DNA Computing: Implications for Theoretical Computer Science

1
DNA Computing Implications for Theoretical
Computer Science

• Lila Kari
• Dept. of Computer Science
• University of Western Ontario
• London, ON, Canada
• http//www.csd.uwo.ca/lila/
• lila_at_csd.uwo.ca

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From DNA to TCS

• The genetic code
• Splicing systems
• Optimal encodings for DNA Computing
• Sticker systems
• Watson-Crick automata
• Combinatorics on DNA words
• Cellular computing
• DNA computation by self-assembly

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1953 Watson and Crick discover DNA structure
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DNA

• DNA structure

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The RNA Tie Club

• 1954 Solve the riddle of the RNA structure and
  to understand how it builds proteins (clockwise
  from upper left Francis Crick, L. Orgel, James
  Watson, Al. Rich)
• There are 20 aminoacids that build up proteins

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The Diamond Code

• G.Gamow - double stranded DNA acts as a template
  for protein synthesis various combinations of
  bases could form distinctively shaped cavities
  into which the side chains of aminoacids might fit

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Comma-Free Codes(the prettiest wrong idea in
20-th century science)

• The RNA piglet model

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The prettiest wrong idea in all of 20th century
science

• Suckling-pig model of protein synthesis
• Construct a code in which when two sense codons
  (triplets) are catenated, the subword codons are
  nonsense codons
• If CGU and AAG are sense codons, then GUA and UAA
  must be nonsense because they appear in CGUAAG

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Comma-free codes (Crick 1957)

• How many words can a comma-free code include?
• For n4 and k3 the size of a maximal comma-free
  code is the magic number 20
• For an alphabet of n letters grouped into
  k-letter words, if k is prime, the number of
  maximal comma-free codes is (nk n)/k
• For n4 and k3 this equals 408

10
Reality Intrudes

• News from the lab bench Nirenberg,Matthaei 61
  synthesize RNA, namely poly-U, coding for
  phenylalanine
• By 1965 the genetic code was solved
• The code resembled none of the theoretical
  notions
• The extra codons are merely redundant

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The Genetic Code
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Splicing Systems (Head 1987)

• 5 CCCCCTCGACCCCC 3
• 3GGGGGAGCTGGGGG5
• 5AAAAAGCGCAAAAA 3
• 3 TTTTTCGCGTTTTT 5
• Enzyme 1 Enzyme 2
• 5TCGA3 5GCGC3
• 3AGCT5 3CGCG5

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Splicing Systems

• 5 CCCCCT CGACCCCC 3
• 3GGGGGAGC TGGGGG5
• 5AAAAAG CGCAAAAA 3
• 3 TTTTTCGC GTTTTT 5
• DNA strands with compatible sticky ends
• recombine to produce two new strands

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Splicing operation

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Splicing system sample results

• Theorem (Paun95, Freund,Kari,Paun ,99)
• Every type-0 language can be generated by a
  splicing system with finitely many axioms and
  finitely many rules.
• Theorem (Freund,Kari,Paun 99)
• For every given alphabet T there exists a
  splicing system, with finitely many axioms and
  finitely many rules, that is universal for the
  class of systems with terminal alphabet T.

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From DNA to TCS

• The genetic code
• Splicing systems
• Optimal encodings for DNA Computing
• Sticker systems
• Watson-Crick automata
• Combinatorics on DNA words
• Cellular computing
• DNA computation by self-assembly

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DNA Computing (Adleman94)

• Input / Output (DNA)
• Data encoded using the DNA alphabet A, C, G, T
  and synthesized as DNA strands
• Bio-operations
• Cut
• Paste
• Recombination
• Anneal / Melt
• Copy

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Biomolecular (DNA) Computing

• Hamiltonian Path Problem Adleman, Science, 1994
• DNA-based addition Guarnieri et al, Science,
  1996
• Maximal Clique Problem Ouyang et al, Science,
  1997
• DNA computing by self-assembly Winfree et al,
  Nature 1998
• Computations by circular insertions, deletions
  Daley, Kari, Gloor, Siromoney, SPIRE99
• DNA computing on surfaces Liu et al, Nature,
  2000
• Molecular computation by DNA hairpin
  formationSakamoto et al, Science, 2000
• 20-variable Satisfiability Braich et al.,
  Science 2002
• An autonomous molecular computer for logical
  control of gene expression Benenson et al,
  Nature, 2004
• Folding DNA to create nanoscale shapes and
  patterns Rothemund, Nature, 2006
• Efficient Turing-universal computation with DNA
  polymers Qian, Soloveichik, Winfree, DNA
  Computing and Molecular Programming, 2010
• Molecular robots guided by prescriptive
  landscapes Lund et al., Nature, 2010

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Encoding Information for DNA Computing

• DNA strands should form desired bonds
• DNA strands should be free of undesirable
  intra-molecular bonds
• DNA strands should be free of undesirable
  inter-molecular bonds

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Intramolecular Bonds

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Intra- and inter-molecular bonds
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DNA-complementarity model (Kari,Kitto,Thierrin02
)
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Bond-free languages

• Bonds between DNA strands

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Sample Results (Hussini/Kari/Konstantinidis/Losse
va/Sosik 03)
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Sticker Systems (Freund,Paun,Rozenberg,Salomaa98
, Kari,Paun,Rozenberg,Salomaa,Yu98,
Hoogeboom,van Vugt00, Kuske,Weigel04,
Paun,Rozenberg 98)

• Given a complementarity relation, define an
  alphabet of double-stranded columns
• 
  

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Sticking operation
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Complex Sticker Systems

• Sakakibara,Kobayashi 01 Sticker systems based
  on hairpins
• Alhazov,Cavaliere 05 Observable sticker
  systems

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Watson-Crick Automata (Freund,Paun,Rozenberg,Salo
maa99Paun,Rozenberg98 MartinVide,Paun,Rozenber
g,Salomaa98Czeizler,Czeizler06
Paun,Paun99Czeizler,Czeizler,Kari,Salomaa08)
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From DNA to TCS

• The genetic code
• Splicing systems
• Optimal encodings for DNA Computing
• Sticker systems
• Watson-Crick automata
• Combinatorics on DNA words
• Cellular computing
• DNA computation by self-assembly

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Combinatorics on DNA Words

• IDEA Consider the word w and its WK- complement,
  WK(w), as equivalent
• The word ACTG CAGT CAGT can be considered
  repetitive (periodic) because it can be written
  as ACGT WK(ACGT)2
• Generalize classical notions such as power of a
  word, border, primitive word, palindrome,
  conjugacy, commutativity

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Identity gt Antimorphic involution f

• Pseudo-palindrome (de Luca,De Luca06,
  Kari,Mahalingam09) u f(u)
• Pseudo-commutativity(Kari,Mahalingam08)
• u v f(v) u
• Pseudo-bordered word (Kari,Mahalingam07)
• w v x y f(v)
• Pseudoknot-bordered word (Kari,Seki09)
• w u
  v x y f(u) f(v)
• Pseudo-conjugacy of u, v (Kari,Mahalingam08)
• u x f(x) v

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Fine and Wilf Theorem

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Extended Fine and Wilf Theorem

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Extended Fine and Wilf Theorem
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Lyndon-Schutzenberger Equation
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Extended Lyndon-Schuzenberger
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Extended Lyndon-Schutzenberger
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Cellular Computing
Photo courtesy of L.F. Landweber
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Ciliates Genetic Info Exchange
Photo courtesy of L.F. Landweber
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Ciliates Gene Rearrangement
Photo courtesy of L.F. Landweber
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Ciliates Bio-operations
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Ciliate Computing

• Guided Recombination System A formal
  computational model based on contextual circular
  insertions and deletions
• Such systems have the computational power of
  Turing Machines (Landweber,Kari 99,Kari,Kari99)

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Other ciliate computing models

• Ld, hi, dlad model (Harju,Rozenberg 03,
  Harju,Petre,Rozenberg 03, Prescott,
  Ehrenfeucht,Rozenberg03)
• Template guided recombination model
• (Angeleska,Jonoska,Saito,Landweber07,
• Daley,McQuillan 06, Kari,Rahman 10)
• RNA guided recombination model
• (Nowacki et. al, 07)

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From DNA to TCS

• The genetic code
• Splicing systems
• Optimal encodings for DNA Computing
• Sticker systems
• Watson-Crick automata
• Combinatorics on DNA words
• Cellular computing
• DNA computation by self-assembly

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DNA Computation by Self-Assembly (Mao, LaBean,
Reif, , Seeman, Nature, 2000)
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DNA self-assembly model (Adleman00, Winfree98)

• Tile square with the edges labelled from a
  finite alphabet of glues (Wang 61)

• Tiles cannot be rotated
• Two adjacent tiles on the plane stick if they
  have the same glue at the touching edges

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Dynamic Self-Assembly

• Tile System T Finite set of tiles, unlimited
  supply of each tile type
• Supertiles self-assemble with tiles from T
• Start with an arbitrary single tile seed
• Proceed by incremental additions of single tiles
  that stick

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Self-Assembly Problem

• Given a tile system T, can arbitrarily large
  supertiles self-assemble with tiles from T?
• Equivalent to
• Given a tile system T, does there exist an
  infinite ribbon of tiles from T?

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Sample Results

• Undecidability of existence of an infinite ribbon
  (L.Adleman, J.Kari, L.Kari, D.Reishus, P.Sosik
  09)
• Consequence Undecidability of existence of
  arbitrarily large supertiles that self-assemble
  from a given tile set, starting from an arbitrary
  seed
• Self-assembly model with variable strength and
  negative strength (repelling) glues (Doty, Kari,
  Masson, 10)

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DNA Nanotechnology(Chen, Seeman, Nature, 01)
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DNA Clonable Octahedron (Shih, Joyce, Nature 04)
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Nanoscale DNA Tetrahedra(Goodman, Turberfield,
Science, 05)
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DNA Origami(Rothemund, Nature, 2006)
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From DNA to TCS

• The genetic code
• Splicing systems
• Optimal encodings for DNA Computing
• Sticker systems
• Watson-Crick automata
• Combinatorics on DNA words
• Cellular computing
• DNA computation by self-assembly

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Impact of DNA Computing on Theoretical Computer
Science

• Novel computing paradigms abstracted from
  biological phenomena
• Alternative physical substrates on which to
  implement computations, e.g. DNA
• Viewing natural processes as computations has
  become essential, desirable, and inevitable
• These developments challenge our assumptions, and
  our very definition of computation
• Biology and Computer Science life and
  computation are related (Adleman)

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Our Challenge

• Discover a new, broader notion of computation
• Understand the world around us in terms of
  information processing
• Biology and Computer Science
• life and computation are related.
• I am confident that at their interface great
  discoveries await whose who seek them.
  (Adleman98)