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*Supported by AFOSR and Air Force Research Lab, Rome NY

SynDCode: A Tool for Biomolecular Nanotechnology and Engineering. Anthony J. Macula, Morgan Bishop, Thomas Renz. Undergraduate Students: Jackie Dresch, Niels Hanson. *Supported by AFOSR and Air Force Research Lab, Rome NY. Outline. DNA Hybridization/Cross Hybridization DNA Codes

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*Supported by AFOSR and Air Force Research Lab, Rome NY

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  1. SynDCode: A Tool for Biomolecular Nanotechnology and Engineering Anthony J. Macula, Morgan Bishop, Thomas Renz Undergraduate Students: Jackie Dresch, Niels Hanson *Supported by AFOSR and Air Force Research Lab, Rome NY

  2. Outline • DNA Hybridization/Cross Hybridization • DNA Codes • Nearest Neighbor Thermodynamics • complete computations • bounds • Overview of Applications and Purposes • DNA Bitstring Library • Biomolecular Computing • Specific Design Techniques and Tools • SynDCode • Comparison to Other Tools • SLSDesinger

  3. This research addresses the development of a engineering tool that generates blueprints for synthetic DNA for biomolecular nanotechnology,computing and medical applications. In this research, we developed methods and tools for of generating of large collections of single stranded DNA sequences called a DNA code.

  4. DNA Hybridization • DNA strands are modeled by directed 3’--> 5’ sequences of letters from the alphabet {A, C, G, T} • (A, T) and (C, G) are complementarypairs. • Two oppositely directed DNA sequences are capable of coalescing into a duplex. • Because an A (C) in one strand can (usually) only bind to a T (G) in the oppositely directed strand, the greatest energy of duplex formation is obtained when the two sequences are reverse-complements (complements)

  5. A DNA Code Coding Strands for Ligation Probing Complement Strands for Reading TACGCGACTTTC GAAAGTCGCGTA ATCAAACGATGC GCATCGTTTGAT TGTGTGCTCGTC GACGAGCACACA ATTTTTGCGTTA, TAACGCAAAAAT CACTAAATACAA TTGTATTTAGTG GAAAAAGAAGAA, TTCTTCTTTTTC 5’ 3’ 5’ 3’ Watson Crick (WC) Duplexes 5’TACGCGACTTTC3’ ATCAAACGATGC Must Have 5’GAAAGTCGCGTA3’ GCATCGTTTGAT TACGCGACTTTC Cross Hybridized (CH) Duplexes ATTTTTGCGTTA Must Avoid GCATCGTTTGAT GAAAAAGAAGAA

  6. x=5’ggCaCaTcatAct3’ 5’ggCaCaTcatAct3’ 5’ AggTTaaCcatct3’ y=5’agatgGttAAccT3’ 5’ggCaCaTcatAct3’ 3’ TccAAttGgtaga5’ 5’agatgGttAAccT3’ =y

  7. Watson-Crick Nearest Neighbor Computation 1.44 2.24 WC Duplex 5’g g c a c a3’ 3’c c g t g t 5’ 5’g g c a c a3’ 5’g g c a c a3’ NNFE=8.42 5’g g c a c a3’ 5’g g c a c a3’ 1.84 1.45 1.45

  8. Cross Hybridized Nearest Neighbor Upper Bound Computation 1.45 1.28 5’ggCaCaTcatAct3’ 3’ TccAAttGgtaga5’ 5’g gC aCaTcatAct3’ 3’ Tc cA AttGgtaga5’ 5’g gC aC a T c a t A ct3’ 5’ A g g T T a a C c a t ct3’ .27 1.84 0.88 NNFE~<5.45 5’ggCaCaTcatAct3’ 5’ AggTTaaCcatct3’ NNFE~<5.72

  9. Intermolecular Interactions Duplexes loop symmetric loop asymmetric 2.90 (5.3) 2.20 (5.3)

  10. Intramolecular Interactions CAAGACTTTTTGGTAGTAAA ***TTTCCC*********GGAA***GGGAAA***********TTCC***

  11. NNFE~<5.66 NNFE~<5.66+ .59 + .32=6.57

  12. correlation=.737 Our FE bound Precise FE Length 16 435 random

  13. DNA codes serve as universal components for biomolecular computing. DNA codes are closed under reverse-complementation. The strands in a DNA code have such binding specificity that a code strand will only hybridize with its reverse-complement and will not cross hybridize with any other code strand in the DNA code Such collections of strands are crucial to the success biomolecular computing and biomolecular nanotechnology. Basic idea is to have correct, parallel and autonomous addressing

  14. Characterization of synthetic DNA bar codes in Saccharomyces cervisiae gene-deletion strains” (Eason et al., PNAS). DNA codes for self-assembly of any components that can be attached to DNA. Their size presents the potential for increased complexity and location control in nanostructures produced by assembly that is driven by DNA duplex formation. Fundamentalphysical limits and increasing costs of fabrication facilities will force alternatives to conventional microelectronics manufacturing to be developed. In self-assembly, weak, local interactions among molecular components spontaneously organize those components into aggregates with properties that range from simple to complex DNA memory:The capacity and storage density of such memories is potentially very large. Information could be mined through massively parallel template-matching reactions. In addition, information could be processed based upon context, and information matched associatively based upon content.

  15. DNA Computing Potential • Advantages of DNA Computing • Massive parallelism of DNA strands • High density of information storage • Ease of constructing many copies of huge data • New data structures (very long words, non volatile) • New operations (cut, paste, adjoin, insert, delete, multiply…) • New algorithms and computability • Reconfigurable hardware and hybrid computers: DNA, cell, optical, electronic • “DNA Computer” Performance Evaluation • Information density: 1015 CDs per cm3 • Massively parallel information processing: • 106 ops/sec for PCs 1012 ops/sec for supercomputers 1020 ops/sec possible for DNA DNA computers would be > 1,000,000 times faster than any computer today. • Energy efficiency: 2 * 1019 operations/joule for DNA 109 operations/joule for silicon-based computers

  16. DNA Code and DNA Bitstring Library A A A A A A A A C C=T1 G G T T T T T T T T =BEAD PROBE (T1) T T T C C A A A A A =F1 T T T T T G G A A A = BEAD PROBE (F1) T T T C T T A A C C=T2 G G T T A A G A A A= BEAD PROBE (T2) A C T A A C A A A A=F2 T T T T G T T A G T= BEAD PROBE (F2) C A T A A A A C A C=T3 G T G T T T T A T G= BEAD PROBE (T3) A T C T T T T C A A=F3 T T G A A A A G A T= BEAD PROBE (F3) C A A T C C A T T A=T4 T A A T G G A T T G= BEAD PROBE (T4) C C T T C T A A A T=F4 A T T T A G A A G G= BEAD PROBE (F4) A C T C C T A A T A=T5 T A T T A G G A G T= BEAD PROBE (T5) T C T C T C T A C T=F5 A G T A G A G A G A= BEAD PROBE (F5) 1. A A A A A A A A C C -T T T C T T A A C C-C A T A A A A C A C-T4-T5 2. A A A A A A A A C C -T T T C T T A A C C-C A T A A A A C A C-T4-F5 3. A A A A A A A A C C -T T T C T T A A C C-C A T A A A A C A C-F4-T5 4. A A A A A A A A C C -T T T C T T A A C C-C A T A A A A C A C-F4-F5 5. A A A A A A A A C C ­-T T T C T T A A C C -A T C T T T T C A A-T4-T5 6. A A A A A A A A C C ­-T T T C T T A A C C -A T C T T T T C A A-T4-F5 7. A A A A A A A A C C -T T T C T T A A C C -A T C T T T T C A A-F4-T5 8. A A A A A A A A C C -T T T C T T A A C C -A T C T T T T C A A-F4-F5 9. A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-T4-T5 10. A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-T4-F5 11. A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-F4-T5 12. A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-F4-F5 13. A A A A A A A A C C-A C T A A C A A A A-A T C T T T T C A A-T4-T5 14. A A A A A A A A C C-A C T A A C A A A A-A T C T T T T C A A-T4-F5 15. A A A A A A A A C C-A C T A A C A A A A-A T C T T T T C A A-F4-T5 16. A A A A A A A A C C-A C T A A C A A A A-A T C T T T T C A A-F4-F5 17. T T T C C A A A A A -T T T C T T A A C C-C A T A A A A C A C-T4-T5 18. T T T C C A A A A A -T T T C T T A A C C-C A T A A A A C A C-T4-F5 19. T T T C C A A A A A -T T T C T T A A C C-C A T A A A A C A C-F4-T5 20. T T T C C A A A A A -T T T C T T A A C C-C A T A A A A C A C-F4-F5 21. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-T4-T5 22. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-T4-F5 23. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-F4-T5 24. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-F4-F5 25. T T T C C A A A A A -A C T A A C A A A A-C A T A A A A C A C-T4-T5 26. T T T C C A A A A A -A C T A A C A A A A-C A T A A A A C A C-T4-F5 27. T T T C C A A A A A -A C T A A C A A A A-C A T A A A A C A C-F4-T5 28. T T T C C A A A A A -A C T A A C A A A A-C A T A A A A C A C-F4-F5 29. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-T4-T5 30. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-T4-F5 31. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-F4-T5 32. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-F4-F5 DNA LIBRARY= DNA BITSTRINGS DNA CODE

  17. DNA Computing Strand Engineering No codeword-codewode CH (cc-CH) No codeword-probe CH (cp-CH) No probe-probe CH (pp-CH) A A A A A A A A C C=T1 G G T T T T T T T T =BEAD PROBE (T1) T T T C C A A A A A =F1 T T T T T G G A A A = BEAD PROBE (F1) T T T C T T A A C C=T2 G G T T A A G A A A= BEAD PROBE (T2) A C T A A C A A A A=F2 T T T T G T T A G T= BEAD PROBE (F2) C A T A A A A C A C=T3 G T G T T T T A T G= BEAD PROBE (T3) A T C T T T T C A A=F3 T T G A A A A G A T= BEAD PROBE (F3) C A A T C C A T T A=T4 T A A T G G A T T G= BEAD PROBE (T4) C C T T C T A A A T=F4 A T T T A G A A G G= BEAD PROBE (F4) A C T C C T A A T A=T5 T A T T A G G A G T= BEAD PROBE (T5) T C T C T C T A C T=F1 A G T A G A G A G A= BEAD PROBE (F5) Only Allowed Hybridizations T T T T T T G G T T G G=Probe(T1) G G T G G T T T T T T T=Probe(F1) T G G A A G G A A A A A=Probe(T2) G G T T T G A G G T A A =Probe(F2) G G A G T T G T G A A A=Probe(T3) C C A A C C A A A A A A = T1 A A A A A A A C C A C C=F1 T T T T T C C T T C C A =T2 T T A C C T C A A A C C =F2 T T T C A C A A C T C C=T3 No cp-CH T T G T G G A T T G A A=Probe(F3) T T G A G A G A G T G A=Probe(T4) A G A G G A G A A A G A=Probe(F4) G A T G G T G A G A T G=Probe(T5) G T G T G T A G T G T T=Probe(F5) T T C A A T C C A C A A =F3 T C A C T C T C T C A A =T4 T C T T T C T C C T C T=F4 C A T C T C A C C A T C =T5 A A C A C T A C A C A C =F5 No cc-CH No pp-CH

  18. DNA Computing Strand Engineering No codeword cp-CH T T C A A T C C A C A A =F3 T T G T G G A T T G A A=Probe(F3) T C A C T C T C T C A A =T4 T T G A G A G A G T G A=Probe(T4) T C T T T C T C C T C T=F4 A G A G G A G A A A G A=Probe(F4) C A T C T C A C C A T C =T5 G A T G G T G A G A T G=Probe(T5) A A C A C T A C A C A C =F5 G T G T G T A G T G T T=Probe(F5) C C A A C C A A A A A A = T1 T T T T T T G G T T G G=Probe(T1) A A A A A A A C C A C C=F1 G G T G G T T T T T T T=Probe(F1) T T T T T C C T T C C A =T2 T G G A A G G A A A A A=Probe(T2) T T A C C T C A A A C C =F2 G G T T T G A G G T A A =Probe(F2) T T T C A C A A C T C C=T3 G G A G T T G T G A A A=Probe(T3) PROBE(F2) G G T T T G A G G T A A C A A C C A A A A A A- T T A C C T C A A A C C- T T C A A T C C A C A A- T C A C T C T C T C A A - C A T C T C A C C A T C Yes WC bonding Yes, bitstring is F2 Good read T1-F2-F3-T4-T5 1 0 0 1 1 PROBE(T2) G G A G T T G T G A A C A A C C A A A A A A- T T A C C T C A A A C C- T T C A A T C C A C A A- T C A C T C T C T C A A - C A T C T C A C C A T C Darn! CH bonding No, bitstring is not T2 Bad read T1-F2-F3-T4-T5

  19. DNA Computing Strand Engineering No codeword pp-CH, cc-CH PROBE(F2) pp-CH interferes with reading G G T T T G A G G T A A T T G A G A G A GT G PROBE(T4) PROBE(F2) G G T T T G A G G T A A bonding site competition T T G A G A G A GT G C A A C C A A A A A A- T T A C C T C A A A C C- T T C A A T C C A C A A- T C A C T C T C T C A A - C A T C T C A C C A T C cc-CH interferes with separation and leads to unwanted library strand interaction T1-F2-F3-T4-T5 F1-F2-T3-T4-f5 C A A C C A A A A A A- T T A C C T C A A A C C- T T C A A T C C A C A A- T C A C T C T C T C A A - C A T C T C A C C A T C T T T C C A A A A-AT T A C C T C A A A C C- T T T C A C A A C T C C-T C A C T C T C T C A A - A A C A C T A C A C A C

  20. DNA Computing Strand Engineering No junction CH A A A A A A -T T T T T C=T1T2 A C C A C C-T T T T T C= F1T2 A A A A A A-T T A C C T =T1F2 A C C A C C -T T A C C T=F1F2 C T T C C A- T T T C A C=T2T3 C A A A C C -T T T C A C = F2T3 C T T C C A-T T C A A T =T2F3 C A A A C C- T T C A A T,=F2F3 A A C T C C- T C A C T C=T3T4 C C A C A A-T C A C T C =F3T4 A A C T C C-T C T T T C =T3F4 C C A C A A -T C T T T C=F3F4 T C T C A A- C A T C T C=T4T5 T C C T C T-C A T C T C =F4T5 T C T C A A-A A C A C T =T4F5 T C C T C T -A A C A C T=F4F5 T T T T T T G G T T G G=Probe(T1) G G T G G T T T T T T T=Probe(F1) T G G A A G G A A A A A=Probe(T2) G G T T T G A G G T A A =Probe(F2) G G A G T T G T G A A A=Probe(T3) C C A A C C A A A A A A = T1 A A A A A A A C C A C C=F1 T T T T T C C T T C C A =T2 T T A C C T C A A A C C =F2 T T T C A C A A C T C C=T3 No CH T T G T G G A T T G A A=Probe(F3) T T G A G A G A G T G A=Probe(T4) A G A G G A G A A A G A=Probe(F4) G A T G G T G A G A T G=Probe(T5) G T G T G T A G T G T T=Probe(F5) T T C A A T C C A C A A =F3 T C A C T C T C T C A A =T4 T C T T T C T C C T C T=F4 C A T C T C A C C A T C =T5 A A C A C T A C A C A C =F5 probes coding library intra-strand junctions from coding strands PROBE(T2) G G A G T T G T G A A C A A C C A (A A A A A- T T A C C T)( C A A A C C- T T C A A T)( C C A C A A- T C A C T C)(T C T C A A - C A T C T C) A C C A T C T1-(T1F2)(F2F3)(F3T4)(T4T5)T5 T1-F2-F3-T4-T5 Darn! Junction CH bonding No, bitstring is not T2 Bad read

  21. DNA Computing Tools: SynDCode

  22. Verified and Extended codewords • Both the original and “improved” codewords examined by Feldkamp et al. were then run through SynDCode and our uniqueness parameters were obtained. • Then we extended these codes, using SynDCode’s “Extend” feature.

  23. Verified and Extended codewords Make Extend [T,G,A,G,G,C,C,G,A,A,T,A,T,G,G,G,A,T,T,G], [T,G,A,T,G,C,T,T,T,C,A,G,G,G,G,G,T,A,G,T], [A,C,T,A,C,C,C,C,C,T,G,A,A,A,G,C,A,T,C,A], [C,C,A,C,A,C,A,G,A,A,G,T,G,G,C,G,T,T,T,A], [T,A,A,A,C,G,C,C,A,C,T,T,C,T,G,T,G,T,G,G], [T,G,A,G,T,T,C,C,A,G,A,G,G,G,C,A,A,A,A,A], [T,T,T,T,T,G,C,C,C,T,C,T,G,G,A,A,C,T,C,A], [G,G,T,T,A,A,C,T,C,C,T,G,G,T,C,A,G,G,G,A], [T,C,C,C,T,G,A,C,C,A,G,G,A,G,T,T,A,A,C,C], [G,G,G,C,T,C,T,G,G,A,T,T,T,A,A,G,G,T,C,C], [G,G,A,C,C,T,T,A,A,A,T,C,C,A,G,A,G,C,C,C], [G,G,T,T,T,G,G,A,G,A,T,T,T,G,C,C,T,G,C,T], [A,G,C,A,G,G,C,A,A,A,T,C,T,C,C,A,A,A,C,C], [T,T,T,C,C,C,G,C,A,T,A,C,A,T,T,C,C,A,G,G], [C,C,T,G,G,A,A,T,G,T,A,T,G,C,G,G,G,A,A,A], [T,C,T,A,A,T,T,C,C,C,C,G,C,C,A,A,G,A,C,T], [A,G,T,C,T,T,G,G,C,G,G,G,G,A,A,T,T,A,G,A], [T,G,T,G,G,T,G,T,T,T,A,G,T,G,G,A,A,C,C,C], [G,G,G,T,T,C,C,A,C,T,A,A,A,C,A,C,C,A,C,A], [A,A,G,G,G,G,C,T,T,A,C,G,T,T,C,A,G,A,A,G], [C,T,T,C,T,G,A,A,C,G,T,A,A,G,C,C,C,C,T,T], [G,C,C,T,A,T,T,T,T,T,C,G,T,C,G,G,A,T,C,G], [C,G,A,T,C,C,G,A,C,G,A,A,A,A,A,T,A,G,G,C], [A,A,A,A,C,A,C,A,C,G,T,T,C,G,A,C,C,A,A,A], [T,T,T,G,G,T,C,G,A,A,C,G,T,G,T,G,T,T,T,T], [A,A,A,G,T,G,C,T,A,C,C,A,A,G,T,A,G,G,C,C], [G,G,C,C,T,A,C,T,T,G,G,T,A,G,C,A,C,T,T,T], [G,G,A,G,A,G,T,C,C,A,G,C,T,T,C,A,G,T,T,C], [G,A,A,C,T,G,A,A,G,C,T,G,G,A,C,T,C,T,C,C], [C,C,C,A,A,C,G,A,G,A,T,T,G,A,C,A,G,A,G,G], [C,C,T,C,T,G,T,C,A,A,T,C,T,C,G,T,T,G,G,G], [C,C,A,A,A,T,A,G,C,A,A,G,G,A,C,C,G,A,C,T], [A,G,T,C,G,G,T,C,C,T,T,G,C,T,A,T,T,T,G,G], [C,T,G,G,G,A,A,G,G,A,A,A,A,T,C,G,C,C,T,A], [T,A,G,G,C,G,A,T,T,T,T,C,C,T,T,C,C,C,A,G], [C,A,A,C,T,C,G,G,A,C,A,G,G,T,C,T,T,C,A,T], [A,T,G,A,A,G,A,C,C,T,G,T,C,C,G,A,G,T,T,G], [T,T,G,G,A,A,A,C,T,G,A,T,C,C,A,C,C,G,A,C], [G,T,C,G,G,T,G,G,A,T,C,A,G,T,T,T,C,C,A,A], [C,C,C,T,G,T,T,G,T,T,G,A,T,T,C,C,C,T,C,C], [G,G,A,G,G,G,A,A,T,C,A,A,C,A,A,C,A,G,G,G], [C,T,T,C,C,T,T,T,A,A,G,G,C,T,T,G,C,A,C,C], [G,G,T,G,C,A,A,G,C,C,T,T,A,A,A,G,G,A,A,G], C,A,C,C,C,A,C,A,T,G,A,T,C,C,G,T,A,T,C,G], [G,T,G,C,A,T,G,G,T,T,G,C,A,T,A,A,C,T,C,G], [C,G,A,G,T,T,A,T,G,C,A,A,C,C,A,T,G,C,A,C], [G,G,A,C,A,G,A,C,G,G,T,T,T,T,T,A,C,G,A,G], [C,T,C,G,T,A,A,A,A,A,C,C,G,T,C,T,G,T,C,C], [A,T,C,G,T,C,A,G,G,G,C,T,C,T,A,C,C,C,T,A], [T,A,G,G,G,T,A,G,A,G,C,C,C,T,G,A,C,G,A,T], [C,A,G,T,A,G,A,G,T,T,G,A,G,T,G,T,G,C,C,A], [T,G,G,C,A,C,A,C,T,C,A,A,C,T,C,T,A,C,T,G], [G,G,A,C,C,C,A,G,T,G,C,A,G,T,C,T,G,A,T,A], [T,A,T,C,A,G,A,C,T,G,C,A,C,T,G,G,G,T,C,C], [T,T,A,C,C,A,A,T,T,C,T,G,C,C,A,G,C,A,G,G], [C,C,T,G,C,T,G,G,C,A,G,A,A,T,T,G,G,T,A,A], [T,G,A,C,C,C,C,T,C,G,T,T,C,T,C,C,T,T,A,A], [T,T,A,A,G,G,A,G,A,A,C,G,A,G,G,G,G,T,C,A], [T,G,T,T,A,C,A,G,G,C,C,A,C,C,A,G,A,A,T,C], [G,A,T,T,C,T,G,G,T,G,G,C,C,T,G,T,A,A,C,A], [C,T,T,T,C,G,G,T,T,C,G,C,A,G,T,C,T,A,A,C], [G,T,T,A,G,A,C,T,G,C,G,A,A,C,C,G,A,A,A,G], [A,A,A,A,T,C,G,A,A,A,A,C,G,A,G,A,C,C,C,G], [C,G,G,G,T,C,T,C,G,T,T,T,T,C,G,A,T,T,T,T], [G,C,G,A,A,A,G,G,A,A,T,T,C,G,A,T,G,C,A,T], [A,T,G,C,A,T,C,G,A,A,T,T,C,C,T,T,T,C,G,C], [G,A,A,G,T,A,T,A,T,C,C,C,G,C,T,C,T,G,C,G], [C,G,C,A,G,A,G,C,G,G,G,A,T,A,T,A,C,T,T,C], [G,G,A,A,G,A,A,G,A,G,T,A,C,A,A,C,C,C,C,C], [G,G,G,G,G,T,T,G,T,A,C,T,C,T,T,C,T,T,C,C], [A,A,A,A,A,T,G,G,G,G,T,G,C,A,A,A,G,C,A,C], [G,T,G,C,T,T,T,G,C,A,C,C,C,C,A,T,T,T,T,T], [G,A,A,A,A,G,C,T,A,G,C,G,A,G,C,A,T,G,G,A], [T,C,C,A,T,G,C,T,C,G,C,T,A,G,C,T,T,T,T,C], [T,T,C,C,G,A,G,T,A,G,T,A,G,G,G,A,A,G,G,G], [C,C,C,T,T,C,C,C,T,A,C,T,A,C,T,C,G,G,A,A], [C,T,G,A,C,A,C,G,A,C,T,C,C,A,A,T,G,G,A,A], [T,T,C,C,A,T,T,G,G,A,G,T,C,G,T,G,T,C,A,G], [C,C,C,T,T,A,C,G,C,C,T,G,T,T,C,C,T,A,T,T], [A,A,T,A,G,G,A,A,C,A,G,G,C,G,T,A,A,G,G,G], [G,C,C,T,C,G,T,T,T,C,A,C,A,A,C,A,G,A,A,A], [T,T,T,C,T,G,T,T,G,T,G,A,A,A,C,G,A,G,G,C], [A,T,T,G,G,C,C,G,C,A,A,G,A,G,T,A,G,A,T,C], [G,A,T,C,T,A,C,T,C,T,T,G,C,G,G,C,C,A,A,T], [C,G,C,T,G,A,T,C,T,C,C,C,A,T,C,A,C,A,A,G], [C,T,T,G,T,G,A,T,G,G,G,A,G,A,T,C,A,G,C,G], [T,T,C,A,A,G,C,T,C,G,T,G,C,C,A,T,A,A,A,C], [G,T,T,T,A,T,G,G,C,A,C,G,A,G,C,T,T,G,A,A], [A,A,T,A,A,C,C,G,G,A,G,C,T,A,G,A,A,C,G,C], [G,C,G,T,T,C,T,A,G,C,T,C,C,G,G,T,T,A,T,T], [C,A,A,C,G,T,T,A,A,C,A,T,C,A,C,A,C,G,C,T], [A,G,C,G,T,G,T,G,A,T,G,T,T,A,A,C,G,T,T,G], [T,G,C,A,C,T,G,A,A,A,A,A,G,A,G,C,C,T,G,T], [A,C,A,G,G,C,T,C,T,T,T,T,T,C,A,G,T,G,C,A], [T,C,A,G,T,T,T,G,T,A,A,G,C,G,C,G,T,T,C,T], [A,G,A,A,C,G,C,G,C,T,T,A,C,A,A,A,C,T,G,A], [C,C,A,A,G,C,A,A,T,G,T,T,C,A,C,A,G,T,C,C], [G,G,A,C,T,G,T,G,A,A,C,A,T,T,G,C,T,T,G,G], [A,T,T,A,C,G,C,T,T,C,G,G,T,T,T,G,A,G,C,T], [A,G,C,T,C,A,A,A,C,C,G,A,A,G,C,G,T,A,A,T], [C,G,T,A,C,A,T,G,G,G,T,C,G,G,A,A,C,A,A,T], [A,T,T,G,T,T,C,C,G,A,C,C,C,A,T,G,T,A,C,G], [C,T,A,C,C,A,C,T,G,G,G,C,T,T,G,A,G,T,T,G], [C,A,A,C,T,C,A,A,G,C,C,C,A,G,T,G,G,T,A,G], [T,C,C,G,A,G,A,C,A,C,A,A,C,C,T,T,C,A,A,A], [T,T,T,G,A,A,G,G,T,T,G,T,G,T,C,T,C,G,G,A], [C,G,A,T,A,C,G,G,A,T,C,A,T,G,T,G,G,G,T,G], [G,G,G,G,G,G,G,G,G,G,A,A,A,A,A,A,A,A,A,A], [T,T,T,T,T,T,T,T,T,T,C,C,C,C,C,C,C,C,C,C], [G,G,G,C,C,A,A,A,A,G,G,G,G,T,T,T,T,T,T,T], [A,A,A,A,A,A,A,C,C,C,C,T,T,T,T,G,G,C,C,C], [C,C,C,T,T,C,T,T,T,T,T,T,T,G,G,G,G,G,G,G], [C,C,C,C,C,C,C,A,A,A,A,A,A,A,G,A,A,G,G,G], [G,G,T,T,T,T,G,G,C,T,T,T,T,T,A,C,C,G,G,G], [C,C,C,G,G,T,A,A,A,A,A,G,C,C,A,A,A,A,C,C], [G,G,G,C,C,C,C,C,C,T,T,T,A,T,T,A,A,A,C,C], [G,G,T,T,T,A,A,T,A,A,A,G,G,G,G,G,G,C,C,C], [T,G,C,G,G,A,A,A,G,G,G,T,T,T,G,A,A,A,A,G], [C,T,T,T,T,C,A,A,A,C,C,C,T,T,T,C,C,G,C,A], [T,T,T,G,G,G,G,A,A,A,T,C,C,C,G,G,A,A,G,T], [A,C,T,T,C,C,G,G,G,A,T,T,T,C,C,C,C,A,A,A], [A,A,A,A,T,T,G,G,G,G,G,A,G,G,G,T,T,G,T,T], [A,A,C,A,A,C,C,C,T,C,C,C,C,C,A,A,T,T,T,T], [T,T,T,C,C,C,C,G,G,G,T,T,T,G,G,G,T,T,A,T], [A,T,A,A,C,C,C,A,A,A,C,C,C,G,G,G,G,A,A,A], [C,C,G,G,C,G,G,C,T,T,T,A,A,C,A,A,A,T,T,T], [A,A,A,T,T,T,G,T,T,A,A,A,G,C,C,G,C,C,G,G], [G,G,G,G,A,G,G,A,G,A,A,G,G,C,A,A,T,T,T,T], [A,A,A,A,T,T,G,C,C,T,T,C,T,C,C,T,C,C,C,C], [C,G,C,A,T,T,T,A,A,C,C,G,C,C,C,T,A,A,A,A], [T,T,T,T,A,G,G,G,C,G,G,T,T,A,A,A,T,G,C,G], [A,A,A,C,A,A,A,C,A,A,A,G,G,G,C,C,A,A,G,C], [G,C,T,T,G,G,C,C,C,T,T,T,G,T,T,T,G,T,T,T], [C,C,C,A,G,G,G,A,A,C,C,T,G,A,A,C,T,T,T,T], [A,A,A,A,G,T,T,C,A,G,G,T,T,C,C,C,T,G,G,G], [C,G,G,A,G,G,A,A,A,C,C,T,T,T,A,G,G,A,C,C], [G,G,T,C,C,T,A,A,A,G,G,T,T,T,C,C,T,C,C,G], [G,C,C,C,A,T,T,C,C,A,A,A,A,T,C,T,T,G,C,T], [A,G,C,A,A,G,A,T,T,T,T,G,G,A,A,T,G,G,G,C], [T,T,A,T,T,T,T,C,G,A,G,G,C,A,A,G,G,C,C,T], [A,G,G,C,C,T,T,G,C,C,T,C,G,A,A,A,A,T,A,A], [C,A,C,C,G,T,T,G,G,A,G,G,T,A,A,A,A,G,G,T], [A,C,C,T,T,T,T,A,C,C,T,C,C,A,A,C,G,G,T,G], [A,A,G,G,T,G,G,G,C,G,A,A,A,A,A,C,C,A,T,T], [A,A,T,G,G,T,T,T,T,T,C,G,C,C,C,A,C,C,T,T], [A,A,T,T,A,G,T,T,G,G,G,T,A,C,C,A,C,C,C,G], [C,G,G,G,T,G,G,T,A,C,C,C,A,A,C,T,A,A,T,T], [T,T,C,A,A,A,A,C,G,T,G,G,G,A,T,G,G,C,T,T], [A,A,G,C,C,A,T,C,C,C,A,C,G,T,T,T,T,G,A,A], [C,G,G,G,G,T,A,A,T,G,A,T,T,T,C,T,G,G,G,G], [C,C,C,C,A,G,A,A,A,T,C,A,T,T,A,C,C,C,C,G], [T,G,A,C,C,G,T,T,T,T,T,T,G,A,C,T,T,G,C,C], [G,G,C,A,A,G,T,C,A,A,A,A,A,A,C,G,G,T,C,A], [A,A,C,C,C,G,G,T,T,T,C,A,A,T,A,G,T,C,G,G], [C,C,G,A,C,T,A,T,T,G,A,A,A,C,C,G,G,G,T,T], [T,T,C,G,C,T,A,A,A,A,G,G,A,A,C,A,A,C,G,G], [C,C,G,T,T,G,T,T,C,C,T,T,T,T,A,G,C,G,A,A], [C,A,A,T,C,C,C,A,T,A,T,T,C,G,G,C,C,T,C,A], [A,A,A,G,C,C,G,T,C,G,T,T,T,A,A,G,G,A,C,C], [G,G,T,C,C,T,T,A,A,A,C,G,A,C,G,G,C,T,T,T], [A,C,C,A,T,T,T,T,G,G,A,G,G,T,G,G,A,A,C,G], [C,G,T,T,C,C,A,C,C,T,C,C,A,A,A,A,T,G,G,T], [T,A,T,A,T,C,G,T,A,G,A,G,C,C,A,C,A,C,G,C], [G,C,G,T,G,T,G,G,C,T,C,T,A,C,G,A,T,A,T,A], [T,C,C,G,C,G,T,A,C,T,G,A,T,A,A,T,C,C,T,C], [G,A,G,G,A,T,T,A,T,C,A,G,T,A,C,G,C,G,G,A], [A,T,A,T,G,C,T,T,A,G,G,C,A,C,G,G,T,T,G,G], [C,C,A,A,C,C,G,T,G,C,C,T,A,A,G,C,A,T,A,T], [T,C,T,C,G,T,G,A,A,T,T,G,G,T,C,T,G,G,A,C], [G,T,C,C,A,G,A,C,C,A,A,T,T,C,A,C,G,A,G,A], [T,T,A,C,T,C,A,T,C,T,C,T,G,T,G,A,C,G,C,C], [G,G,C,G,T,C,A,C,A,G,A,G,A,T,G,A,G,T,A,A], [C,C,C,C,C,C,C,C,C,C,A,A,A,A,A,A,A,A,A,A], [T,T,T,T,T,T,T,T,T,T,G,G,G,G,G,G,G,G,G,G], [C,C,C,G,G,G,G,G,G,G,A,A,A,T,T,T,T,T,T,T], [A,A,A,A,A,A,A,T,T,T,C,C,C,C,C,C,C,G,G,G], [C,C,C,C,C,T,T,T,G,G,T,T,C,C,C,T,T,T,T,T], [A,A,A,A,A,G,G,G,A,A,C,C,A,A,A,G,G,G,G,G], [T,T,T,T,T,T,A,A,A,C,C,G,C,C,C,A,C,C,C,T], [A,G,G,G,T,G,G,G,C,G,G,T,T,T,A,A,A,A,A,A], [T,T,T,T,A,G,G,A,T,T,T,T,C,G,G,C,C,C,C,C], [G,G,G,G,G,C,C,G,A,A,A,A,T,C,C,T,A,A,A,A], [A,A,G,G,T,T,G,G,G,G,T,T,T,T,C,C,C,A,T,G], [C,A,T,G,G,G,A,A,A,A,C,C,C,C,A,A,C,C,T,T], [A,A,G,A,A,A,A,T,G,G,G,G,G,G,C,A,A,A,C,A], [T,G,T,T,T,G,C,C,C,C,C,C,A,T,T,T,T,C,T,T], [A,G,C,C,C,C,A,A,A,C,T,T,T,T,A,A,C,G,G,G], [C,C,C,G,T,T,A,A,A,A,G,T,T,T,G,G,G,G,C,T], [C,T,T,G,A,A,A,C,C,C,T,C,C,A,G,G,G,G,A,A], [T,T,C,C,C,C,T,G,G,A,G,G,G,T,T,T,C,A,A,G], [A,A,A,A,C,C,C,G,G,C,T,C,T,C,G,A,A,A,A,A], [T,T,T,T,T,C,G,A,G,A,G,C,C,G,G,G,T,T,T,T], [G,G,G,C,T,T,T,T,T,T,C,T,C,C,T,T,C,C,C,C], [G,G,G,G,A,A,G,G,A,G,A,A,A,A,A,A,G,C,C,C], [A,A,A,A,G,G,C,C,A,C,C,G,T,T,T,C,T,T,T,G], [C,A,A,A,G,A,A,A,C,G,G,T,G,G,C,C,T,T,T,T], [A,C,G,A,A,A,G,T,G,T,T,T,T,G,G,T,C,C,C,C], [G,G,G,G,A,C,C,A,A,A,A,C,A,C,T,T,T,C,G,T], [C,C,C,A,A,T,T,C,C,C,A,A,A,G,G,T,C,C,A,A], [T,T,G,G,A,C,C,T,T,T,G,G,G,A,A,T,T,G,G,G], [A,A,G,T,C,T,C,T,C,C,C,C,A,A,C,A,T,C,C,C], [G,G,G,A,T,G,T,T,G,G,G,G,A,G,A,G,A,C,T,T], [C,C,T,T,G,G,C,A,A,C,T,T,A,A,C,C,C,G,T,A], [T,A,C,G,G,G,T,T,A,A,G,T,T,G,C,C,A,A,G,G], [C,T,T,T,T,G,T,T,G,A,G,C,A,A,A,G,G,G,C,C], [G,G,C,C,C,T,T,T,G,C,T,C,A,A,C,A,A,A,A,G], [A,A,T,T,G,A,A,A,T,T,G,T,C,G,G,C,G,G,T,T], [A,A,C,C,G,C,C,G,A,C,A,A,T,T,T,C,A,A,T,T], [A,A,A,C,A,A,A,A,A,C,A,A,C,A,G,G,C,C,C,C], [G,G,G,G,C,C,T,G,T,T,G,T,T,T,T,T,G,T,T,T], [A,T,C,A,C,A,A,T,C,C,C,C,C,C,T,G,T,G,T,T], [A,A,C,A,C,A,G,G,G,G,G,G,A,T,T,G,T,G,A,T], [T,T,A,T,G,G,T,A,A,A,T,C,C,G,C,T,G,G,G,C], [G,C,C,C,A,G,C,G,G,A,T,T,T,A,C,C,A,T,A,A], [C,A,A,T,T,T,T,C,C,T,C,C,A,G,C,T,T,C,G,G], [C,C,G,A,A,G,C,T,G,G,A,G,G,A,A,A,A,T,T,G], [T,C,A,A,T,G,G,T,G,C,C,C,G,G,A,A,T,A,A,A], [T,T,T,A,T,T,C,C,G,G,G,C,A,C,C,A,T,T,G,A], [A,A,A,A,G,T,A,A,G,C,G,G,A,A,A,C,T,G,C,G], [C,G,C,A,G,T,T,T,C,C,G,C,T,T,A,C,T,T,T,T], [G,T,G,G,G,G,A,G,G,T,A,A,T,G,C,A,A,T,G,T], [A,C,A,T,T,G,C,A,T,T,A,C,C,T,C,C,C,C,A,C], [C,T,T,T,C,G,A,A,G,A,T,G,G,C,G,A,T,C,C,A], [T,G,G,A,T,C,G,C,C,A,T,C,T,T,C,G,A,A,A,G], [A,C,C,G,T,G,A,T,G,A,A,G,G,G,T,G,A,A,T,T], [A,A,T,T,C,A,C,C,C,T,T,C,A,T,C,A,C,G,G,T], [C,A,G,G,A,A,G,T,G,A,A,G,G,C,T,A,G,T,C,C], [G,G,A,C,T,A,G,C,C,T,T,C,A,C,T,T,C,C,T,G], [T,C,C,C,T,C,C,G,G,C,T,C,A,G,T,A,T,T,T,C], [G,A,A,A,T,A,C,T,G,A,G,C,C,G,G,A,G,G,G,A], [T,T,G,C,T,G,C,C,C,T,A,A,A,G,A,A,C,A,C,T], [A,G,T,G,T,T,C,T,T,T,A,G,G,G,C,A,G,C,A,A], [C,T,C,C,T,T,C,T,G,G,G,G,A,C,C,T,C,T,A,A], [T,T,A,G,A,G,G,T,C,C,C,C,A,G,A,A,G,G,A,G], [C,C,C,G,C,A,T,A,T,A,G,C,A,A,G,A,A,A,C,C], [G,G,T,T,T,C,T,T,G,C,T,A,T,A,T,G,C,G,G,G], [A,A,C,C,G,A,T,T,T,A,G,G,C,C,T,T,C,C,T,C], [G,A,G,G,A,A,G,G,C,C,T,A,A,A,T,C,G,G,T,T], [G,A,G,A,C,C,T,C,T,T,T,T,G,C,C,C,G,A,T,C], [G,A,T,C,G,G,G,C,A,A,A,A,G,A,G,G,T,C,T,C], [A,T,T,C,A,T,C,G,G,G,G,C,T,T,T,A,T,G,G,C], [G,C,C,A,T,A,A,A,G,C,C,C,C,G,A,T,G,A,A,T], [C,A,A,C,T,G,G,G,T,T,C,T,G,G,C,T,C,A,T,T], [A,A,T,G,A,G,C,C,A,G,A,A,C,C,C,A,G,T,T,G], [T,T,T,G,G,C,C,G,C,T,T,G,T,T,A,A,G,A,T,C], [G,A,T,C,T,T,A,A,C,A,A,G,C,G,G,C,C,A,A,A], [G,G,G,T,T,C,A,A,A,C,T,T,G,G,T,G,G,T,T,G], [C,A,A,C,C,A,C,C,A,A,G,T,T,T,G,A,A,C,C,C], [G,C,T,G,A,C,G,A,T,A,A,A,G,G,A,T,C,C,G,G], [C,C,G,G,A,T,C,C,T,T,T,A,T,C,G,T,C,A,G,C], [G,C,C,A,G,G,T,T,C,T,A,A,A,A,T,T,C,G,C,G], [C,G,C,G,A,A,T,T,T,T,A,G,A,A,C,C,T,G,G,C], [A,C,C,T,T,C,T,C,A,C,T,G,A,C,G,T,C,G,A,T], [A,T,C,G,A,C,G,T,C,A,G,T,G,A,G,A,A,G,G,T], [G,A,A,A,A,A,A,C,G,C,A,C,G,A,C,C,T,A,G,T], [A,C,T,A,G,G,T,C,G,T,G,C,G,T,T,T,T,T,T,C], [A,C,T,A,A,T,G,A,G,G,G,G,C,T,C,C,G,T,A,G], [C,T,A,C,G,G,A,G,C,C,C,C,T,C,A,T,T,A,G,T], [T,C,G,A,C,T,C,G,A,A,C,G,T,C,T,T,T,G,T,T], [A,A,C,A,A,A,G,A,C,G,T,T,C,G,A,G,T,C,G,A], [C,C,T,G,C,A,C,C,C,C,T,T,G,T,C,A,A,A,T,A], [T,A,T,T,T,G,A,C,A,A,G,G,G,G,T,G,C,A,G,G], [C,C,A,C,C,G,G,G,G,A,A,T,A,G,T,A,A,C,A,G], [C,T,G,T,T,A,C,T,A,T,T,C,C,C,C,G,G,T,G,G], [T,G,A,A,A,G,G,A,G,G,A,C,G,T,G,G,T,T,A,C], [G,T,A,A,C,C,A,C,G,T,C,C,T,C,C,T,T,T,C,A], [A,A,T,A,A,T,G,C,C,C,C,A,T,A,G,T,G,G,C,C], [G,G,C,C,A,C,T,A,T,G,G,G,G,C,A,T,T,A,T,T], [C,C,C,C,C,A,C,G,A,A,G,A,T,T,G,T,T,A,G,T], [A,C,T,A,A,C,A,A,T,C,T,T,C,G,T,G,G,G,G,G], [C,C,C,A,A,G,A,A,A,G,A,A,T,G,C,C,C,T,C,A], [T,G,A,G,G,G,C,A,T,T,C,T,T,T,C,T,T,G,G,G], [A,T,T,G,G,T,C,G,T,C,A,A,A,A,A,C,C,G,A,G], [ G,A,T,C,T,A,A,C,G,G,A,T,C,G,T,T,C,C,C,G], [C,G,G,G,A,A,C,G,A,T,C,C,G,T,T,A,G,A,T,C], [G,A,A,C,G,T,A,T,A,A,C,C,C,T,G,C,G,A,C,A], [T,G,T,C,G,C,A,G,G,G,T,T,A,T,A,C,G,T,T,C], [C,G,G,T,T,C,G,G,A,T,T,T,G,T,T,G,C,T,T,A], [T,A,A,G,C,A,A,C,A,A,A,T,C,C,G,A,A,C,C,G], [A,A,C,C,C,A,C,T,T,G,G,A,G,A,T,C,T,T,G,C], [G,C,A,A,G,A,T,C,T,C,C,A,A,G,T,G,G,G,T,T], [A,G,T,C,C,C,C,T,T,A,C,T,A,A,G,C,C,A,G,C], [G,C,T,G,G,C,T,T,A,G,T,A,A,G,G,G,G,A,C,T], [T,C,G,A,A,A,C,A,C,C,C,A,T,C,T,A,C,A,G,C], [G,C,T,G,T,A,G,A,T,G,G,G,T,G,T,T,T,C,G,A], [T,C,T,C,A,A,A,A,C,C,A,G,G,G,T,A,G,C,T,G], [C,A,G,C,T,A,C,C,C,T,G,G,T,T,T,T,G,A,G,A], [T,G,C,A,C,T,A,G,G,A,C,A,T,C,G,C,A,C,T,A], [T,A,G,T,G,C,G,A,T,G,T,C,C,T,A,G,T,G,C,A], [A,G,T,T,G,G,T,A,C,A,C,C,A,T,A,G,A,G,C,G], [C,G,C,T,C,T,A,T,G,G,T,G,T,A,C,C,A,A,C,T], [A,G,T,T,G,A,G,T,C,A,G,A,T,T,C,G,C,C,T,C], [G,A,G,G,C,G,A,A,T,C,T,G,A,C,T,C,A,A,C,T], [T,A,T,A,T,G,G,T,G,G,T,G,A,G,G,C,G,A,G,A], [T,C,T,C,G,C,C,T,C,A,C,C,A,C,C,A,T,A,T,A], [T,C,A,G,T,G,C,G,A,G,G,A,T,G,G,A,T,T,T,T], [A,A,A,A,T,C,C,A,T,C,C,T,C,G,C,A,C,T,G,A], C,T,C,G,G,T,T,T,T,T,G,A,C,G,A,C,C,A,A,T], [C,T,A,C,G,C,C,T,G,G,A,A,A,A,A,C,G,A,A,A], [T,T,T,C,G,T,T,T,T,T,C,C,A,G,G,C,G,T,A,G], [G,A,A,G,C,A,A,T,G,T,T,T,C,G,C,C,C,A,A,G], [C,T,T,G,G,G,C,G,A,A,A,C,A,T,T,G,C,T,T,C], [A,G,A,A,C,T,T,C,T,G,C,T,G,T,G,T,C,A,G,G], [C,C,T,G,A,C,A,C,A,G,C,A,G,A,A,G,T,T,C,T], [C,C,A,T,A,C,G,G,A,A,C,A,C,T,G,G,G,A,A,G], [C,T,T,C,C,C,A,G,T,G,T,T,C,C,G,T,A,T,G,G],

  24. Verified and Extended codewords • In addition, the same “verify” feature of SynDCode was used to obtain our parameters for the yeast primer tags in “Characterization of synthetic DNA bar codes in Saccharomyces cervisiae gene-deletion strains” (Eason et al., PNAS). • PNAS used 5992 unique “uptags” • Using SynDCode, we were able to generate an equivalent code containing over 20,000 sequences • The tagging of each deletion strain allows identification of genes without prior knowledge of gene function • Parallel hybridization to a microarray was used to analyze assays • SynDCode parameters: • Free Energy Upper Bound • WC Upper Bound • WC Lower Bound • t-stems and thresholds

  25. Results In each instance, we could generate more codewords in less time than SlsDesigner

  26. SynDCode Conclusions SynDCode provides the means to create collections of synthetic DNA strands (i.e., a DNA code) with controlled properties such as resistance to crosshybridization. The user has the ability to either verify the properties of an existing DNA code, expand a given DNA code or create an entirely new DNA code. The models built into SynDCode allow for the specification of thermodynamic properties of the generated DNA code and for collections of concatenated combinations of strands taken from the generated code. All pairwise strand computations, including the computation of the bound on free energy of formation, ΔG(x:y), of the x:y duplex have complexity O(n²). This is significant, as other DNA code software tools use ΔG(x:y) approximation algorithms with complexity O(n³). These more computationally complex algorithms give more accurate pairwise ΔG(x:y) computations, but pairwise accuracy is not necessarily the most important consideration when the primary objective is maximizing the size of a code for global thresholds.

  27. A DNA Computing Paradigm The identification of maximal frequent sets in data fields are the computational bottleneck in association rule discovery. This is an important problem and the independent sets and maximal cliques problems fit this paradigm.

  28. Example: Independent Sets and Cliques 3 Edges in G are {1,2}, {2,3}, {3,4}, {4,5},{1,4},{2,5} Edges in G’ are {1,3}, {1,5}, {2,4}, {3,5}, 4 2 3 3 2 2 4 G = G’= 4 5 1 1 5 1 5 An independent set is a collection of vertices that contains no edge. A clique is a subgraph were every pair of vertices has an edge between them. For a graph G, its complement G’ is the set of edges not in G A maximal independent set in G is a maximal clique in G’, e.g., {1,3,5}. 3 1 5

  29. Example: Independent Sets and Cliques 3 Edges in G are {1,2}, {2,3}, {3,4}, {4,5},{1,4},{2,5} Edges in G’ are {1,3}, {1,5}, {2,4}, {3,5}, 4 2 3 3 2 2 4 G = G’= 4 5 1 1 5 1 5 An independent set is a collection of vertices that contains no edge. A clique is a subgraph were every pair of vertices has an edge between them. For a graph G, its complement G’ is the set of edges not in G A maximal independent set in G is a maximal clique in G’, e.g., {1,3,5}. 3 1 5

  30. DNA Computing for Independent Sets and Cliques 3 3 2 2 4 G = G’= 4 5 1 1 5

  31. 1. A A A A A A A A C C -T T T C T T A A C C-C A T A A A A C A C-T4-T5 2. A A A A A A A A C C -T T T C T T A A C C-C A T A A A A C A C-T4-F5 3. A A A A A A A A C C -T T T C T T A A C C-C A T A A A A C A C-F4-T5 4. A A A A A A A A C C -T T T C T T A A C C-C A T A A A A C A C-F4-F5 5. A A A A A A A A C C ­-T T T C T T A A C C -A T C T T T T C A A-T4-T5 6. A A A A A A A A C C ­-T T T C T T A A C C -A T C T T T T C A A-T4-F5 7. A A A A A A A A C C -T T T C T T A A C C -A T C T T T T C A A-F4-T5 8. A A A A A A A A C C -T T T C T T A A C C -A T C T T T T C A A-F4-F5 9. A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-T4-T5 10. A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-T4-F5 11. A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-F4-T5 12. A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-F4-F5 13. A A A A A A A A C C-A C T A A C A A A A-A T C T T T T C A A-T4-T5 14. A A A A A A A A C C-A C T A A C A A A A-A T C T T T T C A A-T4-F5 15. A A A A A A A A C C-A C T A A C A A A A-A T C T T T T C A A-F4-T5 16. A A A A A A A A C C-A C T A A C A A A A-A T C T T T T C A A-F4-F5 17. T T T C C A A A A A -T T T C T T A A C C-C A T A A A A C A C-T4-T5 18. T T T C C A A A A A -T T T C T T A A C C-C A T A A A A C A C-T4-F5 19. T T T C C A A A A A -T T T C T T A A C C-C A T A A A A C A C-F4-T5 20. T T T C C A A A A A -T T T C T T A A C C-C A T A A A A C A C-F4-F5 21. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-T4-T5 22. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-T4-F5 23. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-F4-T5 24. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-F4-F5 25. T T T C C A A A A A -A C T A A C A A A A-C A T A A A A C A C-T4-T5 26. T T T C C A A A A A -A C T A A C A A A A-C A T A A A A C A C-T4-F5 27. T T T C C A A A A A -A C T A A C A A A A-C A T A A A A C A C-F4-T5 28. T T T C C A A A A A -A C T A A C A A A A-C A T A A A A C A C-F4-F5 29. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-T4-T5 30. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-T4-F5 31. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-F4-T5 32. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-F4-F5 DNA Library 2^( # Coding Strands / 2) # Coding Strands / 2 Bits T T T T T G G A A A 24. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-F4-F5 T T T T G T T A G T 10.A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-T4-F5 X1=F or X2=F T T T T G T T A G T T T T T T G G A A A 29. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-T4-T5 All subsets not containing {1,2} T T T T T G G A A A=Probe(F1) T T T T G T T A G T=Probe(F2) Edge {1,2} STM 9. A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-T4-T5 10. A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-T4-F5 11. A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-F4-T5 12. A A A A A A A A C C-A C T A A C A A A A-C A T A A A A C A C-F4-F5 13. A A A A A A A A C C-A C T A A C A A A A-A T C T T T T C A A-T4-T5 14. A A A A A A A A C C-A C T A A C A A A A-A T C T T T T C A A-T4-F5 15. A A A A A A A A C C-A C T A A C A A A A-A T C T T T T C A A-F4-T5 16. A A A A A A A A C C-A C T A A C A A A A-A T C T T T T C A A-F4-F5 17. T T T C C A A A A A -T T T C T T A A C C-C A T A A A A C A C-T4-T5 18. T T T C C A A A A A -T T T C T T A A C C-C A T A A A A C A C-T4-F5 19. T T T C C A A A A A -T T T C T T A A C C-C A T A A A A C A C-F4-T5 20. T T T C C A A A A A -T T T C T T A A C C-C A T A A A A C A C-F4-F5 21. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-T4-T5 22. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-T4-F5 23. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-F4-T5 24. T T T C C A A A A A -T T T C T T A A C C -A T C T T T T C A A-F4-F5 25. T T T C C A A A A A -A C T A A C A A A A-C A T A A A A C A C-T4-T5 26. T T T C C A A A A A -A C T A A C A A A A-C A T A A A A C A C-T4-F5 27. T T T C C A A A A A -A C T A A C A A A A-C A T A A A A C A C-F4-T5 28. T T T C C A A A A A -A C T A A C A A A A-C A T A A A A C A C-F4-F5 29. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-T4-T5 30. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-T4-F5 31. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-F4-T5 32. T T T C C A A A A A -A C T A A C A A A A-A T C T T T T C A A-F4-F5 X1=T and X2=T 1. A A A A A A A A C C -T T T C T T A A C C-C A T A A A A C A C-T4-T5 2. A A A A A A A A C C -T T T C T T A A C C-C A T A A A A C A C-T4-F5 3. A A A A A A A A C C -T T T C T T A A C C-C A T A A A A C A C-F4-T5 4. A A A A A A A A C C -T T T C T T A A C C-C A T A A A A C A C-F4-F5 5. A A A A A A A A C C ­-T T T C T T A A C C -A T C T T T T C A A-T4-T5 6. A A A A A A A A C C ­-T T T C T T A A C C -A T C T T T T C A A-T4-F5 7. A A A A A A A A C C -T T T C T T A A C C -A T C T T T T C A A-F4-T5 8. A A A A A A A A C C -T T T C T T A A C C -A T C T T T T C A A-F4-F5

  32. DNA Library {1,2} {2,4} {1,3} {2,5} {1,4} {3,4} {1,5} {3,5} {2,3} {4,5} Black ON, Red OFF =Independent Sets in G Black OFF, Red ON =Cliques in G

  33. Universal DNA Computer for any Graph on n Vertices DNA Library Every Graph G on n vertices has G union G’= all possible pairs on n vertices. This enables the construction of a universal device. {1,2} {1,3} Each possible edge is an STM. Then depending on the problem, the flow is directed by the edges present (or absent) in the given graph . {n-2,n} {n-1,n} Edges in G ON, Edges in G’ OFF =Independent Sets in G when flow completed Edges in G OFF, Edges in G’ ON =Cliques in G when flow completed

  34. We use the concept (t-gap) block isomorphic subsequences couple with classical sequence alignment ideas to describe new abstract weighted string metrics that are similar to the weighted Levenshtein insertion-deletion metric. These metrics for DNA code design capture key aspects of the nearest neighbor thermodynamic model for hybridized DNA duplexes. One of the versions of the metric gives the maximum number of stacked pairs of hydrogen bonded nucleotide base pairs that can be present in any secondary structure in a hybridized DNA duplex without pseudoknots. The SynDCode generates a collection of DNA blueprints such that certain conditions hold for strands, pairs of strands, and concatenation of certain pairs of strands. What is generated is a DNA code C such that: WC complement of each strand in the code is also in the code. The maximum number of ti- stems in each CH duplex from C is at most si. Each CH duplex in C has a free energy of formation above -∆GCH Each WC duplex in C has a free energy of formation between -∆Gwcand -∆Gwc.

  35. Script for Comparing Results read_input SlsDnaDesigner We made this program to ask the user to specify parameter settings to be used in the University of British Columbia’s SlsDnaDesigner to initially generate codewords. pairfold complement get_threshold

  36. Script for Comparing Results read_input SlsDnaDesigner This is the University of British Columbia’s SlsDnaDesigner which uses the specified parameters to generate a pool of codewords. pairfold complement get_threshold

  37. Script for Comparing Results read_input SlsDnaDesigner pairfold complement We made this program to take the codewords that SlsDnaDesigner output and create a complemented pool of codewords. get_threshold

  38. Script for Comparing Results read_input SlsDnaDesigner pairfold complement This is the University of British Columbia’s pairfold program, which uses the complemented pool of codewords and does pairwise comparisons to obtain thermodynamic values. get_threshold

  39. Script for Comparing Results read_input SlsDnaDesigner We made this program to take the output from pairfold, find the thermodynamic upper bound, and store this value to be used later. pairfold complement get_threshold

  40. Script for Comparing Results get_params read_params We made this program to read in the parameters that get_params outputs and output them in the correct format to be read in by SynDCode. pairfold SynDCode Subcode

  41. Script for Comparing Results get_params read_params pairfold SynDCode Morgan Bishop made this program which extends the pool of codewords, given the inputted constraints, creating new codewords. Subcode

  42. Script for Comparing Results get_params read_params pairfold SynDCode This is the University of British Columbia’s pairfold program, which uses the pool of codewords that was extended by SynDCode and does pairwise comparisons to obtain thermodynamic values. Subcode

  43. Script for Comparing Results We made this program to take the output from pairfold and create a binary matrix of sequence comparisons using the thermodynamic upper bound stored earlier. It then uses a Greedy algorithm to parse the matrix and obtain a new pool of codewords, with sequences that “violate” the thermodynamic upper bound deleted. get_params read_params pairfold SynDCode Subcode

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