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Algorithms for Biochip Design and Optimization Ion Mandoiu Computer Science & Engineering Department University of Connecticut
Overview ,[object Object],[object Object],[object Object],[object Object]
Driver Biochip Applications ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],Single Nucleotide Polymorphisms … ataggtcc C tatttcgcgc C gtatacacggg T ctata … … ataggtcc G tatttcgcgc A gtatacacggg A ctata … … ataggtcc C tatttcgcgc C gtatacacggg T ctata …
Watson-Crick Complementarity ,[object Object],[object Object],[object Object]
SNP genotyping via direct hybridization Hybridization ,[object Object],[object Object],Array with 2 probes/SNP Labeled sample A C T C G A A C T C G A Optical scanning used to identify alleles present in the sample
In-Place Probe Synthesis CG AC CG AC ACG AG G AG C Probes to be synthesized A A A A A
In-Place Probe Synthesis CG AC CG AC ACG AG G AG C Probes to be synthesized A A A A A C C C C C C
In-Place Probe Synthesis CG AC CG AC ACG AG G AG C Probes to be synthesized A A A A A C C C C C C G G G G G G
Simplified DNA Array Flow Probe Selection Array Manufacturing Hybridization Experiment Gene expression levels, SNP genotypes,… Analysis of Hybridization Intensities Mask Manufacturing Physical Design: Probe Placement & Embedding Design Manufacturing End User
Unwanted Illumination Effect ,[object Object],[object Object]
Border Length Minimization Objective ,[object Object],A A A A A C C C C C C G G G G G G border CG AC CG AC ACG AG G AG C
Synchronous Synthesis ,[object Object],[object Object], # border conflicts b/w adjacent probes = 2 x Hamming distance T G C A T G T G C A … C A period C T A C G T
2D Placement Problem ,[object Object],[object Object],Edge cost = 2 x Hamming distance probe
2D Placement: Sliding-Window Matching ,[object Object],[object Object],[object Object],1 3 2 5 4 Select mutually nonadjacent probes from small window 2 2 3 1 4 Re-assign optimally
2D Placement: Epitaxial Growth ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
2D Placement: Recursive Partitioning ,[object Object],[object Object],[object Object]
Asynchronous Synthesis A A A C C C T T T G G G A C T G A G T G T G A A Deposition Sequence Probes Synchronous Embedding A G T A G G T A G A A G T A G T ASAP Embedding G
[object Object],Optimal Single-Probe Re-Embedding A C T A C G T A C G T Source Sink
In-Place Re-Embedding Algorithms ,[object Object],[object Object],[object Object],[object Object],CPU %LB CPU %LB CPU %LB 121.4 120.5 Chessboard 1423 54 127.1 125.7 Greedy 120.9 119.9 Sequential 1535 943 500 64 40 100 Chip size
Integration with Probe Selection Probe Selection Physical Design: Placement & Embedding Probe Pools Chip size 100x100 Pool Row-Epitaxial Pool Size 7515 15.2 16 3645 11.8 8 1796 8.2 4 1040 4.3 2 217 - 1 CPU sec. % Improv
Overview ,[object Object],[object Object],[object Object],[object Object]
Universal Tag Arrays ,[object Object],[object Object],[object Object],[object Object]
Universal Tag Array Advantages ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
SNP Genotyping with Tag Arrays Tag + Primer G A G C antitag ,[object Object],2. Solution phase hybridization 3. Single-Base Extension (SBE) 4. Solid phase hybridization G A G G A G T G A T C C T C C
Tag Set Design Problem ,[object Object],[object Object],t1 t1 t2 t2 t1 t2 t1 Tag Set Design Problem: Find a maximum cardinality set of tags satisfying (H1)-(H2)
Hybridization Models ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Hybridization Models (contd.)
c-h Code Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],c-h Code Problem [Ben-Dor et al.00] Given c and h, find maximum cardinality c-h code
Algorithms for c-h Code Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Token Content of a Tag ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Tag  sequence of c-tokens End pos: 2 3 4 5 6 7 c-token: CC  CCA  CAG  AGA  GAT  GATT
Layered c-token graph for length-l tags s t c 1 c N l l-1 c/2 (c/2)+1 …
Integer Program Formulation [MPT05] ,[object Object],[object Object]
Packing LP Formulation
Garg-Konemann Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[GK98] The algorithm computes a factor (1-  ) 2 approximation to the optimal LP solution with (N/  )* log 1+  N shortest path computations
LP Based Tag Set Design ,[object Object],[object Object],[object Object]
Periodic Tags [MT05] ,[object Object],[object Object],[object Object],[object Object]
c-token factor graph, c=4 (incomplete) CC AAG AAC AAAA AAAT
Vertex-disjoint Cycle Packing Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Cycle Packing Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Experimental Results h
More Hybridization Constraints… ,[object Object],[object Object],[object Object],t1 t2 t1
Herpes B Gene Expression Assay GenFlex Tags Periodic Tags % Util. # arrays % Util. # arrays % Util. # arrays 76.10 1 99.80 2 97.80 4 5 76.10 1 98.90 2 96.73 4 1 1522 70 78.00 1 99.90 2 98.00 4 5 78.00 1 98.70 2 96.53 4 1 1560 67 72.30 1 100.00 2 96.13 4 5 72.30 1 97.20 2 94.06 4 1 1446 60 2000 tags 1000 tags 500 tags Pool size # pools T m % Util. # arrays % Util. # arrays % Util. # arrays 70.30 2 91.10 2 92.26 4 5 65.40 2 73.65 3 88.46 4 1 1522 70 67.20 2 76.00 3 91.86 4 5 61.15 2 69.70 3 86.33 4 1 1560 67 63.55 2 70.95 3 88.26 4 5 57.05 2 65.35 3 82.26 4 1 1446 60 2000 tags 1000 tags 500 tags Pool size # pools T m
Overview ,[object Object],[object Object],[object Object],[object Object]
Digital Microfluidic Biochips [Srinivasan et al. 04] ,[object Object],[object Object],[object Object],[Su&Chakrabarty 06] I/O I/O Cell
Design Challenges ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Merging Interference
Concurrent Testing Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Defect model: test droplet gets stuck at defective electrode [Su et al. 04] ILP-based solution for single test droplet case & heuristic for multiple input-output pairs with single test droplet/pair
ILP Formulation for Unconstrained Number of Droplets ,[object Object],[object Object],[object Object],[object Object],[object Object]
Special Case ,[object Object],[object Object],[object Object],[object Object]
Lower Bound ,[object Object],Proof: In each cycle, each of the k droplets place 1 dollar in current cell  3k(k-1)/2 dollars paid waiting to depart  3k(k-1)/2 dollars paid waiting for last droplet  k dollars in each diagonal  1 dollar in each cell
Stripe Algorithm with N/3 Droplets Stripe algorithm has approximation factor of
Stripe Algorithm with Obstacles of width Q ,[object Object],[object Object],[object Object],[object Object]
Results for 120x120 Chip, 2x2 Obstacles ~20x decrease in completion time by using multiple droplets 19x 570 736.6 1071 1501 10800 25% 20x 580.8 738.4 1046.8 1501 11520 20% 21x 588.2 730.8 1025.8 1501 12240 15% 22x 592.6 734.8 1010.8 1490 12960 10% 23x 596.2 725 982.8 1473 13680 5% 24x 598.8 715.2 953.4 1420 14256 1% 24x 593 710 944 1412 14400 0% k=40 k=30 k=20 k=12 k=1 k=40 vs. k=1 speed-up Average completion time (cycles) Obstacle Area
Overview ,[object Object],[object Object],[object Object],[object Object]
Conclusions ,[object Object],[object Object],[object Object]
Acknowledgments ,[object Object],[object Object],[object Object],[object Object]
Questions?

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Biochip

  • 1. Algorithms for Biochip Design and Optimization Ion Mandoiu Computer Science & Engineering Department University of Connecticut
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7. In-Place Probe Synthesis CG AC CG AC ACG AG G AG C Probes to be synthesized A A A A A
  • 8. In-Place Probe Synthesis CG AC CG AC ACG AG G AG C Probes to be synthesized A A A A A C C C C C C
  • 9. In-Place Probe Synthesis CG AC CG AC ACG AG G AG C Probes to be synthesized A A A A A C C C C C C G G G G G G
  • 10. Simplified DNA Array Flow Probe Selection Array Manufacturing Hybridization Experiment Gene expression levels, SNP genotypes,… Analysis of Hybridization Intensities Mask Manufacturing Physical Design: Probe Placement & Embedding Design Manufacturing End User
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18. Asynchronous Synthesis A A A C C C T T T G G G A C T G A G T G T G A A Deposition Sequence Probes Synchronous Embedding A G T A G G T A G A A G T A G T ASAP Embedding G
  • 19.
  • 20.
  • 21. Integration with Probe Selection Probe Selection Physical Design: Placement & Embedding Probe Pools Chip size 100x100 Pool Row-Epitaxial Pool Size 7515 15.2 16 3645 11.8 8 1796 8.2 4 1040 4.3 2 217 - 1 CPU sec. % Improv
  • 22.
  • 23.
  • 24.
  • 25.
  • 26.
  • 27.
  • 28.
  • 29.
  • 30.
  • 31.
  • 32. Layered c-token graph for length-l tags s t c 1 c N l l-1 c/2 (c/2)+1 …
  • 33.
  • 35.
  • 36.
  • 37.
  • 38. c-token factor graph, c=4 (incomplete) CC AAG AAC AAAA AAAT
  • 39.
  • 40.
  • 42.
  • 43. Herpes B Gene Expression Assay GenFlex Tags Periodic Tags % Util. # arrays % Util. # arrays % Util. # arrays 76.10 1 99.80 2 97.80 4 5 76.10 1 98.90 2 96.73 4 1 1522 70 78.00 1 99.90 2 98.00 4 5 78.00 1 98.70 2 96.53 4 1 1560 67 72.30 1 100.00 2 96.13 4 5 72.30 1 97.20 2 94.06 4 1 1446 60 2000 tags 1000 tags 500 tags Pool size # pools T m % Util. # arrays % Util. # arrays % Util. # arrays 70.30 2 91.10 2 92.26 4 5 65.40 2 73.65 3 88.46 4 1 1522 70 67.20 2 76.00 3 91.86 4 5 61.15 2 69.70 3 86.33 4 1 1560 67 63.55 2 70.95 3 88.26 4 5 57.05 2 65.35 3 82.26 4 1 1446 60 2000 tags 1000 tags 500 tags Pool size # pools T m
  • 44.
  • 45.
  • 46.
  • 47.
  • 48.
  • 49.
  • 50.
  • 51. Stripe Algorithm with N/3 Droplets Stripe algorithm has approximation factor of
  • 52.
  • 53. Results for 120x120 Chip, 2x2 Obstacles ~20x decrease in completion time by using multiple droplets 19x 570 736.6 1071 1501 10800 25% 20x 580.8 738.4 1046.8 1501 11520 20% 21x 588.2 730.8 1025.8 1501 12240 15% 22x 592.6 734.8 1010.8 1490 12960 10% 23x 596.2 725 982.8 1473 13680 5% 24x 598.8 715.2 953.4 1420 14256 1% 24x 593 710 944 1412 14400 0% k=40 k=30 k=20 k=12 k=1 k=40 vs. k=1 speed-up Average completion time (cycles) Obstacle Area
  • 54.
  • 55.
  • 56.