Efficient Algorithms for Locating the Length-Constrained Heaviest Segments, with Applications to Biomolecular Sequence Analysis

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Efficient Algorithms for Locating the
Length-Constrained Heaviest Segments, with
Applications to Biomolecular Sequence Analysis

• Yaw-Ling Lin Tao Jiang Kun-Mao Chao
• Dept CSIM, Providence Univ, Taiwan
• Dept CS and Engineering, UC Riverside, USA
• Dept Life Science, Nat. Yang-Ming Univ, Taiwan

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Outline

• Introduction.
• Applications to Biomolecular Sequence Analysis.
• Maximum Sum Consecutive Subsequence.
• Maximum Average Consecutive Subsequence.
• Implementation and Preliminary Experiments
• Concluding Remarks

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Introduction

• Two fundamental algorithms in searching for
  interesting regions in sequences
• Given a sequence of real numbers of length n and
  an upper bound U, find a consecutive subsequence
  of length at most U with the maximum sum --- an
  O(n)-time algorithm.
• Given a sequence of real numbers of length n and
  a lower bound L, find a consecutive subsequence
  of length at least L with the maximum average.
  --- an O(n log L)-time algorithm.

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Applications to Biomolecular Sequence Analysis (I)

• Locating GC-Rich Regions
• Finding GC-rich regions an important problem in
  gene recognition and comparative genomics.
• CpG islands ( 200 1400 bp )
• Huang94 O(n L)-time algorithm.
• Post-Processing Sequence Alignments
• Comparative analysis of human and mouse DNA
  useful in gene prediction in human genome.
• Mosaic effect bad inner sequence.
• Normalized local alignment.
• Post-processing local aligned subsequences

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Applications to Biomolecular Sequence Analysis
(II)

• Annotating Multiple Sequence Alignments
• Stojanovic99 conserved regions in
  biomolecular sequences.
• Numerical scores for columns of a multiple
  alignment each column score shall be adjusted by
  subtracting an anchor value.
• Ungapped Local Alignments with Length Constraints
• Computing the length-constrained segment of each
  diagonal in the matrix with the largest sum (or
  average) of scores.
• Applications in motif identification.

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Maximum Sum Consecutive Subsequence
lt-4,1,-2,3gt is left-negative
lt 5, -3, 4, -1, 2, -6 gt is not.
lt5gt lt-3,4gt lt-1,2gt lt-6gt is minimal left-negative
partitioned.
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Minimal left-negative partition
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MLN-partition linear time
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Max-Sum with LC
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Analysis of MSLC
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Max Average Subsequence
lt4,2,3,8gt is right-skew
lt 5, 3, 4, 1, 2, 6 gt is not.
lt5gt lt3,4gt lt1,2,6gt is decreasing right-skew
partitioned.
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Decreasing right-skiew partition
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DRS-partition linear time
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Max-Avg-Seq with LC
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Locate good-partner
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Analysis of MaxAvgSeq
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Implementation and Preliminary Experiments
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Implementation and Preliminary Experiments
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Conclusion

• Find a max-sum subsequence of length at most U
  can be done in O(n)-time.
• Find a max-avg subsequence of length at least L
  can be done in O(n log L)-time.
• Is there a linear-time algorithm to find a
  max-avg subsequence of length at least L?

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Future Research

• Best k (nonintersecting) subsequences?
• Normalized local alignment?
• Measurement of goodness?