"Membrane Systems and Their Application to Systems Biology "

by

Giancarlo Mauri

Università di Milano – Bicocca

P-systems, or membrane systems, were introduced by George Paun as a class of unconventional computing devices of distributed, parallel and nondeterministic type, inspired by the compartmental structure and the functioning of living cells. The basic model consists of a membrane structure, described by a finite string of well matching parentheses, and graphically represented as regions on the plane, hierarchically embedded within an external region. Each membrane contains a multiset of objects (representing chemical substances) that evolve according to given evolution rules (representing reactions). Objects are described as symbols or strings over a given alphabet, evolution rules are given as rewriting rules. The rules act on objects, by modifying and moving them, and they can also affect the membrane structure, by dissolving the membranes. A computation in P systems starts from an initial configuration, identified by the membrane structure, the objects and the rules initially present inside each membrane, and then letting the system evolve. The evolved objects are then communicated to the regions specified by the rules. When no rule can be further applied, the computation halts and the output is defined in terms of the objects sent out of the external membrane or, alternatively, collected inside a specified membrane.

As a model of computation inspired by biological mechanisms, P systems have been extensively studied in the area of Natural Computing from the point of view of their computational power, and compared with other models like DNA computing or splicing systems. However, they can also be considered as a powerful tool to model complex systems and to simulate processes taking place inside them. In this view, they have been applied in various research areas, ranging from Biology to Linguistics to Computer Science, but very promising results have been obtained in simulating cellular phenomena, hence returning meaningful and useful information to biologists, in the frame of systems biology.