Advances in Breast Cancer Research, 2012, 1, 21-29 Published Online October 2012 (
Computing a Predictor Set Influence Zone through a
Multi-Layer Genetic Network to Explore the Role of
Estrogen in Breast Cancer
Leandro de A. Lima1,2, Marcelo Ris¹, Junior Barrera³, Maria M. Brentani2,4, Helena Brentani4*
1Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil
2Hospital A.C. Camargo, São Paulo, Brazil
3Departamento de Física e Matemática da FFCLRP, Universidade de São Paulo, Ribeirão Preto, Brazil
4Faculdade de Medicina, Universidade de São Paulo, São Paulo, Brazil
Email: *
Received July 5, 2012; revised August 10, 2012; accepted August 20, 2012
Modeling inter-relationships of genes over a specific genetic network is one of the most challenging studies in systems
biology. Among the families of models proposed one commonly used is the discrete stochastic, based on conditionally
independent Markov chains. In practice, this model is estimated from time sequential sampling, usually obtained by
microarray experiments. In order to improve the accuracy of the estimation method, we can use biological knowledge.
In this paper, we decided to apply this idea to study the role of estrogen in breast cancer proliferation. The n-influence
zone of a set S of genes in a given multi-layer genetic network is a set L of genes regulated, directly or indirectly, by
genes in S, after at most n-1 layers. In this manuscript we describe a new approach for computing the n-influence zone
of S through the estimation of a multi-layer genetic network from gene expression time series, measured by microarrays,
and biological knowledge. Using seed genes related to cell proliferation, our method was able to add to the third layer
of the network other genes related to this biological function and validated in the literature. Using a set of genes directly
influenced by estrogen, we could find a new role for cell adhesion genes estrogen dependent. Our pipeline is
user-friendly and does not have high system requirements. We believe this paper could contribute to improve the data
mining for biologists in microarray time series.
Keywords: Genetic Regulatory Networks; Estrogen; Time-Course Microarrays
1. Introduction
Genes are translated into proteins, which in turn can react
to create complexes that regulate genes. This feedback
process generates dynamical systems, known as genetic
regulatory networks (GRN) that regulate metabolic path-
ways. In general, GRNs are very complex due to the in-
trinsic nonlinearity of the phenomena and the huge
amount of variables (e.g. genes and proteins) involved.
A requirement for understanding quantitatively this
natural phenomenon is the capacity of measuring it. In
order to do that, we can use microarray [1] or RNA-Seq
[2], which are technologies that permit to measure si-
multaneously the expressions of thousands of genes. This
technology can be used to get instantaneously the state of
nature under the experimental conditions defined by sci-
entists. Thus, using a large experimental preparation and
extracting relatively small volumes periodically, it is
possible to measure gene expression profiles that are
samples of the dynamical behavior of genes. The result-
ing data is the source for the explosion of molecular pro-
filing studies and permit the understanding of regulation
mechanisms and, consequently, of biological phenomena
associated to a specific organism or a cell culture [3].
When the study needs the measurement of expression
profiles for a period of time, the time-course microarray
experiment usually is the option. The analysis of these
data permits to cluster genes sharing similar temporal
profiles [4] and to estimate the architecture of GRNs [5].
There are several studies trying to model and estimate
GRNs. A review of them can be found in [6-9]. The ar-
chitecture of a GRN indicates the dependence of a gene
dynamics to other genes dynamics. The model parame-
ters can be estimated from promoter region structure
analysis, gene expression profiles and biological knowl-
edge. However, investigating large networks is very hard
due to the small samples of the dynamical behavior of
network genes (i.e. short gene expression profile) avail-
able. Studying specific gene networks is a more tractable
*Corresponding author.
opyright © 2012 SciRes. ABCR
problem [10]. The first model adopted to represent GRNs
were Boolean state machines [11], also called Boolean
Networks. Probabilistic Boolean Networks (PBNs) [12]
are an extension of Boolean Networks in which the Boo-
lean function to determine the next state in the network is
not deterministic, being chosen each iteration from a
family of Boolean functions according to a given prob-
ability distribution. Probabilistic Genetic Networks (PGNs)
[13] is another mathematical view of PBNs that focus
only on the probability distributions that characterize the
PBNs. In fact, a PGN is a discrete Markov chain, whose
states are vectors of gene expression, which obey some
axioms: 1) the transition function is time-independent, i.e.
the probability of a state, given a previous one, does not
vary in time; 2) all the transition probabilities are positive,
i.e. all the states given a previous one can occur; 3) the
transition function is conditionally independent; 4). the
transition function is almost deterministic, i.e. there is a
state almost determined given a previous one. These
axioms are motivated by a compromise between biologi-
cal phenomena representation and difficulties with esti-
mation from the available data.
In fact, any chosen model needs to be estimated from
the available data, which is usually small. This is an im-
portant constraint in the choice of models, since complex
models with many parameters would be impossible to
estimate from reduced data sets. In these conditions,
PBNs or PGNs are good options.
In this work, we used PGN to model GRNs and pro-
posed a new algorithm to estimate them. The input data
for this algorithm is a time-course microarray experiment,
a subgroup of initial genes (the initial set of predictors,
also called seed genes) and some prior knowledge of
genes involved with the studied phenomena, whereas the
output is a graph representing the architecture of the
network designed. The genes that appear in the network
are the influence zone of the seed genes (i.e. the genes
influenced by the seed genes). Several manners of esti-
mating GRNs have been proposed. Some of them pro-
pose, instead of computing the relationship between
every pair of genes, to grow the network around specific
genes [5,14]. And some propose to study the networks in
specific contexts [10,15]. In this paper, we modified
some aspects of the model for network estimation from
seed genes: 1) designing the network through a sequen-
tial multi-layer estimation; 2) measuring the prediction
capacity by the estimated mean conditional entropy; 3)
proposing a formal model for using categorical biological
knowledge to diminish the prediction estimation errors.
Besides, the results were tested in microarray time series
for studying genes regulated by estrogen.
Estrogen has a fundamental importance in the repro-
ductive tissues [16]—the growing of mammary glands
and endometry during pregnancy are estrogen-dependent
[17]—and it can also be related to the growing of tumor
cells. There are more than 300 known genes with regula-
tion positive or negative by estrogen [18-23]. These
genes can be classified in categories by their bio- logical
functions. Genes addressed to biological func- tions as-
sociated to cell proliferation are related to cancer [24]
and estrogen can up-regulate or down-regulate those
genes [19]. Taking it into account, we chose a dataset
related to estrogen to test our method. Two examples of
application will be shown. The input data is a time-
course microarray experiment of estrogen response in
T47-D cells [22] treated with estrogen (E2) during 24
hours. In both experiments, a subgroup of genes (seed
genes) regulated by estrogen was selected to start the
network. The output is a graph representing interactions
among genes and their predictors. The genes in the esti-
mated network are the influence zone of the seed genes
and their biological functions are analyzed in the context
of the seed genes biological function
2. Methods
2.1. Overview
The n-influence zone of a set S of genes in a given
multi-layer genetic network is a set L of genes regulated,
directly or indirectly, by genes in S, after at most n 1
layers. We present an approach for computing the n-in-
fluence zone of the genes in S through the estimation of a
multi-layer genetic network from gene expression time
series and biological knowledge.
The set S chosen is composed of genes that participate
of a given biological function. An n-layer network is
estimated sequentially. The estimation of a layer Li con-
sists in ranking, based in some estimated cost function,
the genes influenced by some subset of the genes in the
previous layer Li1 and choosing a subset of these genes,
based on the rank and on their known relation with the
phenomena studied. This process is repeated n 1 times
and L0 = S. In each step i, the biological functions of Li
layer genes are recorded from GO [25] or, eventually,
from other functional analysis. This procedure permits to
investigate the relation of the phenomena associated to
the biological function of S and L genes.
2.2. Time-Course Microarray
The input data for our study comes from [22] experiment.
This is a time-course microarray experiment, that sam-
pled T-47D cells over 24 hours through Compugen 19K
human oligonucleotide array. The total are 16 experi-
ments: the 8 first every hour and the 8 reminders every
two hours. The whole experiment was repeated in three
different conditions: 1) treated with estrogen (17β-estra-
diol (E2)); 2) treated with estrogen (E2) plus ICI (anti-es-
trogen component); 3) treated with estrogen (E2) plus
Copyright © 2012 SciRes. ABCR
ICI plus CHX-Cycloheximide (protein synthesis inhibitor
component). Each experiment was compared with the
T-47D cells not treated with estrogen. The experiment
obtained: 386 genes, estrogen responsive; 139 genes,
estrogen responsive and ICI sensitive; 89 genes, estrogen
responsive, ICI sensitive and CHX insensitive. These
genes were identified as estrogen directly regulated
2.3. Normalization, Quantization and Filtering
Let M be the time-course microarray matrix, with n
genes in m instants of time. In order to find the best pre-
dictors subset of a gene, the pipeline (Figure 1) needs to
compute for each subset a cost function associated to it.
This process requires that the expression values be dis-
crete values instead of real numbers contained in the
output of the microarray experiment. Of several methods
to do that, we used a method based on [26]. It consists in
two steps:
Normalization of matrix M into the matrix MN. It
consists in normalizing each gene signal to a signal with
normal distribution with expectation equals to 0 and
standard deviation equals to 1. After that, all the genes
will have the same distribution and their expressions can
be compared. The normalization consists in calculating
the expectation Ei and the standard deviation σi of the
signal for each gene G given. The resulting elements of
the normalized matrix MN are given by
Figure 1. The pipeline steps.
ik E
i = 1, ···, n and k = 1, ···, m.
Quantization of matrix MN into the matrix MQ. This
process is equivalent to map the normalized signal values
in previous step to some qualitative expression levels. In
this work, we use three qualitative expression levels: 1,
indicating that the gene is under expressed, 0, indicating
that the gene is null, and 1, indicating that the gene is
over expressed in relation to the reference. A threshold
mapping is used to perform the quantization as in [26].
For each gene G a lower li and an upper ui thresholds are
obtained by
 
,0 ,
,:, 0
,0 ,
,: 0
In other words, li and ui are the expectation of, respec-
tively, the negative and positive signals. The elements of
the quantized matrix MQ are given by:
1, ,
,0,if ,
1, if,
ifMi kl
iklM iku
Mik u
 
 
 
for i = 1, ···, n and k = 1, ···, m.
Filtering. In order to avoid further errors, the entries
in a time-course microarray experiment must be filtered.
To do so, we have to analyze two cases: 1) the expres-
sion signal cannot be determined and 2) the gene expres-
sion during the experiment is constant. For the first case,
we simply set this entry with the null value. In both cases,
the genes do not give any new information for the re-
sulted network and for this reason they are removed from
the data set.
2.4. Seed Genes Analysis
The algorithm pipeline requires at each step a set of
genes called seed genes. This set contains the predictors
to be found for each gene in the whole data set.
For cells treated with estrogen, for example, in order to
test estrogen regulation network, good candidate for seed
genes can be genes directly regulated by estrogen, i.e.
genes in which estrogen could act as a transcription fac-
tor. It is possible to use many tools for analyzing genes
biological functions. In this work, we used FunNet [27]
software, which calculates the significance P-value of the
gene enrichment, of the considered GO/KEGG category,
Copyright © 2012 SciRes. ABCR
Copyright © 2012 SciRes. ABCR
with a unilateral Fisher exact test. The genes best pre-
dicted by each current set of seed genes are used as pre-
dictors for the next step.
2.5. Cost Function
For each gene in the whole data set and a given set of
seed genes, we try to find the subset of the seed genes
that best predict the expression of this gene, which we
call target gene.
It is possible to use our method inferring the prediction
interactions using several manners (for example, Bayes-
ian networks, ordinary differential equations or other
information-theoretic approaches, shown in [6,7].
However, in our tests, we have used the mean condi-
tional entropy as cost function. This measure, which var-
ies between 0 and 1, indicates the dispersion of a prob-
ability distribution function, i.e. the entropy has small
values for distributions with mass concentration in one of
the possible instances and the biggest value for a uniform
distribution. For our case, we are interested in the distri-
bution of the expression G of a gene given the vector
expression A of a subset of seed genes. Let Q be the set
of the discrete values used to quantize the gene expres-
sions (e.g. Q = {1, 0, +1}). And also let a Q|A| be an
instance of A and g Q be an instance of G. The mean
conditional entropy E(H(G|A)) is given by:
aQ gQ
EHGppG g
pG g
ated mean conditional entropy Ê(H(G|A)) is
given by:
Based just in the input data one can only calculate an
estimation of the cost function in place of its real value.
The estim
pG gpG g
ance a of A which
occurs less than f. It is equivalent to:
The Equation (2) requires estimation of P(A = a) and
P(G = g|A = a). Let f be a frequency threshold used to
separate instances a of A that do not occur frequently.
Let N+ be the sum of the frequencies of each instance a
of A which occurs more or equal than f and N be the
sum of the frequencies of each inst
pG g
So, the estima of Aa
pG g
Aa is given by:
 
 
#G g,# f
pG g
#Gg ,#
 
Aa Aa
and the estimator
a of
a is given by:
NN 'Q:#' f'
 
 
Aa Aa
The estimator
gh the ins
distributes uniformly the
est predicted than a gene G’ by
seed genes set. We present here some of them:
quency N throutances that do not occur or
occur less than f times.
2.6. Ranking Results
We say that a gene G is b
the seed genes, if the cost of the best predictor subset of
the seed genes to G is lower than the cost of the best pre-
dictor subset to G’. Ranking the genes of the data set by
the costs associated to their best predictor subsets pro-
duces a list in which the initial elements are the genes
best predicted by the seed genes. This procedure is the
key to obtain a new set of genes to the next step of the
pipeline. Some methods can be used to choose the next
Defining a threshold value e to the cost function and
extracting only the genes with predictor subset cost lower
, depend-than e. This value can be updated each iteration
ing on the number of genes extracted by this value.
Extracting a fixed number of genes from the top of the
ranking list that share some biological function (GO
and/or KEGG entries). For example, extract the first 30
genes that have one or more of these biological functions:
cell division, cell proliferation and cell cycle.
Simply extracting a fixed number of genes from the
top of the ranking list, which can be defined as a per-
centage of the whole set.
These methods can be grouped to obtain the next seed
s. For example, set a threshold value e and some
biological functions to extract the genes sharing these
biological functions and with best predictor subset cost
on was processed by an algorithm using
seed genes. For each gene G in
e algorithm executes the follow-
Cytoscape software.
Database relating the gene to its aliases and
Opteron™ with 4GB of RAM. The resulting
e same data.
ompugen 19K human oligonucleotide array)
T-47D cells treated with estrogen (E2) [22]
undefined. For the un-
es, we searched for
n Figure 2 we see the whole network of this
wer than e.
2.7. Implementation
P The pipeline was composed by the following steps:
Each iterati
Python that received the
the set of seed genes, th
ing processes:
sub-matrix extraction containing the expressions of the
seed genes and the target gene G;
execution of the algorithm to find the best predictor
results storage in an HTML page and in a text file as
the source to create the graph on
is HTML page has, for each gene, a link to Stanford
own information about it.
The FunNet [27] website ( was
used to get the GO Biological Process most enriched
The Cytoscape software
as used to build the network graph image.
The experimental results were processed in an Dual
Core AMD
aph, the seed genes for each iteration and the source
code can be downloaded at
3. Results
We performed two experiments based on th
The input for the experimental results was a tim
microarray (C
experiment of
in 16 experiments over 24 hours.
Some genes were removed from the whole process: 1)
the genes not found in GO Biological Process; 2) genes
with constant signal expression and 3) genes with more
than half of the signal expression
fined signals the entries were marked with null values
and ignored during the whole process. The GO entry was
assigned to each gene, the complete data were normal-
ized and quantized according to the methods discussed
previously and we used 3 levels of quantization: 1, 0
and +1. We used f = 1 as the frequency threshold ex-
plained in Section 2.5. In our experiments, we chose a
general maximum threshold value of 0.15, because we
want to be restrictive in relation to the cost function. An-
other general restriction is that in each iteration the
method permits to adjoin to the network less than 5% of
the whole set of candidate genes. In order to do that, the
threshold of 0.15 may be decreased.
The initial seed genes were obtained from the 386
genes E2-responsive in [22]. As we are interested in the
role of estrogen in proliferation of cancer cells, in our
first experiment, from these 386 gen
e ones with GO Biological Process related to “Cell
proliferation” and found 30 genes (level 9, P-value of
This biological function used to filter the initial seed
genes was obtained from the work in [19] as one of the
functional categories of genes stimulated or inhibited by
estrogen. I
periment. By using the 30 “Cell proliferation” related
seed genes, we grew the network over 3 layers, of which
the first one corresponds to the seed genes. In order to
find the second layer we added to the network the genes
that were predicted by the seed genes with mean condi-
tional entropy lower than 0.15, resulting in a layer with
572 genes, from which 105 have GO Biological Process
annotation. Then, from these 572, we performed a search
for the genes also related to “Cell proliferation” (in GO
Biological Process), finding 8 genes (level 6, P-value of
0.0299). After that, these 8 genes were also used as seed
genes to grow the third layer. The third layer is composed
by the genes predicted with mean conditional entropy
lower than 0.15, a set of 28 genes. We searched in the lit-
erature for these genes that were related to cancer, and
found 18 of them, as shown in Supplementary Table 11.
Figure 2. The “Cell proliferation” 3 layers network. The
diamond nodes are the seed genes. The black nodes are the
second layer genes related to “Cell proliferation” in GO
Biological Process or their predictors. The white genesre a
the seed genes that are not predictors of genes related to
“Cell proliferation”, that are the gray ones. The darker
arrows indicate the predictions from second to third layer
genes. The size of the nodes are proportional to the number
of linkages.
Copyright © 2012 SciRes. ABCR
In the group of 386 genes that [22] discovered as in-
fluenced by estrogen, they performed an experiment us-
ing chromatin immunoprecipitation (ChIP) to characterize
the interaction between ER and the regulatory elements of
candidate target genes. Through this experiment they
found 89 genes. As we previously explained, it is our
interest to discover what and how genes directly regu-
lated by estrogen are related to each other and to other
genes. Therefore, we used these 89 genes as seed genes
in our second experiment. We performed the search of all
of them in GO Biological Process in order to find the
annotated ones. This search resulted in a group of 53
genes, which were used as the seed genes. Then, we
added to the network (Figure 3), which has only two
layers, the genes that were predicted by the seed genes
with mean conditional entropy lower than 0.08 (as de-
scribed previously, this threshold adds to the network
less than 5% of the whole set of genes). It resulted in a
layer with 412 genes.
After that, we performed a search among the biologi-
cal functions of these 412 genes in Gene Ontology. Sev-
eral biological functions known to be related to estrogen
(like “Cell proliferation” and “Cell differentiation”) were
found. In some levels of the GO classification (Figure 4),
we discovered a function related to estrogen that is not so
prominent in the literature. Out of the 412 genes pre-
dicted by the 53 initial seed genes, 27 are related to “Cell
adhesion”. In the first levels of GO enrichment analysis,
“Cell adhesion” appeared as the most enriched biological
function category. This is an important discovery, be-
cause it is known that cell adhesion has a direct relation-
ship to cancer morphogenesis [28]. Roughly speaking,
Figure 4. List of 12 most enriched “GO Biological Process”
categories (level 8), in which “Cell adhesion” is present. Of
the 412 genes predicted by the first layer, 27 of the anno-
tated ones (183) are related to “Cell adhesion”.
reduced intercellular adhesiveness allows cancer cells to
disobey the social order, resulting in destruction of his-
tological structure, which is the morphological hallmark
of malignant tumors.
4. Discussion
Our pipeline is suitable for small data sets, takes into
account the biological knowledge and contributed for
understanding the physiopathology of breast cancer in-
duced by estrogen. It also has not high system require-
ments (for example, the user can easily run the program
in a 256 MB of system memory, a 2 GHz processor and 1
GB of disk space). Using the predicted genes by seeds
related to cell proliferation we can propose new genes
involved in the tumor proliferation. It is important to note
that from 28 genes proposed as important genes reted
the second
to tumor proliferation in breast cancer 18 have been
validated in the literature as cancer proliferating genes.
Another important information to cite is that in the first
experiment (Figure 5) we can observe that
Figure 3. “Cell adhesion” network. The white nodes are the
seed genes. The gray ones are the genes predicted by the
seed genes and the black ones are the predicted genes re-
lated to “Cell adhesion” in GO Biological Process.
Copyright © 2012 SciRes. ABCR
Copyright © 2012 SciRes. ABCR
Figure 5. The GO Biological Process 12 most enriched categories by the genes of our first experiment. Each column corre-
sponds to one layer. In the first and in the second layer we chose only the genes related to “Cell proliferation” to be the pre-
dictor genes of the next step. Figure genera te d by F unnet [27].
layer “Cell proliferation” related genes predictors are the
ones with more linkages (the hub ones). It confirms the
importance that these genes have in the network [29].
The metastasis process consists in a complex sequence
of events involving the tumor cells and properties of the
host organism [30]. The detachment of the tumor cells of
the primary tumor is considered the first and more im-
grow and promote spontaneous metastasis have, in gen-
eral, demonstrated an inverse relation to cell adhesion
function and metastatic ability. The relation of estrogen
as regulator of genes related to cell adhesion is not very
prominent in the literature. In this work, we could obtain,
from a time-course microarray experiment using cells
submitted to estrogen, a strong evidence of estrog
related to cell adhesion. For each one of these 27 genes, a
portant event in the metastatic process. The tumor cells
can be easier separated from a compact tumor tissue than
normal cells near a normal tissue [31]. This separation of
mor cells is regulated by the cell adhesion property of
regulating genes related to cell adhesion. From an initial
list of 53 genes directly regulated (also called direct tar-
gets) by estrogen [22], we obtained a list with 27 genes
the tumor. The cell adhesion biological function is ap-
plied to genes related to adhesion molecules, those acting
as positive or negative modulators in the metastasis
process [32,33]. Despite the rapid progress in the under-
standing of cell adhesion biology, the few available data
turns hard the proposition of a simple model in which the
cell adhesion molecules can be related to the tumor
growing and metastasis. Studies where tumor cells are
injected intravenously have, in general, shown an in-
crease in the adhesion function of these cells and had a
positive correlation to the metastatic ability. Those stud-
ies have a bias in determining that the high adhesion
property of these cells makes that they have more facility
to bind to circulation cells and be deposited in different
regions of the organism. On the other hand, studies that
implant tumor tissues in organisms allowing them to
prediction table, relating the gene to the initial list, was
These results indicate a strong relation between estro-
gen and cell adhesion genes, which could have a role in
metastasis. The most of those genes have been related to
invasion and metastatic process in cancer as can be seen
in Supplementary Table 22. Five have already been asso-
ciated with breast cancer validating our approach to
search for genes related to breast cancer proliferationin-
duced by estrogen: BCAR3 regulates Src/p130 Cas asso
ciation, Src kinase activity, and breast cancer adhesion
ropilin-2 expression in breast cancer correlates with ly-
mph node metastasis and poor prognosis. Tumour-asso-
ciated tenascin-C isoforms promote breast cancer cell in-
vasion and growth by matrix metalloproteinase-depend-
ent and independent mechanisms. SPOCK (SPARC) is a
proteoglycan reported to be associated to poor outcome
in breast cancer [34] and resistance to first-line ta-
moxifen treatment [35]. It is also interesting to note that
some genes related to families of proteins implicated in
the developing nervous system may play an important
role in cancer [36,37] and we found some of them:
5. Acknowledgements
The authors are grateful to FAPESP (99/12765-2, 01/094
01-0, 04/03967-0 and 05/00587-5), CNPq (300722/98-2,
468 413/00-6, 521097/01-0 474596/04-4 and 491323/
05-0) and CAPES for financial support. This work was
partially supported by grant 1 D43 TW07015-01 from
the National Institutes of Health, USA.
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