DNA Computing: Mathematics with Molecules

Russell DeatonProfessorComp. Sci. & Engr.The University of ArkansasFayetteville, AR 72701rdeaton@uark.edu

What is DNA Computing (DNAC) ?

The use of biological molecules, primarily DNA, DNA analogs, and RNA, for computational purposes.

Why Nucleic Acids?• Density (Adleman, Baum):

– DNA: 1 bit per nm3, 1020 molecules– Video: 1 bit per 1012 nm3

• Efficiency (Adleman)– DNA: 1019 ops / J– Supercomputer: 109 ops / J

• Speed (Adleman):– DNA: 1014 ops per s– Supercomputer: 1012 ops per s

What makes DNAC possible?• Great advances in molecular biology

– PCR (Polymerase Chain Reaction)– DNA Microarrays– New enzymes and proteins– Better understanding of biological molecules

• Ability to produce massive numbers of DNA molecules with specified sequence and size

• DNA molecules interact through template matching reactions

What is a the typical methodology?

• Encoding: Map problem instance onto set of biological molecules and molecular biology protocols

• Molecular Operations: Let molecules react to form potential solutions

• Extraction/Detection: Use protocols to extract result in molecular form

PHYSICAL STRUCTURE OF DNA

Nitrogenous Base

34 Å

MajorGroove

Minor Groove

Central Axis

Sugar-PhosphateBackbone

20 Å5’ C

3’ OH

3’ 0HC 5’

5’

3’

3’

5’

What is an example?

• “Molecular Computation of Solutions to Combinatorial Problems”

• Adleman, Science, v. 266, p. 1021.

Algorithm

• Generate Random Paths through the graph.

• Keep only those paths that begin with vin and end with vout.

• If graph has n vertices, then keep only those paths that enter exactly n vertices.

• Keep only those paths that enter all the vertices at least once.

• In any paths remain, say “Yes”; otherwise, say “No”

INTER-STRAND HYDROGEN BONDING

Adenine Thymine

to Sugar-PhosphateBackbone

to Sugar-PhosphateBackbone

(+) (-)

(+)(-)

Hydrogen Bond

Guanine Cytosine

to Sugar-PhosphateBackbone

to Sugar-PhosphateBackbone

(-) (+)

(+)(-)

(+)(-)

STRAND HYBRIDIZATION

A B

a b

A B

ab

b

B

a

A

HEAT

COOL

ba

A B

OR

100° C

DNA LIGATION

’ ’

’ ’

Ligase Joins 5' phosphateto 3' hydroxyl

’ ’

Encoding0

1

2

‘GCATGGCC

‘AGCTTAGG

‘ATGGCATG

CCGGTCGA’

CCGGTACC’

‘GCATGGCCAGCTTAGG CCGGTCGA’

‘GCATGGCCATGGCATG CCGGTACC’

00 21

Massively Parallel SearchV1

E0->1

V0 V2 V3 V4 V5 V6

E1->2 E2->3 E3->4 E4->5 E5->6

V6

E0->6

V0

V3

E0->3

V0 V2 V3 V4 V5 V6

E3->2 E2->3 E3->4 E4->5 E5->6

V5

E4->5

V4 V1 V2

E5->1 E1->2

Algorithm

• Generate Random Paths through the graph.

• Keep only those paths that begin with vin and end with vout.

• If graph has n vertices, then keep only those paths that enter exactly n vertices.

• Keep only those paths that enter all the vertices at least once.

• In any paths remain, say “Yes”; otherwise, say “No”

DNA Polymerase

POLYMERASE CHAIN

REACTION

Start = V0, Stop = V6V1

E0->1

V0 V2 V3 V4 V5 V6

E1->2 E2->3 E3->4 E4->5 E5->6

V6

E0->6

V0

V3

E0->3

V0 V2 V3 V4 V5 V6

E3->2 E2->3 E3->4 E4->5 E5->6

V5

E4->5

V4 V1 V2

E5->1 E1->2

Algorithm

• Generate Random Paths through the graph.

• Keep only those paths that begin with vin and end with vout.

• If graph has n vertices, then keep only those paths that enter exactly n vertices.

• Keep only those paths that enter all the vertices at least once.

• In any paths remain, say “Yes”; otherwise, say “No”

GEL ELECTROPHORESIS - SIZE SORTING

BufferGel

Electrode

Electrode

Samples

Faster

Slower

Right LengthV1

E0->1

V0 V2 V3 V4 V5 V6

E1->2 E2->3 E3->4 E4->5 E5->6

V6

E0->6

V0

V3

E0->3

V0 V2 V3 V4 V5 V6

E3->2 E2->3 E3->4 E4->5 E5->6

Algorithm

• Generate Random Paths through the graph.

• Keep only those paths that begin with vin and end with vout.

• If graph has n vertices, then keep only those paths that enter exactly n vertices.

• Keep only those paths that enter all the vertices at least once.

• In any paths remain, say “Yes”; otherwise, say “No”

ANTIBODY AFFINITY

CACCATGTGAC

GTGGTACACTG B

PMP

+

Anneal

CACCATGTGAC

GTGGTACACTG B+

CACCATGTGAC

GTGGTACACTG B PMP

Bind

Add oligo withBiotin label

Heat and cool

Add Paramagnetic-Streptavidin

Particles

Isolate with MagnetN

S

Every VertexV1

E0->1

V0 V2 V3 V4 V5 V6

E1->2 E2->3 E3->4 E4->5 E5->6

V3

E0->3

V0 V2 V3 V4 V5 V6

E3->2 E2->3 E3->4 E4->5 E5->6

Algorithm

• Generate Random Paths through the graph.

• Keep only those paths that begin with vin and end with vout.

• If graph has n vertices, then keep only those paths that enter exactly n vertices.

• Keep only those paths that enter all the vertices at least once.

• In any paths remain, say “Yes”; otherwise, say “No”

Hamiltonian PathV1

E0->1

V0 V2 V3 V4 V5 V6

E1->2 E2->3 E3->4 E4->5 E5->6

Mismatches

DNA Word Design

• Importance of Template-Matching Hybridization Reactions in DNA Computing (DNAC)

• Sequence design should implement DNAC architecture.– Planned Hybridizations– Problem Size– Subsequent Processing Reactions

• Designed sequences should minimize unplanned “cross-hybridizations.”

• Consequences of Bad Designs: Errors and Poor Efficiency

DNA Word Design

• Design problem is hard.

• As number of sequences required to represent the problem increases, this constraints increasingly conflicts with the requirement of non-crosshybridization.

• How much of DNA sequence space is available for computation?

Why In Vitro?

• In Vitro Selection and Evolution• PCR as tool for selection• Ability to synthesis huge, random starting

populations• Mutagenesis• Oligos manufactured under conditions for use• Use massive parallelism of DNAC to solve

word design problem

Protocol Outline

• Start with huge population of random sequences with attached primers.

• Anneal rapidly to quench oligos in mismatched configurations.

• Using temperature as a control, melt most mismatched pairs.

• Amplify and purify• Repeat

Experimental Results

Experimental Results

Latest Results

DNA Memories

OverviewInput DNAs

(Unknown Seq.)Sequences Comple-

mentary to Input DNAs

Memory DNA Strands(With the 3’ end Comple-

mentary to the Input DNAs)

New UnknownInput DNAs

Learning Recall Output

Tag1Random

Probe

Separates Memory DNA Strands that Match orPartially Match the

New Inputs from ThoseThat Don’t Match

Labeled Tag Sequence Complements

Learning

• Learning: Information acquired from examples rather than programmed

• Protocol to store input DNAs (possibly of unknown sequence)

• Higher level representation of the input sequences• Not individual sequence memories but whole populations• Clustering of input sequences in vitro• Massively random and parallel copying or sampling

depending on number of inputs and probes

Base-by-Base Amplification

Input DNA

Tag Probe Extension

Sampling

Input DNA

Tag Probe Extension

Energy Surface Manipulation through Learning

Energy

Input Sequence

Energy

Input Sequence

Before Learning After Learning

Tags

• Non-Crosshybridizing Sequences• Convenient for Input/Output in absence of input

sequence information• Manipulate memory without input sequences• Implement DNA2DNA Computations (Landweber

and Lipton, DNA 3)

Recall

• Hybridization to retrieve memories

• Similar sequences patterns matched

• Pattern matching done against whole memory

• Single memory associated with single tags

• Memory composite of output on multiple tags

Experiments

• Test learning and recall with plasmid

• Test of sensitivity in concentration

• Test coverage of input sequence space with:– Plasmids (5k bp)– E. Coli (5M bp)

• Test sequence resolution of protocols

LearningInput 1 is a 3 kb linear DNA

(pBluescript)

Input 2 is a 5 kb linear DNA(x 174)

I1 I2 I1 I2

Input DNAs40

60

100

M1 M2

Memory DNAs

Input 1 Input 2

Stained Gel Blot with Memory 1(pBluescript)

Blot with Memory 2(x 174)

Plasmid inputs learned, similar sequences recalled, and dissimilar not matched.

Recall

Concentration Sensitivity

1. Plasmids digested with Hpa II

2. 1 g pBluescript3. 10ng - 800ng x 1744. Blotted with x 174

memory5. 1% x 174 detected in

background of pBluescript

Input Space Coverage

• Randomly digested input

• Learning on both inputs

• Blots nearly identical

E. coli

1. E. coli digested

2. 219bp fragment of x 174 added

3. Learning with and without fragment

4. Fragment distinguished when learned

Application

Team

• Russell Deaton, University of Arkansas, Computer Science and Engineering

• Junghuei Chen, University of Delaware, Chemistry and Biochemistry

• Hong Bi, University of Delaware, Chemistry and Biochemistry

• Max Garzon, University of Memphis, Computer Science• Harvey Rubin, University of Pennsyvania, School of

Medicine• David Wood, University of Delaware, Computer and

Information Science

Acknowledgement

• This work was supported by the NSF QuBIC program, award number EIA-0130385