact on the performance of the deep learning model: the height of the CNN filter, the number of filters in the convolutional layer, the output dimension of BiLSTM, and Dropout rate. Finally, the four optimal parameters are set to (2, 14, 14, 0.1).

We compared the performance of the pLoc_Deep-mHum model with seven state-of-the-art methods in Table 3, including Rake1D [281], LabelPowerset [282], ML-SVM [283], MLARAM{Benites, 2015 #8224}, RandomForestClassifier [284], MLKNN [285], BRkNNaClassifier{Spyromitros, 2008 #8227}. It

can be found that the performance of the pLoc_Deep-mHum model is significantly better than its cohorts in the multi-label metrics scores.

As pointed out in [286], user-friendly and publicly accessible web-servers represent the future direction for developing practically more useful predictors. Actually, user-friendly web-servers as given in a series of recent publications (see, e.g., Song, 2018 #3338; Wang, 2018 #3353}) will significantly enhance the impacts of theoretical work because they can attract the broad experimental scientists [287]. In view of this, the web-server of the current pLoc_Deep-mHum predictor has also been established at http://www.jci-bioinfo.cn/pLoc_Deep-mHum/, by which the majority of experimental scientists can easily get the data they need.