(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, 2009
FJ Romero-Campero, N Krasnogor, CiE 2009
F Bernardini,M Gheorghe,FJ Romero-Campero,N Walkinshaw,WMC 2007
“Natural” modelling -Membrane computing
Membranes
b
Objects
b
a
a
a
b
a
c
c
b
Cell
Membrane (P) system
Regions
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 → ;
•
Execution strategies
a, b, d, x – multisets
Modelling molecular interactions
Biochemistry
P systems
Compartment
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
20
!!
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?