DNA Computing: Mathematics with Molecules Russell Deaton Professor Comp. Sci. & Engr. The University of Arkansas Fayetteville, AR

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 nm 3, molecules –Video: 1 bit per nm 3 Efficiency (Adleman) –DNA: ops / J –Supercomputer: 10 9 ops / J Speed (Adleman): –DNA: ops per s –Supercomputer: 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

P HYSICAL S TRUCTURE OF DNA Nitrogenous Base 34 Å Major Groove Minor Groove Central Axis Sugar-Phosphate Backbone 20 Å 5’ C 3’ OH 3’ 0H C 5’ 5’ 3’ 5’

What is an example? “Molecular Computation of Solutions to Combinatorial Problems” Adleman, Science, v. 266, p

Algorithm Generate Random Paths through the graph. Keep only those paths that begin with v in and end with v out. 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”

I NTER-STRAND H YDROGEN B ONDING AdenineThymine to Sugar-Phosphate Backbone to Sugar-Phosphate Backbone (+)(-) (+)(-) Hydrogen Bond GuanineCytosine to Sugar-Phosphate Backbone to Sugar-Phosphate Backbone (-) (+) (-) (+) (-)

S TRAND H YBRIDIZATION A B a b A B a b b B a A HEAT COOL b a A B OR 100° C

DNA L IGATION  ’’ ’’ ’’ ’’ Ligase Joins 5' phosphate to 3' hydroxyl ’’ ’’  

Encoding ‘GCATGGCC ‘AGCTTAGG ‘ATGGCATG CCGGTCGA’ CCGGTACC’ ‘GCATGGCCAGCTTAGG CCGGTCGA’ ‘GCATGGCCATGGCATG CCGGTACC’ 0021

Massively Parallel Search V1V1 E 0->1 V0V0 V2V2 V3V3 V4V4 V5V5 V6V6 E 1->2 E 2->3 E 3->4 E 4->5 E 5->6 V6V6 E 0->6 V0V0 V3V3 E 0->3 V0V0 V2V2 V3V3 V4V4 V5V5 V6V6 E 3->2 E 2->3 E 3->4 E 4->5 E 5->6 V5V5 E 4->5 V4V4 V1V1 V2V2 E 5->1 E 1->2

Algorithm Generate Random Paths through the graph. Keep only those paths that begin with v in and end with v out. 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 = V6 V1V1 E 0->1 V0V0 V2V2 V3V3 V4V4 V5V5 V6V6 E 1->2 E 2->3 E 3->4 E 4->5 E 5->6 V6V6 E 0->6 V0V0 V3V3 E 0->3 V0V0 V2V2 V3V3 V4V4 V5V5 V6V6 E 3->2 E 2->3 E 3->4 E 4->5 E 5->6 V5V5 E 4->5 V4V4 V1V1 V2V2 E 5->1 E 1->2

Algorithm Generate Random Paths through the graph. Keep only those paths that begin with v in and end with v out. 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”

G EL E LECTROPHORESIS - SIZE SORTING Buffer Gel Electrode Samples Faster Slower

Right Length V1V1 E 0->1 V0V0 V2V2 V3V3 V4V4 V5V5 V6V6 E 1->2 E 2->3 E 3->4 E 4->5 E 5->6 V6V6 E 0->6 V0V0 V3V3 E 0->3 V0V0 V2V2 V3V3 V4V4 V5V5 V6V6 E 3->2 E 2->3 E 3->4 E 4->5 E 5->6

Algorithm Generate Random Paths through the graph. Keep only those paths that begin with v in and end with v out. 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”

A NTIBODY A FFINITY CACCATGTGAC GTGGTACACTG B PMP + Anneal CACCATGTGAC GTGGTACACTG B + CACCATGTGAC GTGGTACACTG B PMP Bind Add oligo with Biotin label Heat and cool Add Paramagnetic-Streptavidin Particles Isolate with Magnet N S

Every Vertex V1V1 E 0->1 V0V0 V2V2 V3V3 V4V4 V5V5 V6V6 E 1->2 E 2->3 E 3->4 E 4->5 E 5->6 V3V3 E 0->3 V0V0 V2V2 V3V3 V4V4 V5V5 V6V6 E 3->2 E 2->3 E 3->4 E 4->5 E 5->6

Algorithm Generate Random Paths through the graph. Keep only those paths that begin with v in and end with v out. 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 Path V1V1 E 0->1 V0V0 V2V2 V3V3 V4V4 V5V5 V6V6 E 1->2 E 2->3 E 3->4 E 4->5 E 5->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

Latest Results

DNA Memories

Overview Input DNAs (Unknown Seq.) Sequences Comple- mentary to Input DNAs Memory DNA Strands (With the 3’ end Comple- mentary to the Input DNAs) New Unknown Input DNAs Learning Recall Output Tag 1 Random Probe Separates Memory DNA Strands that Match or Partially Match the New Inputs from Those That 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 ProbeExtension

Sampling Input DNA Tag ProbeExtension

Energy Surface Manipulation through Learning Energy Input Sequence Energy Input Sequence Before LearningAfter Learning

Tags Non-Crosshybridizing Sequences Convenient for Input/Output in absence of input sequence information Manipulate memory without input sequences Implement DNA 2 DNA 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

Learning Input 1 is a 3 kb linear DNA (pBluescript) Input 2 is a 5 kb linear DNA (  x 174) I1 I2 I1I2 Input DNAs 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 pBluescript 3.10ng - 800ng  x Blotted with  x 174 memory 5.1%  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