thermodynamics of irreversible processes. Accordingly, the cancer “phenotype” is concep-
tualized as a self-organized nonlinear dynamical system far from thermodynamic equilib-
rium, as an “emergent,” specific phenomenon belonging to the cluster of cell-phase
transitions. Therefore, the cancer landscape is rebuilt by considering three main parameters:
the production of entropy per unit time, the fractal dimension, and the tumor growth rate.
The consequent mathematical model shows that cancer can self-organize in time and space
far from thermodynamic equilibrium, acquiring high robustness, complexity, and adaptabil-
ity. The former study from C. Simeoni focuses instead on epithelial-mesenchymal transition
(EMT), a key process of cell fate specification as well of cell reprogramming. It is shown that
epithelial to mesenchymal (as well as the opposite occurring during mesenchymal-epithelial
transition, MET) involves an intermediate step, in which the system displays the classical
feature of a “metastable state.” The metastable state is instrumental for enacting EMT and
for identifying the parameters that are interwoven into a framework of fast-slow dynamics
for Ordinary Differential Equations. Noticeably, those parameters are “captured” by look-
ing at the mesoscopic level, i.e., “the realm comprised between the nanometer and the
micrometer, where wonderful things start to occur that severely challenge our understand-
ing” (C. Simeoni). That is to say, at the mesoscopic level, nonlinear effects, as well as
nonequilibrium processes, are more likely to be appreciated and identified. Again, as in
the previous paper from Nieto-Villar, differentiating processes are described as dynamical
phase transitions. Yet, a special attention is paid to evidencing the role of global cues and
constraints that can be properly assessed at levels higher than the molecular one. This
statement “emphasizes the intrinsic limits of studying biological phenomena on the basis
of purely microscopic experiments [...] and, therefore, a multi-scale model (with some
parameters derived from the microscopic analysis) is better suited from a methodological
point of view.”
Limits and opportunities for a general “modeling strategy” are widely discussed in the
chapter by K. Selvarajoo. This chapter reports that even complex response of living cells may
be described by “simple” biochemical models, based on linear and nonlinear differential
equations. For linear models, the reaction topology rather than kinetics plays crucial and
sensitive roles, while a more complicated picture emerges when nonlinear dynamics is
considered. In fact, “for nonlinear dynamics, the parameters need to be precise or the
response cannot be accurately determined due to the stability issue” (K. Selvarajoo). This
means that the influence of the so-called “initial conditions” in shaping a nonlinear dynamics
in no way can be neglected.
A specific application of those concepts to cancer studies is reported by S. Filippi and
P. Ao. The former discusses two principal theories on carcinogenesis—the Somatic Mutation
Theory (SMT) and the Tissue Organization Field Theory (TOFT)—by providing a simula-
tion of a brain cancer cells growth in a realistic NMR imported geometry. The paper from
P. Ao strives to “incorporate” both genetic and epigenetic factors to describe liver cancer
development. Such endeavor is summarized in the “endogenous network hypothesis,”
where a core working network of hepatocellular carcinoma is depicted by means of a
nonlinear dynamical approach. That model allows one to recognize two stable states within
the “hepatic landscape,” and those states reproduce “the main known features of normal
liver and hepatocellular carcinoma at both modular and molecular levels” (P. Ao). It is worth
noting that the model highlights that specific, multiscale positive feedback loops are respon-
sible for the maintenance of normal liver and cancer, respectively. Namely, the model
evidences that by inhibiting proliferation and inflammation related positive feedback
Preface ix