Biology Reference
In-Depth Information
There are two ways of projecting data points to the principal grid (i.e., the grid
approximating the topology of the principal manifold calculated by ViDaExpert).
One way is to project data point to the nodes that are closest to them. The other is
to project data points perpendicularly to the closest surface on the principal
manifold. In analyzing the TL data from budding yeast using ViDaExpert, the
“closest node” method of approximating the principal manifold was employed.
12.8.2 Ribonoscopy: Looking at RNA
In the following discussions, I will distinguish between
RNA molecules
which are
equilibrium structures (i.e.,
equilibrons
) and
RNA trajectories
or
waves
which are
dissipative structures (i.e.,
dissipatons
) by using two different stems -
ribo-
referring
to the former and
ribono
- to the latter. Thus, “ribonoscopy” will denote the study of
the time-dependent RNA concentrations in the cell (i.e.,
RNA trajectories, ribons
or
RNA waves
) using DNA microarrays and computer-assisted analysis of microarray
data, i.e., RNA waves.
About 1,000 genes were selected out of a total of over 6,000 genes whose
transcripts were measured with DNA arrays in budding yeast after switching
the nutrient glucose to galactose (Garcia-Martinez et al. 2004). These genes were
selected for analysis because their transcript levels showed pronounced changes
induced by the nutritional shift. The data set under consideration consists of a table
with ~1,000 rows (each labeled with the name of the gene encoding the transcript
involved) and six columns representing the time points of measurements, i.e., 0, 5,
120, 360, 450, and 850 min after the nutritional shift. Thus, one gene is associated with
a set of six numbers, each representing the average of the triplicate measurements of
the transcript level of the genemeasured at one of the six time points.
We can represent
these data points in an abstract six-dimensional mathematical space
(to be called
the
RNA concentration space
), each axis representing one of the six time points of
measurements. In this six-dimensional space, one point is equivalent to six numbers,
which can be represented as a vector emanating from the origin of the six-dimensional
concentration space and ending at the point whose coordinate is specified by the
six numbers. The position of a point in the concentration space represents an
RNA trajectory in the concentration-time graph (see Fig.
12.1
as an example)
and hence encodes the
shape information
of such a trajectory. In other words,
differently shaped RNA trajectories will occupy different positions in the RNA
concentration space
.
When we inputted our six-dimensional data (typically 10
4
numbers) to the
ViDaExpert program, we obtained a table of numbers indicating the frequencies
(or probabilities) of individual RNA molecules (their names appearing at the
beginning of each row) exhibiting characteristic kinetic behaviors (or node num-
bers) appearing at the top of each column. This result of the ViDaExpert analysis
can be graphically represented in two ways - as a three-dimensional plot
(Figs.
12.10
,
12.11
) or a two-dimensional plot (Fig.
12.12
).
