1Introduction 2Theoretical background Biochemistry/molecular biology 3Theoretical background computer science 4History of the field 5Splicing systems 6P systems 7Hairpins 8Detection techniques 9Micro technology introduction 10Microchips and fluidics 11Self assembly 12Regulatory networks 13Molecular motors 14DNA nanowires 15Protein computers 16DNA computing - summery 17Presentation of essay and discussion Course outline

More serious

 There is a solid theoretical foundation for splicing as an operation on formal languages.  In biochemical terms, procedures based on splicing may have some advantages, since the DNA is used mostly in its double stranded form, and thus many problems of unintentional annealing may be avoided.  The basic model is a single tube, containing an initial population of dsDNA, several restriction enzymes, and a ligase. Mathematically this is represented as a set of strings (the initial language), a set of cutting operations, and a set of pasting operations.  It has been proved to a Universal Turing Machine. Tom Head – splicing systems

These are the techniques that are common in the microbiologist's lab and can be used to program a molecular computer. DNA can be:  synthezisedesired strands can be created  separatestrands can be sorted and separated by length  mergeby pouring two test tubes of DNA into one to perform union  extractextract those strands containing a given pattern  melt/annealbreaking/bonding two ssDNA molecules with complementary sequences  amplifyuse of PCR to make copies of DNA strands  cutcut DNA with restriction enzymes  rejoinrejoin DNA strands with 'sticky ends'  detectconfirm presence or absence of DNA Tom Head – splicing systems

 Initial set (finite or infinite) consists of double-stranded DNA molecules  Specific classes of enzymatic activities considered-those of restriction enzymes  Recombinant behavior modeled and associated sets analyzed by new formalism called Splicing Systems  Attention focused on effect of sets of restriction enzymes and a ligase that allow DNA molecules to be cleaved and Re-associated to produce further molecules. Tom Head – splicing systems

Circular DNA and Splicing Systems DNA molecules exist not only in linear forms but also in circular forms. Splicing systems

SPLICING LINEAR CIRCULAR Splicing systems

Linear splicing

…ATTGACCC… …CAATCAGG… G|AG|A AT | C ligase …ATTG ACCC… …CAAT CAGG… …ATTGCAGG… …CAATACCC… Splicing in nature

V alphabet r = u1u1 u2u2 u4u4 u3u3 splicing rule u 1, u 2, u 3, u 4  V * (x, y) x, y, z, w  V * x = x 1 u 1 u 2 x 2 y = y 1 u 3 u 4 y 2 x 1, x 2, y 1, y 2  V * (z, w) r r x 1 u 1 u 4 y 2 = z y 1 u 3 u 2 x 2 = w Splicing in DNA computing

 = (V, T, A, R) L(  ) =  * (A)  T * if A, R  FIN then L(  )  REG … with permitting context u1u1 u2u2 u4u4 u3u3 C1C1 C2C2  R if A, R  FIN then L(  )  RE V alphabet T  V terminal alphabet A  V * set of strings R splicing rules C 1, C 2  V * Extended H-system

tAtA h A a t 1 hAhA h A bs 1 cAt A h 1 a At A t1t1 h1ah1a h A At A hAhA h 1 abs 1 ct 1  h 1 bs 1 cAt 1 {s 1 }  {h 1, s 1 }  {h A, s 1 }  {s 1, t A }  h 1 a bs 1 ct 1 h A bs 1 c t 1 h 1 bs 1 cA t A h 1 bs 1 cAt h1ah1a h A At A t1t1 tAtA 3 Rotation h 1 a At A h 1 at 1 h A a t 1 h A at A h A At A h 1 at 1

 : (x u 1 u 2 y, wu 3 u 4 z) r = u 1 |u 2 $ u 3 |u 4 rule (x u 1 u 4 z, wu 3 u 2 y) xy wz x w zcut paste y sites Pattern recognition u1u1 u2u2 u3u3 u4u4 u1u1 u2u2 u3u3 u4u4 x u1u1 z u4u4 w u3u3 u2u2 y Păun’s linear splicing operation (1996)

Circular splicing

restriction enzyme 1restriction enzyme 2 ligase enzymes Circular splicing

Conjugacy relation on A* w, w  A*, w ~ w  w = xy, w = yx Example abaa, baaa, aaab, aaba are conjugates A o = A* o = set of all circular words o w = [w] o, w  A* Circular languages

Circular language C  A o set of equivalence classes A* A*  o  L Cir(L) = { o w | w  L} (circularization of L) C L C {w  A*| o w  C}= Lin(C) (Full linearization of C) (A linearization of C, i.e. Cir(L)=C ) Circular languages

FA o ={ C  A o |  L  A*, Cir(L) = C, L  FA, FA  Chomsky hierarchy} Definition Theorem [Head, Păun, Pixton] C  Reg o  Lin (C)  Reg Circular languages

Păun’s definition (A= finite alphabet, I  A o initial language) SC PA = (A, I, R) R  A* | A* $ A* | A* rules ohu1u2,ohu1u2, oku3u4oku3u4  A o r = u 1 | u 2 $ u 3 | u 4  R u2hu1u2hu1 u4ku3u4ku3 o u 2 hu 1 u 4 ku 3 Circular splicing systems

Definition A circular splicing language C(SC PA ) (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. Circular splicing systems

Head’s definition SC H = (A, I, T) T  A*  A*  A* triples  A o (p, x, q ), (u,x,v)  T vkux o hpx vkux q o hpxq, o kuxv q hpx SC PI = (A, I, R)  A o ( ,  ;  ), ( ,  ;  )  R oh  h oh  h  oh,oh, o  h h h  Pixton’s definition R  A*  A*  A* rules h  Other splicing systems (A= finite alphabet, I  A o initial language)

Characterize FA o  C(Fin, Fin) C(Reg, Fin) class of circular languages C= C(SC PA ) generated by SC PA with I and R both finite sets. Problem

Theorem [Păun96] F  {Reg o, CF o, RE o } R +add. hyp. (symmetry, reflexivity, self-splicing) Theorem [Pixton95-96] R  Fin+add. hyp. (symmetry, reflexivity) C(F, Fin)  F F  {Reg o, CF o, RE o } C(F, Reg)  F C(Reg o, Fin)  Reg o, Problem

CS o CF o Reg o o ((aa)*b) o (aa)* o (a n b n ) I= o aa  o 1, R={aa | 1 $ 1 | aa}I= o ab  o 1, R={a | b $ b | a} Circular finite splicing languages

Circular automata

J. Kari and L. Kari Context-free Recombinations, words, sequences, languages where computer science, biology and linguistics meet, C. Martin-Vide, V. Mitrana (Eds.). Kluwer, the Netherlands. Finite automata for circular languages

Definition  Finite automaton A, circular language K-accepted by A, L( A ) o K, all words w o such that A has a cycle labeled by w  K–Acceptance Circular/linear language accepted by a finite automaton A, defined as L(A)  o L(A), L(A) linear language accepted by automaton A defined in the usual way Definition A circular/linear language L   *  o is regular if there is a finite automaton A that accepts the circular and linear parts of L, i.e. that accepts L  * and L   o Finite automata for circular languages

The following definition is equivalent to a definition given by Pixton: the circular language accepted by a finite automaton is a set of all words that label a loop containing at least one initial and one final state. Definition Given a finite automaton A, the circular language accepted by A, L(A) o P is the set of all words o w such that A has a cycle labeled by w that contains at least one final state. P-acceptance

The circular languages accepted by finite automaton by the following definition coincide with the regular circular languages introduced by Head. Given a finite automation A, the circular language accepted by A, L( A ) o H is the set of all words o w such that w = u v and v u  L( A ) Pixton has shown that if in addition we assume that the family of languages is closed under repetition (i.e., w n is in the language whenever w is) H – acceptance and P – Acceptance are equivalent H-acceptance

Advantages of K-acceptance The same automaton accepts both the linear and circular components of the language K-acceptance

Counting problem

T. Head, Circular Suggestions for DNA Computing, in: Pattern Formation in Biology, Vision and Dynamics, Eds. A.Carbone, M Gromov and P. Prusinkiewicz, World Scientific, Singapore, 2000, pp J. Kari, A Cryptosystem Based on Propositional Logic, in: Machines, Languages and Complexity, 5th International Meeting of Young Computer Scientists, Czeckoslovakia, Nov , 1988, Eds. J. Dassow and J.Kelemen, LNCS 381, Springer, 1989, pp Rani Siromoney, Bireswar Das, DNA Algorithm for Breaking a Propositional Logic Based Cryptosystem, Bulletin of the EATCS, Number 79, February 2003, pp Sources

Introducing CUT-DELETE-EXPAND-LIGATE (C-D-E-L) model Combine features in Divide-Delete-Drop (D-D-D) (Leiden) and CUT-EXPAND-LIGATE (C-E-L) (Binghamton) to form CUT-DELETE- EXPAND-LIGATE (C-D-E-L) model This enables us to get an aqueous solution to 3SAT which is a counting problem and known to be in IP. 3SAT Defined as follows: Instance: F a propositional formula of form F = C 1  C 2  …C m where C i are clauses and i = 1, 2, …, m. Each C i is of the form ( l i1  l i2  l i3 ) where l i j, j = 1, 2, 3 are literals from the set of variables {x 1, x 2, …, x n } Question What is the number of truth assignments that satisfy F? C-D-E-L model

Standard double stranded DNA cloning plasmid are commercially available. A plasmid is a circular molecule approximately 3 kb. It contains a sub-segment, MCS (multiple cloning site) of approximately 175 base pairs that can be removed using a pair of restriction enzyme sites that flank the segment. The MCS contains pair-wise disjoint sites at which restriction enzymes act such that each produces a 5’ overhang. Data register molecule

In C-D-E-L, a segment of the plasmid used is of the form …c 1 s 1 c 1 …c 2 s 2 c 2 …c n s nn c n … Where c i are called sites, such that no other subsequence of plasmid matches with this sequence and s i are called stations and i=1,…,n In D-D-D, lengths of stations are required to be the same However in C-D-E-L, lengths of stations all different which is fundamental in solving #3SAT Bio-molecular operations used in C-D-E-L are similar to the operations in C-E-L C-D-E-L model

x 1, …, x n the variables in F,  x 1, …,  x n their negations s i station associated with x i  s i station associatd with  s i c i site associated with station s i  c i site associated with station  s i v i length of station associated with x i, i=1, …, n v n+j length of station associated with literal  x j, j=1,…, n Choose stations in such a way that the sequence [ v 1, …, v 2n ] satisfies the property k  v i < v k+1, k = 1, …, 2n-1 i=1 i.e. an Super-increasing (Easy) Knapsack Sequence From sum, sub-sequence efficiently recovered. Design

 Solution in C n is analyzed by gel separation  If more than one solution is present, they will be of different lengths, thus will form separate bands  By counting number of bands we count the number of satisfying assignments.  Furthermore, from lengths of satisfying assignment,exact assignment is read.  This can be done since stations have lengths from easy knapsack sequence any subsequence of an easy knapsack sequence has different sum from the sums of other subsequences. Solution

C-D-E-L model

Thus solution to 3–SAT viz. finding the number of satisfying assignments is effectively done. Moreover, reading the truth assignments is a great advantage to break the cryptosystem based on propositional logic Solution

Advantage over previous method of attack  In the cryptanalytic attack proposed earlier, modifying D-D-D, it was required to execute the DNA algorithm for each bit in the crypto-text  But in the present method proposed, using C-D-E-L (combining features of C-C-C and C-E-L ) apply 3-SAT on P and read any satisfying assignment from the final solution  This gives an equivalent public key, which amounts to breaking the cryptosystem Advantage

 H-system  Lipton[94-95a-95b] Formalization and generalization of Adleman’s approach to other NP-complete problems.  Ex H-system  Circular H-system  Sticker system  P-system Splicing systems so far

For computational strength  Turing Equivalence Expansion  Finiteness & Regularity  More Operator Formalization To confirm homogeneity  HPP solving & AGL Splicing systems so far

Molecular application

 Separating and fusing DNA strands  Lengthening of DNA  Shortening DNA  Cutting DNA  Multiplying DNA Operations of DNA molecules

Denaturation  separating the single strands without breaking them  weaker hydrogen than phosphodiester bonding  heat DNA (85° - 90° C) Renaturation  slowly cooling down  annealing of matching, separated strands Separating and fusing DNA strands

Machinery for Nucleotide Manipulation  Enzymes are proteins that catalyze chemical reactions.  Enzymes are very specific.  Enzymes speed up chemical reactions extremely efficiently (speedup: 1012)  Nature has created a multitude of enzymes that are useful in processing DNA. Enzymes

 DNA polymerase enzymes add nucleotides to a DNA molecule Requirements  single-stranded template  primer,  bonded to the template  3´-hydroxyl end available for extension  Note: Terminal transferase needs no primer. Lengthening DNA

DNA nucleases are enzymes that degrade DNA. DNA exonucleases  cleave (remove) nucleotides one at a time from the ends of the strands  Example: Exonuclease III 3´- nuclease degrading in 3´- 5´direction Shortening DNA

DNA nucleases are enzymes that degrade DNA. DNA exonucleases  cleave (remove) nucleotides one at a time from the ends of the strands  Example: Bal31 removes nucleotides from both strands Shortening DNA

DNA nucleases are enzymes that degrade DNA. DNA endonucleases  destroy internal phosphodiester bonds  Example: S1 cuts only single strands or within single strand sections Restriction endonucleases  much more specific  cut only double strands  at a specific set of sites (EcoRI) Cutting DNA

 Amplification of a „small“ amount of a specific DNA fragment, lost in a huge amount of other pieces.  „Needle in a haystack“  Solution: PCR = Polymerase Chain Reaction  devised by Karl Mullis in 1985  Nobel Prize  a very efficient molecular copy machine Multiplying DNA

Start with a solution containing the following ingredients:  the target DNA molecule  primers (synthetic oligo- nucleotides), complementary to the terminal sections  polymerase, heat resistant nucleotides PCR - initialisation

 Solution heated close to boiling temperature.  Hydrogen bonds between the double strands are separated into single strand molecules. PCR – denaturation

 The solution is cooled down (to about 55° C).  Primers anneal to their complementary borders. PCR - priming

 The solution is heated again (to about 72° C).  Polymerase will extend the primers, using nucleotides available in the solution.  Two complete strands of the target DNA molecule are produced. PCR - extension

2n copies after n steps PCR – copying

Measuring the Length of DNA Molecules  DNA molecules are negatively charged.  Placed in an electric field, they will move towards the positive electrode.  The negative charge is proportional to the length of the DNA molecule.  The force needed to move the molecule is proportional to its length.  A gel makes the molecules move at different speeds.  DNA molecules are invisible, and must be marked (ethidium bromide, radioactive) Gel electrophoresis

 reading the exact sequence of nucleotides comprising a given DNA molecule  based on  the polymerase action of extending a primed single stranded template  nucleotide analogues  chemically modified e.g., replace 3´-hydroxyl group (3´-OH) by 3´-hydrogen atom (3´-H)  dideoxynucleotides: - ddA, ddT, ddC, ddG  Sanger method, dideoxy enzymatic method Sequencing

Objective  We want to sequence a single stranded molecule a. Preparation  We extend a at the 3´ end by a short (20 bp) sequence g, which will act as the W-C complement for the primer compl(g). l Usually, the primer is labelled (radioactively, or marked fluorescently)  This results in a molecule b´= 3´- ga. Sequencing 5' ATTAGACGTCCGTGCAATGC 3' 3'ACGTTACG 5'

Sequencing

4 tubes are prepared  Tube A, Tube T, Tube C, Tube G  Each of them contains  b molecules  primers, compl(g)  polymerase  nucleotides A, T, C, and G.  Tube A contains a limited amount of ddA.  Tube T contains a limited amount of ddT.  Tube C contains a limited amount of ddC.  Tube G contains a limited amount of ddG. Sequencing

Structure of ddTTP

Termination with ddTTP

Reaction in Tube A  The polymerase enzyme extends the primer of b´, using the nucleotides present in Tube A: ddA, A, T, C, G.  using only A, T, C, G:  b´ is extended to the full duplex.  using ddA rather than A:  complementing will end at the position of the ddA nucleotide. Sequencing

Sequencing - stopping

Tube C  GCCTGCAGATTA  C  CGGAC  CGGACGTC Tube G  GCCTGCAGATTA  CG  CGG  CGGACG Sequencing -results Tube A  GCCTGCAGATTA  CGGA  CGGACGTCTA  CGGACGTCTAA Tube T  GCCTGCAGATTA  CGGACGT  CGGACGTCT  CGGACGTCTAAT

Sequencing – reading the results