Modeling Biochemical Pathways - Mathematical Approaches to Polymer Sequence Analysis and Related Problems - page 112

The integration of data provided by sequence analysis approaches yields
important knowledge for the reconstruction of the “molecular circuits,” which
exploit metabolic (related to mass and energy flows), signal transduction (con-
cerning the transmission of signals) and gene regulatory processes (describing the
regulation of gene expression). The understanding of the structural and dynamical
properties of molecular networks is mainly important since biological functions
arise from the activity of these circuits. In order to reach this goal, it is necessary
to define mathematical models that permit numerical simulations; in fact, analytical
solutions are available only in the few cases in which the modeled pathway is
composed of a small number of molecular species.
In this chapter, we will discuss the definition of mathematical models for the
analysis of molecular pathways. Models can be defined starting from data provided
by sequence analysis methods and represent a relevant application of these data to
shed light on the functioning of living organisms.
Section 6.2 introduces systems biology and underlies the importance of the quan-
titative study of biological systems; Section 6.3 describes the steps involved in
building a mathematical model; Section 6.4 illustrates the representation of molecu-
lar circuits structure and its analysis; Section 6.5 describes the modeling approaches
that can be used to study the system time evolution; Section 6.6 copes with the prob-
lem of the estimation of model parameters; Section 6.7 summarizes the message of
the chapter.

6.2 Complexity of Living Organisms and Systems Biology

Living organisms are intrinsically complex. This concept can be easily visualized
considering the molecular scale, in which biological processes are controlled by
the activity of intricate and heterogeneous regulatory networks established by the
interactions among DNA, RNAs, proteins, metabolites and other organic and inor-
ganic elements. These networks exhibit complex dynamics and, in general, regulate
biological processes determining a response that may vary across many orders
of magnitudes [ 24 ]. Moreover, molecular circuits are sensitive to environmental
changes and are spatially regulated by means of the intracellular structures. The
complexity increases considering that cells organize in tissues, tissues in organs
and organs in the whole organism, and all these scales control biological functions.
Biological systems have been tuned by the evolution process to be robust, but also
to be evolvable (for instance, DNA replication is a process with an astonishing effi-
ciency, but some errors occur and are crucial for life evolvability). During evolution
this phenomenon generated complex and very improbable structures, like the so-
called bowtie architecture [ 8 ] of the molecular processes.
Complex systems show emergent properties . This properties can appear when a
number of elements operate in an environment, resulting in more complex behaviors
as a collective. Considering living systems, swarms show complex behaviors mani-
festing structures, patterns and properties during the process of self-organization [ 7 ],