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3.8
The Ubiquity of Metabolism
The French mathematician Rene Thom quotes in his topic Structural Stability and
Morphogenesis [155] a statement by the Greek philosopher Eraclitus saying that
“fire rests by changing” ( Metabollon anapauetai ). Existence is transformation, and
metabolism is the basis of biochemical transformation. However, metabolism is not
only an important kind of transformation, but can be considered a paradigm within
which many kinds of dynamical systems can be represented. We have already seen
that real functions can be approximated by means of suitable MP systems (see Sect.
3.3), and we discussed in many points the prominent role of metabolism in cell
functionalities and its link with DNA replication. Here, we want to point out some
other fields, where the metabolic perspective could be naturally applied to analyze
phenomena from observed behaviors.
The solution of many problems consists in the ability to discover discrete dy-
namical systems that generate time series of an observed phenomenon. This yields
the identification of an internal state transition logic from an external phe-
nomenalistic evolution . The algorithm LGSS, which we presented in Sect. 3.4.2
provides a method for solving dynamical inverse problems by means of MP gram-
mars. Its resolution schema follows a pattern illustrated in Fig. 3.39. Therefore,
if we are able to describe a phenomenon in “metabolic terms”, within a suitable
class of MP grammars, the discovery of specific MP grammars modeling it can
be developed by means of LGSS. In Sect. 3.8.2, a very general notion of MP
grammar will be presented, which suggests a large applicability of this concept
for a wide class of dynamical systems. Of course, this enlarges the fields where
MP theory and LGSS methodology could be applied for solving dynamical in-
verse problems: from the time series of meteorological variables, to time series
of economic, or of ecological nature. What are the evolution rules that are re-
sponsible for the series we observe? Sometimes, some basic principles are known,
but many detailed aspects are missing or are difficult to be deduced in a reliable
manner.
In this section we outline an example, where a crucial phenomenon of gene
expression is analyzed by means of MP grammars. In the next section, examples
are given where distributed computations are expressed in terms of suitable MP
grammars.
Two relevant cases of biological interest are represented by signal transduction
and regulation networks . The first case is a sort of metabolism where no matter
conservation principles are applicable. Namely, signals (for their intrinsic nature)
propagate by changing places and forms of appearance, but they can also be ampli-
fied or reduced, and this is a peculiarity very important in their transformation and
communication.
The second case, which we report shortly, concerns a research in progress on
gene expression analysis in a cancer cell [109, 140, 141]. Assume that a given
perturbation, of a pharmacological nature, is activated on this cell, and the gene-
expressions of around 20,000 genes are given along a sequence of time points.
An important problem to solve is the effect of this perturbation on the gene-
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