DNA algorithm is an optimizing algorithm.

1. DNA
ALGORITHM
PRESENTED BY: GUIDE:
T. KRISHNA MURTHY Dr. C. S. P. RAO
PROFESSOR
NITW

2. Objectives
Introduction to DNA
DNA computing
DNA operations
Definition of Hamiltonian path problem.
Steps involved in DNA operation
Application of DNA algorithm to solve
AHPP
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3. Introduction to DNA
 The (deoxyribonucleic acid) DNA stand is
encodes the genetic information of cellular
organisms.
 Consists of polymer chains, commonly referred to
as DNA strands.
 Strand lengths are measured in base pairs (b.p.)
 composed of basic blocks called nucleotides.
 two pairs of bases form hydrogen bonds
between each other
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4. continued…
 Two bonds between A and T, and three
between G and C
 A single DNA strand can pair with another strand
 Example
CCCAATGAACCCCATTT
GGGTTACTTGGGGTAAA
 Every natural species have unique DNA identity.
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5. 5
Introduction to DNA
Computing
 DNA computing uses : DNA, biochemistry,
and molecular biology, instead of the
traditional silicon-based computer
technologies.
 Manipulations with DNA strands, basic
biological transformations
 DNA computing solves NP complete problems
much faster than modern silicon-based
computers

6. 6
continued..
 DNA computing uses : DNA, biochemistry,
and molecular biology, instead of the
traditional silicon-based computer
technologies.
 Manipulations with DNA strands, basic
biological transformations
 DNA computing solves NP complete problems
much faster than modern silicon-based
computers

7. 7
DNA Operations
 Synthesis
- making millions of copies
 Denaturing, Annealing and Ligation
- double strand to single strand
- annealing with complementary strand
- unified strand formation
 Affinity purification
 Gel electrophoresis
 Polymerase Chain Reaction

8. 8
A directed Graph. An s-t Hamiltonian path is (s,2,4,6,3,5,t).Here Vin=s and
Vout=t.
Introduction to AHPP

9. Introduction to AHPP
 A directed Graph G=(V,E)
 |V|=n, |E|=m and two distinguished vertices
Vin = s and Vout = t.
 Verify whether there is a path (s,v1,v2,….,t)
 which is a sequence of “one-way” edges that begins in
Vin and Vout
 whose length (in no. of edges) is n-1 and
(i.e. enters all vertices.)
 Whose vertices are all distinct
(i.e. enters every vertex exactly once.)
A CLASSIC NP-COMPLETE PROBLEM!!!
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10. Steps for solving AHPP
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11. 1. Random Path Generation
 Assumptions
 Random single stranded DNA sequences with 20
nucleotides are available.
 Vertex representation
 Each vertex v is represented with a random 20-mer
sequence of DNA denoted by Sv..
 For each such sequence obtain its complement Sv.
 Generate many copies of each Sv sequence .
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12. For example, the sequences chosen to
represent vertices 2, 4 and 5 are :
S2 = GTCACACTTCGGACTGACCT
S4 = TGTGCTATGGGAACTCAGCG
S5 = CACGTAAGACGGAGGAAAAA
The reverse complement of these sequences are:
S2 = AGGTCAGTCCGAAGTGTGAC
S4 = CGCTGAGTTCCCATAGCACA
S5 = TTTTTCCTCCGTCTTACGTG
20 mer
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13. 13
S2 S4
Edge(2,4)
S5S4
Edge(4,5)

14. Examples of random paths
formed
S2 S4 S6 sS2 S3
E24 E46 E62 E2s Es3
S6 tS5S3
E5tE35E63
s S2
Es2
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15. 1.Random Path Generation
 Path Construction
 Both vertex complimentary and edge strands
ligase reactions will take place.
(Ligase Reaction or ligation: There is an enzyme
called Ligase, that causes concatenation of
two sequences in a unique strand.)
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16. Formation of Paths from Edges
and compliments of vertices
Edge uv Edge vw
Su SwSv
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17. 2.Keep only those that start at s
and end at t.
 Product of step 1 was amplified by PCR using
primers Ss and St.
 By this, only those molecules encoding paths that
begin with vertex s and end with vertex t were
amplified.
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18. 3. Keep only those that visit
exactly n vertices
 Product of step 2 is run on agarose gel and
the 140bp (since 7 vertices) band was excised
and soaked in doubly distilled H2O to extract
DNA.
 This product is PCR amplified and gel purified
several times to enhance its purity.
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19. 3. Keep only those that visit
exactly n vertices
 DNA is negatively charged.
 Place DNA in a gel matrix at the
negative end. (Gel Electrophoresis)
 Longer strands will not go as far as
the shorter strands.
 In our example we want DNA that
is 7 vertices times 20 base pairs, or 140
base pairs long.
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20. 4.Keep only those that visit each
vertex at least once
 From the double stranded DNA product of step3,
generate single stranded DNA.
 Incubate the single stranded DNA with S2
conjugated to the magnetic beads.
 Only single stranded DNA molecules that
contained the sequence S2 annealed to the
bound S2 and were retained
 Process is repeated successively with S4,S6,S3,S5
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21. Contd…..
 Filter the DNA searching for one vertex at
a time.
 Do this by using a technique called
Affinity Purification. (think magnetic
beads)
s 2 t4 6 3 5
5
compliment
Magnetic bead
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22. 5. Obtaining the Answer
 This was done by amplifying the results of
step 4 by polymerase chain reaction and
then determining the DNA sequence of
the amplified molecules.
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23. 23

24. LIMITATIONS

25. DNA Vs Electronic computers
 At Present, NOT competitive with the state-of-the-
art algorithms on electronic computers
 Only small instances of HDPP can be solved.
Reason?..for n vertices, we require 2^n molecules.
 Time consuming laboratory procedures.
 Good computer programs that can solve TSP for 100
vertices in a matter of minutes.
 No universal method of data representation.
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26. Size restrictions
 Adleman’s process to solve the traveling
salesman problem for 200 cities would
require an amount of DNA that weighed
more than the Earth.
 The computation time required to solve
problems with a DNA computer does not
grow exponentially, but amount of DNA
required DOES.
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27. References
 “Solving Shortest Hamiltonion Path Problem
Using DNA Computing”- by Hala Mohammed
Alshamlan, Mohammed El Bachir Menai.
 “DNA algorithms for computing shortest
paths” by Ajit Narayanan,Spiridon Zorbalas.
 “NPTEL video on DNA computing ” by Kamala
Krithivasan.
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