1. Tutor: Prof. Lucia Pomello Supervisors: Prof. Giancarlo Mauri Dr. Luciano Milanesi PhD Thesis Proposal Membrane systems: a framework for stochastic processes analysis and modelling Dr. Ettore Mosca Bioinformatics Istituto Tecnologie Biomediche – CNR

2. Natural computing A field of research which tries to imitate nature in the way it computes Evolutionary computing Neural computing DNA computing Membrane computing Evolution Neurons, synapses DNA, enzymes Cell(s)

3. P systems: definition 1.V is an alphabet, elements are called objects 2.µ is a membrane structure of degree n 3.w i, are strings from V * representing multisets over V 4.R i, are finite sets of evolution rules over V; ρ i is a partial order relation over R i ; Evolutio n rule is a pair (u,v), u  v, u is a string over V and v=v ’ or v=v ’ δ v ’ is a string over (V x {here,out}) U (V x { in j |1 ≤ j ≤ n }) 5.i 0 specifies the output membrane (G. P ă un, 2000) Evolution: at each step apply all the possible rules in parallel and non-deterministically

4. P systems: facts Several variants exist: cell like: symport and antiport, active membranes, rewriting, splicing cells are nodes of an arbitrary graph: tissue, population, neuronal Applications (Ciobanu, Pérez-Jiménez, Paŭn, 2006): Computer science: computer graphics, sorting, criptography, evolutionary computing, computationally hard problems Linguistic: parsing Bio-applications: molecular pathways, cell populations Initial studies related to area of formal languages, grammars and computational models. “a fast Emerging Research Front in Computer Science” (2003, Thompson Institute for Scientific Information) 39 open problems and research topics (G. P ă un, 2007)

5. Research proposal topics 1.Introduce the spatial ingredient ( physical dimensions or spatial coordinates) in membrane systems Up to now: space included only topologically 2.Q35: “define and examine P systems with ‘approximate’ components, in terms of probabilistic, fuzzy, or rough set theory. [...] this direction of research [...] is expected to have an important development and significant applications”. 3.Q31: “compare P systems with other distributed computing systems” gain alredy developed theory for the analysis of certain system properties (G. Păun, 2007)

6. Applications: systems biology “However, not planned at beginning, membrane computing turned out to be a useful framework for represent biological processes” Molecular biology Biochemistry Physiology (Life Sciences) Computer Science Physics Mathematics Engeenering Inherent compartimentalization Discreteness Stochasticity Easy extensibility (modularity) Non-linear behaviuor Direct understandability Easy programmability (G. P ă un and Pérez-Jiménez, 2006) A DYNAMICAL APPROACH IS REQUIRED How to simulate the evolution? How to analyse the dynamics of a stochastic, discrete system? USEFUL PROPERTIES (G. P ă un and J. Romero-Campero, 2006)

7. Stochastic Discrete Systems Simulation Quantitative simulation based on modifications of the Stochastic Simulation Algorithm (SSA) (D.T. Gillespie, 1977) Analysis of the dynamics Repeated simulation with different initial conditions Reformulate the problem in different modelling framework (s) for which there is the theory already developed

8. Project Plan p-systems formalization (space, fuzzy) Compare P systems with other formal methods Parameter estimation EA Model checking Sensitivity Analysis Analysis of dynamics implementation of the simulation algorithm (space, fuzzy) Selection of a biological process (application) P systems implementation Is the model fitted to data? no yes

9. References G. P ă un, 2000, Computing with membranes, Journal of Computer and System Sciences, 61, 108-143 G. Ciobanu, M. Pérez-Jiménez, G. Paŭn, 2006, Applications of Membrane Computing, Natural Computing Series, ISBN 978-3-540-25017-3 G. P ă un, 2007, Tracing Some Open Problems in Membrane Computing, Romanian Journal of Information Science and Technology, 10,4 G. P ă un and M. Pérez-Jiménez, 2006, Membrane computing: Brief introduction, recent results and applications, Biosystems, 85, 11-22 D.T. Gillespie, 1977, Exact stochastic simulation of coupled chemical reactions, Journ. Phys. Chem., 81, 2340-2361