1 / 20

Towards the sequence design preventing pseudoknot formation

Towards the sequence design preventing pseudoknot formation. 2 nd International Workshop on Natural Computing, Dec. 10-12, 2007 Noyori Conference Hall, Nagoya University, Japan. Lila Kari and Shinnosuke Seki. Biocomputing Laboratory Department of Computer Science,

wilda
Download Presentation

Towards the sequence design preventing pseudoknot formation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Towards the sequence design preventing pseudoknot formation 2nd International Workshop on Natural Computing, Dec. 10-12, 2007 Noyori Conference Hall, Nagoya University, Japan Lila Kari and Shinnosuke Seki Biocomputing Laboratory Department of Computer Science, University of Western Ontario, London, ON, Canada http://www.csd.uwo.ca/~lila/, ~sseki lila, sseki@csd.uwo.ca

  2. DNA computing: brief overview • Process flow • Information is encoded into DNA strings over adenine (A), cytosine (C), guanine (G), and thymine (T) • Succession of intermolecular reactions among encoding DNA strings (bio-operations) in an expected manner based on the base-pairing A-T and C-G (Watson-Crick complementarity) • Resulting DNA strings are decoded using such techniques as Gel-electrophoresis and PCR (polymerase chain reaction). • Advantages • Parallelism • NP-complete problem solvable • Massive storage capacity • Energy efficiency

  3. Watson-Crick complementarity • C - G, A - T (or A - U in RNAs) • Two DNA single strands with opposite orientation (5’ -> 3’) can bind to each other via Watson-Crick complementarity • Bio-operations of DNA computing strongly depend on this biochemical property. 5’ A C C G T A G 3’ 3’ 5’ T G G C A T C

  4. 0 6 3 1 4 2 5 Adleman’s first DNA computing [Adleman, 1994] A solution of Hamiltonian Path Problem (NP-complete problem) • Hamiltonian Path • A path which visits each vertex exactly once. • Hamiltonian Path Problem • Whether a Hamiltonian path exists in a given graph. • How to encode this problem into a test tube called DNA computer?

  5. Encoding oligonucleotides O2TATCGGATCGGTATATCCGA O3GCTATTCGAGCTTAAAGCTA O2->3 6 3 1 4 2 5 0 O2 O3 TATCGGATCGGTATATCCGA GCTATTCGAGCTTAAAGCTA CTCGAATAGC TCGGATATAC O2->3 Adleman’s first DNA computing [Adleman, 1994] A solution of Hamiltonian Path Problem (NP-complete problem) encode CTCGAATAGCTCGGATATAC

  6. What’s the challenges in DNA computing? • How to design encoding DNA strands? • Any kind of intramolecular structures are undesirable for encoding DNA single strands; • Intramolecular structures deprive strands of their ability to interact with another strand (bio-operations) • On the other hand, DNA single strands tend to form intramolecular structures for thermodynamic stability.

  7. Intramolecular structures • E coli transfer-messenger RNA • hairpin loops • bulge loops • internal loops • multiple loops • pseudoknots

  8. Intramolecular structure freeness problem Formal language theoretic approach • DNA alphabet: • d-morphic involution • Antimorphism: (cf. morphism: ) • Involution: • Watson-Crick complementarity • Antimorphic involution A T C T A G

  9. ACG AA CGT θ Intramolecular structure freeness problem Formal language theoretic approach • Hairpin structure • The hairpin structure is the most well-known, and hence intensively investigated intramolecular structure (e.g. [2]). • A DNA strand which forms a hairpin can be modeled as A C G AA T G C

  10. θ-bordered words [Kari et al. 2007] • θ-border • v is said to be θ-border of w if • w is said to be θ-bordered if w has a non-empty θ-border; otherwise, it is called θ-unbordered. • A DNA strand which forms a hairpin is modeled as • Therefore, θ-unbordered words do not form hairpins in this sense. • : the set of all θ-borders of w

  11. Pseudoknots 3’ y θ(y) • Generic term of cross-dependent structures: the right figure is the simplest and hence most popular type pseudoknot. • From the viewpoint of formal language, a strand which forms a pseudoknot of this type can be modeled as: • In this paper, we consider the case where ρ x α y γ θ(x) δ θ(y) σ θ(x) x 5’

  12. θ-Pseudoknot-bordered words • θ-pseudoknot-border • v is said to be θ-pseudoknot-border of w if • w is said to be θ-pseudoknot-bordered if w has a non-empty θ-pseudoknot-border; otherwise it is called θ-pseudoknot-unbordered. • In particular, for an antimorphic θ, if xy is a θ-pseudoknot-border of w, then • θ-pseudoknot-unbordered words never form a pseudoknot of the type • : the set of all θ-pseudoknot-borders of w

  13. A A T A T T T y θ(y) Example of θ-Pseudoknot-bordered words • Let • θ: Watson-Crick complementarity • In fact, by letting • Also by letting x θ(x)

  14. θ-border and θ-pseudoknot border • Lemma 2 • Let θ be a d-morphic involution, and . Then • Let be the set of all θ-unbordered words. • Let be the set of all θ-pseudoknot unbordered words. • Proposition 1 • Let θ be a d-morphic involution. Then

  15. Properties of θ-unbordered words [Kari et al. 1997] • Pref(u), Suff(u): the set of all prefixes (suffixes) of u. • Lemma [Kari et al. 1997] • Let θ be an antimorphism and . Then u is θ-unbordered, i.e, , iff • Lemma 5 • Let θ be an antimorphism and . Then • Corollary 2 • Let θ be an antimorphism and . Then

  16. x θ(x) y θ(y) Properties of θ-pseudoknot unbordered words • We cannot say generally • Example 7 • Let • uu is θ-pseudoknot bordered because for AATTTTATA AATTTTATA

  17. Repetitions of a word and their θ-pseudoknot unbordered property (cont.) • Proposition 2 • Let θ be an antimorphism. Then for , if , then for any , • Corollary 3 • For a word ,

  18. Primitive & θ-pseudoknot unborderd words • A word u is primitive if u = wi implies i = 1. • Lemma 7 • Let θ be an antimorphism and . If u2 is θ-pseudoknot bordered, then u is primitive. • Corollary 4 • If and it is not primitive, then u2 is θ-pseudoknot unbordered, i.e., . This implies • Example 8 • Let . Neither u nor uu are θ-pseudoknot-bordered. This implies that

  19. Primitive & θ-pseudoknot unborderd words (cont.) • Theorem 1 • Let θ be an antimorphism and satisfying Then any θ-pseudoknot border of u2 is primitive. • Proposition 3 • Let θ be an antimorphism and . If w is a θ-pseudoknot border of u2, then the factorization of w into x and y s.t. is unique.

  20. Future work • How to ease the condition ? • The current condition is too strict for practical use. • How to guarantee the θ-pseudoknot unbordered property for the concatenation of two different θ-pseudoknot unbordered words? • Concatenation is a basic manipulation used in DNA computing. • How to model more complicated pseudoknots?

More Related