Protein Annotation from Protein Interaction Networks and Gene Ontology

Abstract

We introduce a novel method for annotating protein function that combines Naïve Bayes and association rules, and takes advantage of the underlying topology in protein interaction networks and the structure of graphs in the Gene Ontology. We apply our method to proteins from the Human Protein Reference Database (HPRD) and show that, in comparison with other approaches, it predicts protein functions with significantly higher recall with no loss of precision. Specifically, it achieves 51% precision and 60% recall versus 45% and 26% for Majority and 24% and 61% for χ²–Statistics, respectively.

1. Introduction

Understanding protein function is one of the most challenging problems in biology. While many genome sequences have been generated, a large fraction of the newly discovered genes lack functional characterization. This is particularly true for higher eukaryotes. While many experimental approaches, including both individual protein or gene-specific efforts and large scale, whole-genome projects, are used successfully, these are time consuming and expensive. Large scale, computational methods to predict protein function, therefore, can potentially play important roles.

Early computational methods inferred functions of novel proteins from their amino acid sequence similarity to proteins of known function [1] or from observations of pairs of interacting proteins that had orthologs in another organism fused into a single protein chain [2]. Correlated evolution, correlated RNA expression patterns, plus patterns of domain fusion, have also been used to predict similarities in protein functions [3,4]. Several other approaches have annotated proteins based on phylogenetic profiles of orthologous proteins [5–9]. Bayesian reasoning was used to combine large-scale yeast two-hybrid (Y2H) screens and multiple microarray analyses [10] and Support Vector Machines were used to combine protein sequence and structure data [11] to produce functional predictions. Other methods related features extracted from protein 3D structures to function [12,13]. Recently, a consensus method, GOPred [14] predicted protein function by combining three different classifiers, namely, BLAST k-nearest neighbor, Subsequence Profile Map and Peptide statistics combined with support vector machine. While each of these approaches has had some success, generally they produce high false positive rates because their underlying principles/assumptions are valid for only a small number of proteins [15,19]. In addition, many methods were appropriate largely for prokaryotic sequences [15].

Protein-protein interaction (PPI) data have proven valuable for inferring protein function from functions of interaction partners. Facilitating this work, whole genome interaction data have been and/or are being generated for E. coli, yeast, worm, fly and human [16–24]. The curated databases consolidate these datasets [25–29] that have been used by several methods. The Majority method annotated yeast proteins based on the most frequent functional properties of nearest neighbors [19]. However, because the whole network was not considered, a function that occurred at a very high frequency was not annotated when it did not occur in the nearest neighbor set. In an approach that extended the Majority method, functions were annotated by exploiting indirect neighbors and using a topological weight [30], and χ²–statistics were used to look at all proteins within a particular radius, although it did not consider any aspect of the underlying topology of the PPI network [31]. FunctionalFlow considered each protein as a source of functional flow for its associated function, which spread through the neighborhoods of the source [35]. Proteins receiving the highest amount of flow of a function were assigned that function. This algorithm did not take into account the indirect flow of functions to other proteins after labeling them. Markov random fields (MRF) and belief propagation in PPI networks were combined to assign protein functions based on a probabilistic analysis of graph neighborhoods [32–34]. This assumed that the probability distribution for the annotation of any node was conditionally independent of all other nodes, given its neighbors. These methods were sensitive to the neighborhood size and the parameters of the prior distribution. The MRF methods were later extended by combining PPI data, with gene expression data, protein motif information, mutant phenotype data, and protein localization data to specify which proteins might be active in a given biological process [36,37]. Other global approaches integrated PPI network with more heterogeneous data sources (such as large-scale two-hybrid screens and multiple microarray analyses) [10,38]. Our algorithm ClusFCM [39] assigned biological homology scores to interacting proteins and performed agglomerative clustering on the weighted network to cluster the proteins by known functions and cellular location; functions then were assigned to proteins by a Fuzzy Cognitive Map. PRODISTIN formulated a distance function (the Czekanowski-Dice distance) that uses information on shared interactome to mirror a functional distance between proteins [15]. Other approaches predicted protein functions via the patterns found among neighbors of proteins within a network [40,41]. Recently, a network-based method combined the likelihood scores of local classifiers with a relaxation labeling technique [42]. Several approaches applied clustering algorithms to PPI networks to predict functional modules, protein complexes and protein functions, however, the performance of these algorithms differs substantially when run on the same network which leads to uncertainties regarding the reliability of their results [43].

Here, we extend our previous work [44] by exploring the hierarchical structure of the Gene Ontology database. For each of protein, a predicted function will be considered as a true positive if the function is a parent of any function in the annotated set of the protein. Thus, this work is a less conservative approach than our previous work. We use Naïve Bayes combined with association rules and take into account the underlying topology of a PPI network. Predicted functions are analyzed by association rules to discover relationships among the assigned functions, i.e., when one set of functions occurs in a protein then the protein may be annotated with an additional set of other specific functions at some confidence level. We test our method on human protein data and compare its performance with the Majority [19] and χ2 statistics [31] methods.

2. Materials

Gene Ontology (GO) database

The Gene Ontology (GO) [45] was established to provide a common language to describe aspects of the biology of a gene product. The use of a consistent vocabulary allows genes from different species to be compared based on their GO annotations. GO terms are composed of the three structured controlled vocabularies (ontologies): the molecular function of gene products, their associated biological processes, and their physical location as cellular components. Each ontology is constructed as a directed acyclic graph through a parent-child “is-a” relationship (see Figure 1). We used the GO database (version 1.1.940 released 1/2010).

Fig. 1.

A hierarchical structure of GO terms: many-to-many parent-child relationships are allowed in the ontologies. A gene may be annotated to any level of ontology, and to more than one term within an ontology [45].

Human interaction dataset

The human interaction data were retrieved from HPRD [29] (release 7/2009). The entire dataset contains 38,788 direct molecular interactions from three types of experiments (in vivo, in vitro, and in Y2H). There are 9,630 distinct proteins annotated with 433 GO functions in the three categories. Because some estimates suggest that more than half of all current Y2H data are spurious [46,47], we first excluded interactions supported only by the Y2H experiments, leaving 29,557 interactions from in vivo and in vitro experiments, and 422 GO functions annotating the 7,953 unique proteins. A more recent study showed that Y2H data for human proteins were actually more accurate than literature-curated interactions supported by a single publication. Therefore, we also separately analyzed the complete HPRD PPI dataset.

Note that we use the “is-a” relationships to eliminate all parent GO terms annotated for a protein, i.e. suppose there are two GO terms A and B annotated for a protein, and if A “is-a” B, then B is removed from the annotated GO terms of the protein.

3. Methods

3.1 Notation

• G=(V,E): an undirected graph to define the PPI network, where V is a set of proteins and E is a set of edges connecting proteins u and v if the corresponding proteins interact physically;

• K: the total number proteins in the PPI network

• F: the whole GO function collection set and |F|: the cardinality of the set F

• f_i: a function in the set F (i=1‥|F|)

• O(f_i) is the parent ontology set of f_i, that is ∀g∈O, f_i “is-a” g

• C_u: the cluster coefficient of protein u

• N_u: the neighbor set of protein u (proteins interacting directly with protein u)

• $N_u^{f_i}$: the number of proteins annotated with function f_i in N_u and $N_u^{{\overline{f}}_i}$: the number of proteins un-annotated with function f_i in N_u where $|N_u|=N_u^{f_i}+N_u^{{\overline{f}}_i}$.

3.2 Posing the Problem: From Annotation to Classification

For a function of interest f_i, we want to annotate the function f_i to the proteins in a PPI network. We pose the functional annotation problem as a classification problem. The training data are in the form of observations d ∈ R^k (k dimensions) and their corresponding class information. For each protein u in the network, a function of interest f_i is considered as a class label 1 if the protein u is annotated with f_i, and otherwise as 0. The features to deduce class information are selected as follows. Exploiting the fact that proteins of known functions tend to cluster together [19], the first feature we take into account, A₁, is the number of proteins annotated with the function f_i in the neighborhood set of protein u (i.e. $A_1=N_u^{f_i}$). The second feature (A₂) is the number of proteins not annotated with the function f_i in the neighborhood set of the protein u (i.e. $A_2=N_u^{{\overline{f}}_i}$). Several studies indicate that other features can be useful to predict functions and drug targets for a protein, such as the number of functions annotated in proteins in the neighborhood set at level 2 of the protein [31], the connectivity (the total number of incoming and outgoing arcs of a protein, which is equal to $N_u^{f_i}+N_u^{{\overline{f}}_i}$), the betweenness (the number of times a node appears in the shortest path between two other nodes) and the clustering coefficient C_u (the ratio of the actual number of direct connections between the neighbors of protein u to the maximum possible number of such direct arcs between its neighbors) [48]. To select the best features for a robust learning method, we use a feature selection method. First, we form a sub set, S, containing two features: $A_1=N_u^{f_i}\text{ and }{A}_2=N_u^{{\overline{f}}_i}$. Second, we perform a heuristic search by iteratively adding one feature at a time to the set S (without using class information) to form a new subset, S’. Next, we classify the HPRD data with the selected S’ features by the Radial Basis Function, Support Vector Machine, Logistic Regression and Naïve Bayes. The feature to be added to S’ is the feature that achieves the maximum average value of the harmonic mean of the four classification methods. The heuristic search terminates when the average of the harmonic mean of the four methods does not increase. At the end of this process we came up with three selected features, namely, $A_1=N_u^{f_i},A_2=N_u^{{\overline{f}}_i}$ and A₃=C_u. We use Weka [49] to implement the four classifiers with default parameters. Performance in terms of recall, precision, and harmonic mean of the four classifiers on the HPRD data using the three selected features using 10-fold cross validation is shown in Table 1. Because Naïve Bayes performs the best in terms of the harmonic mean, we use it in our predictive modeling.

Table 1.

Performance of the Radial Basic Function, Support Vector Machine, Logistic Regression and Naïve Bayes methods on the HPRD data set using 10-fold cross validation.

	Precision	Recall	Harmonic Mean
Radial Basis Function	0.63	0.11	0.19
Support Vector Machine	0.81	0.04	0.09
Logistic Regression	0.68	0.15	0.24
Naïve Bayes	0.53	0.27	0.36

3.3 Predictive modeling

Phase I: Naïve Bayes

If d=<A₁, A₂, A₃> is an observation for a protein u, we decide a class membership for the observation d (corresponding to a function of interest f_i) by assigning d to the class with the maximal probability computed as follows:

$$\mu \mathit{(}d,f_i\mathit{)}\mathrm{\alpha }{\mathit{\text{argmax}}}_{c\in \mathit{\{}\mathit{0},\mathit{1}\mathit{\}}}\widehat{P}\mathit{(}c|d,f_i\mathit{)}\mathrm{\alpha }{\mathit{\text{argmax}}}_{c\in \mathit{\{}\mathit{0},\mathit{1}\mathit{\}}}\frac{\widehat{P}\mathit{(}d|c,f_i\mathit{)}\widehat{P}\mathit{(}c|f_i\mathit{)}}{\widehat{P}\mathit{(}d|f_i\mathit{)}}$$ (1)

Note that P(d | f_i) can be ignored because it is the same for all classes:

$$\mu \mathit{(}d,f_i\mathit{)}\propto {\mathit{\text{argmax}}}_{c\in \{0,1\}}\widehat{P}(d|c,f_i)\widehat{P}(c|f_i)$$ (2)

The likelihood P(d | c, f_i) is the probability of obtaining the observation d for a protein u in class c and is calculated as:

$$\widehat{P}\mathit{(}d|c,f_i\mathit{)}=\mathit{(}{N}_u^{f_i}+N_u^{{\overline{f}}_i}+C_u\mathit{)}\mathit{!}\frac{\widehat{P}{\mathit{(}{A}_{\mathit{1}}|c,f_i\mathit{)}}^{N_u^{f_i}}}{N_u^{f_i}\mathit{!}}\frac{\widehat{P}{\mathit{(}{A}_{\mathit{2}}|c,f_i\mathit{)}}^{N_u^{{\overline{f}}_i}}}{N_u^{{\overline{f}}_i}\mathit{!}}\frac{\widehat{P}{\mathit{(}{A}_{\mathit{3}}|c,f_i\mathit{)}}^{C_u}}{C_u\mathit{!}}$$ (3)

Thus equation (2) becomes:

$$\mu \mathit{(}d,f_i\mathit{)}\propto {\mathit{\text{argmax}}}_{c\in \mathit{\{}\mathit{0},\mathit{1}\mathit{\}}}\mathit{(}{N}_u^{f_i}+N_u^{{\overline{f}}_i}+C_u\mathit{)}\mathit{!}\frac{\widehat{P}{\mathit{(}{A}_{\mathit{1}}|c,f_i\mathit{)}}^{N_u^{f_i}}}{N_u^{f_i}\mathit{!}}\frac{\widehat{P}{\mathit{(}{A}_{\mathit{2}}|c,f_i\mathit{)}}^{N_u^{{\overline{f}}_i}}}{N_u^{{\overline{f}}_i}\mathit{!}}\frac{\widehat{P}{\mathit{(}{A}_{\mathit{3}}|c,f_i\mathit{)}}^{C_u}}{C_u\mathit{!}}\widehat{P}\mathit{(}c|f_i\mathit{)}$$ (4)

Because the factorials in equation (4) are constant, we can rewrite the maximum a posteriori class c as follows:

$$\mu \mathit{(}d,f_i\mathit{)}\propto {\mathit{\text{argmax}}}_{c\in \mathit{\{}\mathit{0},\mathit{1}\mathit{\}}}\widehat{P}{\mathit{(}{A}_{\mathit{1}}|c,f_i\mathit{)}}^{N_u^{f_i}}\widehat{P}{\mathit{(}{A}_{\mathit{2}}|c,f_i\mathit{)}}^{N_u^{{\overline{f}}_i}}\widehat{P}{\mathit{(}{A}_{\mathit{3}}|c,f_i\mathit{)}}^{C_u}\widehat{P}\mathit{(}c|f_i\mathit{)}$$ (5)

Two key issues arise here. First, the problem of zero counts can occur when given class and feature values never appear together in the training data. This can be problematic because the resulting zero probabilities will eliminate the information from all other probabilities. We use the Laplace correction to avoid this [50]. Second, in equation (5), the conditional probabilities are multiplied and this can result in a floating point underflow. Therefore, it is better to perform the computations using logarithms of the probabilities. Equation (5) then becomes:

$$\mu \mathit{(}d,f_i\mathit{)}\propto {\mathit{\text{argmax}}}_{c\in \mathit{\{}\mathit{0},\mathit{1}\mathit{\}}}\mathit{\text{ exp }}\mathit{[}{N}_u^{f_i}\mathit{\text{ log }}\widehat{P}\mathit{(}{A}_{\mathit{1}}|c,f_i\mathit{)}+N_u^{{\overline{f}}_i}\mathit{\text{ log }}\widehat{P}\mathit{(}{A}_{\mathit{2}}|c,f_i\mathit{)}+C_u\mathit{\text{ log }}\widehat{P}\mathit{(}{A}_{\mathit{3}}|c,f_i\mathit{)}\mathit{]}\widehat{P}\mathit{(}c|f_i\mathit{)}$$ (6)

The parameters of the model, in our case, P̂(A₁ | c, f_i), P̂ (A₂ | c, f_i), P̂ (A₃ | c, f_i) and P̂(c | f_i) can be estimated as follows:

$$\widehat{P}\mathit{(}{A}_{\mathit{1}}|c=\mathit{1},f_i\mathit{)}=\mathit{(}{\displaystyle \sum }{N}_u^{f_i}+{\mathit{\text{lc}}}_{\mathit{1}}\mathit{)}/\mathit{(}{\displaystyle \sum }{N}_u^{f_i}+N_u^{{\overline{f}}_i}+C_u+{\mathit{\text{lc}}}_{\mathit{1}}\mathit{)}\mathit{\text{ where }}u\in \mathit{\{}\mathit{\text{proteins annotated with}}{f}_i\mathit{\}}$$ (7)

$$\widehat{P}\mathit{(}{A}_{\mathit{1}}|c=\mathit{0},f_i\mathit{)}=\mathit{(}{\displaystyle \sum }{N}_u^{f_i}+{\mathit{\text{lc}}}_{\mathit{1}}\mathit{)}/\mathit{(}{\displaystyle \sum }{N}_u^{f_i}+N_u^{{\overline{f}}_i}+C_u+{\mathit{\text{lc}}}_{\mathit{1}}\mathit{)}\mathit{\text{ where }}u\in \mathit{\{}\mathit{\text{proteins not annotated with}}{f}_i\mathit{\}}$$ (8)

$$\widehat{P}\mathit{(}c=\mathit{1}|f_i\mathit{)}=\mathit{(}|\mathit{\text{proteins annotated with}}{f}_i|+{\mathit{\text{lc}}}_{\mathit{1}}\mathit{)}/\mathit{(}K+{\mathit{\text{lc}}}_{\mathit{2}}\mathit{)}$$ (9)

$$\widehat{P}\mathit{(}c=\mathit{0}|f_i\mathit{)}=\mathit{(}|\mathit{\text{proteins not annotated with}}{f}_i|+{\mathit{\text{lc}}}_{\mathit{1}}\mathit{)}/\mathit{(}K+{\mathit{\text{lc}}}_{\mathit{2}}\mathit{)}$$ (10)

where lc₁=1 and lc₂=2 are the Laplace corrections and the attributes A₂ and A₃ can be similarly estimated.

Phase II: Association Rules

Association rules are statements of the form {f_X} => {f_Y}, meaning that if we find all of {f_X} in a protein, we have a good chance of finding {f_Y} with some user-specified confidence (derived as an estimate of the probability P({f_Y} | {f_X})) and support (the fraction of proteins that contain both functions {f_X} (in the antecedent) and {f_Y} (in the consequent) of the rule in the entire network). With 0.1% support and 75% confidence thresholds, we found 900 association rules in the HPRD, and 1,154 rules in the HPRD without Y2H. For example, the rule GO:0004894 → GO:0006955 was found with 100% confidence. Next, we derive new functions from the predicted functions in Phase I by using the mined rules and the following axioms [52]:

1. if X ⊇ Y then X → Y,

2. if X → Y then XZ → YZ for any Z, and

3. if X → Y and Y → Z then X → Z.

Below we briefly describe the Majority and χ2 statistics methods used in comparisons.

Majority

For each protein u in a PPI network, we count the number of times each function f_i ∈ F occurs in neighbors of the protein u. The functions with the highest frequencies are assigned to the query protein u.

χ2 statistics

For each function of interest f_i we derive the fraction π_fi (number of proteins annotated with function f_i / K). Then, we calculate e_fi as the expected number for a query protein u annotated with f_i: e_fi = N_u π_fi. The query protein u is annotated with the function with the highest χ2 value among the functions of all proteins in its neighbors, where $\mathrm{\chi }2={(N_u^{f_i}-e_{f_i})}^2/e_{f_i}$.

The assessment of the proposed method, Majority and χ2 statistics, which takes into account the many-to-many relationships of GO terms, is performed as follows. For a protein, a predicted function will be i) a true positive if it exists in the annotated functions or the set O(annotated functions), and ii) a false positive if it does not exists in the annotated set. A function existing in the annotated set but not existing in the predicted set will be considered as a false negative while functions in the entire GO set not existing in both annotated and predicted sets will be true negatives.

4. Results and Discussions

We implement our method in Java as a combination of Naïve Bayes and the association rule algorithm. In addition, we implement the Majority and χ2 statistics methods and test all on the HPRD data (with and without interactions identified by Y2H). To compare the performance of our method we use implicit thresholds, τ. We normalize the posterior probability of a query protein u annotated with the function f_i: P(c=1| d, f_i) and decide the protein u to be annotated with the function f_i if the normalized P(c=1| d,f_i) > τ, where τ assumes a value between 0 and 1, in increments of 0.1.

Our method assumes that a newly annotated protein propagates its newly acquired function(s) to its direct neighbors. Thus, the method is repeated in two iterations. In the second iteration, to calculate the value $A_1=N_u^{f_i}$ for a protein u, we count both the number of proteins in its neighborhood annotated with f_i and predicted with f_i in the first iteration. In the Majority and χ2 statistics methods top k functions having the highest scores (k ranges from 0, 1, … 20) are selected and those functions are assigned to the query protein.

We use the leave-one-out method to evaluate the predictions. For each query protein u in a PPI network we assume that it is not annotated. Then, we the methods described above to predict protein functions for protein u. For each method, we choose the threshold which yields the highest Matthews Correlation Coefficient (MCC) values. Figure 2 shows the relationship between precision and recall using different thresholds for the normalized probabilities of query proteins on the HPRD data sets. The threshold resulting in the highest MCC measures for the HPRD and HPRD without Y2H data sets is 0.3. Because functional annotations for proteins are incomplete at present, a protein may have a function that has not yet been experimentally detected. Our goal is to decrease the number of annotated functions that are not predicted and increase the number of predicted functions that are actually annotated. The fact that the values of recall are always higher than the values of precision in all datasets increases confidence in our method.

Fig. 2.

Precision and recall results of our method on a) the HPRD network data and b) HPRD without two-hybrid network data.

The Figure 3 shows that, for any precision, the recall of our method outperforms Majority and χ2 statistics. Performance measures of the three methods are shown in Table 2. Our method performs equally well in both data sets. To gauge the robustness of the algorithms’ performance (the MCC value), we use the ANOVA one-way-test for statistical significance from the leave one out cross validation. The ANOVA statistics shown in Table 3 confirm that our method indeed performed better than the compared methods.

Fig. 3.

Precision and recall of the three methods on a) the HPRD network data and b) HPRD without two-hybrid network data.

Table 2.

Performance of the three methods on two datasets using leave-one-out validation^*; (1): Our method (2): Majority (3): χ2 statistics.

	HPRD			HPRD without Y2H
	(1)	(2)	(3)	(1)	(2)	(3)
Precision	0.51	0.45	0.24	0.52	0.49	0.23
Recall	0.60	0.26	0.61	0.61	0.28	0.58
MCC	0.55	0.34	0.37	0.56	0.36	0.36

^*The selected implicit thresholds for our method, Majority, χ2 statistics are .3, 3, and 12, respectively.

Table 3.

Results from one way ANOVA test for MCC value on the two datasets; (1): Our method (2): Majority (3): χ2 statistics.

	HPRD			HPRD without Y2H
	(1)	(2)	(3)	(1)	(2)	(3)
Average	0.55	0.34	0.37	0.56	0.36	0.36
Variance	0.07	0.08	0.03	0.07	0.07	0.03
F	1841.2			1581.16
P	0			0

In addition to providing statistics tests to cement our method, it is worth noting that this work takes into account the hierarchical structure of GO database for predicting functions of a protein. If a new function of a protein exists in the set O(annotated functions) of the protein, it will be a true positive. Thus we expect to sacrifice the cost of recall (sensitivity) to increase precision. However, the performance (i.e. recall and precision) of our method was not significantly changed in comparison with our previous work. The reason is probably that in comparison with an average of 1.56 (1.77) shared functions per each interactome, there is only an average of 0.19 (0.15) functions in the O(annotated functions) per each interactome in the HPRD (HPRD without Y2H) dataset. Thus, those functions account for a minor proportion of the performance measures.

Because protein functional annotation is incomplete, it is possible that novel predicted functions that are at present false positives may eventually be discovered to be true positives. We list in Table 4 some proteins from the HPRD without Y2H dataset that are annotated with novel functions at very high probabilities (>.9). The full list of predicted functions for human proteins and Java source code are shown at http://chr21.egr.vcu.edu/bayesian

Table 4.

Novel protein functions predicted by the Naive Bayes.

HPRD ID	Symbol	Protein Name	GO Term ID	GO Name	Predicted Probability
00010	ACHE	Acetylcholinesterase	GO:0005201	extracellular matrix structural constituent	0.99
00010	ACHE	Acetylcholinesterase	GO:0004872	receptor activity	0.92
00015	ACTC1	Actin alpha, cardiac muscle	GO:0008092	cytoskeletal protein binding	1.00
00017	ACTG1	Actin gamma 1	GO:0008092	cytoskeletal protein binding	1.00
00019	ACTN2	Actinin alpha 2	GO:0005194	cell adhesion molecule activity	0.99
00019	ACTN2	Actinin alpha 2	GO:0005554	molecular_function	0.96
00021	ACVR1	Activin A receptor, type I	GO:0003924	GTPase activity	1.00
00023	PML	PML	GO:0003700	transcription factor activity	1.00
00025	ACVR2A	Activin A receptor, type II	GO:0005102	receptor binding	1.00
00030	ACTA1	Actin alpha, skeletal muscle 1	GO:0008092	cytoskeletal protein binding	1.00
00030	ACTA1	Actin alpha, skeletal muscle 1	GO:0005200	structural constituent of cytoskeleton	1.00
00032	ACTB	Actin beta	GO:0008092	cytoskeletal protein binding	1.00
00038	ADA	Adenosine deaminase	GO:0004930	G-protein coupled receptor activity	0.99
00043	ADORA2A	Adenosine A2 receptor	GO:0008092	cytoskeletal protein binding	0.92
00054	ARF1	ADP ribosylation factor 1	GO:0015457	auxiliary transport protein activity	1.00
00059	FDX1	Adrenodoxin	GO:0003824	catalytic activity	1.00
00061	ADM	Adrenomedullin	GO:0005179	hormone activity	0.96
00070	ALDOA	Aldolase 1	GO:0003824	catalytic activity	0.98
00072	A2M	Macroglobulin, alpha 2	GO:0008236	serine-type peptidase activity	0.97
00082	LRPAP1	RAP	GO:0004872	receptor activity	1.00
00097	SAA1	Serum Amyloid A1	GO:0005201	extracellular matrix structural constituent	1.00
00098	SAA2	Serum amyloid A2	GO:0005201	extracellular matrix structural constituent	0.97
00101	APCS	Serum amyloid P	GO:0004872	receptor activity	0.96
00106	AGT	Angiotensin I	GO:0008236	serine-type peptidase activity	1.00
00106	AGT	Angiotensin I	GO:0004177	aminopeptidase activity	0.96
00106	AGT	Angiotensin I	GO:0004180	carboxypeptidase activity	0.92
00113	CD19	CD19	GO:0004713	protein-tyrosine kinase activity	1.00
00113	CD19	CD19	GO:0030159	receptor signaling complex scaffold activity	0.98
00114	CD22	SIGLEC2	GO:0030159	receptor signaling complex scaffold activity	0.99
00114	CD22	SIGLEC2	GO:0004713	protein-tyrosine kinase activity	0.95
00116	CD38	Cyclic ADP ribose hydrolase	GO:0004872	receptor activity	0.97
00120	SERPINA3	Alpha 1 antichymotrypsin	GO:0008236	serine-type peptidase activity	1.00
00121	SLPI	Secretory leukocyte protease inhibitor	GO:0008236	serine-type peptidase activity	0.98
00123	SLC9A1	Solute carrier family 9, isoform A1	GO:0005509	calcium ion binding	0.93
00125	CD3EAP	Antisense ERCC1	GO:0003899	DNA-directed RNA polymerase activity	0.91
00126	IFNAR1	Interferon, alpha receptor	GO:0005125	cytokine activity	1.00
00133	APOB	Apolipoprotein B	GO:0003754	chaperone activity	1.00
00135	APOE	Apolipoprotein E	GO:0004872	receptor activity	0.98
00138	LRP1	Low density lipoprotein receptor-related protein 1	GO:0008236	serine-type peptidase activity	0.98
00139	NR2F2	Nuclear receptor subfamily 2, group F, member 2	GO:0003700	transcription factor activity	1.00
00139	NR2F2	Nuclear receptor subfamily 2, group F, member 2	GO:0030528	transcription regulator activity	1.00
00146	ARRB1	Beta arrestin 1	GO:0004930	G-protein coupled receptor activity	1.00
00147	ARRB2	Beta arrestin 2	GO:0004930	G-protein coupled receptor activity	1.00
00120	SERPINA3	Alpha 1 antichymotrypsin	GO:0008236	serine-type peptidase activity	1.00
00121	SLPI	Secretory leukocyte protease inhibitor	GO:0008236	serine-type peptidase activity	0.98
00123	SLC9A1	Solute carrier family 9, isoform A1	GO:0005509	calcium ion binding	0.93
00125	CD3EAP	Antisense ERCC1	GO:0003899	DNA-directed RNA polymerase activity	0.91
00126	IFNAR1	Interferon, alpha receptor	GO:0005125	cytokine activity	1.00
00133	APOB	Apolipoprotein B	GO:0003754	chaperone activity	1.00

5. Conclusions

We have described a novel method for protein functional annotation that combines Naïve Bayes and association rules. The method used global optimization that took into account the following features of interaction networks: direct and indirect interactions, the underlying topology (cluster coefficients), and functional protein clustering, as well as the many-to-many relationships of the GO terms in the GO database. We have shown the robustness of our method by testing it on two interaction data sets using the leave-one-out cross-validation. The results showed that our method consistently outperformed the Majority and the χ2–statistics methods in predicting protein functions. In addition, our method predicts new relationships among the predicted functions that can provide new experimental directions. Finally, in comparison with previous work, the results empirically showed that our approach does not depend on the GO’s hierarchy.