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Computing with DNA

L. Adelman, Scientific American, pp. 54-61 (Aug 1998)

Note: This ppt file is based on a student presentation given in October, 1999 by Jae

yeon Jung and Jaehong Lim, Department of Computer Science, KAIST, Korea

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Overview

1. Introduction

2. Hamiltonian Path Problem

3. Finding Solution with DNA Experiment

4. Summary & Conclusion

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1. INTRODUCTION

Computing with computer:

CPU, memory, I/O

Binary coding

Serial processing

Universal Turing Machine

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Computing with DNA

Invented (discovered?) by Dr. Leonard M. Adleman of US

C in 1994, a computer scientist and mathematician

Basic Idea: Perform molecular biology experiment to

find solution to math problem.

“DNA Computer”

“Biological Computation” vs “computational biology”

“Molecular Computer”

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2. HAMILTONIAN PATH PROBLEM

(Posed by William Hamilton)

Given a network of nodes and directed connections

between them, is there a path through the network

that begins with the start node and concludes with

the end node visiting each node only once

(“Hamiltonian path")?

“Does a Hamiltonian path exist, or not?”

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Detroit

BostonChicago

Atlanta

Start city

End cityHamiltonian path does exist!

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Detroit

BostonChicago

Atlanta

End city

Start cityHamiltonian path does not exist!

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Solving the Hamiltonian Problem

Generation-&-Test Algorithm:

Step 1: Generate random paths on the network.

Step 2: Keep only those paths that begin with start city and

conclude with end city.

Step 3: If there are N cities, keep only those paths of length N.

Step 4: Keep only those that enter all cities at least once.

Step 5. Any remaining paths are solutions (I.e., Hamiltonian

paths).

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[X] D -> B -> A

[X] B -> C -> D -> B -> A -> B

[X] A -> B -> C -> B

[X] C -> D -> B -> A

[X] A -> B -> A -> D

[O] A -> B -> C -> D

[X] A -> B -> A -> B -> C -> D

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Does a Hamiltonian path exist for the following network?

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Combinatorial Explosion

The total number of paths grows exponentially as the

network size increases (i.e., NP-hard problem):

(e.g.) 106 paths for N=10 cities, 1012 paths (N=20),

10100 paths!! (N =100)

The Generation-&-Test algorithm takes “forever”. Some sor

t of smart algorithm must be devised; none has been foun

d so far (NP-hard).

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3. FINDING SOLUTION WITH DNA EXPERIMENT

DNA is a double-strand polymer

made up of alternating series of

four bases, A, T, C, G.

DNA makes multiple copies of

itself during cell differentiation.

A

G C

T

T A

C G

G

A T

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DNA for Hamiltonian Problem

The key to solving the problem is using DNA to

perform the five steps of the Generation-&-Test

algorithm in parallel search, instead of serial

search.

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DNA Polymerase

- Protein that produces complementary DNA strand

- A -> T, T -> A, C -> G, G -> C

- Enables DNA to reproduce

A

G

T

T

C

G

A

C

A

G

T

A

G

T

T

C

G

A

DNA Polymerase

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Polymerase in Action

The “bio” nano-machine:

– hops onto DNA strand

– slides along

– reads each base

– writes its complement onto new

strand

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Ingredients and tools needed:

- DNA strands that encode city names and connectio

ns between them

- Ligase, water, salt, other ingredients

- Polymerase chain reaction (PCR) set

- Gel electrophoresis tool (that filters out non-solution

strands)

DNA Experiment Set-up

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Gel Electrophoresis

http://www.life.uiuc.edu/molbio/geldigest/equipment.html

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Detroit

BostonChicago

Atlanta

Start city

End city

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CITY DNA NAME COMPLEMENT ATLANTA ACTTGCAG TGAACGTC BOSTON TCGGACTG AGCCTGAC

CHICAGO GGCTATGT CCGATACA DETROIT CCGAGCAA GGCTCGTT

CONNECTING PATH DNA PATH ATLANTA-BOSTON GCAGTCGG ATLANTA-DETROIT GCAGCCGA BOSTON-CHICAGO ACTGGGCT BOSTON-DETROIT ACTGCCGA BOSTON-ATLANTA ACTGACTT CHICAGO-DETROIT ATGTCCGA

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DNA encoding of city-network

TGAACGTC AGCCTGACGCAGTCGG

Atlanta Boston

Atlanta -Boston

Atlanta

Boston

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Detroit

BostonChicago

Atlanta

Start city

End city

Atlanta-Boston Boston-Chicago

Chicago*

Chicago-Detroit

Detroit*Atlanta* Boston*

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Detroit

BostonChicago

Atlanta

Start city

End city

Boston-Atlanta Atlanta-Detroit

Detroit*Boston* Atlanta*

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1. In a test tube, mix the prepared DNA pieces together

(which will randomly link with each other, forming all different paths).

2. Perform PCR with two ‘start’ and ‘end’ DNA pieces as

primers (which creates millions’ copies of DNA strands with the

right start and end).

3. Perform gel electrophoresis to identify only those pieces

of right length (e.g., N=4).

DNA Experiment

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4. Use DNA ‘probe’ molecules to check whether their paths

pass through all intermediate cities.

5. All DNA pieces that are left in the tube should be

precisely those representing Hamiltonian paths.

- If the tube contains any DNA at all, then conclude that a

Hamiltonian path exists, and otherwise not.

- When it does, the DNA sequence represents the

specific path of the solution.

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4. SUMMARY & CONCLUSION

- Why does it work?

Enormous parallelism, with 1023 DNA pieces working in

parallel to find solution simultaneously.

Takes less than a week (vs. thousands yrs for supercomputer)

- Extraordinary energy efficient

(10-10 of supercomputer energy use)

- Future work:

Weather forecasting, robot brain, …, using DNA computers?

(Note: DNA is a Universal Turing machine.)