DNA Computing on a ChipDNA Computing on a Chip

Mitsunori Ogihara and Animesh Ray

Nature, vol. 403, pp. 143-144

Cho, Dong-Yeon

AbstractAbstract

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 et al., 2000] Liu, Q. et al., “DNA computing on a chip,” Nature, vol.

403, pp. 175-179, 2000.

Arriving at the truth by Arriving at the truth by eliminationelimination Problem classes

Polynomial time or P problems O(1), O(n), O(nlogn), O(n2), O(n3), …

Non-deterministic polynomial time or NP problems ‘Hard’ NP problems have running times that grow exponential

ly with the number of the variables. O(2n), O(3n), O(n!) …

New technology for massively parallel elimination [Liu et al., 2000] This algorithm harnesses the power of DNA chemistry

and biotechnology to solve a particularly difficult problem in mathematical logic.

Adleman’s experimentsAdleman’s experiments

Hamilton path problem Millions of DNA strands, diffusing i

n a liquid, can self-assemble into all possible path configurations.

A judicious series of molecular manoeuvres can fish out the correct solutions.

Adleman, combining elegance with brute force, could isolate the one true solution out of many probability.

Liu’s experimentsLiu’s experiments

Satisfiability Problem Find Boolean values for variab

les that make the given formula true

3-SAT Problem Every NP problems can be see

n as the search for a solution that simultaneously satisfies a number of logical clauses, each composed of three variables.

)or or ( AND )or or (

)or or ( AND )or or (

321321

654321

xxxxxx

xxxxxx

)()()( 324431 xxxxxx

ProcedureProcedure

Step 1. Attach DNA strings encoding all possible answers to a

specially treated gold surface.

Step 2. Complementary DNA strands that satisfy the first

clauses are added to the solution. The remaining single strands are destroyed by enzymes. The surface is then heated to melt away the

complementary strands. This cycle is repeated for each of the remaining clauses.

Step 3. The surviving strands first have to be amplified using

the PCR. Their identities are then determined by pairing with an

ordered array of strings identical to the original set of sequences.

O(3k+1) vs. O(1.33n), O(2n) k: the number of clauses n: the number of variables

ProblemsProblems

Scaling up this technique to solve larger 3-SAT problems is still unrealistic. Correcting errors arising from the inherent sloppiness

of DNA chemistry High cost of tailor-made DNA sequences

50-variable 3-SAT: 1015 unique DNA strands

Designing enough unique DNA strands Exponentially increasing number of DNA molecules

A compromise may be achieved by reducing the search space through heuristics.

ConclusionsConclusions

The ideal application for DNA computation does not lie in computing large NP problems There may be a need for fully organic computing

devices implanted within a living body that can integrated signals from several sources and compute a response in terms of an organic molecular-delivery device for a drug or signal.