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

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 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 Mipnets Liverpool 06/03 Comparison between a microscope picture of a fern gametophyte Microsorium linguaeforme (left) and a simulated model using L systems (right).

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: a Rules:a → aba a; aba; abababa; abababababababa … Definition. Example

Verification and Testing Group, DCS, University of Sheffield Mipnets Liverpool 06/03 Axiom: A Rules: A → F[+A][-A]FA F → FF Graphics

Mipnets Liverpool 06/03 Verification and Testing Group, DCS, University of Sheffield

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

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 thymine guanine cytosine x and y are complementary elements on a DNA sequence

Mipnets Liverpool 06/03 Definition Verification and Testing Group, DCS, University of Sheffield Alphabet: Σ DNA = {a, g, t, c}; a=t’, g=c’ Ideal DNA sequence entails pairing between nucleotide basis of Σ DNA Let w = agtgc then u=gcact (the reversed complement)=w‘ R a g t g c t c a c g

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 Σ DNA b’ its complement and ε is the empty word – generates the language agtgcgcact is obtained as S=>aSt=>agSct=>agtSact=>agtgScact=> agtgcgcact

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 contain i) unpaired elements and ii) arbitrarily folded branches (i) obtained by adding to G: S → bSb’|ε, rules S → A and A → bA| ε

Mipnets Liverpool 06/03 Verification and Testing Group, DCS, University of Sheffield

Mipnets Liverpool 06/03 …folded branches Verification and Testing Group, DCS, University of Sheffield agag tctc a t a agag tctc t a g t c

Mipnets Liverpool 06/03 Derivation-like Verification and Testing Group, DCS, University of Sheffield agag tctc a t a agag tctc t a g t c S S S S S S S S S S SS S S

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 rule S → SS The derivation and derivation tree are used to model secondary structures of biological macromolecules

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 w 1 δw 2 … δw n then the language contains sets {w 1,w 2,…w n } Recombinant behaviour of DNA molecules (splicing systems)

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

Mipnets Liverpool 06/03 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

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

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

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…

Mipnets Liverpool 06/03 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k  1 …  k …  n  1 …  k Memory mm’  h-1 (m”,  k-1 )= (  k-1,m) ;  k (m,  k )= (  k,m’ ) ; m 0 – initial memory  k-1 kk Mipnets Liverpool 06/03 X (Eilenberg) machines

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 parallel in various parts of the memory

Verification and Testing Group, DCS, University of Sheffield (R i,1,…, R i,m ) (R j,1,…, R j,m ) Variant 1: structured memory distributed rules Mipnets Liverpool 06/03

Verification and Testing Group, DCS, University of Sheffield Variant 2: set of machines derived components

Mipnets Liverpool 06/03 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

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

Mipnets Liverpool 06/03 Links Verification and Testing Group, DCS, University of Sheffield Molecular X machines Membrane computing DNA computing