DNA Computing: Mathematics with Molecules

1. DNA Computing: Mathematics with Molecules Russell DeatonProfessor Comp. Sci. & Engr.The University of Arkansas Fayetteville, AR 72701 rdeaton@uark.edu

2. What is DNA Computing (DNAC) ? The use of biological molecules, primarily DNA, DNA analogs, and RNA, for computational purposes.

3. 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

4. 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

5. 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

6. PHYSICAL STRUCTURE OF DNA 20 Å 3’ OH 5’ C Minor Groove 34 Å 5’ 3’ Sugar-Phosphate Backbone Major Groove 5’ 3’ Nitrogenous Base C 5’ 3’ 0H Central Axis

7. What is an example? • “Molecular Computation of Solutions to Combinatorial Problems” • Adleman, Science, v. 266, p. 1021.

9. 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”

10. (-) (+) (+) (-) to Sugar-Phosphate Backbone (+) (-) to Sugar-Phosphate Backbone Guanine Cytosine Hydrogen Bond INTER-STRAND HYDROGEN BONDING (+) (-) (-) (+) to Sugar-Phosphate Backbone to Sugar-Phosphate Backbone Adenine Thymine

11. B A a b A B a b B A a b B A a b STRAND HYBRIDIZATION 100° C HEAT COOL OR

12. DNA LIGATION   ’ ’   ’ ’ ’ ’ Ligase Joins 5' phosphate to 3' hydroxyl

13. Encoding ‘GCATGGCC 0 CCGGTCGA’ 1 CCGGTACC’ ‘AGCTTAGG 2 ‘ATGGCATG 0 1 0 2 ‘GCATGGCCATGGCATG CCGGTACC’ ‘GCATGGCCAGCTTAGG CCGGTCGA’

15. V0 V1 V2 V3 V4 V5 V6 E0->1 E1->2 E2->3 E3->4 E4->5 E5->6 V4 V5 V1 V2 V0 V6 E4->5 E5->1 E1->2 E0->6 V0 V3 V2 V3 V4 V5 V6 E0->3 E3->2 E2->3 E3->4 E4->5 E5->6 Massively Parallel Search

16. 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”

17. DNA Polymerase

18. POLYMERASE CHAIN REACTION

19. V0 V1 V2 V3 V4 V5 V6 E0->1 E1->2 E2->3 E3->4 E4->5 E5->6 V4 V5 V1 V2 V0 V6 E4->5 E5->1 E1->2 E0->6 V0 V3 V2 V3 V4 V5 V6 E0->3 E3->2 E2->3 E3->4 E4->5 E5->6 Start = V0, Stop = V6

20. 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”

21. GEL ELECTROPHORESIS - SIZE SORTING Electrode Samples Slower Gel Buffer Electrode Faster

22. V0 V1 V2 V3 V4 V5 V6 E0->1 E1->2 E2->3 E3->4 E4->5 E5->6 V0 V6 E0->6 V0 V3 V2 V3 V4 V5 V6 E0->3 E3->2 E2->3 E3->4 E4->5 E5->6 Right Length

23. 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”

24. CACCATGTGAC CACCATGTGAC PMP CACCATGTGAC N B PMP S ANTIBODY AFFINITY Add oligo with Biotin label + B GTGGTACACTG Anneal Heat and cool Add Paramagnetic-Streptavidin Particles + B GTGGTACACTG Bind Isolate with Magnet GTGGTACACTG

25. V0 V1 V2 V3 V4 V5 V6 E0->1 E1->2 E2->3 E3->4 E4->5 E5->6 V0 V3 V2 V3 V4 V5 V6 E0->3 E3->2 E2->3 E3->4 E4->5 E5->6 Every Vertex

26. 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”

27. V0 V1 V2 V3 V4 V5 V6 E0->1 E1->2 E2->3 E3->4 E4->5 E5->6 Hamiltonian Path

28. Mismatches

29. 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

30. 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?

31. 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

32. 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

35. Experimental Results

36. Experimental Results

37. Latest Results

38. DNA Memories

39. Overview Sequences Comple- mentary to Input DNAs New Unknown Input DNAs Labeled Tag Sequence Complements Input DNAs (Unknown Seq.) Tag1 Random Probe Learning Recall Output Memory DNA Strands (With the 3’ end Comple- mentary to the Input DNAs) Separates Memory DNA Strands that Match or Partially Match the New Inputs from Those That Don’t Match

40. 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

42. Base-by-Base Amplification Input DNA Tag Probe Extension

43. Sampling Input DNA Tag Probe Extension

44. Energy Energy Input Sequence Input Sequence Energy Surface Manipulation through Learning Before Learning After Learning

45. 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)

46. 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

49. 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