1. Universal DNA Arrays Ion Mandoiu Computer Science & Engineering Department

2. High-Throughput Genomic Assays Growing number of applications –Focus shifting from basic research to healthcare, forensics, environmental monitoring,… Increasingly stringent requirements –Reproducibility, sensitivity, cost Assay design and optimization become critical –Source of challenging combinatorial problems Multiplex PCR primer set selection Probe selection Fidelity probes Mask design … –This talk: design and optimization of universal tag arrays

3. Overview  Background on DNA Microarrays  Universal Tag Arrays  Tag Set Design Problem  Tag Assignment Problem  Conclusions

4. Watson-Crick Complementarity Four nucleotide types: A,C,T,G A’s paired with T’s (2 hydrogen bonds) C’s paired with G’s (3 hydrogen bonds)

5. DNA Microarrays Images courtesy of Affymetrix. Labeled DNA/RNA mixture flushed over array of probes Laser activation of fluorescent labels Optical scanning used to identify probes with complements in the mixture

6. Applications Gene expression (transcription analysis) Genomic-based microorganism identification Single Nucleotide Polymorphism (SNP) genotyping

7. Gene Expression Cells express different subsets of genes under different environments Gene (DNA) mRNA Protein Transcription Translation

8. Two-Color Technique Sample labeled RED Control labeled GREEN YELLOW YELLOW probes hybridize to both sample and control BLACK probes hybridize to neither Cy3 Cy5 cell type 2 cell type 1 RNA 2 RNA 1 target 1 target 2

9. Microarray Technologies Arrays of cDNAs –Obtained by reverse transcription from Expressed Sequence Tags (ESTs) Oligonucleotide arrays –Short (20-60bp) synthetic DNA strands

10. Ink jet Technology Pin TechnologyQuill Pen Technology Pin Ring Technology Robotic cDNA Arrayers

11. VLSIPS Array Synthesis Images courtesy of Affymetrix.

12. VLSIPS Array Synthesis CG AC CG AC ACG AG G C Probes to be synthesized A A A A A

13. VLSIPS Array Synthesis CG AC CG AC ACG AG G C Probes to be synthesized A A A A A C C C C C C

14. VLSIPS Array Synthesis CG AC CG AC ACG AG G C Probes to be synthesized A A A A A C C C C C C G G G G G

15. Oligonucleotide Arrays Pros –Highly versatile –Very high integration (VLSIPS ~10 6 probes/cm 2 ) Cons –Higher cost Significant problem for low production volumes

16. Overview  Background on DNA Microarrays  Universal Tag Arrays  Tag Set Design Problem  Tag Assignment Problem  Conclusions

17. Universal Arrays Key idea –Array consisting of application independent tags –Two-part “reporter” probes: aplication specific primers ligated to antitags –Detection carried by a sequence of reactions separately involving the primer and the antitag part of reporter probes Brenner 97, Morris et al. 98

18. Universal Array Experiment +

19. Universal Array Advantages Cost effective –Same array type used for large number of experiments  can be produced in large quantities Rapid design – Only need to synthesize new set of reporter probes Reliable –Solution phase hybridization better understood than hybridization on solid support

20. Overview  Background on DNA Microarrays  Universal Tag Arrays  Tag Set Design Problem  Tag Assignment Problem  Conclusions

21. Tag Set Requirements Hybridization constraints (H1) Antitags hybridize strongly to complementary tags (H2) No antitag hybridezes to a non-complementary tag (H3) Antitags do not cross-hybridize to each other t1 t2 t1t2t1

22. Hybridization Model Melting temperature Tm: temperature at which 50% of duplexes are in hybridized state 2-4 rule Tm = 2 #(As and Ts) + 4 #(Cs and Gs) More accurate models exist, e.g., the near- neighbor model

23. Tag Set Design Problem [Ben-Dor et al. 00] Conservative formalization of (H1)+(H2) based on nucleation complex theory and 2-4 rule (C1) Every tag must have total weight  h (C2) No 2 tags share a common substring of weight  c Where –w(A)=w(T)=1, w(C)=w(G)=2 –c, h are given constant

24. c-h codes c-token: left-minimal DNA string of weight  c, i.e., –w(x)  c –w(x’) < c for every proper suffix of x [Ben-Dor et al. 00] A set of tags is called c-h code if (C1) Every tag has weight  h (C2*) Every c-token is used at most once c-h code problem: given c and h, find largest c-h code

25. c-h code problem [Ben-Dor et al. 00] give a constructive upper- bound on largest c-h code size and a near- optimal algorithm based on DeBruijn sequences [MT05] c-h code problem can be formulated as a maximum integer flow problem with capacity constraints on (disjoint) sets of vertices –Solvable in practical time for small values of c

26. Token Content of a Tag c=4 CCAGATT CC CCA CAG AGA GAT GATT

27. Tag of length l  sequence of c-tokens c=4, l=7 tag = CCAGATT CC  CCA  CAG  AGA  GAT  GATT

28. Layered c-token graph st c1c1 cNcN ll-1 c/2(c/2)+1…

29. Integer Program Formulation O( hN) constraints and variables, where N = #c-tokens

30. ILP Results

31. Number of c-tokens W=A or T, S=C or G G n = #strings of weight n  G 1 = 2; G 2 = 6; G n = 2G n-2 + 2G n-1 Token typeNum tokens S2 G c-2 S 4 G c-3 W2 G c-1 S W4 G c-2 TotalG c + 2 G c-1

32. Number of c-tokens cNum c-tokens 5208 6568 71552 84240 911584 1031648

33. Periodic Tags If multiple c-token copies are not allowed in a tag, every tag uses roughly one c-token per letter (except for first up to c-1 letters) A tag t is periodic if it is the prefix of (  )  for some string  –t periodic with period   t uses at most |  | c-tokens –Advantageous to use periodic tags with short period

34. Portion of c-token factor graph, c=4 CC AAG AAC AAAA AAAT

35. Tag Set Design Algorithm 1.Construct c-token factor graph G 2.T  {} 3.For all cycles C defining periodic tags, in increasing order of cycle length, do –If C has no c-tokens in common with T, then Add a tag defined by C to T Remove C from G 4.Perform a pruned alphabetic tree search and add to T tags with no c-tokens in common with T 5.Return T

36. Vertex-disjoint Cycle Packing Problem Given directed graph G, find maximum number of vertex disjoint directed cycles in G [MT 05] APX-hard even for regular directed graphs with in-degree and out-degree 2 –h-c/2+1 approximation factor for tag set design problem [Salavatipour and Verstraete 05] –Quasi-NP-hard to approximate within  (log 1-  n) –O(n 1/2 ) approximation algorithm

37. Experimental Results

38. Antitag-to-Antitag Hybridization Additional practical constraint: antitags do not cross-hybridize (including self) –Ignored by Ben-Dor et al Formalization in c-token hybridization model: (C3) No two (anti)tags contain complementary substrings of weight  c Cycle packing and tree search extend easily

39. Results w/ Extended Constraints

40. Overview  Background on DNA Microarrays  Universal Tag Arrays  Tag Set Design Problem  Tag Assignment Problem  Conclusions

41. More Possible Mis-Hybridizations Degrees of freedom: partition of primers on multiple arrays, tag assignment within an array (may be forced to leave tags unassigned) Here we focus on avoiding case (a), primer-to-tag hybridization

42. Constraints on tag assignment If primer p hybridizes with tag t, then either p or t must be left un-assigned, unless p is assigned to t p t t’ p’

43. Characterization of Assignable Sets [Ben-Dor 04] Set P is assignable to T iff X+Y  |P|, where, in the hybridization graph induced by P+T –X = number of primers incident to a degree 1 tag –Y = number of degree 0 tags Y=2 X=1

44. MAPS Problem Maximum Assignable Primer Set (MAPS) Problem: given primer set P and tag set T, find maximum size assignable subset of P [Ben-Dor 04] Greedy deletion heuristic: repeatedly delete primer of maximum weight from P until it becomes assignable, where –Potential of tag t is 2 -|P(t)| –Potential of primer p is sum of potentials of conflicting tags

45. Multiplexing Problem Universal Tag Array Multiplexing Problem: given primer set P and tag set T, find partition of P into minimum number of assignable sets [Ben-Dor 04] Repeatedly find approximate MAP using greedy deletion

46. Integration with Probe Selection In practice, several primer candidates with equivalent functionality –In SNP genotyping, can pick primer from either forward and reverse strand –In gene expression/identification applications, many primers have desired length, Tm, etc.

47. Pooled Array Multiplexing Problem [MPT 05] Given set of primer pools P and tag set T, find a primer from each pool and a partition of selected primers into minimum number of assignable sets

48. X+Y Characterization no Longer Holds

49. Pooled Multiplexing Algorithms 1.Primer-Del = greedy deletion for pools similar to [Ben-Dor et al 04] 2.Primer-Del+ = same but never delete last primer from pool unless no other choice 3.Min-Pot = select primer with min potential from each pool, then run Primer-Del 4.Min-Deg = select primer with min conflict degree, then run Primer-Del

50. Results: GenFlex Tags, c=7

51. Results: GenFlex Tags, c=8

52. GenFlex vs. PerTags, c=8 (|T|=213)

53. Overview  Background on DNA Microarrays  Universal Tag Arrays  Tag Set Design Problem  Tag Assignment Problem  Conclusions

54. Conclusions Novel combinatorial techniques for tag set design and tag assignment lead to significant improvement in overall assay throughput Other applications of DNA tags: –Lab-on-chip, DNA-directed assembly of nanostructures (e.g., carbon nano-tubes), DNA computing [Brenneman&Condon 02] Other applications of assignment techniques: –Genotyping by mass-spectroscopy [Aumann et al 05] –Genotyping using l-mer arrays

55. Ongoing Work Special type of universal arrays: l-mer arrays –Initially introduced for sequencing by hybridization, but proved impractical –Currently investigated for use in resequencing by hybridization –More promising application: SNP genotyping –Isothermal prefix sets instead of l-mer arrays? Deeper integration between tag assignment and probe selection, e.g., in string barcoding Extend algorithms to more accurate near-neighbor hybridization model –monotonic Tm  c-tokens  successor graph

56. Open Problems Settle approximation complexity of (vertex) disjoint cycle packing ([Salavatipour and Verstraete 05] show approximation preserving reductions between edge and vertex disjoint versions) Establish better approximation bound for special instances arising in tag set design Improved approximation algorithms for maximum assignable tag set and the tag assignment problems

57. Acknowledgments Claudia Prajescu and Dragos Trinca UCONN Research Foundation