Engineering, 2013, 5, 181-188
http://dx.doi.org/10.4236/eng.2013.510B039 Published Online October 2013 (http://www.scirp.org/journal/eng)
Semi-Global Inference in Phenotype-Protein Network
Siliang Xia1, Guangri Quan2, Yon gb o Zhao3, Xuhui Jia4
1Institute of Architecture of Application Systems, University of Stuttgart, Stuttgart, Germany
2School of Computer Science, Harbin Institute of Technology at Weihai, Weihai, China
3Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China
4Department of Computer Science, The University of Hong Kong, Hong Kong, China
Received May 2013
ABSTRACT
Discovering genetic basis of diseases is an important goal and a challenging problem in bioinformatics research. In-
spired by network-based global inference approach, Semi-global inference method is proposed to capture the complex
associations between phenotypes and genes. The proposed method integrates phenotype similarities and protein-protein
interactions, and it establishes the profile vectors of phenotypes and proteins. Then the relevance between each candi-
date gene and the target phenotype is evaluated. Candidate genes are then ranked according to relevance mark and
genes that are potentially associated with target disease are identified based on this ranking. The model selects nodes in
integrated phenotype-protein network for inference, by exploiting Phenotype Similarity Threshold (PST), which throws
lights on selection of similar phenotypes for gene prediction problem. Different vector relevance metrics for computing
the relevance marks of candidate genes are discussed. The performance of the model is evaluated on Online Mendelian
Inheritance in Man (OMIM) data sets and experimental evaluation shows high performance of proposed Semi-global
method o ut performs existing global i n fe r ence methods.
Keywords: Diseases Gene Prioritization; Phenotype-Protein Network; Se mi-Global Inference; Phenotype Similarity
Threshold
1. Introduction
It is challenging for biomedical research to figure out the
genetic basis of diseases. Traditional biology researchers
adopt linkage analysis and association studies [1] to dis-
cover disease genes, which firstly locate disease g enes in
a chromosome region. However, the resolution of this
approach is low and further analysis of candidate genes
in a large genomic region is an expensive task, which
prevents gene identification even after a region has been
detected.
Many studies have tried to discover disease genes with
computational methods. Some work related was based on
annotations [2-4], or based on sequences [5]. But, the
methods rely on functional annotations are limited be-
cause only a small part of genes in the genome have been
annotated currently and methods based on sequencing is
an expensive task. Moreover, they treated disease genes
as separate and independent, however, biological pro-
cesses are not realized by a single molecule, but rather by
the complex interactions of proteins, and the breakdown
in protein interaction networks could result in diseases
[6]. Moreover, some research indicates that phenotypi-
cally similar diseases are caused by functionally related
genes [7], and the proteins coded by these functionally
related genes usually have direct or indirect interactions
[8]. From this perspective, disease genes could then be
investigated through the interaction networks of disease
proteins.
Recently, researchers took advantage of the computing
method to build biological network to help explore the
relationship among biological information in multiple
granularity, and netwo rk approach in biology is pro posed
and under active research [9], which also facilitates dis-
ease gene discovery. A wide range of methods are pro-
posed based on network methods for disease gene priori-
tization [10-16]. A method utilizing Bayesian predictor
and ranking of protein complexes linked to human dis-
eases is proposed by Kasper Lage et al. to predict genes
of human’s inherited phenotypes [13]. Xuebing Wu et al.
proposed network-based global inference approach [14].
These methods achieve some accomplishments in disease
gene prioritization, which primarily relies on analysis of
the topological properties of PPI networks and the ex-
pectation that the products of genes that are associated
with similar diseases interact heavily with each other.
Motivated by these existing network based approaches,
we propose a network based Semi-global inference model
for disease gene prioritization, which selects diseases in

S. L. XIA ET AL.
182
integrated phenotype-protein network for building profile
vectors of candidate genes and target disease, by ex-
ploiting Phenotype Similarity Threshold (PST). The
model evaluates the relevance between candidate genes
and the given target phenotype. Candidate genes are then
ranked according to relevance marks. Genes that are po-
tentially associated with target disease are prioritized
based on this ranking. To evaluate the effectiveness of
the model, the proposed model is tested on known phe-
notype and gene pairs from OMIM. Our research has
three contributions:
• Semi-global inference method with Phenotype Simi-
larity Threshold (PST) is proposed to prioritize candi-
date disease genes. The experimental result shows the
proposed Semi-global method outperforms existing
global infe r ence method.
• Phenotype Similarity Threshold (PST) is defined to
make a difference between high similarities and low
similarities and to distinguish between diseases closely
related to target disease and diseases less related,
which specifies phenotypes in the network to be con-
sidered and exploited for inference. Two methods
(S-PST, D-PST) to get PST are introduced and com-
pared.
• Performance of proposed model with different vector
relevance metrics (Pearson correlation coefficient,
Euclidean distance and Cosine similarity) are eva-
luated and compared. We show that Semi-global infe-
rence works well with Euclidean distance and Cosine
similarity.
In Section 2, we briefly introduce the background of
network based candidate gene prioritization by describ-
ing the problem formally and discussing the related work
and their limitations. Section 3 presents Semi-global in-
ference model and explains strategies of PST to select
nodes in phenotype-protein network. Section 4 shows
experimental results of proposed Semi-global inference
model with variation of relevance metrics and PST，and
comprehensively compares the performance of proposed
model against an existing global inference method. In
Section 5, we draw some conclusions and point out fur-
ther wor k.
2. Background
2.1. Network Based Candidate Gene
Prioritization
Here is a brief d escription of network -based disease gene
prioritization problem referring to [17]: given target dis-
ease d, the input to the candidate disease gene prioritiza-
tion problem consists of two sets of genes, known set K
and candidate set C. The known set K contains prior
knowledge of the disease d, e.g., it is the set of genes
known to be associated with d and diseases similar to d.
Each gene g
∈
K is associated with a similarity score
σ(g, d), indicating the known degree of association be-
tween g and d. The candidate set C contains candidate
genes, one or more of which is potentially associated
with target disease d (e.g., these genes might be in the
linkage interval of d that is identified by association stu-
dies). The purpose of network based disease prioritiza-
tion is to use a PPI network G = (V, E), to compute a
score φ(v, D) for each gene g
∈
C that represents the
likelihood of g to be associated with d.
The PPI network G = (V, E) consists of a set of gene
products V and a set of undirected inter actions E between
these gene products, in which uv
∈
E represents an
interaction between u
∈
V and v
∈
V. In this ne t work,
the set of interacting partners of a gene product v
∈
V is
defined as N(v) = {u
∈
V: uv
∈
E}.
Global prioritization methods use this network infor-
mation to compute φ by propagating σ over G. Candidate
genes with high relev ance to target disease of interest are
ranked in the top and are regarded as the disease genes.
2.2. Related Work
Xuebing Wu et al. have proposed network-based global
inference approach called CIPHER algorithm [14], in
which Pearson correlation coefficient is adopted to eva-
luate the relevance between candidate genes and the tar-
get disease. Another global inference method is proposed
based on a network propagation algorithm to formulate
constraints on the prioritization function [16].
Although these existing global network based methods
to some extent throw ligh ts on disease gene prioritization
problems, they have some drawbacks and limitations.
Research of Xuebing Wu et al. is based on the assump-
tion of the linear correlation between profiles of pheno-
types and disease genes, which shows some bias against
genes whose related proteins have few interactions with
other peers [14]. Moreover, as reported in literatures,
network based global inference methods, favor genes
whose products are highly connected in the network and
perform poorly in identifying loosely connected disease
genes, due to centrality of target disease genes [17] and
incomplete and noisy nature of the PPI data [18].
In global inference method, all the diseases in the
phenotype similarity network are exploited to generate a
prediction, including less related diseases to profile a
target disease, which fails to take into consideration that
more similar diseases may play more important roles in
inference. No work has been done for disease gene pri-
oritization using only parts of diseases in phenotype
network , and nodes selection strategy has not been ex-
plored. Secondly, phenotype similarities vary. A target
disease has different phenotype similarities to other dis-
eases in the network. No selection criteria is made to
treat roles of diseases differently in phenotype network,

S. L. XIA ET AL.
183
no methods make a difference between high similarities
and low similarities, which might be considered to de-
termine which related d iseases to refer in gene pr ioritiza-
tion pro bl e ms.
Our research aims at exploring the uncovered areas
mentioned and overcoming limitations of global infe-
rence methods. We propose Semi-global inference me-
thod by exploiting PST as the criteria to select pheno-
types in network for inference, which is the essential
difference between proposed Semi-global model and
existing global inference methods.
3. Methodology
In this section we present the mathematical model and
show the general framework of gene prioritization algo-
rithm of Semi-global inference. Furthermore, we explain
how Phenotype Similarity Threshold is exploited for
nodes selection in phenotype network, which is the core
of Semi -global inference model.
It is important to note that the purpose here is to infer
functional associations between genes from functional
and physical interactions between their products. For this
reason, any reference to interactions between genes in
this paper refers to the interactions between their prod-
ucts. Meanwhile, disease gene prioritization is inferred
from phenotypically similar diseases, term disease and
term phenotypes deliver identical conception in this pa-
per.
3.1. Mathematical Model
• Undirect ed gra ph
(1)
is defined as phenotype similarity network;
is a subset of all the phenotypes,
; and the element
is the similarity of phenotypes .
• Undirect ed gra ph
(2)
is defined as protein interaction network;
is a subset of all the proteins,
; and the element
denotes the interaction of proteins .
• Given a phen oty pe , , set
(3)
is defined as association set of ; each element
in is an association of ;
set
(4)
is defined as global association set, which contains all
phenotype-protein associations.
• Given phenotype similarity network GPhenotype, pro-
tein interaction network and global asso-
ciation set , set
(5)
is phenotype -pr otein network.
• Given a phenotype and a protein ,
,
(6)
denotes one dimension of the profile vector of protein
.
• Phenotype Similarity Threshold (PST) is a manually
set similarity value that satisfies
(7)
• Given a phen oty pe , set
(8)
contains the phenotypes that have similarities higher or
equals to PST with . Each element in is de-
fined as a Closely Related P henotype of .
• Given a phen oty pe , , if
, then is used as a dimension in pro-
file vector of ; vector
j
p
(9)
characterizes the profile of in phenotype similarity
network , in which . Means only the similar-
ities of Closely Related Phenotypes (higher than PST)
are used to build the profile vector of a target phenotype
of interest.
• Given a phenotype and a protein ,
, if , thenis used as
a dimens ion of vector o f ; vector
k
g
(10)
characterizes the profile ofin Protein Network, in
which .
Given a phenotype and a protein, let
denote a relevance metric of vector
j
p
and
vector
k
g
. Three different metrics are defined, which
characterize the correlation between profile vectors of
protein and phenotype and thus indicate the
relevance of candidate protein and target phenotype
. Let denote Euc l idean dis t a nc e of t w o ve c t ors ,
(11)
Cosine similarity is a metric measuring the included
angle of two vectors, which is denoted as ,
,
p
GPhenotypP E=<>
123
{, ,}
m
P ppp p= …
Pm=
p
{,}
jkj k
ES pp P=|∈
jk
S
,
jk
pp
g
GProtein =<G,E>
123
{, ,}
n
G gggg= …
Gn=
g
{,}
jkj k
EI ggG=|∈
jk
I
,
jk
gg
j
pP∈
k
gG
∀∈
j
CAssociation
={<, is associated with }
jk kkj
pggG gp>|∈ ∧
j
p
,
jk
pg<>
j
CAssociation
j
p
1
=
m
j
j
CAssociation CAssociation
=

GProtein
CAssociation
,,NGPhenotype GProtein CAssociation=<>
j
pP∈
k
gG∈
xy
p Pg G∀ ∈∀∈
(,){ |,}
kxkyx yx
fgpMax IpgCAssociation=< >∈
k
g
{|, }{|, }
jkj kjkj k
Minsp pPPSTMaxsp pP∈≤ ≤∈
j
pP∈
{| }
jkkjk
CRPp pP sPST=∈∧ ≥
j
p
j
CRP
j
p
j
pP∈
1rm∀≤ ≤
r
ji
s PST≥
r
ji
s
j
p
123
(,,)
r
ji jijiji
SSS S= …
j
p
12
...
r
ii i<<
j
pP∈
k
gG∈
1rm∀≤ ≤
r
ji j
p CRP∈
(, )
r
ki
fg p
k
g
123
((,),(, ),(, )(, ))
r
ki kikiki
fg pfgpfg pfg p= …
k
g
12
...
r
ii i<<
j
pP∈
kj
gG∈
(,)
jk
pg ϕ
k
g
j
p
k
g
j
p
1
ϕ
1
22
1,
1
(,)((()) )
m
jkjiki
i
p gSfgd ϕ
=
= −
∑
2
ϕ

S. L. XIA ET AL.
184
(12)
Pearson correlation coefficient indicates linear correla-
tion between two vectors, which is denoted as ,
(13)
3.2. Phenotype Similarity Threshold (PST)
According to the biological assumption that phenotypi-
cally similar diseases are caused by functionally related
genes [7], the proposed Sem i-global inference model
takes into consideration only phenotypes that are highly
similar to target disease, with similarities higher than
PST. We use only those Closely Related Phenotypes (re-
fer to (8)) of and exploit corresponding similarities
to characterize the target phenotype. Therefore, In (9)
and (10), given a phenotype, the dimensions of profile
vector
j
p
are determined by the number of phenotypes
in , the dimensions of profile vector of candidate
genes are reduced correspondingly.
3.3. Semi-Global Inference
Based on the mathematical model above, here we give
the computation framework of proposed semi-global
inference method, which consists of two algorithms to
prioritize candidate disease genes.
Algorithm 1 Relevance Mark Calculation calculates
the relevance mark for a given pair of target phenotype
and candidate protein . Algorithm 2 Disease
Gene Prioritization takes a target phenotype as the input
and evaluates relevan ce mark for all candidate proteins in
linkage interval, then prioritizes the candidate proteins
based on their relevance marks. Proteins with high re-
levance mark are regarded highly related to target phe-
notype and thus genes associate with these top ranked
proteins are the underlying causing genes of target dis-
ease, as the predictive result of Semi-global inference
model.
In practice, each of metrics (11) or (12) (13) ar e tested
respectively in Algorithm 1 as relevance evaluation of
candidate proteins. Algorithm 2 is invoked to prioritize
candidate genes for all phenotypes we are interested in.
4. Results
In this section, we comprehensively evaluate the perfor-
mance of proposed Semi-global inference model with
different setting of metrics and PSTs. Then we compare
proposed model to global inference method.
4.1. Datasets
To evaluate the proposed model, data sets needed are
listed as follows: Phenotype set and quantified similari-
ties between each pair of phenotypes. Protein set and
quantified protein interaction between each pair of pro-
teins. Set of known pairs (associations) of phenotypes
and associated proteins, which serves as the validation
set.
Phenotype set and their linkage intervals are obtained
from Online Mendelian Inheritance in Man (OMIM)
Morbid Map [19], which provides a publicly accessible
and comprehensive database of genotype-phenotype re-
lationship in humans; phenotype similarities come from
the research of van Driel et al. [20]; quantified protein
interaction marks are extracted from STRING database
[21] to build PPI network; chromosome mapping of pro-
teins are extracted from Ensembl database [22]; valida-
tion set can be built from phenotype-protein network, by
extracting the phenotype-gene mapping from OMIM
Morbid Map and gene-protein mapping from bioDBnet
database [23] and mapping phenotype network to PPI
network.
Those phenotypes that can not be mapped to proteins
are removed, due to lack of known associated genes or
incomplete information of proteins coded by genes in the
linkage interval. We finally get 1897 phenotypes and
84652 proteins in total, while only 156584 protein-pro-
tein interactions are available. Those missing PPI records
are regarded as zero. 2549 known phenotype-gene pairs
are maintained for evaluation.
4.2. Experimental Setting
We apply leave-one-out cross-validation in order to eva-
luate the performance of different methods in terms of
accuracy of disease gene prioritization. For each disease
of interest, we conduct following experiment:
• We remove all associations of this targ et disease from
global association set (refe r t o (4)).
• All the genes in the linkage interval are regarded as
candidate genes to be prioritized. On average, there
are 750 candidate genes in the linkage interval of a
disease.
• In practice, w e exploit Po sition Parameter to get
PST: Phenotype similarities are sorted in an array in
ascending order, then PST is assigned as the value re-
trieved from the array with index of (array size * ),
so PST is determined by assigning a value from
zero to one. It is important to note that when ,
all the nodes in phenotype network are considered in
inference. In this case, Semi-global model degenerates
into global inference. Thus, global inference method is
a case of proposed Semi-global model when .
We conduct experiment with two methods to ge t PST:
Static method (S-PST). All the phenotyp e similarities
are sorted in one array. PST is a global static value for all
target diseases during the experiment.
2( ,) cos( ,) ||| |
jk
jk jk
jk
pg
pg pg
pg
ϕ
⋅
= =
3
ϕ
3
cov( ,)
(,) ( )( )
jk
jk
jk
pg
pg
pg
ϕσσ =
j
p
j
p
j
CRP
j
p
k
g
λ
λ
λ
0 λ =
0 λ =

S. L. XIA ET AL.
185
Dynamic method (D-PST) . PST is retrieved from a
smaller phenotype similarity set containing only the si-
milarities related to current targ et disease. Different PSTs
are gained for prediction of different target diseases, ac-
cording to the similarity range of that target disease.
• We conduct the experiment with each combination of
relevance metrics and PST met hods.
• In order to systematically compar e the performance of
proposed model, we use following evaluation criteria:
Average Rank. Average rank in proposed model of
known dise a s e genes.
Fold Enrichment. Ability to enrich known disease
genes ove r ra n dom selection [13].
Distribution of Cases. Percentage of the test cases
ranked within top 1%, top 5% and top 10%.
4.3. Experiment with Variation of PST and
Relevance Metri cs
Proposed model with Euclidean distance shows a rapid
increase of average rank with the increase of λ, though
the performance is always poorer than that of model with
the other two relevance metrics. The model exhibits a
high average rank with high PST (high Position Parame-
ter λ) using S-PST, in spite of relevance metrics adopted.
For model with Euclidean distance and Cosine simi-
larity, fold enrichment gets higher along with the in-
crease of . On the other hand, Figure 1 to Figure 4
show that proposed model with Cosine similarity gets
higher performance than the other two relevance metrics.
Moreover, the trend of the performance with increasing λ
shows that the model gains better performance when
highly similar diseases are referred to profile target dis-
ease and candidate genes, in which the profile vectors
consist of only a few dimensions and only small part of
nodes (eg. diseases holding top 5% highest similarities in
whole phenotype network in S-PST and diseases holding
Figure 1. Average rank to compare the performance of pro-
posed model using S-PST with differen t rel ev a n ce m et rics.
Figure 2. Average rank to compare the performance of pro-
posed model using D-PST with different releva n ce m et rics.
Figure 3. Fold enrichment to compare the performance of
S-PST model with different metrics .
Figure 4. Fold enrichment to compare the performance of
S-PST model with different metrics .
λ

S. L. XIA ET AL.
186
top 5% highest similarities to the tar get disease in D-PST)
are exploited. Therefore it indicates the strategy that re-
ferring only part diseases in proposed Semi -global model
works well with these two relevance metrics (especially
with Euclidean distance) and nodes selection with PST
and dimension reduction of profile vectors achieves per-
formance improvement.
Model with Pearson correlation coefficient reaches its
best performance when λ = 0 (global inference method)
and shows a decline with increase of λ. Therefore, pro-
posed Semi-global inference does not increase the per-
formance if Pearson correlation is adopted as the relev-
ance metric.
4.4. Comparison to Global Inference Method
Here we discuss the cases when D-PST is exploited with
a certain λ assigned to get the relative high performance
using different relevance metrics and compare them to
global inference method using CIPHER algorithm [14]
with the same relevance metric.
Table 1 and Table 2 demonstrate that Semi-global
model with D-PST and high λ outperforms global infe-
rence method using same relevance metrics. Especially
for Euclidean distance, when λ is assigned with a high
value, Semi-global model shows much higher perfor-
mance than global inference.
D-PST and Cosine similarity work as the best combi-
nation, with which proposed model reaches a high per-
formance with fold enrichment being 217.62 when
0.96 λ =
and average rank being 16.29 when
0.92 λ =
.
In this configuration, Semi-global model takes into ac-
count top 4% most similar diseases of the target disease
for inference, outperforms the highest fold enrichment of
197.60 and average rank of 22.31 in global inference
method.
Table 3 shows that with same relevance metrics, more
known disease genes are ranked within top 1%, top 5%
Table 1. Fold enrichment to compare performance of pro-
posed Semi-global model to a global inference method.1
ED CS PCC
Global inference
(CIPHER) 55.44 159.71 197.60
Semi-global inference
(D-PST)
177.03
(
0.991 λ =
)
217.62
(
0.96 λ =
)
197.60
(
0 λ =
)
Table 2. Average rank to compare performance of proposed
Semi-global model to a global inference method.1
ED CS PCC
Global inference
(CIPHER) 1172.60 22.31 67.94
Semi-global inference
(D-PST)
81.46
(
0.995 λ =
)
16.29
(
0.92 λ =
)
56.43
(
0.1 λ =
)
Table 3. Percentage of the known disease genes ranked
within top 1%, top 5% and top 10% in proposed Semi-
global model and a global inference model.1,2
Top 1% Top 5% Top 10%
Global inference
(CIPHER)
ED 0.21 0.25 0.26
CS 0.64 0.93 0.97
PCC 0.72 0.91 0.94
Semi-global
inference
(D-PST)
ED (
0.995 λ =
) 0.59 0.82 0.85
CS (
0.96 λ =
) 0.75 0.94 0.98
PCC (
0 λ =
) … … …
and top 10% in proposed Semi-global model using
D-PST than that in global inference method. It also
shows D-PST and Cosine similarity in proposed model
achieves better performance than other combinations of
PST methods and relevance metrics.
Then, we compare distribution and accumulation of
test cases between proposed Semi-global model and
global method when they reach their respective high
performance with particular experimental settings.
Figures 5 and 6 are general views about distribution
and accumulation of test cases of proposed Semi-global
model and global inference method with particular set-
tings to reach their high performance which are Semi-
global model using D-PST with Euclidean distance and
, Semi-global model using D-PST with Co-
sine similarity and and CIPHER algorithm
with Pearson correlation coefficient as a representative of
global inference. Semi-global model using D-PST and
Cosine similarity not only gets better performance in
terms of average rank and fold enrichment than global
inference, but also generates a more desirable distribu-
tion of test cases. It ranks more than 75% cases within
top 1%, and the accumulated ratio of test cases is higher
than global inference method.
5. Conclusions
In this paper, a S emi-global inference model with PST is
proposed for disease gene prioritization, which applies
profile vectors in phenotype-protein network to charac-
terize target disease and candidate genes. The model is
evaluated comprehensively on OMIM dataset and the
experimental result shows proposed Semi-global model
outperforms existing global inference method.
Phenotype Similarity Threshold (PST) is proposed and
Closely Related Phenotypes are defined. It is adopted as
a criterion to select diseases in phenotype network to pro-
file the target disease. Thus, by considering only highly
similar diseases, proposed PST has significance in nodes
0.995 λ =
0.96 λ =
1ED = Euclidean distance, CS = Cosine similarity, PCC
= Pearson
correlation coefficient.
2Last row in Table 3
is blank because proposed model with Pearson
correlation coefficient reaches best performance when λ = 0
, which
degenerates into global inference.

S. L. XIA ET AL.
187
Figure 5. Comparison of distribution of test cases between
proposed Semi-global model using D-PST and a global infe-
rence method.1
Figure 6. Comparison of accumulation of test cases between
proposed Semi-global model using D-PST and a global infe-
rence method.1
selection in phenotype-protein network for gene prioriti-
zation problem, which as a trial demonstrates a novel
understanding of the well accepted belief that phenotyp-
ically similar diseases are caused by functionally related
genes.
Effect of different relevance metrics o f profile vectors,
different methods and variation of PST on the proposed
model are discussed. The proposed model with Cosine
similarity as relevance metric shows higher performance
than model using other two metrics. Moreover, proposed
model achieves performance improvement along with the
increase of PST when Cosine similarity and Euclidean
distance are adopted as relevance metrics. We have also
shown proposed Semi-global model using D-PST exhi-
bits higher average rank, fold enrichment and more ad-
mirable distribution than global method .
Further research includes configurations of Semi-
global model (proper PST, Position Parameter and re-
levance metric) t o ach iev e better performance, sensitivity
of proposed model to noise of PPI data, and the issue of
bias occurs in global inference.
6. Acknowledgements
This research is supported by National Science Founda-
tion of China 60973077.
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