Graphics Reference
In-Depth Information
sickorlethal(SSL)to SIS
(Tongetal.,
;Tongetal.,
)waspredicted;checked
against the quantitative RT-PCR, the inferred results are satisfactory.
Visualization for Genetic Network
Reconstruction
1.3
Clustering and Graphical Models
1.3.1
Cell cycle regulated genes display periodicity through two cell cycles in the alpha,
cdc
and cdc
data sets of Spellman et al. (
). For genes that show periodic
expression across phases, the target gene B may be enhanced in the S phase but it
may be repressed or there may be no interaction with the gene B in other phases.
his suggests that the interaction between two given genes may vary from phase to
phase over a cell cycle. Due to data limitations, most of the approaches used so far
have assumed that genetic interactions are invariant across time or phase, but there
are some approaches that have dealt with genetic interactions that vary with phase,
e.g., Toh and Horimoto (
) and Aburatani et al. (
). hese authors utilized
clustering and a graphical model to infer interactions of pseudogenes that may vary
across phases, where a pseudogene denotes a group of genes clustered via similar
gene expression patterns.
Modelinggeneticinteractionsthatvarywithphaserequiresmore(fourtimesmore
for four phases in a cell cycle) data than those that have interactions that are invari-
ant with phase. To reduce the huge number of interactions among genes in a given
genome, graphical model requires that clustering is performed as a preprocessing
step.Namely, coexpressed genes are grouped into clusters,and each cluster is treated
asarandomvariable toinferitsinteraction withotherclusters.Forinstance, ahierar-
chical clustering analysis was applied in Toh and Horimoto (
)to aggregate
genes into
clusters. he averaged expression profile of each cluster was then ana-
lyzed by a graphical Gaussian model (GGM). Inevitably, this makes it more di
cult
to interpret the meaning of such interactions. his GGM inferred direct interactions
between variables based on their partial correlations, which is a function of the ele-
ments in Σ
−
, where Σis the covariance matrix.
AgraphG
,whereV and E denote a set of vertices (variables) and a set
of orderededges (the associations between pairs of variables), represents the interac-
tions among M clusters. Note that G assumes the Markov property. he chain graph
model (Aburatani et al.,
) consists of the following steps. First, the variables are
partitioned intoafeworderedblocks,e.g.,fourblocksforfourphases.Second,within
each block, the conditional independence of each pair of variables is tested by a like-
lihood ratio test given the rest of the variables in the block. his likelihood ratio test
is based on the inverse of the covariance matrix Σ
−
, If the conditional direct associ-
ation of two given variables is significant, then an undirected edge is drawn between
them. hird, one can similarly test for the conditional independence between any
=(
V, E
)
