U.S. patent application number 13/534578 was filed with the patent office on 2012-11-15 for computational analysis of the synergy among multiple interacting factors.
Invention is credited to Dimitris Anastassiou, Vinay Varadan.
Application Number | 20120290218 13/534578 |
Document ID | / |
Family ID | 38694700 |
Filed Date | 2012-11-15 |
United States Patent
Application |
20120290218 |
Kind Code |
A1 |
Anastassiou; Dimitris ; et
al. |
November 15, 2012 |
Computational Analysis of the Synergy Among Multiple Interacting
Factors
Abstract
A method is provided for selecting two or more genes from gene
expression data. In the method, gene expression data for a
plurality of genes is provided, where the gene expression data
include expression levels for each of the plurality of genes. The
gene expression data is discretized. Based on the discretized gene
expression data, the synergy among the plurality of genes with
respect to a phenotype, for example, presence or absence of a
disease in a tissue, is evaluated. Two or more genes whose synergy
exceeds a predetermined threshold are selected. A system
implementing the method is also provided.
Inventors: |
Anastassiou; Dimitris;
(Tenafly, NJ) ; Varadan; Vinay;
(Hastings-on-Hudson, NY) |
Family ID: |
38694700 |
Appl. No.: |
13/534578 |
Filed: |
June 27, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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12307694 |
May 4, 2009 |
8234077 |
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PCT/US2007/068666 |
May 10, 2007 |
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13534578 |
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60799271 |
May 10, 2006 |
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60885349 |
Jan 17, 2007 |
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Current U.S.
Class: |
702/19 ;
702/189 |
Current CPC
Class: |
C12Q 1/6883 20130101;
C12Q 2600/158 20130101 |
Class at
Publication: |
702/19 ;
702/189 |
International
Class: |
G06F 19/22 20110101
G06F019/22; G06F 15/00 20060101 G06F015/00 |
Claims
1. A method for selecting factors from a data set of measurements,
the measurements including values of the factors and outcomes,
comprising: identifying two or more factors that are jointly
associated with one or more outcomes from the data set; and
analyzing each of the two or more factors to determine at least one
cooperative interaction among the factors with respect to an
outcome.
2. The method of claim 1, wherein the two or more factors comprise
a module of factors.
3. The method of claim 1, wherein the two or more factors comprise
a sub-module of factors.
4. The method of claim 1, wherein the at least one interaction
comprises a structure of interactions.
5. The method of claim 1, wherein the two or more factors comprise
two or more genes, the data includes gene expression data
comprising expression levels for each of the two or more genes, and
the one or more outcomes includes presence or absence of a
disease.
6. The method of claim 5, wherein the two or more genes comprise a
module of genes.
7. The method of claim 6, wherein the module of genes comprise a
smallest cooperative module of genes with joint expression levels
that can be used for a prediction of the presence of disease.
8-16. (canceled)
17. A system for selecting factors from a data set of measurements,
each measurement comprising values of the factors and outcomes
comprising: at least one processor, and a computer readable medium
coupled to the at least one processor, having stored thereon
instructions which when executed cause the at least one processor
to: identify two or more factors that are jointly associated with
one or more outcomes or factors from the data; and analyze each of
the two or more factors to determine at least one cooperative
interaction among the factors with respect to an outcome or
factor.
18. The system of claim 17, wherein the two or more factors
comprise a module of factors.
19. The system of claim 18, wherein the module of factors comprises
at least one sub-module of factors.
20. The system of claim 18, wherein the at least one cooperative
interaction comprises a structure of interactions.
21. The system of claim 20, wherein the at least one cooperative
interaction comprises a logic function.
22. The system of claim 21, wherein the two or more factors
comprise two or more genes, the data comprises gene expression data
comprising expression levels for each of the two or more, and the
one or more outcomes comprise presence or absence of a disease.
23. The system of claim 22, wherein the two or more genes comprise
a module of genes.
24. The system of claim 23, wherein the module of genes comprises
at least one sub-module of genes.
25. The system of claim 23, wherein the module of genes comprises a
smallest module of genes with joint expression levels that can be
used for a prediction of the presence of disease with high
accuracy.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] The present application claims priority to U.S. Provisional
Application Ser. No. 60/799,271 filed May 10, 2006 and U.S.
Provisional Application Ser. No. 60/885,349 filed Jan. 17, 2007,
the entire contents of which are incorporated by reference
herein.
BACKGROUND
[0002] The disclosed subject matter relates generally to systems
and methods for factor selection, including factors useful in gene
expression analysis.
[0003] The expression levels of thousands of genes, measured
simultaneously using DNA microarrays, can provide information
useful for medical diagnosis and prognosis. However, gene
expression measurements have not provided significant insight into
the development of therapeutic approaches. This can be partly
attributed to the fact that while traditional gene selection
techniques typically produce a "list of genes" that are correlated
with disease, they do not reflect interrelationships.
[0004] Gene selection techniques based on microarray analysis often
involve individual gene ranking depending on a numerical score
measuring the correlation of each gene with particular disease
types. The expression levels of the highest-ranked genes tend to be
either consistently higher in the presence of disease and lower in
the absence of disease, or vice versa. Such genes usually have the
property that their joint expression levels corresponding to
diseased tissues and the joint expression levels corresponding to
healthy tissues can be cleanly separated into two distinct
clusters. These techniques are therefore convenient for
classification purposes between disease and health, or between
different disease types. However, they do not identify cooperative
relationships or the synergy among multiple interacting genes.
[0005] There is therefore a need for the ability to analyze genes
in terms of the cooperative, as opposed to independent, nature of
their contributions towards a phenotype.
SUMMARY
[0006] The disclosed subject matter provides techniques for the
analysis of the cooperative interactions or synergy among multiple
interacting factors. The factors can be features, elements or
outcomes that are cooperatively associated with one or more factors
or outcomes by their joint presence or absence.
[0007] In some embodiments of the disclosed subject matter, methods
for selecting factors from a data set of measurements are provided.
The measurements can include values of factors and/or outcomes. Two
or more factors that are jointly associated with one or more
outcomes from the data set are identified. Each of the two or more
factors are analyzed to determine at least one cooperative
interaction among the factors with respect to an outcome or factor.
The factors can be a module of factors or a sub-module of factors.
The interaction can be a structure of interactions.
[0008] The factors can include two or more genes. The data set can
include gene expression data including expression levels for each
of the genes. The outcomes includes presence or absence of a
disease, and the genes can be a module of genes, preferably a
smallest cooperative module of genes with joint expression levels
that can be used for a prediction of the presence of a disease with
high accuracy.
[0009] In other embodiments of the disclosed subject matter,
methods for selecting two or more genes from gene expression data
are provided. The gene expression data can include expression
levels for each of the two or more genes. The method includes
providing gene expression data for two or more genes, discretizing
the gene expression data, identifying the two or more genes with a
high synergy, and identifying a cooperative interaction that
connects the expression levels in the two or more genes with
presence or absence of a disease. The gene expression data can be
derived from at least one microarray of gene expression data. The
genes can be a module of genes. The cooperative interaction can be
modeled using a Boolean function, a parsimonious Boolean function,
or the most parsimonious Boolean function. The high synergy can be
a maximum synergy.
[0010] In other embodiments of the disclosed subject matter,
systems for selecting two or more genes from gene expression data
are provided. The gene expression data includes expression levels
for each of the two or more genes. The system includes at least one
processor, a computer readable medium coupled to the processor
including instructions which when executed cause the processor to
provide gene expression data for the genes. The instructions also
cause the processor to discretize the gene expression data, choose
a single threshold for each of the two or more genes, identify the
two or more genes with a high synergy, and identify a cooperative
interaction that connects the expression levels in the two or more
genes with presence of a disease. The gene expression data can be
derived from a microarray of gene expression data. The two or more
genes can be a module of genes. The high synergy can be a maximum
synergy.
[0011] In other embodiments of the disclosed subject matter,
systems for selecting factors from a data set of measurements are
provided. Each measurement can include values of the factors and
outcomes. The system includes at least one processor and a computer
readable medium coupled to the at least one processor. The computer
readable medium includes instructions which when executed cause the
processor to identify two or more factors that are jointly
associated with one or more outcomes or factors from the data, and,
analyze each of the two or more factors to determine at least one
cooperative interaction among the factors with respect to an
outcome or factor. The factors can be a module of factors. The
module of factors can include at least one sub-module of factors.
The cooperative interaction can include a structure of
interactions, such as a logic function.
[0012] The two or more factors can be two or more genes, the data
can include gene expression data including expression levels, and
the outcomes can be the presence or absence of a disease. The genes
can be a module of genes. The module of genes can include at least
one sub-module of genes. The module of genes can be a smallest
module of genes with joint expression levels that can be used for a
prediction of the presence of disease.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] FIG. 1 is a diagram according to some embodiments of the
disclosed subject matter.
[0014] FIG. 2 is a diagram according to some embodiments of the
disclosed subject matter.
[0015] FIG. 3 is a diagram according to some embodiments of the
disclosed subject matter.
[0016] FIG. 4 is a schematic diagram according to some embodiments
of the disclosed subject matter.
DETAILED DESCRIPTION
[0017] According to some aspects of the disclosed subject matter, a
method for selecting factors from a data set of measurements is
provided. The method includes identifying factors cooperatively
associated with an outcome from a data set for two or more factors,
and analyzing each of the factors or modules of factors to
determine cooperative or synergistic interactions among the factors
or outcomes with respect to the outcome. The data set can be a set
of measurements that includes values of the factors and the
outcomes.
[0018] One application of the disclosed subject matter is where the
factors are genes and the inference of the cooperative relationship
or synergy among multiple interacting genes is desired. Although
the following will describe disease data it can be more generally
applicable to other data sets.
[0019] Other applicable data sets include other biological data
such as how cells are influenced by stimuli jointly, financial
data, internet traffic data, scheduling data for industries,
marketing data, and manufacturing data, for example. Table 1,
below, specifies other data sets relevant to various objectives,
including factors and outcomes, to which the disclosed subject
matter can also be applied:
TABLE-US-00001 TABLE 1 Objective Factors Outcomes Disease pathway
Gene expression Disease identification Synaptic specificity Gene
expression Neural synapses factors Disease susceptibility Single
Nucleotide Disease of specific genotypes Polymorphisms (SNPs)
Genotypic basis SNPs Gene expression for gene expression profiles
Gene regulation Gene expression Gene expression factors Gene
expression Gene expression SNP association with individual SNPs
Pharmacogenomics SNPs Drug resistance Drug side-effect SNPs Side
effect of drug modeling Stocks/bonds/currency Stocks/bonds/currency
price Sell/Buy at given selling/buying price time series data price
identification Macroeconomic Macroeconomic time series Federal
interest rate models such as consumer index, increase/decrease
housing market index, trade balance, etc
[0020] Referring to FIG. 1, gene expression data for two or more
genes is provided 101 in the form of, for example, a microarray of
expression data. The gene expression data is then discretized 102.
For example, the data can be binarized into two levels. Other
levels of discretization, such as trinarization, can also be
used.
[0021] Rather than independently binarizing each gene's expression
level, which can be more appropriate for an individual gene ranking
approach, single thresholds are used for the genes. This approach
is consistent with the fact that finding global interrelationships
among genes is desirable and that the microarray data have already
been normalized across the tissues and genes. Therefore, a choice
of high threshold will identify the genes that are "strongly"
expressed, while a choice of a low threshold will identify the
genes that are expressed even "weakly." Entropy Minimization and
Boolean Parsimony ("EMBP") analyses can be performed across several
thresholds and to determine the threshold levels that provide
optimized performance, as disclosed in International Application
No. PCT/US06/61749, the disclosure of which is incorporated herein
by reference.
[0022] Following binarization, each gene can be assumed to be
either expressed or not expressed in a particular tissue. It can
also be assumed that there are two types of tissues, either healthy
ones or tissues suffering from a particular disease. For example,
Table 2, below shows results from hypothetical microarray
measurements of three genes, G.sub.1, G.sub.2, and G.sub.3 in both
the presence and absence of a particular cancer C. N.sub.0 and
N.sub.1 represent the presence and absence of cancer,
respectively.
TABLE-US-00002 TABLE 2 G.sub.1 G.sub.2 G.sub.3 N.sub.0 N.sub.1 0 0
0 2 6 0 0 1 0 24 0 1 0 2 7 0 1 1 0 26 1 0 0 1 7 1 0 1 0 25 1 1 0 76
1 1 1 1 19 4
[0023] The latter assumption can also be generalized to include
more than two types of tissues, or modified to be used for
classification among several types of cancer. According to one
aspect of the disclosed subject matter, two or more genes with a
high synergy are identified 103, as detailed below.
[0024] Cooperative or synergistic interactions between multiple
genes can then be determined 104, as shown in FIG. 1. Because
systems biology is based on a holistic view of biological systems,
synergy is important.
[0025] A gene set of n genes can have expression levels G.sub.1,
G.sub.2, . . . , G.sub.n and a particular outcome C can be any
phenotype, such as the presence of a particular disease or the
differentiation of stem cells into a particular cell type when
analyzing expression data of human tissues. The synergy
Syn(G.sub.1, G.sub.2, . . . , G.sub.n;C) of the gene set with
respect to the phenotype C is defined by equation (1):
I ( G 1 , G 2 , , G n ; C ) - max all partitions { S i } such that
i S i = { G 1 , , G n } and i S i = .0. i I ( S i ; C ) ( 1 )
##EQU00001##
[0026] The partition of the gene set that is chosen in equation (1)
above is the one that maximizes the sum of the amounts of mutual
information connecting the subsets of that partition with the
phenotype 104 as shown in FIG. 1, and it is referred to as the
"synergistic partition" of the gene set {G.sub.1, G.sub.2, . . . ,
G.sub.n} with respect to the phenotype C. The definition is
consistent with the intuitive concept that synergy is the
additional amount of contribution for a particular task provided by
an integrated "whole" compared with what can best be achieved,
after breaking the whole into "parts," by the sum of the
contributions of these parts. The above quantity can be divided by
the entropy H(C) from EMBP analysis, in which case the maximum
possible thus normalized synergy will be +1.
[0027] For the special case of n=2, the synergy is defined as shown
in equation (2):
Syn(G.sub.1,G.sub.2;C)=I(G.sub.1,G.sub.2;C)-[I(G.sub.1,C)+I(G.sub.1,C)].
(2)
[0028] Equation (2) is symmetric with respect to the three random
variables and equal to the opposite of the mutual information
I(G.sub.1;G.sub.2;C) common to the three variables G.sub.1,
G.sub.2, C. Contrary to the mutual information common to two
variables, the mutual information common to three variables is not
necessarily a nonnegative quantity. This allows for a strictly
positive synergy.
[0029] In one example, it can be assumed that each of the genes
G.sub.1 and G.sub.2 is equally (50% of the time) expressed when C=1
and C=0. In that case, it would appear that the two genes are
uncorrelated with the phenotype C, because
I(G.sub.1;C)=I(G.sub.2;C)=0, and the genes would not be found high
up in any typical "gene ranking" computational method. However, C
can to be determined with absolute certainty from the joint state
of the two genes, for example when C=1 if G.sub.1=G.sub.2, and C=0
if G.sub.1.noteq.G.sub.2, in which case I(G.sub.1, G.sub.2;C)=1,
and the synergy is positive and equal to +1. On the other hand, if
G.sub.1=G.sub.2=C then the synergy is negative and equal to -1.
More generally, if G.sub.1=G.sub.2= . . . =G.sub.n=C (ultimate
redundancy) then the multivariate synergy can become even more
negative and equal to -(n-1).
[0030] Since H(C|G.sub.1, G.sub.2, . . . , G.sub.n)=H(C)-I(G.sub.1,
G.sub.2, . . . , G.sub.n;C), EMBP analysis naturally tends to find
high-synergy results, although not necessarily the most synergistic
ones.
[0031] In another example, as shown in Table 2, equation (3) can be
used for n=3 and is simplified by omitting the phenotypes.
Syn.sub.123=I.sub.123-max(I.sub.1+I.sub.23,I.sub.2+I.sub.13,I.sub.3+I.su-
b.12,I.sub.1+I.sub.2+I.sub.3) (3)
[0032] The values for mutual information between gene subsets and
the phenotype can then be found in this example as follows:
I.sub.123=0.7963; I.sub.12=0.7152; I.sub.13=0.5094;
I.sub.23=0.5163; I.sub.1=0.3235; I.sub.2=0.3335; and
I.sub.3=0.2782.
[0033] Positive synergy implies some form of direct or indirect
interaction of the genes, as a system. This definition of synergy
also allows for insight into the structure of potential pathways by
making iterative use of the "synergistic partition," defined
earlier, to generate a hierarchical decomposition of the gene set
into smaller modules. In particular, consider a rooted and not
necessarily binary tree with n leaves, each of which represents one
of the genes. Each node of the tree represents a subset or
sub-module of genes, which contains the genes represented by the
leaves of the Blade formed by the node. Therefore the root
represents the whole gene set. The synergistic partition of the
whole gene set, as defined above, can then be represented by the
branching of the root, so that the nodes that are neighboring to
the root represent the gene subsets or sub-modules defined by the
synergistic partition 105, 106 as shown in FIG. 1. Some of these
nodes can be leaves, representing a single gene. If they are not
leaves, then they represent a subset of genes, which has its own
synergistic partition, defined and evaluated as above, with respect
to the phenotype. This methodology can be repeated for all gene
subsets, until the full tree is formed 107 as outlined in FIG. 1.
This is referred to as the tree of synergy of the gene set
{G.sub.1, G.sub.2, . . . , G.sub.n} with respect to the phenotype
C. Each intermediate node of the tree of synergy identifies a gene
subset or sub-module with nonnegative synergy.
[0034] As shown in FIG. 2, G.sub.1 and G.sub.2 can be a subset of
genes or a module or sub-module of genes that together have a
nonnegative synergy 202 and a third independent gene G.sub.3 with a
negative synergy 201 between itself and the subset of G.sub.1 and
G.sub.2. In the example of Table 2, the synergy between G.sub.1 and
G.sub.2 is +0.0582 and the synergy between the subset of G.sub.1
and G.sub.2 and G.sub.3 is -0.1971.
[0035] The synergy, as defined above, refers to the combined
cooperative participation of all n genes. If, for example, the
expression of one of these genes is independent of all the other
genes including the phenotype, then the synergy of the n-gene set
will be zero, even if the set contains synergistic subsets or
sub-modules. Therefore, for a thorough synergistic analysis of a
gene set, it can be desirable to also identify the most synergistic
subsets of size n-1, n-2, . . . , 2, which may not necessarily
appear in the tree of synergy. For n=3, however, it can be proved
that the most synergistic subset of size 2, if it has positive
synergy, is defined by an existing clade of the full tree of
synergy. In this way, the disclosed subject matter identifies a
cooperative or synergistic interaction that connects the expression
levels in two or more genes with the presence or absence of
disease. The interaction can be modeled using, for example, using a
most parsimonious Boolean function as disclosed in International
Application No. PCT/US06/61749.
[0036] For small gene set sizes n, such as 3 or 2, it is possible
to identify all the synergistic sets of genes by doing a search of
possible gene sets of size n. However, as the size increases,
searches of all gene sets become computationally expensive and
therefore heuristic methods can be employed to find a collection of
gene sets with positive synergy, as shown in FIG. 3. Starting with
the binarized gene expression data 301 an initial random gene set
is first chosen 302 and the synergy of the gene set is calculated
304. If the synergy is greater than a predetermined threshold 305
the gene set is added to the list of gene sets with synergy. The
predetermined threshold could be zero, for example. The gene set is
then modified using a heuristic algorithm such as simulated
annealing 303 to identify a new gene set whose synergy is evaluated
303. If the synergy of the new gene set is positive, it is added to
the list of existing gene sets 306. This process is repeated until
the desired number of gene sets is reached. The gene sets are then
selected based on the statistical significance of their synergy
values 307.
[0037] For small sizes of gene sets, synergistic analysis can be
done with algorithms that list all the partitions of a particular
set of genes. The total number of partitions of a set with n
elements is given by the "Bell number." As the values of n
increase, however, the increased computational complexity makes the
problems more complex and heuristic solutions can be used to do the
analysis.
[0038] The techniques of the disclosed subject matter can be
implemented by way of off-the-shelf software such as MATLAB, JAVA,
C++, or other software. Machine language or other low level
languages can also be utilized. Multiple processors working in
parallel can also be utilized.
[0039] As illustrated in the embodiment depicted in FIG. 4, a
system in accordance with the disclosed subject matter can include
a processor or multiple processors 404 and a computer readable
medium 401 coupled to the processor or processors 404. The computer
readable medium includes data such as factors and outcomes 402 and
can also include programs for synergy analysis and/or EMBP analysis
403. The system leads to the identification of the synergy,
synergies or cooperative interaction(s) among multiple interacting
factors 405. Multiple processors 404 working in parallel can also
be utilized.
[0040] The foregoing merely illustrates the principles of the
disclosed subject matter. Various modifications and alterations to
the described embodiments will be apparent to those skilled in the
art in view of the teachings herein. It will thus be appreciated
that those skilled in the art will be able to devise numerous
techniques which, although not explicitly described herein, embody
the principles of the disclosed subject matter and are thus within
the spirit and scope of the disclosed subject matter.
* * * * *