13th International Conference on Membrane Computing - MTA Sztaki

<strong>13th</strong> <strong>International</strong> <strong>Conference</strong> on Membrane Computing, CMC13,
Budapest, Hungary, August 28 - 31, 2012. Proceedings, pages 55 - 57.
MP Systems for Systems Biology
Vincenzo Manca
University of Verona
Abstract. MP systems concepts will be revisited, in more general terms,
by stressing their special role in solving dynamical inverse problems.
Then, a main application of MP systems to Systems Biology will be
outlined, which concerns gene expression in breast cancer (in cooperation
with Karmanos Cancer Institute, Wayne State University, Detroit
MI, USA). From recent experimental results developed at KCI, it follows
that MP systems can provide ”good” models of pathological phenomena,
where good, in this case, means useful to oncologists. In fact, the MP systems
methodology has identified previously unknown intermediaries in a
breast cancer cell-specific signaling circuit. This could provide a significant
contribution to the task of mapping complete oncogenic signaling
networks to improve cancer treatments.
1 Introduction
The theory of MP systems (Metabolic P systems) started in first years of
2000s as a discrete mathematical method, inspired from P systems (an unconventional
computation model based on abstract membranes, [1]), for describing
biological dynamics. In the following years, algorithms and software were developed
for simulating and reconstructing many biological phenomena [2-11], but
the main problem addressed in the theory, and systematically solved in many
significant cases, is the so called dynamical inverse problem [10], which is a very
old problem in science (it was the starting problem of differential models of
planetary orbits). Its discrete formulation and solution is crucial in many biological
situations. First, let us recall that a dynamical system is given by a set
of real variables changing in time and a set of invariants, that is, conditions
(constraints) which are satisfied by the variables during their change. Let us observe
the variables of a (discrete) dynamical system along a number of (equally
spaced) time points (steps). The sequences of these values constitute a set of
time series representing the behavior of the observed system. We pose the following
question: can we reconstruct these time series as generated by certain
kinds of interactions/transformations among the variables of the system? If this
reconstruction is possible (even with some approximations), then we are able to
infer an internal logic that is responsible of what we observe. Therefore, we can
deduce a mechanism ruling the observed phenomenon, by passing from the time
manifestation of the system to its state causation law.
In the MP theory this internal mechanism is expressed by means of a grammar,
that is, a set of rules transforming quantities (metabolite quantities, gene
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