Graphics Reference
In-Depth Information
histime-lagged correlation approachresultedinapredictednetworkcomprising
groups of
genes; a simplified network, obtained at iteration
,is shown in Fig.
.
.
he graph illustrates zero-lagged highly correlated groups at the same time point.
Moreover, it depicts groups that are correlated between different time points, which
demonstratesthedynamicinteractionsbetweengroupsacrosstimemuchmoreclear-
ly than when any analytical method is used. Among the predicted groups, several
have known light-stimulated gene clusters - for example carbon dioxide fixation
pathways - while others are novel findings.
A Smooth Response Surface Approach
1.3.3
Let A, R and T denote the activator (enhancer), the repressor and their regulated
target gene, respectively. Woolf and Wang (
) proposed that the interaction re-
lation of A, R and T could be elucidated via a fuzzy logic algorithm, where A and
R are inputs and T is the output. he fuzzy logic function used is discrete and has
the drawback that it can map two adjacent boundary inputs to two quite different
outputs. hefuzzylogic algorithm wasimproved bythe smooth response surface ap-
proach (Xu et al.,
), which provides a continuous regulatory influence that has
biological bearing. Xu and his colleagues proposed that the triplets could be fitted to
the following response surface:
A
(
−
R
)
A
.
,
.
R
S
(
A, R
)=
(
.
)
A
R,
.
A
,
R
.
−
(
−
)
A
R
.
,
otherwise.
−
+
his approach captures the basic idea that an activator increases its regulated target
gene'sexpressionlevelwhilearepressordecreasesitstargetgene'sexpressionlevel.To
fitgeneexpressionlevelsoftripletsintocertainfixedsurfaces(WuandHamada,
and Xu et al.,
), gene expression levels (in log
scale) were transformed into the
interval
. he minimum and maximum values of each gene were transformed
into
and
, respectively.
If a given triplet fits the (A, R, T) relation specified by the response surface in (
.
)
well, the predicted target gene's expression over time should be close to the observed
one's, and the mean squared error should be small compared tothe target gene's vari-
ance. hus the lack-of-fit and diagnostic functions are defined as follows:
[
,
]
T
t
T
t
=
(
T
t
−
)
)=
RT
(
A, R, T
(
.
)
T
T
t
=
(
T
t
−
)
and
T
T
t
=
RT
(
t
)
(
A, R, T
)−
RT
(
A, R, T
)
Diag
(
A, R, T
)=
(
.
)
RT
(
A, R, T
)
