Bacteria can be divided into two groups: Gram-positive and Gram-negative. Gram-positive bacteria are those that are stained dark blue or violet by Gram staining; while Gram-negative bacteria cannot retain the stain, instead taking up the counter-stain and appearing red or pink.

It has special meaning for both basic research and drug design to study bacteria because (1) they are the workhorses for the fields of molecular biology, biochemistry, and genetics due to their ability to quickly grow and being relatively easier to be manipulated, and (2) they are both harmful and useful. With the explosion of protein sequences generated in the post-genomic era, we are challenged to develop computational methods for timely and accurately identifying the subcellular locations of newly discovered bacterial proteins based on their sequence information alone because this kind of knowledge will be very useful for selecting proper bacterial proteins for a special target, or screening and prioritizing candidates in drug design.

Actually, numerous predictors were developed for identifying subcellular localization of proteins in various organisms (see [1], [2] as well as the long list of references cited in the two review papers). However, those that are specialized for dealing with Gram-negative proteins are only a few. They are called “PSORT” [1], [3], [4], “PSORT-B” [5], and PSORTb v.2.0 [6]. All these methods have played important roles in stimulating the development of this area. To improve the prediction coverage scope and the quality of benchmark datasets, the predictor called Gneg-PLoc [7] was developed. Compared with the previous methods, Gneg-PLoc extended the coverage scope from five to eight subcellular location sites. Also, the benchmark datasets used to train and test the predictor have been significantly refined. For instance, the benchmark datasets used in PSORT-B [5] contain many proteins with pairwise sequence identity higher than 90%, while in the benchmark datasets of Gneg-PLoc [7] none of the proteins included has pairwise sequence identity to any other in a same subcellular location; i.e., the latter is much more stringent and rigorous than the former in excluding the homology bias and redundancy. Also, Gneg-PLoc was able to yield higher success rates.

However, all the aforementioned predictors cannot be used to deal with multiplex proteins that may simultaneously exist at, or move between, two or more different subcellular locations. Proteins with multiple locations or dynamic feature of this kind are particularly interesting because they may have some very special biological functions intriguing to investigators in both basic research and drug discovery [8], [9]. Particularly, as pointed out by Millar et al. [10], recent evidences have indicated that an increasing number of proteins have multiple locations in the cell.

To make Gneg-PLoc [7] be able to deal with multiplex Gram-negative proteins as well, a predictor called Gneg-mPLoc [11] was developed recently, where the character “m” in front of “PLoc” stands for “multiple”, meaning that it can be also used to deal with Gram-negative bacterial proteins with multiple locations.

However, Gneg-mPLoc has the following shortcomings. (1) In predicting the number of subcellular location sites for a query Gram-negative protein, an optimal threshold factor (see Eq.48 of [2]) was adopted without providing its statistical implication and detailed learning process. It would be more instructive if we could find a more intuitive approach to determine this with a more natural manner. (2) In formulating the protein samples, only the integer numbers 0 and 1 were used to reflect the GO (gene ontology) information [12], [13]. Such an over-simplified formulation might cause some useful information lost so as to limit the prediction quality. (3) Although a web-server for Gneg-mPLoc has been established at http://www.csbio.sjtu.edu.cn/bioinf/Gneg-multi/, only one query protein sequence at a time is allowed when using the web-server to conduct prediction. For the convenience of users in handling many query Gram-negative protein sequences, such a rigid limit should be improved.

The present study was dedicated to develop a new and more powerful predictor, called iLoc-Gneg, for predicting Gram-negative bacterial protein subcellular localization by addressing the above three problems.

To establish a really useful statistical predictor for protein system, we usually need to consider the following procedures [14]: (1) select or construct a valid benchmark dataset to train and test the predictor; (2) formulate the protein samples with an effective mathematical expression that can truly reflect their intrinsic correlation with the attribute to be predicted; (3) introduce or develop a powerful algorithm (or engine) to operate the prediction; (4) properly perform cross-validation tests to objectively evaluate the anticipated accuracy of the predictor; (5) establish a user-friendly web-server [15] for the predictor that is accessible to the public. Below, let us describe how to realize these steps one by one.

Here, we choose to use the same dataset in establishing Gneg-mPLoc [11] as the benchmark dataset for the current study. The reasons doing so are as follows. (1) The dataset was constructed specialized for Gram-negative bacterial proteins and it can cover 8 subcellular location sites; compared with the other datasets such as the one in PSORTb v.2.0 [6] that only covered 5 subcellular locations, the coverage scope of the dataset from [11] is much wider. (2) None of proteins included in has pairwise sequence identity to any other in a same subcellular location; compared with most of the other benchmark datasets in this area, the dataset is much more rigorous in excluding homology bias and redundancy. (3) It contains both singleplex and multiplex proteins and hence can be used to train and test a predictor developed aimed at being able to deal with proteins with both single and multiple location sites. (4) Using the dataset will also make it easier to compare the new predictor with the existing one because the tested results by Gneg-mPLoc on have been well documented and reported [11].

The dataset contains 1,392 Gram-negative bacterial protein sequences, of which 1,328 belong to one subcellular location, 64 to two locations, and none to three or more locations. The dataset covers 8 subcellular locations (Fig. 1), as can be formulated by(1)where represents the subset for the subcellular location of cell inner membrane, for cell outer membrane, for cytoplasm, for extracellular, and so forth (Table 1); while represents the symbol for “union” in the set theory. To avoid homology bias and redundancy, none of the proteins in has pairwise sequence identity to any other in a same subset. For convenience, hereafter let us just use the subscripts of Eq.1 as the codes of the 8 location sites; i.e., “1” for “cell membrane”, “2” for “cell wall”, “3” for “chloroplast”, and so forth (Table 2).

For readers' convenience, the corresponding accession numbers and protein sequences in are given in Supporting Information S1.

Note that because some proteins may occur in two or more locations, the 1,392 Gram-negative proteins actually correspond to 1,456 locative proteins. The concept of “locative proteins” was introduced for studying proteins with multiple subcellular location sites, as elaborated in [2].

To develop a powerful method for statistically predicting protein subcellular localization according to the sequence information, one of the most important things is to formulate the protein sequences with an effective mathematical expression that can truly reflect the intrinsic correlation with their subcellular localization [14]. However, it is by no means an easy job to realize this because this kind of correlation is usually deeply “buried” or hidden in piles of complicated sequences.

The most straightforward method to formulate the sample of a query protein was just using its entire amino acid sequence, as can be generally written by(2)where represents the 1^st residue of the protein , the 2^nd residue, …, the residue, and they each belong to one of the 20 native amino acids. In order to identify its subcellular location(s), the sequence-similarity-search-based tools, such as BLAST [16], [17], was utilized to search protein database for those proteins that have high sequence similarity to the query protein . Subsequently, the subcellular location annotations of the proteins thus found were used to deduce the subcellular location(s) for . Unfortunately, although it was quite intuitive and able to contain the entire information of a protein sequence, this kind of straightforward sequential model failed to work when the query protein did not have significant sequence similarity to any location-known proteins.

Thus, various non-sequential or discrete models to formulate protein samples were proposed in hopes to establish some sort of correlation or cluster manner by which the prediction quality could be improved.

Among the discrete models for a protein sample, the simplest one is its amino acid (AA) composition or AAC [18]. According to the AAC-discrete model, the protein of Eq.2 can be formulated by [19], [20](3)where are the normalized occurrence frequencies of the 20 native amino acids in protein , and the transposing operator. Many methods for predicting protein subcellular localization were based on the AAC-discrete model (see, e.g., [19], [21], [22], [23], [24]). However, as we can see from Eq.3, if using the ACC model to represent the protein , all its sequence-order effects would be lost, and hence the prediction quality might be limited.

To avoid completely lose the sequence-order information, the pseudo amino acid composition (PseAAC) was proposed to represent the sample of a protein, as formulated by [25](4)where the first 20 elements are associated with the 20 elements in Eq.3 or the 20 amino acid components of the protein , while the additional factors are used to incorporate some sequence-order information via a series of rank-different correlation factors along a protein chain. For a brief introduction about PseAAC, please see a Wikipedia article at http://en.wikipedia.org/wiki/Pseudo_amino_acid_composition.

According to [14], the PseAAC for a protein can be generally formulated as(5)where the subscript is an integer, and its value as well as the components , , … will depend on how to extract the desired information from the amino acid sequence of (cf. Eq.2). As a general form, Eq.5 can cover various different modes of PseAAC. For example, when its elements are given by(6)we immediately obtain the formulation of PseAAC as originally introduced in [25], where the meanings for , , and were clearly elaborated and hence there is no need to repeat here.

Below, let us use the general form of PseAAC (Eq.5) to find the formulations to reflect the core and essential features of protein samples that are closely correlated with their subcellular localization.

In statistical prediction, it would be meaningless to simply report a success rate of a predictor without specifying what method and benchmark dataset were used to test its accuracy [14]. As is well known, the following three methods are often used to examine the quality of a predictor: independent dataset test, subsampling test, and jackknife test [36]. Owing to that subsampling test and jackknife test can be performed with one benchmark dataset and that independent dataset test can be treated as a special case of subsampling test, one benchmark dataset would suffice to serve all the three kinds of cross-validation. However, as demonstrated by Eq.1 of [37] and elucidated in [2], among the three cross-validation methods, the jackknife test is deemed the least arbitrary that can always yield a unique result for a given benchmark dataset and hence has been widely recognized and increasingly used to examine the power of various predictors (see, e.g., [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56]). Accordingly, in this study, the jackknife test will be adopted to evaluate the power of iLoc-Gneg as well.

However, even if using the jackknife test to examine the accuracy, a same predictor may still yield obviously different success rates when tested by different benchmark datasets. This is because the more stringent of a benchmark dataset in excluding homologous sequences, the more difficult for a predictor to achieve a high success rate. Also, the more number of subsets (subcellular locations) a benchmark dataset covers, the more difficult to achieve a high overall success rate, as elaborated in a recent review [14].

As mentioned in the Materials section, the benchmark dataset used in this study is (cf. Supporting Information S1), which is the same benchmark dataset constructed in [11] for Gneg-mPLoc.

Actually, for such a dataset containing both single-location and multiple-location Gram-negative proteins distributed among 8 subcellular location sites, so far only one existing predictor, i.e., Gneg-mPLoc [11], had the capacity to deal with it. Therefore, to demonstrate the power of the current predictor, it would suffice to just compare iLoc-Gneg with Gneg-mPLoc [11].

Listed in Table 2 are the results obtained with Gneg-mPLoc [11] and iLoc-Gneg on the aforementioned benchmark dataset by the jackknife test. As we can see from Table 2, for such a stringent and complicated benchmark dataset, the overall success rate achieved by iLoc-Gneg is over 91.4%, which is about 6% higher than that by Gneg-mPLoc [11].

Note that during the course of the jackknife test by Gneg-mPLoc and iLoc-Gneg, the false positives (over-predictions) and false negatives (under-predictions) were also taken into account to reduce the scores in calculating the overall success rate. As for the detailed process of how to count the over-predictions and under-predictions for a system containing both single-location and multiple-location proteins, see Eqs.43–48 and Fig. 4 in a comprehensive review [2].

To provide a more intuitive and easier-to-understand measurement, let us introduce a new scale, the so-called “absolute true” success rate, to reflect the accuracy of a predictor, as defined by(26)where represents the absolute true rate, the number of total proteins investigated, and(27)According to the above definition, for a protein belonging to, say, two subcellular locations, if only one of the two is correctly predicted, or the predicted result contains a location not belonging to the two, the prediction score will be counted as 0. In other words, when and only when all the subcellular locations of a query protein are exactly predicted without any underprediction or overprediction, can the prediction be scored with 1. Therefore, the absolute true scale is much more strict and harsh than the scale used previously [2], [11] in measuring the success rate. However, even if using such a stringent criterion on the same benchmark dataset by the jackknife test, the overall absolute true success rate achieved by iLoc-Gneg was 1252/1392 = 89.9%.

Why can iLoc-Gneg enhance the success rate so remarkably? One of the key reasons is that the GO formulation for protein samples in iLoc-Gneg contains more information than that in Gneg-mPLoc [11], as elaborated as follows. For example, for the protein with the access number “P0A8U0” as denoted by , according to Steps 3 and 4 in the Section of “GO (Gene Ontology) Formulation”, we found 47 proteins that were homologous to it; i.e., . Each of the 47 homologous proteins hit GO:0005886 (or GO_compress:00277) and GO:0016020 (or GO_compress:00830), and hence the two GO numbers were hit by a total of 47 times. Only one of the 47 proteins hit GO:0005737 (or GO_compress: 00269). Substituting these data into Eqs.8–9, we have(28)In contrast, if the same protein was represented according to the formulation in Gneg-mPLoc [11], it would be(29)It can be seen by a comparison of Eq.28 with Eq.29 that although the elements in the 269^th, 277^th, and 830^th components are all not zero in both formulations, the differences of their weights are completely ignored in Eq.29 as formulated in Gneg-mPLoc [11]. That is also why, when the sequence of was inputted into iLoc-Gneg and Gneg-mPLoc [11] as a query protein for prediction, the former could accurately predict its both location sites (“cell inner membrane” and “cytoplasm”), while the latter could predict only one site (“cell inner membrane”) but miss the site of “cytoplasm”.