Verification and Testing Group, DCS, University of Sheffield

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


Summary

Formal languages and biology L systems

DNA sequencesMembrane computing; X machinesMolecular X machines



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 …



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

Simulated model



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



LS = (Vocabulary, Axioms, Rules)Rewriting rules are applied in parallel to all occurrences

Axiom: aRules: a → aba

a; aba;abababa; abababababababa …

Definition. Example



Axiom: A

Rules: A → F[+A][-A]FA F → FF

Graphics

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




The language of genes


Formal languages applied to biological sequence analysis

Biologically inspired linguistic formalism extensions


Language based DNA modelling


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


Definition


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


The language definition


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


The intramolecular language of genes


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


…folded branches


a

g

t

cat t

a aa

gt

c

t

ag

tc


Derivation-like


a

g

t

cat t

a aa

gt

c

t

ag

tc

S

SS S

S

S

SS

S

S

S S

S

S


The formal grammar


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


The grammars of intermolecular structure


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)


Language based models of cell


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


Membrane characteristics


Bi-layer structure

Two sides have different electrical charges

Trans-membrane transfer: passive or active

Communication channels


Cell model (membrane computing)


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


A computation in a membrane system


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


The rules


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…


Outcomes


Computing competence

Efficiency (SAT, HPP problems in polynomial time)

Decidability

State machine with input, memory and output sets - and basic processing functions


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


X (Eilenberg) machines


Molecular X machines


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


(Ri,1,…, Ri,m)(Rj,1,…, Rj,m)

Variant 1:

structured memory

distributed rules




Variant 2:

set of machines

derived components


Application


Behaviour of ant colonies (Monomorium pharaonis):Pheromone deposition rate; trail pheromone volatility; attraction to trail; population size

Different individual behaviour


Conclusions


Formal grammars used to model general forms of inter/intra-molecular structure

New approaches, concepts, models

Biological relevance


Links


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/

Verification and Testing Group, DCS, University of Sheffield

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