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Error-Control and Constrained Coding Solutions for DNA Microarrays and Aptamer Arrays Design

USC, November 21st, 2006. 2. Outline. Information theory and genetics. USC, November 21st, 2006. 3. Outline. Information theory and geneticsBrief introduction to gene regulatory networks (GRN). USC, November 21st, 2006. 4. Outline. Information theory and geneticsBrief introduction to gene regulatory networks (GRN)Reverse engineering GRN.

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Error-Control and Constrained Coding Solutions for DNA Microarrays and Aptamer Arrays Design

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    1. Error-Control and Constrained Coding Solutions for DNA Microarrays and Aptamer Arrays Design Olgica Milenkovic University of Colorado, Boulder ITA Center, University of California, San Diego

    2. USC, November 21st, 2006 2 Outline Information theory and genetics

    3. USC, November 21st, 2006 3 Outline Information theory and genetics Brief introduction to gene regulatory networks (GRN)

    4. USC, November 21st, 2006 4 Outline Information theory and genetics Brief introduction to gene regulatory networks (GRN) Reverse engineering GRN

    5. USC, November 21st, 2006 5 Outline Information theory and genetics Brief introduction to gene regulatory networks (GRN) Reverse engineering GRN DNA microarrays Production Quality control coding Error control coding

    6. USC, November 21st, 2006 6 Outline Information theory and genetics Brief introduction to gene regulatory networks (GRN) Reverse engineering GRN DNA microarrays Production Quality control coding Error control coding RNA aptamer arrays SELEX (Systematic Enrichment of Ligands by Exponential Evolution) Structured probe selection RNA folds and grammars

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    30. USC, November 21st, 2006 30

    31. USC, November 21st, 2006 31 Boolean Networks and Gene Interactions

    32. USC, November 21st, 2006 32 Boolean Networks and Gene Interactions

    33. USC, November 21st, 2006 33 Boolean Networks and Gene Interactions

    34. USC, November 21st, 2006 34

    35. USC, November 21st, 2006 35 Boolean Networks and Gene Interactions

    36. USC, November 21st, 2006 36 Boolean Networks and Gene Interactions

    37. USC, November 21st, 2006 37

    38. USC, November 21st, 2006 38

    39. USC, November 21st, 2006 39 DNA Microarrays and Aptamer Arrays

    40. USC, November 21st, 2006 40 DNA Microarrays

    41. USC, November 21st, 2006 41 DNA Microarrays

    42. USC, November 21st, 2006 42 DNA Microarrays

    43. USC, November 21st, 2006 43 DNA Microarrays

    44. USC, November 21st, 2006 44 Probe Selection/Construction

    45. USC, November 21st, 2006 45 Probe Selection/Construction

    46. USC, November 21st, 2006 46 Probe Selection/Construction

    47. USC, November 21st, 2006 47 Probe Selection/Construction

    48. USC, November 21st, 2006 48 Probe Selection/Construction

    49. USC, November 21st, 2006 49 Probe Selection/Construction

    50. USC, November 21st, 2006 50 Minimum Hamming, Reverse and Reverse-Complement Hamming Distance

    51. USC, November 21st, 2006 51 Minimum Hamming, Reverse and Reverse-Complement Hamming Distance

    52. USC, November 21st, 2006 52

    53. USC, November 21st, 2006 53 Constant GC Content

    54. USC, November 21st, 2006 54 Probe Synthesis in Microarrays

    55. USC, November 21st, 2006 55 Probe Synthesis in Microarrays

    56. USC, November 21st, 2006 56 Probe Synthesis in Microarrays

    57. USC, November 21st, 2006 57 Probe Synthesis in Microarrays

    58. USC, November 21st, 2006 58

    59. USC, November 21st, 2006 59

    60. USC, November 21st, 2006 60 Base Scheduling Shortest asynchronous base schedule Shortest common super-sequence of set of M sequences (NP-hard) ESN(M,k) – expected length of a longest common subsequence of M randomly chosen sequences of length N over an alphabet of size k

    61. USC, November 21st, 2006 61 Mask Design

    62. USC, November 21st, 2006 62 Quality Control

    63. USC, November 21st, 2006 63 Relevant Coding-Theoretic Ideas

    64. USC, November 21st, 2006 64 Relevant Coding-Theoretic Ideas

    65. USC, November 21st, 2006 65 Relevant Coding-Theoretic Ideas

    66. USC, November 21st, 2006 66 Error-Correcting Microarray Design Probe multiplexing (Khan et.al, 2003, Shmulevich et.al. 2004)

    67. USC, November 21st, 2006 67 VLSIPS/Analysis for Multiplexed Arrays (Milenkovic, 2006) Features: Multiple polymer synthesis at one given spot Can use two different classes of linkers sensitive to different wavelengths so to select probes for extension (say, `blue’ and `green’ and `cyan’)

    68. USC, November 21st, 2006 68 VLSIPS/Analysis for Multiplexed Arrays

    70. USC, November 21st, 2006 70 Mask Design / Scheduling

    71. USC, November 21st, 2006 71 Quality Control Coding

    72. USC, November 21st, 2006 72 DNA Microarrays and Aptamer Arrays

    73. USC, November 21st, 2006 73 RNA Secondary and Tertiary Structure

    74. USC, November 21st, 2006 74 RNA Secondary and Tertiary Structure

    75. USC, November 21st, 2006 75 Secondary Structures

    76. USC, November 21st, 2006 76 Aptamers SELEX (Systematic Evolution of Ligands by EXponential enrichment) – Archemix (Lary Gold, University of Colorado, Boulder)

    77. USC, November 21st, 2006 77 Aptamers SELEX (Systematic Evolution of Ligands by EXponential enrichment) – Archemix (Lary Gold, University of Colorado, Boulder)

    78. USC, November 21st, 2006 78 Aptamers SELEX (Systematic Evolution of Ligands by EXponential enrichment) – Archemix (Lary Gold, University of Colorado, Boulder)

    79. USC, November 21st, 2006 79 Aptamers SELEX (Systematic Evolution of Ligands by EXponential enrichment) – Archemix (Lary Gold, University of Colorado, Boulder)

    80. USC, November 21st, 2006 80 How Many Possible Shapes for a Secondary Structure Are There?

    81. USC, November 21st, 2006 81 How Many Possible Shapes for a Secondary Structure Are There?

    82. USC, November 21st, 2006 82 How Many Possible Shapes for a Secondary Structure Are There?

    83. USC, November 21st, 2006 83 Results on Secondary Structures

    84. USC, November 21st, 2006 84

    85. USC, November 21st, 2006 85 Can One Do Better?

    86. USC, November 21st, 2006 86 Can One Do Better?

    87. USC, November 21st, 2006 87 Suggested by Vauchaussade &Viennot, 1985 Mapping Secondary Structures to Ternary Sequences

    88. USC, November 21st, 2006 88

    89. USC, November 21st, 2006 89 Interpretations Dyck, Motzkin and Schroeder words

    90. USC, November 21st, 2006 90 Interpretations Dyck, Motzkin and Schroeder words Dyck, Motzkin and Schroeder lattice paths

    91. USC, November 21st, 2006 91 Interpretations Dyck, Motzkin and Schroeder words Dyck, Motzkin and Schroeder lattice paths Incomplete rooted binary trees …

    92. USC, November 21st, 2006 92 Interpretations Dyck, Motzkin and Schroeder words Dyck, Motzkin and Schroeder lattice paths Incomplete rooted binary trees …

    93. USC, November 21st, 2006 93 Mapping RNA Folded Shapes to Lattice Paths Definition: A lattice path of length n is a sequence of points P1,P2,…, Pn with n = 1, such that each point Pi belongs to the plane integer lattice and consecutive points Pi and Pi+1 are connected by a line segment.

    94. USC, November 21st, 2006 94 Mapping RNA Folded Shapes to Lattice Paths Definition: A lattice path of length n is a sequence of points P1,P2,…, Pn with n = 1, such that each point Pi belongs to the plane integer lattice and consecutive points Pi and Pi+1 are connected by a line segment. Definition: A Dyck path is a lattice path in the plane integer lattice consisting of steps (1,1) and (1,-1) which never passes below the x-axis.

    95. USC, November 21st, 2006 95 Mapping RNA Folded Shapes to Lattice Paths Definition: A lattice path of length n is a sequence of points P1,P2,…, Pn with n = 1, such that each point Pi belongs to the plane integer lattice and consecutive points Pi and Pi+1 are connected by a line segment. Definition: A Dyck path is a lattice path in the plane integer lattice consisting of steps (1,1) and (1,-1) which never passes below the x-axis. Definition: A Motzkin path is a lattice path in the plane integer lattice consisting of steps (1,1), (1,-1), and (1,0) which never passes below the x-axis.

    96. USC, November 21st, 2006 96 Mapping RNA Folded Shapes to Lattice Paths Definition: A lattice path of length n is a sequence of points P1,P2,…, Pn with n = 1, such that each point Pi belongs to the plane integer lattice and consecutive points Pi and Pi+1 are connected by a line segment. Definition: A Dyck path is a lattice path in the plane integer lattice consisting of steps (1,1) and (1,-1) which never passes below the x-axis. Definition: A Motzkin path is a lattice path in the plane integer lattice consisting of steps (1,1), (1,-1), and (1,0) which never passes below the x-axis. Definition: A Schroeder path is a lattice path in the plane integer lattice consisting of steps (1,1), (1,-1), and (2,0) which never passes below the x-axis.

    97. USC, November 21st, 2006 97 Lattice Path Examples ( ( ) ( ) ) ||| ( | ( ) ( ( || ) ) | ( ) )

    98. USC, November 21st, 2006 98 Main Idea: View `plausible’ secondary structures as Motzkin paths obeying certain constraints

    99. USC, November 21st, 2006 99 Main Idea: View “plausible” secondary structures as Motzkin paths obeying certain constraints Constraints account for biological properties of RNA molecules

    100. USC, November 21st, 2006 100 Main Idea: View `plausible’ secondary structures as Motzkin paths obeying certain constraints Constraints account for biological properties of RNA molecules Use lattice enumeration techniques based on context-free grammars to find generating functions of counted objects

    101. USC, November 21st, 2006 101 Main Idea: View `plausible’ secondary structures as Motzkin paths obeying certain constraints Constraints account for biological properties of RNA molecules Use lattice enumeration techniques based on context-free grammars to find generating functions of counted objects “Extend” scope of constrained coding: from regular to context-free grammars

    102. USC, November 21st, 2006 102 The Grammars

    103. USC, November 21st, 2006 103 The Grammars Regular : Production rules

    104. USC, November 21st, 2006 104 The Grammars Regular : Production rules Context-free: Production rules Each Xi terminal or non-terminal

    105. USC, November 21st, 2006 105 Regular Grammars and Constrained Coding

    106. USC, November 21st, 2006 106 Regular Grammars and Constrained Coding

    107. USC, November 21st, 2006 107 Regular Grammars and Constrained Coding

    108. USC, November 21st, 2006 108 Regular Grammars and Constrained Coding

    109. USC, November 21st, 2006 109 Regular Grammars and Constrained Coding

    110. USC, November 21st, 2006 110 Regular Grammars and Constrained Coding

    111. USC, November 21st, 2006 111

    112. USC, November 21st, 2006 112 Attribute Grammars: DSV and q-Method for Context Free Languages

    113. USC, November 21st, 2006 113 Attribute Grammars: DSV and q-Method for Context Free Languages

    114. USC, November 21st, 2006 114 Attribute Grammars

    115. USC, November 21st, 2006 115 Attribute Grammars

    116. USC, November 21st, 2006 116 The Stem-Loop Constraint: For a sequence over the alphabet { ( , ) , | }, let ls denote the length of a (maximal) run of ( symbols. The sequence is said to obey a stem-loop constraint if for each such ls, the maximal run ll of | symbols on the right of the ( run satisfies c1 = ll = c2 ls. The Constraints

    117. USC, November 21st, 2006 117 Example

    118. USC, November 21st, 2006 118 Example

    119. USC, November 21st, 2006 119 Example

    120. USC, November 21st, 2006 120 Context-Free Grammar for the Stem-Loop Constraint M = Motzkin words M+ = non-empty Motzkin words T = non-empty trapezoids Tk = non-empty trapezoids of height h>k, smallest width 3 and largest width k Tk = non-empty trapezoids of height 2<h< k+1, smallest width 3 and largest width h N = non-empty non-trapezoids

    121. USC, November 21st, 2006 121 Schutzenberger’s approach

    122. USC, November 21st, 2006 122 Generating Objects Described by Grammars

    123. USC, November 21st, 2006 123 References O. Milenkovic and B. Vasic, “Information theory problems in genetics,” ITW 2004. O. Milenkovic and N. Kashyap, “On the design of codes for DNA computing,” LNCS 2006. O. Milenkovic, N. Kashyap, and B. Vasic, “Coding for DNA computers controlling gene expression levels,” CDC 2005. O. Milenkovic, “Enumerating RNA motifs: a constrained coding approach,” Allerton 2006. Note: Some of the pictures (cells etc) are taken from open Internet sources

    124. USC, November 21st, 2006 124 LDPC Codes as BNs Boolean functions depend on: Code graph; Decoding algorithm; Initial state of network variables (some cases); Compared to random BN in Kaufmann’s model: network graph and functions chosen independently;

    125. USC, November 21st, 2006 125 Properties of LDPC Boolean Networks

    126. USC, November 21st, 2006 126 Properties of LDPC Boolean Networks

    127. USC, November 21st, 2006 127 Properties of LDPC Boolean Networks

    128. USC, November 21st, 2006 128 Robustness of LDPC Decoders

    129. USC, November 21st, 2006 129 Density Evolution for Gene Regulatory Networks

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