verification and testing group, dcs, university of sheffield
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MIPNETS Liverpool06/2003. Language based approach in biological modelling. Marian Gheorghe University of Sheffield. Verification and Testing Group, DCS, University of Sheffield. Mipnets Liverpool 06/03. Summary Formal languages and biology L systems DNA sequences - PowerPoint PPT PresentationTRANSCRIPT
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Verification and Testing Group, DCS, University of Sheffield
Language based approach in biological modelling
Marian Gheorghe
University of Sheffield
MIPNETS Liverpool06/2003
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Mipnets Liverpool 06/03
Verification and Testing Group, DCS, University of Sheffield
Summary
Formal languages and biology L systems
DNA sequencesMembrane computing; X machinesMolecular X machines
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Mipnets Liverpool 06/03
Verification and Testing Group, DCS, University of Sheffield
Formal languages/linguistics and biological models
FL/Linguistics and biology modern era started in 1950sBoth benefited from a mathematical approachAround 30 years of almost independent development1980s – Chomsky-like approach to molecular biologyLater – DNA computing, aqueous computing, membrane computing …
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Verification and Testing Group, DCS, University of Sheffield
Mipnets Liverpool 06/03
L systems introduced as a model of development of simple multicellular organisms, such as blue-green bacteria Anabaena catenula.
axiom or initial set of elementsset of rewriting rulesyields a language
A Lindenmayer
L systems
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Simulated model
Verification and Testing Group, DCS, University of Sheffield
Mipnets Liverpool 06/03
Comparison between a microscope picture of a fern gametophyte Microsorium linguaeforme (left) and a simulated model using L systems (right).
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Mipnets Liverpool 06/03
Verification and Testing Group, DCS, University of Sheffield
LS = (Vocabulary, Axioms, Rules)Rewriting rules are applied in parallel to all occurrences
Axiom: aRules: a → aba
a; aba;abababa; abababababababa …
Definition. Example
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Verification and Testing Group, DCS, University of Sheffield
Mipnets Liverpool 06/03
Axiom: A
Rules: A → F[+A][-A]FA F → FF
Graphics
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http://www.cpsc.ucalgary.ca/Research/bmv/lstudio/whatis.html
Mipnets Liverpool 06/03
Verification and Testing Group, DCS, University of Sheffield
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Mipnets Liverpool 06/03
The language of genes
Verification and Testing Group, DCS, University of Sheffield
Formal languages applied to biological sequence analysis
Biologically inspired linguistic formalism extensions
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Mipnets Liverpool 06/03
Language based DNA modelling
Verification and Testing Group, DCS, University of Sheffield
Use of Chomsky grammars to model structure & interactions of biological macromolecules
Intramolecular and intermolecular interactions
DNA = sequences (strings) of basic nucleotides
adenine thymineguanine cytosine
x and y are complementary elements on a DNA sequence
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Mipnets Liverpool 06/03
Definition
Verification and Testing Group, DCS, University of Sheffield
Alphabet: ΣDNA = {a, g, t, c}; a=t’, g=c’
Ideal DNA sequence entails pairing between nucleotide basis of ΣDNA
Let w = agtgc then u=gcact (the reversed complement)=w‘R
a g t g c
t c a c g
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Mipnets Liverpool 06/03
The language definition
Verification and Testing Group, DCS, University of Sheffield
The language contains words wu, i.e. ww’R
A context-free grammar G: S → bSb’|ε, where b is any element of ΣDNA
b’ its complement and ε is the empty word – generates the language
agtgcgcact is obtained as
S=>aSt=>agSct=>agtSact=>agtgScact=> agtgcgcact
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Mipnets Liverpool 06/03
The intramolecular language of genes
Verification and Testing Group, DCS, University of Sheffield
Previous language is linear (between regular and context-free)
Realistic stem-loop patterns might containi) unpaired elements and ii) arbitrarily folded branches
(i) obtained by adding to G: S → bSb’|ε, rules S → A and A → bA| ε
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Mipnets Liverpool 06/03
Verification and Testing Group, DCS, University of Sheffield
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Mipnets Liverpool 06/03
…folded branches
Verification and Testing Group, DCS, University of Sheffield
a
g
t
cat t
a aa
gt
c
t
ag
tc
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Mipnets Liverpool 06/03
Derivation-like
Verification and Testing Group, DCS, University of Sheffield
a
g
t
cat t
a aa
gt
c
t
ag
tc
S
SS S
S
S
SS
S
S
S S
S
S
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Mipnets Liverpool 06/03
The formal grammar
Verification and Testing Group, DCS, University of Sheffield
The initial grammar rules of G: S → bSb’|ε and the new ruleS → SS
The derivation and derivation tree are used to model secondary structures of biological macromolecules
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Mipnets Liverpool 06/03
The grammars of intermolecular structure
Verification and Testing Group, DCS, University of Sheffield
Restriction enzymes cut DNA sequences at specific substrings
Enzyme MboI cuts just before gatc
Cut language: let w1δw2… δwn then the language contains sets {w1,w2,…wn}
Recombinant behaviour of DNA molecules (splicing systems)
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Mipnets Liverpool 06/03
Language based models of cell
Verification and Testing Group, DCS, University of Sheffield
Cell: complex body containing compartments delimited by membranes; inside of each region: ions, DNA molecules
Cell behaviour: interactions, transfer – biochemical rules
Membrane roles: help compartmentalize, regulate transport
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Membrane characteristics
Verification and Testing Group, DCS, University of Sheffield
Bi-layer structure
Two sides have different electrical charges
Trans-membrane transfer: passive or active
Communication channels
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Mipnets Liverpool 06/03
Cell model (membrane computing)
Verification and Testing Group, DCS, University of Sheffield
A hierarchical arrangement
Each membrane delimits a region
Each region contains a multiset of elements (simple molecules, DNA sequences…)
The elements evolve in time according to some (rewriting/combination) rules specific to each region or may be moved across the membranes
The rules may also dissolve/create membranes
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Mipnets Liverpool 06/03
A computation in a membrane system
Verification and Testing Group, DCS, University of Sheffield
Initial configuration: multisets of initial elements inside of regions
Current configuration: the rules are applied in parallel in each region to the elements obtained in the previous configuration
The result is not a set of words like in usual language based approaches, but a set of multisets
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Mipnets Liverpool 06/03
The rules
Verification and Testing Group, DCS, University of Sheffield
Rewriting/interaction rules but applied to multisets (interactions inside a region)
Communication rules – membrane crossing
Rewriting/interaction rules: catalysts, inhibitors, priorities
Communication rules: different electrical charges, passive (direct) vs active (mediated);symport/antiport…
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Outcomes
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Computing competence
Efficiency (SAT, HPP problems in polynomial time)
Decidability
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State machine with input, memory and output sets - and basic processing functions
Verification and Testing Group, DCS, University of Sheffield
k
1… k … n
1 … k
Memorym m’
h-1 (m”,k-1)= (k-1 ,m) ; k (m ,k)= (k ,m’ ) ; m0 – initial memory
k-1
k
Mipnets Liverpool 06/03
X (Eilenberg) machines
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Mipnets Liverpool 06/03
Molecular X machines
Verification and Testing Group, DCS, University of Sheffield
Computationally complete
Finite state based with input/output streams
Structured hierarchically organized memory
Provide in every state specific sets of rules acting in parallelin various parts of the memory
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Verification and Testing Group, DCS, University of Sheffield
(Ri,1,…, Ri,m)(Rj,1,…, Rj,m)
Variant 1:
structured memory
distributed rules
Mipnets Liverpool 06/03
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Mipnets Liverpool 06/03
Verification and Testing Group, DCS, University of Sheffield
Variant 2:
set of machines
derived components
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Application
Verification and Testing Group, DCS, University of Sheffield
Behaviour of ant colonies (Monomorium pharaonis):Pheromone deposition rate; trail pheromone volatility; attraction to trail; population size
Different individual behaviour
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Mipnets Liverpool 06/03
Conclusions
Verification and Testing Group, DCS, University of Sheffield
Formal grammars used to model general forms of inter/intra-molecular structure
New approaches, concepts, models
Biological relevance
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Links
Verification and Testing Group, DCS, University of Sheffield
Molecular X machineshttp://www.dcs.shef.ac.uk/~bernardf/molxm/index.htm
Membrane computinghttp://psystems.disco.unimib.it/
DNA computinghttp://www.liacs.nl/home/pier/webPagesDNA/