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indicate the numbers of the transcripts clustering at different nodes. The addresses
of the columns on the grid reflect the different shapes of the RNA trajectories
(i.e., different kinetic behaviors of individual transcripts observed over the 850-
min time period), since the different shapes of the average RNA trajectories
of the glycolytic and oxidative phosphorylation genes shown in Fig.
12.2a
are
transformed by ViDaExpert into different distributions of the columns on the
principal grid. (Compare the left and the middle panels on the uppermost row in
Fig.
12.10
.)
Turning to one of the three columns, say, the left column, in Fig.
12.11
, we can
see the effects of changing the grid number from 4 to 25 to 64 (or n
¼
2, 5, and 8)
on the pattern of distributions of transcripts on the principal grid. As one increases
the grid number, the columns tend to get fragmented into smaller ones but their
characteristic pattern of clustering seems to be retained. In general, increasing the
grid number (which is equivalent to increasing the number of clusters in K-means
clustering) is akin to increasing the
resolution power
of a microscope with which
the clusters of the transcript trajectories in the six-dimensional space are viewed.
Figure
12.11
shows the RNA trajectories (i.e.,
ribons
) belonging to a set of eight
different metabolic pathways or functions - glycolysis (22 genes), protein degrada-
tion (15 genes), protein folding (11 genes), protein synthesis (156 genes), secretion
(26 genes), sterol metabolism (11 genes), transcription (15 genes), and RNAs with
unknown functions (294). The number of nodes in the principal grid (i.e., grid
resolution) is fixed at 64. The visual inspection of these plots clearly demonstrates
that the RNA trajectories (i.e.,
RNA dissipatons
or
ribons
) belonging to different
metabolic pathways/functions are distributed in distinct ways on the principal grid.
It has been found that these patterns of distribution of ribons are sensitive to small
variations (typically from 0.01 to 0.1) of the elastic coefficients,
. Thus, we
can express the
Pattern of the Distribution of Ribons
(PDR) associated with a
metabolic function, MF, on the principal grid with node n, stretching coefficient
l
l
and
m
, and bending coefficient
m
as in Eq.
12.20
:
PDR
¼
f(n
;
l
;
m
;
MF
;
EC)
(12.20)
where f is a function or a set of rules, and EC stands for the “experimental or
environmental conditions” under which observations are made such as the
glucose-galactose shift or normal vs. tumor tissues, etc.
Equation
12.20
can be interpreted as the ViDaExert-enabled visualization of the
metabolic pathways in cells in terms of ribons under a given observational condi-
tion. The PDR defined by Eq.
12.20
may provide a useful method for analyzing
microarray data with the goal of identifying
pathway-dependent or pathway-
specific biomarkers
that are the focus of intense current attention among workers
in the field of DNA array technology, because they possess the potential for
facilitating the discovery of drug targets for various diseases and for providing
diagnostic and pharmacotherpeutical tools for personalized medicine (Clarke et al.
2004; Burczynski et al. 2005; Watters and Roberts 2006; Boyer et al. 2006; Sears
