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elements like feedbacks or resonances. But this is the same for sequence with
respect to structure comparisons of different proteins as well as for graph
representations of organic molecules and we know how important both these
research avenues were for the respective fields of investigation. Nevertheless the
problem of the possible link between network topology and its dynamical
properties at large is worth of consideration.
8.3. Network Dynamics
The mathematical description of a dynamical system is a collection of state
variables changing with time according to a set of rules which determine the
future state basing on a given present state. The finding of such rules for various
natural systems is a central problem in science.
Once the dynamics is given, one of the tasks of mathematical dynamical
systems theory is to investigate the patterns of how states change in the long run.
Dynamics is often described by means of differential or difference equations,
which are widely used (and sometimes misused) in virtually all fields of the
applied sciences whenever dynamical aspects,
i.e.
time dependency, come into
action. This is mainly due to its spectacular success in physics that has led many
researchers to apply this mathematical tool to almost everything: economy, social
sciences, analytical chemistry and so on.
The “amount” of differential equations used by a scientific discipline is often
considered as a measure of how “mature” it is. This is a very dangerous attitude,
since the use of differential equations, as any other computational tool, may be
justified by very different paradigms, more or less convincing or appropriate. For
example, in papers dealing with gene expression modeling, it is common to read
that “the underlying molecular machinery is governed by mass action laws” so
that differential equations are necessarily relevant. This argument may be very
misleading, since it assumes a high degree of reductionism at many different
levels, which is not necessarily needed in the context of complex systems, where
the “language” of an emergent level may completely different from the subsiding
level. Actually, some like to define a “complex system” as those systems whose
descriptive items are fundamentally different at different levels.
The opposite approach relies on the fact that since differential equations are
ubiquitous in science, than we can use it "everywhere" even for describing “love
affairs”!. It is clear that such an approach is nothing more than “wishful
thinking”. This preliminary discussion is important to understand the impact of
the differential equations approach to metabolic networks.
