Verification and Testing Group, DCS, University of Sheffield

Language based approach in biological modelling

Marian Gheorghe

University of Sheffield

MIPNETS Liverpool06/2003

Mipnets Liverpool 06/03

Verification and Testing Group, DCS, University of Sheffield

Summary

Formal languages and biology

L systems

DNA sequences

Membrane computing; X machines

Molecular X machines

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Verification and Testing Group, DCS, University of Sheffield

Formal languages/linguistics and biological models

FL/Linguistics and biology modern era started in 1950s

Both benefited from a mathematical approach

Around 30 years of almost independent development

1980s – Chomsky-like approach to molecular biology

Later – DNA computing, aqueous computing, membrane computing …

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 elements

set of rewriting rules

yields a language

A Lindenmayer

L systems

Simulated model

Verification and Testing Group, DCS, University of Sheffield

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Comparison between a microscope picture of a fern gametophyte Microsorium linguaeforme (left) and a simulated model using L systems (right).

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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

Verification and Testing Group, DCS, University of Sheffield

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Axiom: A

Rules: A → F[+A][-A]FA F → FF

Graphics

http://www.cpsc.ucalgary.ca/Research/bmv/lstudio/whatis.html

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Verification and Testing Group, DCS, University of Sheffield

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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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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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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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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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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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Verification and Testing Group, DCS, University of Sheffield

Mipnets Liverpool 06/03

…folded branches

Verification and Testing Group, DCS, University of Sheffield

a

g

t

cat t

a a

a

g

t

c

t

ag

tc

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Derivation-like

Verification and Testing Group, DCS, University of Sheffield

a

g

t

cat t

a a

a

g

t

c

t

ag

tc

S

SS S

S

S

SS

S

S

S S

S

S

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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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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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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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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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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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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

Verification and Testing Group, DCS, University of Sheffield

Computing competence

Efficiency (SAT, HPP problems in polynomial time)

Decidability

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

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X (Eilenberg) machines

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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

Verification and Testing Group, DCS, University of Sheffield

(Ri,1,…, Ri,m)(Rj,1,…, Rj,m)

Variant 1:

structured memory

distributed rules

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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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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/