Tutor: Prof. Lucia PomelloSupervisors: Prof. Giancarlo Mauri

Dr. Luciano Milanesi

PhD Thesis Proposal

Membrane systems: a framework for stochastic processes analysis and modelling

Dr. Ettore MoscaBioinformatics

Istituto Tecnologie Biomediche – CNR

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)

P systems: definition)),,(),...,,(,...,,,( 0111 iRRwwV nnn

1. V is an alphabet, elements are called objects2. µ is a membrane structure of degree n3. wi, are strings from V* representing multisets over V4. Ri, are finite sets of evolution rules over V; ρi is a partial order relation over Ri;

• 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 { inj |1 ≤ j ≤ n })

5. i0 specifies the output membrane

(G. Păun, 2000)

Evolution: at each step apply all the possible rules in parallel and non-deterministically

P systems: facts

Several variants exist:• cell like: symport and antiport, active membranes, rewriting, splicing• cells are nodes of an arbitrary graph: tissue, population, neuronalApplications (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. Păun, 2007)

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)

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. Păun 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. Păun and J. Romero-Campero, 2006)

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

Project Planp-systems formalization (space, fuzzy)

Compare P systems with other formal

methods

Parameterestimation

EA

Model checkingSensitivity 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? noyes

References

• G. Păun, 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. Păun, 2007, Tracing Some Open Problems in Membrane Computing, Romanian Journal of Information Science and Technology, 10,4

• G. Păun 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