investigated by putting that process into the whole context. A true biological understanding
cannot benefit from studying parts in isolation. It is time to fill the gap we create long time
ago by adopting a reductionist stance. Some hints are provided and, among others sugges-
tions, Montevil proposes a different kind of cooperation between biologists, physicists, and
mathematical modelers in order to merge the respective skills and knowledge thereof.
A proper selection among the overwhelming body of biological variables so far provided
by high-throughput analytical technologies constitutes a preliminary, essential task. To recall
a paradigmatic example given by the history of Physics, dynamics took off as a science only
when acceleration was identified as the appropriate parameter instead of velocity. Something
analogous is happening in the realm of Systems Biology where the “golden” parameter
(s) has still to be unveiled.
For the search of proper parameters is at the core of biological modeling, A. Giuliani
sketched a compelling survey on the field. Namely, Giuliani warns us adopting “standar-
dized” procedures, already vindicated in nonbiological contexts. Precisely, as “system’s
parameter estimation in biology asks for a continuous feedback between biological and
procedural information, the data analysis by no way can be considered as a ‘separate
optimized’ set of procedures to be applied to a set of experimental results” (A. Giuliani).
We have therefore to look at those networks linking the different players of the system at
hand. That network can be deemed as the only relevant “causative agent” with the experi-
mental observables acting as probes of the coordinated motion of the underlying network.
However, this approach requires a completely different style of reasoning with respect to the
classical approach of biologists used to a neat dependent/independent variables discrimina-
tion and considering the observables as autonomous players in the game. To “extract” such
observables from the intricacy of the system, the “most fruitful way is letting the network to
suggest us (e.g., by the application of unsupervised techniques like PCA) where to look
avoiding the overfitting/irrelevance traps” (A. Giuliani).
Selection of proper parameters for identification of the systems is a central tenet,
especially if we consider that in most cases the parameters introduced into the set of
equations are completely unknown and/or only rough estimates of their values are available.
The so-called parameter estimation problem is then formulated as an optimization problem
where the objective is finding the parameter set so as to minimize a given cost function that
relates model predictions and experimental data. R. Guzzi et al., striving to conceptualize a
reliable approach to the so-called “inverse problem,” acutely address this question. The
inverse problem is indeed a strategy in identifying a minimal set of parameters that can
describe the system under examination or to extract from the models the information
embedded in the system. Since parameter estimation in dynamic models of biochemical
systems is characterized by limited observability, large number of parameters and a limited
amount of noisy data, the solution of the problem is in general challenging and, even when
using robust and efficient optimization methods, computationally expensive. Yet, the solu-
tion of this problem is mandatory, as the parameter recognition is required to “identify” the
system. As a result, the “parameterization of a subclass of dynamic systems will be called
identifiable if, for any finite but sufficiently long time series of observed input-output
trajectories, there exists an unique element in the subclass of systems which represents
those observations” (R. Guzzi et al.). The inverse problem-based approach could greatly
help in solving that conundrum.
C. Simeoni et al. as well as J.M. Nieto-Villar et al. discuss two worth noting examples of
parameter identification and modeling here. According to Nieto-Villar, the phase space of
cell differentiation is reconstructed mainly by adopting the formalism borrowed from the
viii Preface