To evaluate the prediction model proposed in this study and compare it with state-of-the-art methods, two publicly available datasets are used here [8]. And anyone can freely download it at [13]. The training dataset contains 300 bioluminescent proteins and 300 non-bioluminescent proteins, and the test dataset contains 139 bioluminescent proteins and 18202 non-bioluminescent proteins.

To avoid homology bias and remove the redundant sequences from the benchmark dataset, a cutoff threshold of 25% is imposed by [14,15] to remove those proteins from the benchmark dataset that have ≥ 25% sequence similarity. However, we do not use such a stringent criterion in this study because the number of available protein sequences does not allow us to do so (40% in this paper). In addition, the protein sequences containing less than 50 amino acids are also screened out.

Evolutionary information, one of the most important types of information in assessing functionality in biological analysis, has been widely used in many studies [16–21]. To extract the evolutionary information, the profile of each protein sequence is generated by running Position Specific Iterated BLAST (PSI-BLAST) program [22–24]. Then this information can be represented as a two dimensional matrix which is known as the PSSM of the protein. PSSM has been widely used to predict protein fold pattern [25], protein quaternary structural attribute [26], disulfide connectivity [27,28], half-sphere exposure [29], protein fold recognition and superfamily discrimination [30], ATP binding residues of a protein [31], and catalytic residues [32]. As a result, we also use it to predict bioluminescent proteins.

In this paper, the PSSM of each protein sequence in the constructed dataset is generated against the non-redundant Swiss-Prot database (version 56, released on 22 July 2008) using the PSI-BLAST program with three iterations (−j 3) and e-value threshold 0.0001 (−h 0.0001). This matrix is composed of L × 20 elements, where L is the total number of residues in a peptide, the rows of the matrix represent the protein residues and the columns of the matrix represent the 20 amino acids.

In view of the fact that SVM requires the fixed length feature vectors as their inputs for training [10], we generate a vector of 400 dimensions, called PSSM-400 from the PSSM. PSSM-400 is the composition of occurrences of each type of amino acid corresponding to each type of amino acids in protein sequence. Thus for each column we have a vector of dimension 20. Figure 1 shows the schematic representation of transformation of each protein sequence into PSSM-400. Besides the PSSM-AC encoding strategy, PSSM-400 is also used to encode each protein sequence in this study.

Auto covariance (AC) is a correlation factor coupling adjacent residues along the protein sequence [11]. It’s a kind of variant of auto cross covariance. As a powerful statistical tool used to analyze sequences of vectors [33], the AC transformation has been widely applied in various fields of bioinformatics [34–39]. AC variables are able to avoid producing too many variants. In the PSSM-AC encoding strategy, the AC transformation is applied to each column of PSSM to incorporate the local sequence-order information. In this study, AC is employed to transform the PSSM into equal length vector. Given a protein sequence, AC variables describe the average interactions between residues with a series of lag. Here, lag is the distance between one residue and its neighbors in the protein sequence P. The AC variables can be calculated by Equation (1).

where P represents the PSSM generated by running the PSI-BLAST program, i represents the position, j represents one descriptor and n is the length of the sequence. Thus, the number of AC variables D can be calculated as D = lg × q (lg is the maximum lag (lag = 1, 2, …, lg) and q is the number of descriptors). Using Equation 1, each protein sequence can be represented by a vector of AC variables, whose length equals to the value of D. Here, the value of q is 20, which corresponds to the number of the columns of the PSSM. Ultimately, each protein sequence was characterized by the PSSM-AC model.

Support vector machine (SVM) is a popular learning approach mainly used in pattern recognition areas [40–42]. SVM [43] belongs to the family of margin-based classifier and is assumed to be a very powerful method to deal with prediction, classification, and regression problems. SVM looks for the optimal hyperplane which maximizes the distance between the hyperplane and the nearest samples from each of the two classes. Let x_i ∈ Rⁿ be training instance and y_i ∈ {−1, +1} be the corresponding class labels, i = 1, ..., n. The class label for a new instance x can be determined by the sign of the following function.

where m is the number of training instances, α_i are the obtained by solving a optimization problem on the input instances, and b is the bias term. In this paper, LIBSVM package [44] with radial basis kernels (RBF) is used.

Two parameters, the regularization parameter C and the kernel width parameter γ are optimized based on 10-fold cross-validation using a grid search strategy.

The work flow of the proposed model is described in Figure 2. For the left part of Figure 2, firstly, sequential evolution information in form of PSSM profiles on the training dataset is obtained by PSI-BLAST. Secondly, the AC transformation is applied to the obtained PSSM with optional values of lg to incorporate local sequence order information. Finally, SVM is applied with ten-fold cross validation. With different lg, we can get different prediction models. In this study, we select the one which corresponds to the highest accuracy as the final model. The right part of Figure 2 shows the process of how to predict each one protein sequence using the BLPre predictor.

Ten-fold cross validation [45] is used in this work. The dataset is randomly divided into ten equal sets, out of which nine sets are used for training and the remaining one for testing. This procedure is repeated ten times and the final prediction result is the average accuracy of the ten testing sets. Besides the ten-fold cross validation on the training set, we also utilize independent dataset test [46] to evaluate our model.

Three parameters, sensitivity (S_n), specificity (S_p), and accuracy (AC) are used to measure the performance of our model. They are defined by the following formulas:

where TP, TN, FP and FN stand for true positive, true negative, false positive and false negative, respectively. Moreover, we create ROC (receiver operating curve) for all of the models in order to evaluate the performance of models using different encoding strategies.

As mentioned in Section 2.5, for prediction performance, the value of lg of AC transformation is an important parameter needed to be considered. Generally, the value of lg varies in different datasets, and must be smaller than the length of the shortest protein sequence in the corresponding dataset. Since all the protein sequences collected in this paper contain more than 50 amino acids, a series value of lgs (lg = 1, 5, 10, 15, …, 50) are investigated to construct the optimal prediction model. The results on the training set constructed in this study are presented as Figure 3.

It can be seen in Figure 3, the prediction performance increases from 79.33% to 85.17% when the value of lg increases from 1 to 30 and decreases when the value of lg is larger than 30. The accuracy of the prediction model becomes stable when the value of lg equals 45. It is obvious that the best value of lg is 30 corresponding to a peak with accuracy of 85.17%, so that the value of lg is set to 30 in the rest of this study.

In this section, we compare the PSSM-AC encoding strategy with the PSSM-400 encoding strategy mentioned in Section 2.2, thus to highlight the advantage of our prediction model. The results evaluated by ten-fold cross validation on the training dataset are shown in Table 1 and Figure 4. It can be seen in Table 1, compared with the accuracy of 79.32% gained by PSSM-400 method, the accuracy obtained by our method PSSM-AC is 85.17%.

As shown in Figure 4, we achieve the area under the ROC curve (AUC) of 0.92, which is significantly better than that of the PSSM-400 method with AUC of 0.88. These results indicate that the superior performance of the AC transformation encoding when being applied to the PSSM to incorporate the local sequence-order information.

In this section, the proposed predictor is further compared with a recently reported predictor BLProt [8] on the training dataset and the independent test dataset. As can be seen in Table 1, our model achieves the accuracy of 85.17%, which is about 5% higher than the BLProt method. The number of bioluminescent proteins and non-bioluminescent proteins in the test dataset are highly imbalanced, and this situation is close to reality. Compared with the accuracy of 80.06% gained by Kandaswamy et al. [8], the accuracy obtained by our method is 90.71% which has been significantly improved. The better prediction performance may be credited to the appropriate protein sequence encoding strategy adopted in our prediction model.