Systems Biology (Methods in Molecular Biology)

the healthy (stable) equilibrium (see Fig. 1b). It is worthwhile

stressing that a stable dynamics should not be confused with a

system in a stationary stable phase (namely, when nothing signifi-

cant happens). Indeed, the former may anyway undergo a wide

range of fluctuations without losing its stability. This means that a

stable dynamics is characterized by resilience (robustness) with

respect to external perturbations, given that it is located in the

manifold of a stable attractor. On the contrary, a stationary stable

system lies in a phase where no apparent dynamical changes occur.

Mathematical Modeling is asked to develop criteria to guide the

interpretation of the observations in making “causes” and “effects”

to raise from experiments (seeFig. 3). One wishes to identify lower

order changes that are precursory to phase transitions inside the

biological systems. In fact, identifying the metastable state during a

complex biological process is a challenging task, because the state of

the system may show neither apparent changes nor clear phenom-

ena before a critical transition. Therefore, recognizing specific steps

by means of additional mathematical variables which vary gradually

could help, not only in identifying markers of transformation for

early diagnosis, but also in determining drug targets.

The interaction between Systems Biology and Mathematical

Modeling would have no hope of generating a virtuous circle, if

not for the emergence of a new actor on stage: the computer. The

performance development of modern computers has permitted to

test models even remotely approachable in the past, through

Fig. 2Phenotypic reversal through myo-Ins-induced MET; schematic cell shape profiles are depicted as
extracted from images, highlighting changes occurring during phenotypic transition

102 Chiara Simeoni et al.