Predicting subcellular localization of multisite proteins using differently weighted multi-label k-nearest neighbors sets

1.Introduction

Proteins are more complex and diverse than the DNA sequence that generates them. As protein subcellular localization (PSL) is highly correlated with protein function, effective PSL prediction methods provide information for understanding protein functions that is essential for several research applications such as in molecular biology [1, 2], cell biology [3, 4], and neuroscience [5], as well as in clinical medicine [6, 7, 8]. The prediction and recognition of PSL using bioinformatics methods is one of the fundamental objectives of proteomics and cell biology [9], as PSL information is crucial for discovering protein functions toward helping to understand the complex cellular pathways involved in the process of biological regulation.

In recent decades, high-throughput molecular biology technologies have brought about exponential growth in the number of protein sequences identified. Considering the vast amount of molecular data now available and continuously accumulating, it is vital to develop a fast and available method for identifying the subcellular locations of their sequence information [10, 11, 12, 13]. The basic requirement for a cell to function normally is that the proteins operate in specific subcellular positions [14]. The main limitations of current methods of predicting PSL is that they cannot handle information on multiple proteins simultaneously. Thus, new prediction methods must be able to predict both single- and multiple-point PSLs.

Since a given feature extraction method and dataset will yield different results depending on the prediction algorithm applied, we here propose a new method for extracting protein subcellular information using a feature fusion technique. Feature extraction methods including the entropy density and pseudo amino acid composition (PseAAC) are typically used for protein coding. Considering these two feature extraction methods, we used the multi-label k-nearest neighbors (ML-KNN) algorithm and assigned diverse weights to various attributes for predicting multiplex PSL. We then evaluated the developed algorithms using a variety of well-established performance indexes.

2.Materials and method

2.3Algorithm

To guarantee the accuracy of PSL, a machine-learning algorithm must first be carefully designed. Although there are many algorithms available for predicting PSL, most of these focus only on a single subcellular location of a protein sequence, and cannot handle proteins located at multiple sites. With the increase in the discovery of multisite proteins, it is vital to obtain a fast and convenient method to recognize the subcellular location of proteins that do not have specific features. Here, we explored the use of the ML-KNN algorithm for this purpose, which is known to be beneficial for multi-label learning problems [20, 21, 22, 23]. In a test case t, ML-KNN should identify the K nearest neighbors N⁢(t) within the training set. H1l signifies that t has label l, whereas H0l signifies that t does not have label l. Moreover, the event that exactly j cases among the K nearest neighbors of t have label l is denoted by Ejl. Let y→ be the class vector of x. If l∈Y, then the l-th unit y→x⁢(l) is 1; otherwise, it is 0. The expression of N⁢(x) is similar to N⁢(t). Therefore, according to the neighbor set of tags, the membership count vector can be expressed as:

(10)

C→x⁢(l)=∑a∈N⁢(x)y→a⁢(l),l∈y

where C→x⁢(l) represents the serial number of neighbors of x at the l-th level.

Specifically, the prior probability of all labels is calculated based on whether they are training samples or test samples:

(11)

P⁢(H1l)=s+∑i=1myxi⁢(l)→s×2+m

(12)

P⁢(H0l)=1-P⁢(H1l)

Next, the Bayesian rule is used to compute the posterior probabilities:

(13)

P(Ejl|H1l)=s+c⁢[j]s×(k+1)+∑p=0kc⁢[p]

(14)

P(Ejl|H0l)=s+c′⁢[j]s×(k+1)+∑p=0kc′⁢[p]

where c⁢[j] is the number of instances in which there are exactly j samples labeled l within the k nearest neighbors in the training set; c′⁢[j] is similar to c⁢[j], except that j denotes unlabeled samples.

Finally, we compute the maximum posterior probability using the following two equations:

(15)

y→t(l)=argmaxb∈{0,1}P(Hbl)P(EC→t⁢(l)l|Hbl)

(16)

r→t⁢(l)=P(H1l)P(EC→t⁢(l)l|H1l)∑b∈{0,1}P(Hbl)P(EC→t⁢(l)l|Hbl)

However, the uneven features in the training set will lead to relatively low accuracy. Thus, we developed an improved algorithm to assign suitable weights to each attribute [24]. The weighting factors wt are defined as:

(17)

wt=log⁡(a+𝐴𝑣𝑔𝑁𝑢𝑚𝑁𝑢𝑚⁢(Ct))log⁡(a+1)(1<t<N)

(18)

a=𝑀𝑎𝑥𝑁𝑢𝑚𝐴𝑣𝑔𝑁𝑢𝑚

Figure 1.

Flowchart of the prediction algorithm.

where AvgNum represents the average number of different categories of samples and 𝑁𝑢𝑚⁢(Ct) represents the number of samples in class Ct. This novel ML-KNN method considering weighted prior probabilities was named wML-KNN. A flowchart of the prediction algorithm is shown in Fig. 1.

3.Results

The feature extraction algorithm affects the final accuracy. In this study, the effect of using the entropy density and PseAAC feature extraction methods was examined. The ML-KNN and wML-KNN methods were both applied for comparison of results. The feature fusion method, with simple addition of dimensions, was also used. Overall, better results were obtained when k= 1.

As shown in Tables 1 and 2, the entropy density and PseAAC feature extraction methods wML-KNN showed better performance than ML-KNN in each evaluation measurement. Moreover, the wML-KNN algorithm achieved better performance than ML-KNN for each evaluation criterion.

The comparative results presented in Tables 3 and 4 suggest that using wML-KNN increases the absolute-true rate by approximately 20%. Thus, the same feature extraction algorithm applied to the same dataset gives different results simply by including weight values within the ML-KNN algorithm. Similar changes in the absolute-true rate were observed with both feature extraction algorithms, indicating that the wML-KNN algorithm provides better prediction accuracy.

4.Discussions

Previous PSL prediction studies largely focused on proteins with localization at a single site. Since the discovery of the phenomenon that several proteins have two or more subcellular sites, more attention has been paid to developing multisite subcellular localization prediction and related algorithms. As a multi-label learning method with good generalization ability, the ML-KNN algorithm achieved remarkable results in multisite subcellular localization prediction. Furthermore, using various feature extraction methods and adopting the wML-KNN prediction algorithm can achieve higher accuracy than reported in other studies. For example, using different fusion feature extraction methods, Qu et al. [13] adopted the ML-KNN algorithm to predict multisite subcellular localization in the Gpos-mploc protein dataset, and obtained the best overall accuracy rate of 66.1568%. Lin et al. [9] used ML-KNN as the prediction algorithm to predict a benchmark animal protein dataset and finally obtained an accuracy of 62.88%. Practically, one dataset often contains proteins with both single-site and multisite subcellular localizations. This imbalance in a dataset will inevitably influence the efficiency of the ML-KNN algorithm. Therefore, as an improved version of ML-KNN, we developed the wML-KNN algorithm to reduce the negative effects of this data imbalance in part and to achieve relatively higher prediction accuracy.

The ultimate purpose of studying multisite PSL is to understand a protein’s intrinsic function and obtain new insight into the nature of life. However, to date, the prediction of PSL has stagnated at the theoretical and experimental level. Despite the higher prediction accuracy obtained by adopting our proposed method, more research will be needed combining the results obtained in this study to link the theory to practice in this field. The following details should be considered as a preliminary analysis. First, more standardized protein datasets should be constructed to reduce the imbalance of data and the universality of related algorithms. Second, the entropy density and PseAAC are both effective local feature extraction methods. Thus, effective fusion methods of multiple features is expected to further improve the prediction accuracy. Moreover, the fusion of global and local protein physicochemical features, beyond information of the protein image, may bring breakthroughs in this field. Finally, just as important as the improvement of prediction accuracy described herein, it will be necessary to derive a plausible biological explanation for the results, which can facilitate application of the PSL theory into practice and should be a primary focus of the further work in this field.