DNA computing on a chip
Mitsunori Ogihara and Animesh Ray
Nature, 2000
발표자 : 임예니
Idea

In a DNA computer, the input and output
are both strands of DNA. A computer in
which the strands are attached to the
surface of a chip can now solve difficult
problems quite quickly.
Liu

Report a technique for massively parallel elimination

Harness the power of DNA chemistry to solve a particularly
difficult problem in mathematical logic (NP problems)

Complexity classes

Whether sequential algorithms can solve all NP
problems in polynomial time is still unknown.
Complexity classes



The class P is the set of decision problems that
can be solved by a deterministic sequential
machine in polynomial time.
The class NP is the set of decision problems
that can be solved by a non-deterministic Turing
machine in polynomial time.
The NP-complete problems are the most
difficult problems in NP. A decision version of a
combinatorial optimization problem is proved to
belong to the class of NP-complete problems,
then the optimization version is NP-hard.
Leonard Adleman

Present a DNA-based
polynomial time method
for the Hamilton path
problem

The problem of finding an
airline flight path between
several cities on a map
such that each city is
visited only once.
Hamiltonian path problem

Algorithm for directed Hamiltonian path problem






Step 1: Generate random paths through the graph
Step 2: Keep only those paths that begin with vin and end with
vout
Step 3: If the graph has n vertices, then keep only those paths
that enter exactly n vertices.
Step 4: Keep only those paths that enter all of the vertices of
the graph at least once.
Step 5: If any paths remain, say “Yes”, otherwise, say “No”
In order to achieve the small computation time,
Adleman traded space (the amount of DNA needed) for
time (the number of biochemical steps to be used).
Hamiltonian path problem

Step 1



Cities on a map, paths
between pairs of cities, may
be encoded in strands of
DNA.
Millions of DNA strands,
diffusing in a liquid, can selfassemble into all possible
flight-path configurations.
Step 2 ~ Step 4


From that configurations,
molecular maneuvers can
fish out the correct solution.
PCR amplification, running
on an Agarose gel, magnetic
bead separation
Liu

3-SAT

Every NP problem can be seen as the search for a
solution that simultaneously satisfies a number of
logical clauses, each composed of three variables.


(x1 OR x2 OR ^x3) AND (^x4 OR x5 OR ^x6)
Representation
The variables in a given 3-SAT formula
X1 OR x2 OR ^x3
Binary strings
110
Single-stranded DNA sequence
CTTCG
Surface-based approach

Watson strands


Crick strand


For n variables, there are 2n
unique Watson strands. For small
3-SAT, you need 8 Watson
strands.
For each Watson strand, there is
also a complementary Crick
strand created by the basepairing rule : A-T, C-G.
Goal
 to identify those strings out
of a library of eight that
satisfy all the clauses of a
particular 3-SAT formula.
Surface-based approach
1.
2.
3.
4.
They made 8 Watson strands.
They attached the Watson DNA
strings corresponding to all
candidate solutions on a specially
treated gold surface.
They added all possible Crick
strands that will stick to a Watson
string satisfying the first clause.
Such pairing creates doublestranded DNA.
The remaining single-stranded
molecules are destroyed by
enzymes.
Surface-based approach
5.
6.
The surface is then heated to
melt away the complementary
strands, washed and a fresh
collection of Crick strands is
paired with strings satisfying the
second clause.
The DNA answers are attached
randomly to the surface, to read
out the answer, the surviving
strands first have to be
amplified using the polymerase
chain reaction (PCR).
Polymerase Chain Reaction (PCR)

A molecular biological method for amplifying (creating
multiple copies of) a short, well-defined part of a DNA
strand

3 steps



Melting : The double-stranded DNA has to be heated to 96°C in
order to separate the strands.
Annealing : The temperature is lowered so the primers can
attach themselves to the single DNA strands. The temperature
is usually 5°C below melting temperature of primer.
Elongation : The DNA-Polymerase has to fill in the missing
strands. It starts at the annealed primer and works its way
along the DNA strand.
Polymerase Chain Reaction (PCR)
Computation time

Surface-based approach
 only 3k+1 steps



Best computer algorithm
 1.33n steps


for a brute-force evaluation of all 2n possible answers
where k is the number of clauses
where n is the number of variables
3-SAT problem ( k=30, n=50 )
 could be solved in approximately 1.6 million steps by
an ordinary computer algorithm, but in only 91 steps
by surface-based approach.
Issues



Scaling up this technique to solve larger 3-SAT
problems is unrealistic.
Issue of correcting errors arising from the inherent
sloppiness of DNA chemistry
High cost of tailor-made DNA sequences


50-variable problem will require 1015 unique DNA strands.
The exponentially increasing number of DNA molecules
needed to compute even small 3-SAT problems

A compromise may be achieved by reducing search space
through heuristics
The future of technology

The ideal application for DNA computation does
not lie in computing large NP problems.

Some day there may be a need for fully organic
computing devices implanted within a living
body that can integrate signals from several
sources and compute a response in terms of an
organic molecular delivery device.
References


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
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Q. Liu, L. Wang, A.G. Frutos, A.E. Condon, R.M. Corn, L.M. Smith,
“DNA computing on surfaces, “ Nature 403, 175-179 (2000).
L.M. Adleman, “Molecular Computation of Solutions to
Combinatorial Problems, “ Science 266, 1021-1024 (1994).
M. Ogihara and A. Ray, “DNA-based parallel computation by
counting,” DIMACS Series in Discrete Mathematics and Theoretical
Computer Science Volume 48 , The American Mathematics Society
Press, pages 255--264, 1999
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