The benchmark dataset used in this study is exactly the same as that in pLoc_bal-mAnimal [4]; i.e.,

S = S 1 ∪ S 2 ∪ ⋯ ∪ S u ∪ ⋯ ∪ S 20 (1)

where S 1 only contains the protein samples from the “Acrosome” location, S 2 only contains those from the “Cell cortex” location, and so forth; ∪ denotes the symbol for “union” in the set theory. For readers’ convenience, their detailed sequences and accession numbers (or ID codes) are given in Supporting Information S1 that is also available at http://www.jci-bioinfo.cn/pLoc_bal-mAnimal/Supp1.pdf, where none of proteins included has ≥25% sequence identity to any other in the same subset (subcellular location).

Now let us consider the 2^nd step of the 5-step rule [17]; 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

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 [18] or PseAAC [19] was proposed. Ever since then, the concept of “Pseudo Amino Acid Composition” 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., [20 - 30] as well as a long list of references cited in [31]). Because it has been widely and increasingly used, recently three powerful open access soft-wares, called “PseAAC-Builder” [32], “propy” [33], and “PseAAC-General” [34], were established: the former two are for generating various modes of special PseAAC [35]; while the 3^rd one for those of general PseAAC [17], 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 [36] that have proved very successful as well (see, e.g., [37,38]).

According to the concept of general PseAAC [17], any protein sequence can be formulated as a PseAAC vector given by

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 [4]. Thus, by following exactly the same procedures as described in the Section 2.2 of [4], each of the protein samples in the benchmark dataset can be uniquely defined as a 20-D numerical vector as given in Supporting Information S2, which can also be directly downloaded at http://www.jci-bioinfo.cn/pLoc_bal-mAnimal/Supp2.pdf.

In this study, we use the CNN (Convolutional Neural Network) model to predict the subcellular localization of animal proteins, as illustrated in Figure 1.

The CNN model consists of input layer, convolutional layer, average-pooling layer and fully connected layer. The input layer represents each animal protein with 6 features. The second layer is convolutional layer which extract dependency relationship between features subsequence of animal proteins. The filter stride is set to one. The activation function is set as “relu”. The average-pooling layer down-samples the features and compute the average values of the features. The fully connected layer consists of 2 hidden layers. Finally, the output of connected layer was concatenated into output layer with sigmoid activation function. The label of animal protein was decided by the threshold θ. If the output is greater than 0.5, the outcome was true; otherwise, false.

The other parameters of CNN model are as follows. 1) The algorithm of Adam was used to train the model and the loss function is set to binary cross-entropy. 2) The activation function of full connected layer and convolutional layer is ReLU [39], and the activation function of output layer is sigmoid. 3) Convolutional Layer used the filter size 2 * 1 to extract features of animal proteins. 4) The batch size is 26. 5)

The model is trained for 120 epochs. 6) The metrics is set as “accuracy”.

The new predictor developed via the above procedures is called “pLoc_Deep-mAnimal”, where “pLoc_Deep” stands for “predict subcellular localization by deep learning”, and “mAnimal” for “multi-label animal 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 [40]. To make them more intuitive and easier to understand for most experimental scientists, here we use the following intuitive Chou’s five metrics [41] or the “global metrics” that have recently been widely used for studying various multi-label systems (see, e.g., [42,43]). For the current study, the set of global metrics can be formulated as:

{ Aiming ↑   = 1 N q ∑ k = 1 N q ( ‖ L k ∩ L k * ‖ ‖ L k * ‖ ) ,       [ 0 , 1 ] Coverage ↑   = 1 N q ∑ k = 1 N q ( ‖ L k ∩ L k * ‖ ‖ L k ‖ ) ,       [ 0 , 1 ] Accuracy ↑   = 1 N q ∑ k = 1 N q ( ‖ L k ∩ L k * ‖ ‖ L k ∪ L k * ‖ ) ,       [ 0 , 1 ] Absolutetrue ↑   = 1 N q ∑ k = 1 N q Δ ( L k , L k * ) ,       [ 0 , 1 ] Absolutefalse ↓   = 1 N q ∑ k = 1 N q ( ‖ L k ∪ L k * ‖ − ‖ L k ∩ L k * ‖ M ) ,       [ 1 , 0 ] (4)

where N q is the total number of query proteins or tested proteins, M is the total number of different labels for the investigated system (for the current study it is L cell = 20 ), ‖ ‖ means the operator acting on the set therein to count the number of its elements, ∪ means the symbol for the “union” in the set theory, ∩ denotes the symbol for the “intersection”, L k denotes the subset that contains all the labels observed by experiments for the k-th tested sample, L k * represents the subset that contains all the labels predicted for the k-th sample, and

Δ ( L k , L k * ) = { 1 ,     if   all   the   labels   in   L k *   are   identical   to   those   in   L k 0 ,       otherwise (5)

In Equation (4), the first four metrics with an upper arrow ↑ are called positive metrics, meaning that the larger the rate is the better the prediction quality will be; the 5^th metrics with a down arrow ↓ is called negative metrics, implying just the opposite meaning.

From Equation (4) we can see the following: 1) the “Aiming” defined by the 1^st sub-equation is for checking the rate or percentage of the correctly predicted labels over the practically predicted labels; 2) the “Coverage” defined in the 2^nd sub-equation is for checking the rate of the correctly predicted labels over the actual labels in the system concerned; 3) the “Accuracy” in the 3^rd sub-equation is for checking the average ratio of correctly predicted labels over the total labels including correctly and incorrectly predicted labels as well as those real labels but are missed in the prediction; 4) the “Absolute true” in the 4^th sub-equation is for checking the ratio of the perfectly or completely correct prediction events over the total prediction events; 5) the “Absolute false” in the 5^th sub-equation is for checking the ratio of the completely wrong prediction over the total prediction events.

Listed in Table 1 are the rates achieved by the current pLoc_Deep-mAnimal predictor via the cross validations on the same experiment-confirmed dataset as used in [4]. For facilitating comparison, listed there are also the corresponding results obtained by the pLoc_bal-mAnimal [4], the existing most powerful predictor for identifying the subcellular localization of animal proteins with both single and multiple location sites. As shown in Table 1, the newly proposed predictor pLoc_Deep-mAnimal is remarkably superior to the existing state-of-the-art predictor pLoc_bal-mAnimalin all the five metrics. Particularly, it can be seen from the table that the absolute true rate achieved by the new predictor is over 92%, which is far beyond the reach of any other existing methods [44 - 49]. 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 [4]. 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., [50 - 56]).

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 the “local metrics” [40] or a set of four intuitive metrics that were derived in [57] based on the Chou’s symbols introduced for studying protein signal peptides [58] and that have ever since been widely concurred or justified (see, e.g., [59 - 62]). For the current study, the set of local metrics can be formulated as:

{ Sn ( i ) = 1 − N − + ( i ) N + ( i )                                                                                                                           0 ≤ Sn ≤ 1 Sp ( i ) = 1 − N + − ( i ) N − ( i )                                                                                                                           0 ≤ Sp ≤ 1 Acc ( i ) = 1 − N − + ( i ) + N + − ( i ) N + ( i ) + N − ( i )                                                                                             0 ≤ Acc ≤ 1 MCC ( i ) = 1 − ( N − + ( i ) N + ( i ) + N + − ( i ) N − ( i ) ) ( 1 + N + − ( i ) − N − + ( i ) N + ( i ) ) ( 1 + N − + ( i ) − N + − ( i ) N − ( i ) )           − 1 ≤ MCC ≤ 1 ( i = 1 , 2 , ⋯ , 20 ) (6)

where Sn, Sp, Acc, and MCC represent the sensitivity, specificity, accuracy, and Mathew’s correlation coefficient, respectively, and i denotes the i-th subcellular location (or subset) in the benchmark dataset. N + ( i ) is the total number of the samples investigated in the i-th subset, whereas N − + ( i ) is the number of the samples in N + ( i ) that are incorrectly predicted to be of other locations; N − ( i ) is the total number of samples in any locations but not the i-th location, whereas N + − ( i ) is the number of the samples in N − ( i ) that are incorrectly predicted to be of the i-th location.

Listed in Table 2 are the results achieved by pLoc_Deep-mAnimal for the animal proteins in each of 20 subcellular locations. As we can see from the table, nearly all the success rates achieved by the new predictor for the animal proteins in each of the 20 subcellular locations are within the range of 90% - 100%,

^aSee Equation (4) for the definition of the metrics. ^bSee [4], 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 [4] for pLoc_bal-mAnimal.

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

which is once again far beyond the reach of any of its counterparts.

Meanwhile, as a byproduct, the present paper has also stimulated some kinds of provocative or challenging but very intriguing papers (see, e.g., [63 - 68]).

As pointed out in [69], user-friendly and publicly accessible web-servers represent the future direction for developing practically more useful predictors. Actually, user-friendly web-servers will significantly enhance the impacts of theoretical work because they can attract the broad experimental scientists [31]. In view of this, the web-server of the current pLoc_Deep-mAnimal predictor has also been established at http://www.jci-bioinfo.cn/pLoc_Deep-mAnimal/, by which users can easily get their desired data without the need to go thru the mathematical details.