Predicting Types of Protein-Protein Interactions
Using a Multiple-Instance Learning Model
Hiroshi Yamakawa1 , Koji Maruhashi1 , and Yoshio Nakao1
Fujitsu Laboratories Ltd.
1-1, Kamikodanaka 4-chome, Nakahara-ku, Kawasaki, Kanagawa, 211-8588, Japan{ymkw, maruhashi.koji, ynakao}@jp.fujitsu.com

Abstract. We propose a method for predicting types of protein-protein
interactions using a multiple-instance learning (MIL) model. Given aninteraction type to be predicted, the MIL model was trained using interaction data collected from biological pathways, where positive bags wereconstructed from interactions between protein complexes of that type,and negative bags from those of other types. In an experiment using
the KEGG pathways and the Gene Ontology, the method successfully
predicted an interaction type (phosphorylation) to an accuracy rate of
86.1%.

1

Introduction

In recent molecular biology and its application ﬁelds including drug discovery,
analysis of protein-protein interactions (PPIs) is an emerging issue to elucidate
the mechanism of biological processes. Since PPIs play a central role in numerous
cellular processes, understanding PPIs provides us with clues to determining
potential drug targets in cases where drug targets are identiﬁed from a known
pathway related to a disease. Although a large volume of PPI data has beencollected as described later, many other unknown PPIs are believed to exist(Rhodes et al., 2005). Moreover, only a few PPIs have been elucidated at thefunctional level. In order to resolve this situation, an approach that combines
wet and dry technologies is promising, so that one might construct hypotheses
on a biological mechanism based on conﬁrmed PPI data produced by a wet
technology with plausible PPI data predicted by a dry technology.
As for PPI prediction, Rhodes et al. (2005) proposed a probabilistic methodthat integrates model organism interactome data, protein domain data, genomewide gene expression data and functional annotation data; and Lee et al. (2005)
presented an assessment scheme for the reliability of PPI candidates based on aneural network algorithm. However, the aim of these studies is discovering novel
PPIs or ﬁltering correct PPIs, not identifying the interaction types between
proteins (e.g., activation, inhibition, phosphorylation, or the like).
Although PPI types are essential in describing the mechanism of a biologicalprocess, only a few existing PPI databases provide interaction types (Ekins,
Nikolsky, and Nikolskaya, 2005). For example, the Human Protein Reference

2

Database (HPRD) (Peri et al., 2003), which is one of the most famous databases
providing a large volume of PPI data, does not provide interaction types although
it stores 33,710 entries of PPI data at the time of September 2005 and its size
continues to grow. Although the Kyoto Encyclopedia of Genes and Genomes(KEGG) database (Kanehisa and Goto, 2000) provides pathway data in terms
of protein-protein interaction networks with interaction types, the number of its
PPI entries is only several thousands.
PPI type prediction is, therefore, an important issue to understand biologicalprocesses. In this paper, we propose a method for predicting PPI types basedon a machine learning model using known PPI types provided by the KEGG
database (Kanehisa and Goto, 2000) as training data.

2

A Model of Interaction between a Protein Complex
Pair

A PPI described in existing pathways, as provided by the KEGG database(Kanehisa and Goto, 2000), often corresponds to a pair of protein complexes(see rounded rectangles in Fig. 1), each of which is composed of several subunits(simple proteins). On the other hand, functional annotations, as provided by
the Gene Ontology (Ashburner et al., 2000), have been accumulated mainly forsimple proteins.

Label
Complex L

phosphorylation

Complex R

Subunit
L-A

Subunit
R-B

Subunit
L-B

Subunit
R-C

Subunit
L-C

collection of
pairs

causal pair

Bag
Fig. 1. A MIL Bag Model for PPI Type Prediction: each rounded rectangle depicts aprotein complex; the upper block arrow depicts an interaction type (i.e., a label to belearned) between complexes; each simple arrow depicts a possible subunit pairing (i.e.,
an instance of the MIL model) and the broad arrow indicates the subunit pair that is
the only cause of the process that Complex L phosphorylates Complex R.

In other words, training data for interaction type predictions are given interms of a collection of complex pairs labeled with an interaction type (i.e., the3target variable); while available features (i.e., the input variables) for machinelearning are given for each subunit (simple protein) composing complexes. Figure 1 depicts a case where the target variable is whether the interaction type is
phosphorylation and the input variables are given for each subunit of L-A, L-B,..., and R-B.
It is diﬃcult for a standard supervised learning method to solve a problemof this kind because the relationship between the input variables and the target
variable is ambiguous. With regard to this point, we assume that the interaction type between complexes can be determined by a subunit pair across thosecomplexes. In other words, we ignore those cases, for example, where two or
more subunits of a complex work cooperatively, or where the active site of a
subunit of a complex is hidden by other subunits of that complex. Hereafter,
this assumption is referred to as the subunit reaction assumption.
This assumption can be validated based on the following discussion. Fromthe protein structure viewpoint, an interaction between a protein pair is often
explained by one or a small number of domain1 -level interactions across those
proteins. This fact suggests that an interaction between a protein complex pair
can also be reduced to just a few domain-level interactions even though it cannot
always be reduced to those of a protein pair across those complexes. In molecularbiology, target validation (e.g., validation of a hypothesis that a particular protein causes a particular disease) is often performed by knocking-out the gene that
encodes a target protein. The eﬀectiveness of this approach suggests that many
individual biological functions originate from a speciﬁc protein. Accordingly, thesubunit reaction assumption is almost as valid as the tacit assumption based on
which biologists may take the above-mentioned approach to target validation.
The assumption also has another advantage in that prediction methods basedon it are expected to predict both the interaction types of complex pairs andthose of subunit (protein) pairs, the former of which may describe the behaviorof a biological system while the latter may indicate the molecular function that
could be controlled with chemical substances (i.e., potential drugs).

3

A Method for Predicting Interaction Types Based on
Multiple Instance Learning

In this section, we propose a method for predicting PPI types based on amultiple-instance learning (MIL) scheme. As shown in Fig. 1, the PPI-type prediction task based on the subunit reaction assumption can be formalized as aproblem of MIL as follows: a complex pair (two rounded rectangles) with aninteraction type (the upper block arrow) is formulated as a labeled bag, and apossible subunit pair across a complex pair (the six simple arrows) as an instance.
1

A portion of a protein thought to have speciﬁc molecular functions and often corresponding to a characteristic sequence of amino acids.

4

3.1

Multiple-Instance Learning Scheme

Multiple-instance learning (MIL) is a scheme of semi-supervised learning forproblems with incomplete knowledge concerning the labels of the training data.
In the MIL training data, labels to be learned are only assigned to bags of
instances but not to individual instances, while every training instance is labeled
for supervised learning. For example, in a binary classiﬁcation problem, a bag islabeled positive if at least one instance in that bag is positive, while the bag islabeled negative only if all the instances in it are negative. The goal of MIL is
to predict labels of unseen bags and/or instances based on those labeled bags.
In the pioneering work of (Dietterich, Lathrop, and Lozano-Perez, 1997), MIL
was applied to drug activity estimation. Following this, many MIL methods havebeen proposed and applied to various ﬁelds including image classiﬁcation (Maronand Lozano-Pérez, 1998), stock selection (Maron and Lozano-Pérez, 1998), textclassiﬁcation, face labeling in broadcasting news video (Yang, Yan, and Hauptmann, 2005), Web mining (Zhou, Jiang, and Li, 2005), etc.
3.2

Diverse Density

In this research, we solve the problem using a modiﬁed version of the diverse
density (DD) framework (Maron and Lozano-Pérez, 1998), which is one of thewell-known MIL solutions. The main idea of the DD framework is to ﬁnd adesired concept point (i.e., the point desired for positive identiﬁcation) in thefeature space that is close to at least one instance from every positive bag andfar away from any instances in negative bags. Desired concept points are foundaccording to a score called diverse density (dd), which is a measure of how many
diﬀerent positive bags have instances near the point, and how far the negative
instances are away from that point. The optimal concept point is deﬁned as theone with the maximum dd.
A probabilistic version of dd at a point x is calculated using positive bags
Bi+ and negative bags Bi− by the following formula:dd (x) ∝iPr x|Bi±(1)±
where Bij
denotes the j-th instance in the bag Bi± ; P r(x|Bi± ) denotes a contribution score of an instance in the bag Bi± , which is calculated as a likelihoodscore whether an instance in the bag Bi± is near the location x (described later).
Each bag Bx (i.e., a case whose interaction type is predicted) is evaluated bya score at the optimal concept point in that bag, which can be calculated by thefollowing formula:dd(Bx ) = max dd(x(m) )mwhere x(m) is the point at which instance m is located. It is judged positive if
the score is larger than a threshold value(≥ 0).

5

Every contribution score is calculated using a noisy-or model as follows:





+
1 − Pr x|Bij
Pr x|Bi+ = 1 −
j


 


−
Pr x|Bi− =1 − Pr x|Bij

(2)

j



±
±
denotes the contribution score of an instance Bij, which iswhere Pr x|Bij
calculated using a Gaussian-like distribution as follows:

 


±
(3)
= exp −
Pr x|Bijs (Bijk − xk )2kwhere k denotes the index of the axes of the feature space, and s denotes thescale factor.
3.3

Modified Diverse Density as a Weighted Voting System

In a preliminary experiment, we found that the diverse density score (dd) did
not work well for our problem. We found many false negative cases related to a
few instances from negative bags. This was because the dd score calculated by(1) is very sensitive to the contribution score of a negative bag: i.e., the dd scoreis calculated as very low even in the case where only one negative instance isnear the point x.
Relating this to our particular problem, this could represent a case where asubunit pair with an interacting potential is inhibited from interaction in sucha condition that the active domain of a subunit of a complex is hidden by othersubunits of that complex. Accordingly, a point around which many positive
instances are near should be given a higher score even though there are a few
negative instances near to that point. In this respect, we introduced anotherdiverse density score, vdd, based on the following formula:
⎤
⎡




± ⎦
(4)
signi ⎣1 −1 − Pr x|Bij
vdd(x) ∝ijwhere signi is +1 for positive bags and −1 for negative bags. The vdd score canbe interpreted as a weighted voting system where the absolute value of a voting
weight is a likelihood score of whether any of the instances in a bag are at the
point. Hereafter, this score is referred to as the voting diverse density (vdd).
Each bag Bx is evaluated by a score vdd(Bx ) = maxm vdd(x(m) ) (x(m) is thepoint at which instance m locates). It is judged positive if the score is larger
than a threshold value (≥ 0). The experiments described later used a thresholdvalue of 0.

4

PPI Dataset and Feature SpaceIn this study, we use the KEGG pathways (Kanehisa and Goto, 2000) for dataset
construction, and the Gene Ontology (Ashburner et al., 2000) for feature spaceconstruction.

6

4.1

PPI Dataset Obtained from the KEGG Pathways

The PPI dataset for the experiment was constructed from the KEGG pathways
as of March 2006. Firstly, we obtained human pathway data in XML format fromthe KEGG site2 , and then extracted PPI data, i.e., the relation elements whose
value for the type attribute was PPrel. Each record in the PPI data comprises twogroups of proteins, either or both of which may correspond to a protein complex,
a protein family, or a simple protein, and one or more interaction types, which
is described in the subtype element in the XML ﬁle. As a result, 1,279 diﬀerent
PPI records were obtained.
Table 1 summarizes the distribution of interaction types. The rows from state
to compound individually correspond to an interaction type; the columns from
1 to 17 show the assignment patterns of the interaction types where the cellswith a value of 1 in the same column indicate that all the interaction types
corresponding to those rows were assigned to one or more identical PPI records.
For example, the 6th column indicates that there were six records labeled withboth interaction types of ubiquination and inhibition.
Table 1. Distribution of Interaction Types in PPI Records from the KEGG Pathways
Assignment Pattern [Dataset Type]1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 #[−] [−] [−][+] [+] [+] [−][+][+] [−] Recs.
state
1 . . . . . . . . . . . . . . . .
4. 1 . . . 1 . . . . . . . . . . .
13ubiquination25
dephosphorylation . . 1 . . . 1 . . . . . . . 1 . .
. . . 1 . . . . 1 . . . . . . . .
14dissociation. . . . 1 1 1 . . 1 . . . . . . .
198
inhibition. . . . . . . 1 1 1 . . 1 . . 1 .
249
phosphorylation
181
binding association . . . . . . . . . . 1 . . . . . .
. . . . . . . . . . . 1 1 . . . .
102
indirect. . . . . . . . . . . . . 1 1 1 .
588
activation. . . . . . . . . . . . . . . . 1
27compound#Records
4 7 8 13 145 6 6 150 1 41 181 97 5 525 11 52 27 1,279
Interaction Type

4.2

Feature Space Encoding the Gene Ontology

Feature Vector: A feature vector of each instance, which comprises two proteins and an interaction type, was constructed using the Gene Ontology (GO)(Ashburner et al., 2000). The GO is a vocabulary that describes the attributesof genes. Each term in the vocabulary, called a GO term, represents a possible
attribute value possessed by a gene or a protein encoded by genes. The GO
has a hierarchical structure, i.e., GO terms are connected by is-a relations and2

ftp://ftp.genome.jp/pub/kegg/xml/KGML v0.5/hsa

7construct a directed acyclic graph. GO currently consists of three standard gene
ontologies that describe biological processes, cellular components, and molecularfunctions. Many biological resources use the GO terms to annotate the propertiesof genes or their products (i.e., proteins or RNAs encoded by genes).
An initial feature vector of each instance consists of two components, each ofwhich represents a list of GO terms annotated to one of the proteins composingthat instance. The list of GO terms were obtained from the gene2go ﬁle3 provided
by the National Center for Biotechnology Information (NCBI). The list of GO
terms for each protein was extended by adding all the ancestors in the GO
hierarchy for each term in the initial list.
Feature Space Construction by Singular Value Decomposition: It isdiﬃcult for MIL to use the initial feature vectors. This is because a GO termin the higher layers of the GO hierarchy often relates to too many instances todiscriminate diﬀerent ones, and ones in the lower layers often relate to too few
instances to generalize similar instances. In addition, the large size of the GO
term set4 requires expensive computational cost for MIL.
To overcome these problems, the feature space was compressed by using
Singular Value Decomposition (SVD).
Logarithmic Probability Weighting: The SVD process tends to emphasize
those properties that appear frequently. On the other hand, a GO term in thehigher layers of the GO hierarchy often relates to many instances. If all the GO
terms are equally weighted, an ineﬀective feature space will be obtained thatemphasize those GO terms in the higher layers of the GO hierarchy.
In this respect, each GO term, j, is weighted with a logarithmic probability
weight, Wj , which highlights a moderate abstraction level (depth) in the GO
hierarchy. Wj is calculated using the following formula:
Wj = − log(pj ) = − log(

mj
)
m

(5)

where m is the total number of genes appearing in the gene2go ﬁle, and mj is
the number of genes with term j in that ﬁle. For instance, the topmost termin the hierarchy, which relates to all the genes, is weighted with zero (Wj = 0),
and is then ignored. On the other hand, a term in the middle layers, which is
expected to have an appropriate speciﬁcity, is emphasized.
Singular Value Decomposition (SVD): In preparation for the SVD process,a matrix G that represents the relationship between the instances and the GO
terms was constructed. A cell Gij is set as Wj if the ﬁrst protein of instance i
relates to term j, or is set as Wj  if the second protein of instance i relates to34

ftp://ftp.ncbi.nih.gov/gene/DATA/
The molecular function ontology contains 622 diﬀerent terms.

8term j  where j  = j − n1 (n1 is the number of elements for the ﬁrst proteins of
instances), otherwise it is set as 0.
SVD decomposes matrix G as follows:
G = U SDT

(6)

where U and D are a unitary matrix that satisﬁes U T U = Im and DT D = In
respectively. The column vector of U is called the left singular vector. The column
vector of D is called the right singular vector. The diagonal entries of S are called
singular values.
A compressed feature matrix G̃ can be composed using selected right singular
vectors dx , dy , . . . as follows:G̃ = GD̃ where D̃ = [dx , dy , . . .]5

(7)

Experiments: Binary Classification Task concerning
Phosphorylation

This section reports on an experiment to evaluate the proposed method using
a PPI prediction task as binary classiﬁcation concerning an interaction type ofphosphorylation. In the experiment, the proposed method was implemented on
MATLAB. This is because MATLAB provides an eﬃcient implementation of
SVD for a sparse matrix.
5.1

Binary Classification Task concerning Phosphorylation

Since the GO provides three kinds of ontologies as described in Sect. 4.2, theinput variables (i.e., feature vectors) can be constructed by several diﬀerent approaches concerning which ontologies should be encoded into the feature vectors.
In addition, since there are two proteins comprising an instance, the relation
across the properties of those proteins can be encoded into the feature vectors. On the other hand, since some bags (i.e., PPI records) have two or moreinteraction types (Table 1), we can construct complicated tasks where certain
combinations of interaction types are formalized as the target variable.
Among those possible tasks, we chose one of the simplest ones: the task ofclassifying PPIs into binary classes based on whether the PPI type is phosphorylation or not by using the feature vectors constructed from the molecularfunction ontology. This is because preliminary experiments suggested that thistask is most promising among the simpler ones.
By taking account of the distribution of PPI type assignment patterns shownin Table 1, positive and negative bags were constructed as follows.
A set of positive bags was constructed by selecting those PPI records ofwhich one of the interaction types was phosphorylation. As a result, 249 PPI
records, those columns with a ‘[+]’ mark in Table 1, were selected as positive
bags.

9

A set of negative bags was constructed by selecting those PPI recordsof which neither of the interaction types appeared in any records in the set of
positive bags. As a result, 227 PPI records, those columns with a ‘[-]’ mark in
Table 1, were selected as negative bags.
The remaining 803 PPI records were those whose interaction types included
a type appearing in some positive bags but not phosphorylation. For example,
PPI records that had only one interaction type of activation or inhibition.
5.2

Results

There are two major parameters of the proposed method: the dimension of thefeature space and the scale factor of the Gaussian-like distribution (3) concerning
the voting diverse density. The optimal values of these two parameters were
explored in the range described below.
The compressed feature space based on the ﬁrst few singular vectors by
the SVD process is expected to represent major components of the initial feature space. In the experiment, twelve kinds of feature spaces of diﬀerent dimensions were constructed by (7) with topmost n right singular vectors wheren ∈ {[2..10], 12, 15, 20}.
The experiments also used the following twelve values in exploring the scale
factor s: {500, 1000, 2500, 5000, 10000, 20000, 40000, 80000, 160000, 320000,
640000, 1280000}.
Figure 2 summarizes the results by the accuracy score in leave-on-out crossvalidation for each parameter setting. The best accuracy of 86.1% was obtainedat the point of n = 4 and s = 160, 000. A comparable accuracy of 85.6% was
obtained at the point of n = 10 and s = 10, 000, and local peaks of the accuracy
were found along a line connecting those two points. These observation suggestthat a smaller scale factor is better for the feature space of a higher dimension.
This could be explained by a tendency that the higher the dimension of thefeature space, the longer the distance between instances.
Figure 3 is a scatter graph that plots every instance in the condition when thebest accuracy was obtained (n = 4 and s = 160, 000). The x-axis of this graphindicates the contribution of negative bags by a value of the 0.25th power ofthe negative components obtained by (4); and the y-axis of this graph indicatesthe contribution of positive bags by a value of the 0.25th power of the positive
components obtained by (4).
Since the voting diverse density at a point equals to the diﬀerence of thevalue indicated by the y-axis and that indicated by the x-axis at that point, an
instance located in the area above the dotted line in Fig. 3 is judged positive;
while that located in the area below the dotted line is judged negative.
Note the instances in a positive bag (plotted with ‘*’) and that in a negative
bag (plotted with ‘·’). A signiﬁcant amount (20.5%) of positive instances appear
below the dotted line while most of instances at the optimal concept point (plotted with a small circle) in a positive bag appear above the dotted line. This isbecause the vdd score at the optimal point in a bag, according to its deﬁnition,equals to the maximum score among instances in that bag. For the same reason,

10n = 10s = 10,000
acc.= 0.856

n=4
s = 160,000
acc.= 0.861

0.9Accuracy

0.85
0.8
0.75
5
0.7
0.5

10
2.5

10
Scale F40
actor (s)(x 1/ 160 640
1000)

15

#

m
Di

en

s

s
ion

)
(n

20

Fig. 2. Prediction Accuracy according to Two Parameters

a relatively large amount of instances at the optimal concept point (plotted withsmall rectangles) in a negative bag appear above the dotted line. This is thecause of false positive bags.

6

Conclusion

In this paper, we addressed the issue of PPI type prediction, and pointed out the
problem that it is diﬃcult for a standard supervised learning method to handle
this issue because the relationship between the input variables (annotations forsubunits) and the target variable (PPI type) is ambiguous.
We introduced the subunit reaction assumption and proposed that the PPItype prediction task based on this assumption can be formalized as a problem
of MIL as follows: a complex pair with an interaction type is formulated as alabeled bag, and a possible subunit pair across a complex pair as an instance.
To solve that MIL problem, we proposed a method, a type of weighted voting
system, based on Maron’s Diverse Density (Maron and Lozano-Pérez, 1998), andevaluated it based on a binary classiﬁcation version of that problem.
In the experimental evaluation, we have constructed a dataset, consistingof 1,279 diﬀerent PPI records, from the KEGG pathways (Kanehisa and Goto,
2000), and a feature space for instances using the Gene Ontology (GO) (Ashburner et al., 2000). We then applied the method to a binary classiﬁcation task
concerning phosphorylation and achieved a highest accuracy of 86.1% in leave-11(Positive diverse density)0.25

2.5

2

1.5

1

Inst. in Pos. Bag
Inst. in Neg. Bag

0.5

MaxVDD in Pos. Bag
MaxVDD in Neg. Bag
0

0

0.5

1

1.5

2

2.5

3

(Negative diverse density)0.25
Fig. 3. Contribution of Positive and Negative Bags to Voting Diverse Density Score

one-out cross-validation when using the four major topmost components of thefeature space obtained by SVD.
In the future, we would like to apply this method to the tasks of predicting
other interaction types. In addition, we could improve the method by introducing
a process to discriminate whether the protein group comprising a PPI record
corresponds to a protein complex or a protein family, because the current versionof the algorithm ignored those diﬀerent types of protein groups, which the KEGG
pathways may include in the same format. It will also be a future issue to improve
the feature space, for example, by constructing an appropriate combination offeatures, or by encoding the domain or structural information of a protein, or
relational information across a protein pair.
Acknowledgement
The authors would like to thank Kentaro Doi of Fujitsu Limited for the very
useful discussions on potential applications of this research.

12

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