(Towards a) Modelling Platform for Biological Systems

Marian Gheorghe

University of Sheffield

What the method does

Use computer science models & concepts and software engineering approach & tools

• Formal model – membrane systems: modular and uses “natural” approach (Nott & Sheff)

• Formal analysis + learning mechanisms;

• Automated design – structure and parameters

Simulations, verifications, system restructuring and design

FJ Romero-Campero, J Twycross, M Camara, M Bennett, M Gheorghe, N Krasnogor, IJFCS, 2009FJ Romero-Campero, N Krasnogor, CiE 2009 F Bernardini,M Gheorghe,FJ Romero-Campero,N Walkinshaw,WMC 2007

“Natural” modelling -Membrane computing

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Membranes

Objects

Regions

Cell Membrane (P) system

What is a (basic) membrane system

A membrane system is a computing model consisting of • chemicals are modelled as symbols or strings, called abstract objects• regions (compartments) contain multisets of objects and other membranes• rules are associated to regions• system evolves through transitions

http://ppage.psystems.eu/The Oxford Handbook of Membrane Computing – To appear: 24/12/2009

Rules and computation

(a) transformation: [a → x]c complex formation/dissociation; activators/inhibitors

(b) communication: a[]c → [a]c, [a]c → a[]c ; symport, antiport

(c) cell division: [a]c → [b]c [d]c

(d) cell differentiation: [a]c → [b]e

(e) cell death: [a]c → ; a, b, d, x – multisets

• Execution strategies

Modelling molecular interactions

Biochemistry P systemsCompartment Region

Molecules Objects (symbols, strings)

Molecular population Multiset of objects

Biochemical transformations Various rules

Gene regulatory network - P system model

Lac operon in E coli: Hlavacek, Savageau, 1995

Simulations

Invariants of the model

Initial values:

gene = 1, act = n, rep = m; where n, m either 0 or 10

others = 0

P-invariants

PIPE: http://pipe2.sourceforge.net

Property inference

Daikon tool:

Reverse-engineer specifications from software systems – as preconditions, postconditions and invariants (Ernst et all, 2001) – formal analysis and testing

In the context of biological data, it automatically infers invariants to:

• confirm the model behaves as it should - obvious invariants

• indicate faults – anomalous invariants

• suggest novel relationships

Daikon: Pre-, post-conditions and invariants

Daikon: Pre-, post-conditions and invariants

Daikon: Pre-, post-conditions and invariants

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Daikon: Pre-, post-conditions and invariants

Formal verification - model checking

Use PRISM –

• Probability that the mRNA or the protein is within/under/over some limits

• Monotonic increase of some products

• Relevant properties

M Kwiatkowska et al 2002

P systems in PRISM

P system model

PRISM code

Invariants checking – positive regulation

… more likely rna’s between 0 and 15, proteins between 0 and 150

Check relationships

Relationships between the number of repressors and rna and protein molecules

P(prot>rep) P(rna>rep)

Conclusions and further developments

• Integrated engineering approach

• P systems – modelling approach for molecular interactions;

modular and “natural”

• Automated design

• Property inference

• Formal verification

Thanks?