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Constructing linked gene sets by analyzing
conditional probabilities in microarrays
Jose Pacheco1, Stuart Winter2, Ksenia Matlawska-Wasowska2, Judy Cannon3, and David Torres1
Department of Mathematics, Northern New Mexico College1
Department of Pediatrics, University of New Mexico Health Sciences Center2
Department of Pathology, University of New Mexico Health Sciences Center3
Abstract
In the PLoS ONE publication, “SelfContained Statistical Analysis of Gene
Sets,” [1] we describe a permutation
method that not only computes the pvalue of a gene set but also the
conditional probability or dependence
of genes, P(A|B). P(A|B) is the
probability that gene A is
differentially expressed given that
gene B is differentially expressed.
These dependencies will allow us to
construct gene sets. Our project will
create new gene sets associated with
T-lineage Acute Lymphoblastic
Leukemia (T-ALL) and migration to
the Central Nervous System (CNS)
based on these dependencies using
expression levels from a microarray.
We will use a T-ALL CNS vs nonCNS microarray with 54,675
probes/genes and 49 patients.
Introduction
T-ALL is a heterogeneous disease
characterized largely by
chromosomal translocations which
manifest themselves in the arrested
development of thymocytes.
Treatment of T-ALL is complicated
when the disease migrates to the
Central Nervous System (CNS)
and CNS migration is also
associated with relapse. Genes
associated with T-ALL include
Notch and CD3D, and molecules
associated with CNS relapse
include the chemokine receptor
CCR7 and CARMA1 [2-3]. Yeoh
et al. [2] identify genes associated
with T-ALL relapse and emphasize
that a collection of genes and not a
single gene is necessary for an
accurate prediction of relapse. Our
project continues our work in
identifying and creating gene sets
associated with T-ALL CNS
migration using microarrays since
the progression of the disease may
take multiple pathways and involve
many genes.
Constructing conditional
probabilities using permutations
Given the probability levels of
individual genes, a modified
Fisher’s method can be used to
compute the p-value of a gene set to
set a lower limit pmin given the
individual p-values of its genes pk.
Accounting for Dependencies
Among Genes
Computing Genes Sets
A differentially expressed gene A will
be connected to first generation genes
Ai that show a high level of
dependence. A differentially expressed
gene A can be linked to a gene B
through direct dependence and through
shared dependencies among their
respective first generation genes Ai and
Bi.
Applying the Method to
T-ALL
A microarray was used to
Fisher’s method assumes gene
compare 22 T-ALL CNS patients
independence (i.e. the
with 27 T-ALL non-CNS
differential expression of one
patients and 54,675
gene does not influence the
genes/probes. Dependencies
differential expression of
were calculated using the 22
another gene). However genes
T-ALL CNS patients.
within a gene set are related and
thus may exhibit dependencies.
Results
To overcome this statistical
Gene
p-value
Connections
dilemma, the phenotypic labels PLDN
1.0e-5
of a gene are permuted. The
CEP27
4.4e-4
15
FLJ36840
5.2e-4
14
p-value of the original
CCDC3
1.2e-4
14
unpermuted gene is then
CNTNAP3B
5.2e-4
12
computed by determining its
ADCY5
1.7e-4
14
rank among the large number of CCL18
4.8e-4
12
permutations.
LOC146439
6.2e-4
11
Computing Dependencies
In the permutation procedure, the
number of times that a gene A, a
gene B, and both gene A and B are
differentially expressed is tracked.
The equation p(A and B) =
p(A)p(B|A) is then used to
compute the dependency p(A|B).
Relationship with
Distance Correlation
RTP1
LASS6
C150RF42
TCL6
PRDM13
4.4e-4
1.2e-3
4.8e-4
1.2e-3
7.3e-4
10
9
9
9
9
References
[1] Torres et al. Self-contained statistical
analysis of gene sets. PLoS ONE. 2016, 118. e0163918.
doi:10.1371/journal.pone.0163918
[2] Oruganti, SR et al. CARMA1 is a novel
regulator of T-ALL disease and leukemic cell
migration to the CNS. Leukemia. 2017; 31,
255-238. doi: 10.1038/leu.2016.272
[3] Yeoh E-J et al. Classification, subtype
discovery, and prediction of outcome in
pediatric acute lymphoblastic leukemia by
gene expression profiling. Cancer Cell. 2002;
1, 133-143.
[4] Maiorov EG et al. Identification of
interconnected markers for T-cell acute
lymphoblastic leukemia. BioMed Research
International. 2013; 1-20.
http://dx.doi.org/10.1155/2013/210253.
Acknowledgements
The authors would like to
acknowledge the NM-INBRE.