Intracellular Dissipative Structures (IDSs) - Molecular Theory of the Living Cell - page 251

such as proteins, RNA, and DNA that can form gradients, it would be necessary
to distinguish their dissipatons with appropriate adjectives. Thus, the X dissipaton
(e.g., RNA dissipatons) will denote the dissipaton consisting of the concentration
gradient of X. An X dissipaton comprises two aspects - (1) the static structure of X
which is an equilibrium structure, and (2) the dynamic aspect of X which is a process
derived from or rooted in (1). These two aspects of X form the two of the three
elements constituting a function, the third element being the mechanism of producing
dynamic processes from static structures (see Fig. 6.9 ). Furthermore, it is here
recommended that, whenever convenient, the term “ribons” be used to refer to RNA
dissipatons, the term “ribons” being derived from “ribonucleic acid .” Unlike
equilibrons (e.g., genes defined as sequences of nucleotides), which are stable enough
to be isolated, purified, and sequenced, dissipatons are dynamic and ephemeral
in the sense that, whenever attempts are made to isolate them, they disappear, just as
the flame of a candle disappears if attempts are made to capture it. The main objective
of this section is to describe and use the software known as ViDaExpert to characterize
and classify RNA dissipatons or ribons in cells. The computational method presented
in this topic (see Chaps. 18 1nd 19) should be applicable to studying other
kinds of dissipatons , including pericellular and extracellular concentration gradients
(e.g., gradients of morphogens and cheomoattractants in tissues and hormones in
blood), EEG patterns, and many other time-series data, since they are undoubtedly
instances of dissipative structures (or dissipatons), their existence being dependent on
free energy dissipation.
The software ViDaExpert was developed in (Zinovyev 2001; Gorban and
Zinovyev 2004, 2005) and is freely available at http://bioinfo-out.curie.fr/
projects/vidaexpert/ .
The term ViDaExpert derives from “the visualization of multidimensional
data Expert” program. It is a tool for visualizing high-dimensional data on a
lower-dimensional space for easy visual examination and analysis of their spatio-
temporal patterns and regularities. The main technique implemented in ViDaExpert
is the method of elastic maps, an advanced analog of the method of self-organizing
maps. In addition, it embodies many other methods of data analysis such as
principal component analysis, various clustering methods, linear discriminate anal-
ysis, and linear regression methods (Gorban and Zinovyev 2004, 2005).
The RNA kinetic data can be displayed in an abstract six-dimensional mathe-
matical space wherein each point is associated with six numbers, each representing
the concentration of an RNA molecule (or RNA equilibron) measured at one of
the six time points 0, 5, 120, 360, 450, and 850 min measured after switching
glucose to galactose (Garcia-Martinez et al. 2004). ViDaExpert was used to
visualize the six-dimensional kinetic data of the genome-wide RNA levels of
budding yeast on a two-dimensional principal grid with n 2 nodes where n is the
dimensionality of the grid which was varied from 2 to 15. The elastic coefficients,
that is, stretching coefficient , were also varied from 0 to

50, but, having found no significant improvement in clustering behaviors of the data
points, these elastic coefficients were kept constant at 0 for most analysis.

l and bending coefficient m