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of structures in the body. This motivates researches
to study the glucose-insulin endocrine regulatory sys-
tem.
The intravenous glucose tolerance test focuses on
the metabolism of glucose in a period of 3 hours start-
ing from the infusion of a bolus of glucose at time
t = 0. It is based on the assumption that, in a healthy
person, the glucose concentration decreases exponen-
tially with time followingthe loading dose. In (Manca
et al., 2011) Metabolic P systems theory has been ap-
plied for developing new physiologically based mod-
els of the glucose-insulin system which can be applied
to the IVGTT. In that work, ten data-sets obtained
from literature were considered and, for each of them,
an MP model which fits the data and explains the reg-
ulations of the dynamics was found (see Figure 2).
Figure 2: The calculated insulin dynamics related to four of
the considered data-sets (Manca et al., 2011) (τ = 2 min).
In the differential models proposed in literature,
the delay of the insulin release is approached by
adding artificial substances or by considering a delay
integral kernel. Here, instead, the problem has been
solved by assuming that the insulin production is reg-
ulated by the plasma glucose concentration level both
at the current time and at some previous simulation
steps (glucose memories as introduced in (Manca and
Marchetti, 2010b)). This has permitted to point out,
in a more natural and detailed way, the delays which
act in the insulin production. Moreover, even if dif-
ferences were found in the regulation governing the
release of insulin, it was possible to observe a com-
mon logic which before was only theorized during the
development of the differential models (see (Manca
et al., 2011) for details). These preliminary results
and analysis suggest that MP models seem to pro-
vide comprehensive tools for discovering personal-
ized glucose-insulin dynamics.
4 MP ANALYSIS OF THE HER-2
ONCOGENE-REGULATED
TRANSCRIPTOME IN HUMAN
SUM-225 CELLS
The identification of new gene networks are now
an important part of systems biology. In addition to
high-throughputexperimental methods, mathematical
and computational approaches are indispensable for
the analysis of gene networks. Given the large num-
ber of components of most networks of biological in-
terest, connected by positive and negative feedback
loops, an intuitive comprehension of the dynamics
of the system is often difficult, if not impossible to
obtain. Mathematical modelling supported by com-
puter tools can contribute to the analysis of a regu-
latory network by allowing the biologist to focus on
a restricted number of plausible hypotheses. Many
reviews of the modelling and simulation of gene net-
works have been published in recent years (e.g. (Cao
et al., 2010; Bolouri and Davidson, 2002; Gilman
and Arkin, 2002; Jong, 2002; Hasty et al., 2001;
Smolen et al., 2000)), presenting the wide variety
of formalisms that have been proposed in the liter-
ature, such as oriented graphs, Bayesian networks,
Boolean networks, differential equations, stochastic
master equations and stochastic P systems.
MP systems were initially introduced to model
metabolic processes, but they can be successfully
used in each context where we want to infer models of
a system from a given set of time series. In (Marchetti
and Manca, 2011) an application of the MP theory to
gene expression analysis was developed. In this case,
a standard way for translating MP grammars involv-
ing gene expressions into corresponding quantitative
gene networks was found (see Table 3).
The number of the raw microarray time series
which need to be processed for a generic experiment
on human cells is usually of the order of tens of thou-
sands. Generally, however, only a small part of them
are related to the phenomenon under examination.
For this reason, before to start with the modelling of
the MP model, raw data need to be preprocessed fol-
lowing a methodology which comprises normaliza-
tion, filtering and clustering. This methodology has
been developed during a work in progress where the
MP theory has been successfully applied for defining
the gene network underlying the regulations acting on
the HER-2 oncogene-regulated transcriptome in hu-
man SUM-225 cells in order to define new therapies
for the breast cancer.
HER-2 is an epidermal growth factor receptor
which have been implicated in radioresistance in
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