DNA  and                 splicing
This presentation is the property of its rightful owner.
Sponsored Links
1 / 21

DNA and splicing (circular) PowerPoint PPT Presentation


  • 66 Views
  • Uploaded on
  • Presentation posted in: General

DNA and splicing (circular). circular. Paola Bonizzoni, Clelia De Felice, Giancarlo Mauri, Rosalba Zizza. Dipartimento di Informatica Sistemistica e Comunicazioni, Univ. di Milano - Bicocca ITALY Dipartimento di Informatica e Applicazioni, Univ. di Salerno, ITALY.

Download Presentation

DNA and splicing (circular)

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Dna and splicing circular

DNA and splicing

(circular)

circular

Paola Bonizzoni, Clelia De Felice, Giancarlo Mauri, Rosalba Zizza

Dipartimento di Informatica Sistemistica e Comunicazioni, Univ. di Milano - Bicocca ITALY

Dipartimento di Informatica e Applicazioni, Univ. di Salerno, ITALY

Circular splicing, definitions

State of the art

Our contributions

Works in progress


We apologize

We apologize...

<<An important aspect of this year’s meeting can be summed

up us: SHOW ME THE EXPERIMENTAL RESULT! >>

(T. Amenyo, Informal Report on 3rd Annual

DIMACS Workshop on DNA Computing, 1997)

theoretical results


Before adleman experiment 1994

Before Adleman experiment (1994)...

Tom Head 1987 (Bull. of Math. Biology)

“ Formal Language Theory and DNA:

an analysis of the generative capacity of

specific recombinant behaviors”

Unconventional

models of computation

SPLICING


Dna and splicing circular

LINEAR

SPLICING

CIRCULAR


Circular splicing

CIRCULAR SPLICING

restriction enzyme 2

restriction enzyme 1

ligase enzymes


Circular languages definitions and examples

Circular languages: definitions and examples

w, w A*, w~ w   w=xy, w = yx

  • Conjugacy relation on A*

abaa

Example

abaa, baaa, aaab,aaba are conjugate

  • A~ = A*  ~ =set of all circular words

~w = [w]~ , w A*

  • Circular language

C  A ~ set of equivalence classes

A*

A*  ~

Cir(L) = {~w | w L} (circularization of L)

L

L

C

(A linearization of C, i.e. Cir(L)=C )

{w  A*| ~w C}=Lin(C)

C

(Full linearization of C)


Dna and splicing circular

Definition:

FA~ ={ C A~|  L  A*, Cir(L) = C, L  FA, FA  Chomsky hierarchy}

Theorem [Head, Paun, Pixton]

C  Reg ~ Lin (C)  Reg


Dna and splicing circular

Circular splicing systems

(A= finite alphabet, I A~ initial language)

Paun’s definition

SCPA = (A, I, R)

R A* | A* $ A* | A* rules

r = u1| u2 $ u3 | u4  R

~hu1u2,

~ku3u4

 A~

u2 hu1

u4ku3

~ u2 hu1 u4ku3

Definition

A circular splicing language C(SCPA) (i.e. a circular language generated

by a splicing system SCPA ) is the smallest circular language containing

I and closed under the application of the rules in R


Dna and splicing circular

Other definitions of splicing systems

(A= finite alphabet, I A~ initial language)

Head’s definition

SCH = (A, I, T)

T A*  A*  A* triples

 A~

~hpxq,

~kuxv

(p, x, q ), (u,x,v)  T

vkux

~hpx vkux q

qhpx

Pixton’s definition

SCPI = (A, I, R)

R A*  A*  A* rules

 A~

~h,

~h

(, ;), (, ;  )  R

~ h h 

h 

h 


Dna and splicing circular

Problem:

Characterize

C(Reg, Fin)

FA~ C(Fin, Fin)

class of circular languages C= C(SCPA) generated by SCPA with I and R both finite sets.

Theorem [ Paun96]

F{Reg~, CF~, RE~}

R +add. hyp. (symmetry, reflexivity, self-splicing)

C(F, Fin)  F

Theorem [Pixton95-96]

F{Reg~, CF~, RE~}

R Fin+add. hyp. (symmetry, reflexivity)

C(Reg~, Fin)Reg~,

C(F, Reg)  F


Circular finite splicing languages and chomsky hierarchy

Circular finite splicing languages and Chomsky hierarchy

CS~

CF~

C(Fin, Fin)

Reg~

~((aa)*b)

~(an bn)

~(aa)*

I= ~ab  ~1, R={a | b $ b | a}

I= ~aa  ~1, R={aa | 1 $ 1 | aa}


Our contributions

Our contributions

Reg~ C(Fin, Fin)

C(Fin, Fin)

Fingerprint closed

star languages

Reg~

X*, X regular

group code

cyclic

languages

Cir (X*)

X finite

weak cyclic,

other examples

~ (a*ba*)*


Dna and splicing circular

Our contributions (continued)

Comparing the three definitions of splicing systems

C(SCH )  C(SCPA )  C(SCPI )

~ (a*ba*)*, ~ ((aa)*b)

= ... ?


Star languages

Definition

Star languages

L  A* is star language if L is regular, closed under

conjugacy relation and L=X*, with X regular

Proposition:

SCPA=(A,I,R), I  Cir(X*)  C(SCPA)  Cir (X*)

“Consistence” easily follows!!!

Examples

  • (b*(ab*a)*)* = X*

X=b  ab*a

X= a*ba*

  • (a*ba*)* = X*


Dna and splicing circular

c

q0

q0

y

x

z

x’

y’

z’

Fingerprint closed languages

Definition

For any cycle c, L contains the Fingerprints of c

Fingerprint of a cycle

cnc L

power of the cycle, where the internal cycles are crossed a finite number of times

i n y , j n x

c=(x(y(zz’)jy’)i x’)nc


Dna and splicing circular

Theorem

Fingerprint closed star languages C(Fin,Fin)

Sketch

Take SCPA = (A, I, R) with

I=Cir({successful path containing fingerprint of cycles})

R={1 | 1 $ 1 | ƒ | ƒ fingerprint of cycle c, for any cycle c}

Star languages fingerprint closed

(for example X=b  ab*a)

  • X*, X regular group code

(for example X=Ad )

  • X finite, Cir(X*)

Star languages not fingerprint closed

(a*ba*)*but not generated!!!


Dna and splicing circular

Not Star Languages in C(Fin, Fin)

new!

Cyclic Languages

Definition

Cyclic(z) ={(~(z* p)) | p Pref (Lin( ~z))}

Example

 z = abc  A*

 Lin ( ~z) =Lin (~ abc) ={abc, bca,cab}

 Pref(Lin ( ~z)) =Pref(Lin (~ abc)) =Pref({abc, bca,cba}) = {a, ab, b, bc, c, ca}

Cyclic(abc)= ~(abc)*a~(abc)*ab 

~(abc)*b ~(abc)*bc 

~(abc)*c ~(abc)*ca


Dna and splicing circular

Theorem

For any z, |z|>2, z unbordered word, then

Cyclic(z) C(Fin,Fin)

i.e. z  uA* A*u

The proof is quite technical ...

Example (continued)

Cyclic (abc) is generated by SCPA = (A,I,R) where I,R are defined as follows

I={~ ((abc)i p | 0 i  3, p  Pref(Lin(~ (abc))) }

R={z ab | z $ z | ca z, z ab | z $ z b | c z, z ca | z $ z $ bc z,

z a | z $ z | b z, z b | z $ z $ c z , z c | z $ z | a z }


Dna and splicing circular

Other circular regular splicing languages

  • ~(abc)*a~(abc)*ab ~(abc)*b ~(abc)*bc ~(abc)*c ~(abc)*ca

~(abc)*ac

Cyclic(abc)

weak cyclic languages

  • Cyclic (abca) .... bordered word...


Works in progress

Works in progress

  • Characterize Reg~ C(Fin, Fin)

  • Characterize FA~ C(Fin, Fin)

  • C(SCPI) = Star languages

  • Additional hypothesis

  • r= u1| u2 $ u3 | u4 in R

  • Reflexive:  r’ = u1| u2 $ u1| u2

  • Symmetric:  r” = u3 | u4 $ u1| u2

  • Self-splicing: From ~ xu1u2yu3u4 ,

  • with r,r” as above, generates ~u4 xu1 , ~u2yu3 .


Dna and splicing circular

Conclusions

DNA6

auditorium

Thanks!


  • Login