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2-D and 3-D Coordinates For M-Mers And Dynamic Graphics For Representing Associated Statistics

2-D and 3-D Coordinates For M-Mers And Dynamic Graphics For Representing Associated Statistics. By Daniel B. Carr dcarr@gmu.edu George Mason University. Overview. Background Encoding and self-similar coordinates Examples Rendering software – GLISTEN Closing remarks. Background. Task

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2-D and 3-D Coordinates For M-Mers And Dynamic Graphics For Representing Associated Statistics

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  1. 2-D and 3-D Coordinates For M-Mers And Dynamic Graphics For Representing Associated Statistics By Daniel B. Carr dcarr@gmu.edu George Mason University

  2. Overview • Background • Encoding and self-similar coordinates • Examples • Rendering software – GLISTEN • Closing remarks

  3. Background • Task • Visualize statistics indexed by a sequence of letters • Letter-Indexing • Nucleotides: AAGTAC • Amino Acids: KTLPLCVTL • Terminology: blocks of m letters called m-mers • Statistics: counts or likelihoods for • Short DNA sequence motifs for transcription factor binding: gene regulation • Peptide docking on immune system molecules

  4. Graphical Design Goals • Provide an overview and selective focus • Use geometric structures to • Organize statistics • Reveal patterns • Provide cognitive accessibility • Incorporate scientific knowledge in layout choices • Enhance patterns and simplify comparisons

  5. Common Practice - Tables • Published tables – a linear list • Sorted by values of a statistic • Indexing letter sequences shown as row labels • Only few items shown of thousands to millions

  6. Common Practice - Graphics • 1-D histograms – some examples • Nucleotides: Distribution of promoters by distance upstream from the start codon • Amino acids: • Sequence alignment logo plots are one variant • Docking counts by position • Cell-colored matrices? • More commonly used for microarray data and correlation matrices

  7. Graphical Encoding Ideas:Use Points For M-Mers • Represent m-mers using coordinates • A point stands for an m-mer • A glyph at the point represents statistics for that m-mer. For example point color, size, shape • Challenge • The domain of all letter sequences is exponential in sequence length • Display space is limited

  8. Self-Similar Coordinates • Self-similarity helps us keep oriented • Parallel coordinate plots are increasingly familiar • Coordinates from 3-D geometry • 4 Nucleotides => tetrahedron • 20 Amino acids • Icosahedron face centers • Familiar coordinates => hemisphere • Two kinds of self-similarity • At different scales => fractals • At the same scale => shells, surfaces

  9. Self-Similarity At Different Scales:Nucleotide Example • Represent each 6-mer as a 3-D point • (4 nucleotides)6 = 4096 points • Attractor: tetrahedron vertices • A=(1,1,1), C=(1,-1,-1), G=(-1,1,-1), T=(-1,-1,1) • Computation: • Hexamer position weights: 2^(5,4,3,2,1,0)/63 • ACGTTC -> (.555, .270, .206)

  10. Application:Gene Regulation Studies • Cluster genes based on • Gene expression levels in different situations • Other criteria such as gene family • For each cluster look in gene regulation regions for recurrent nucleotide patterns • Over expressed m-mers: potential transcription factor docking sites • Show frequencies (or multinomial likelihoods)

  11. Sliding hexamer window 300 letters upstream from open reading frames 300 ATATGA 299 TATGAG 298 ATGAGT 297 TGAGTA 29 Genes in a cluster YBL072c YDL130w YDR025w … YCL054w Nucleotides ExampleYeast Gene Regulation

  12. Statistics • Number of genes with hexamer • TTTTTC 22 • GAAAAA 21 • TTTTTT 19 • AAAAAT 19 • TTTTCA 18 • ATTTTT 17 • Total number of appearances, etc.

  13. Extensions • 2-D version (projected gasket) • 10mers => 1024 x 1024 pixel display • Wild card and dimer counts • TACC……GGAA • Include more scientific knowledge • Special representations for known transcription factors • More interactivity • Filtering for regions upstream • Mouseovers, etc.

  14. Self-Similarity At Different Scales:Amino Acids Sequence Coordinates • Represent each 3-mer as a 3-D point • (20 amino acids)3 = 8000 points • Attractor: icosahedron face centers • Let x1= .539, x2=.873, x3=1.412 • A=(x1,x3,0), C=(0,x1,x3), … Y=(-x3,0,-x1) • Computation Position weights: 3.8(2,1,0) scaled to sum to 1. Letters HIT => (-1.26, -1.08, .180)

  15. Graphical Encoding Ideas: Paths • Use paths connecting m-mer points to represent longer sequences • Path features, thickness and color can encode statistics indexed by the concatenated m-mers • Can reuse the m-mers keeping a common framework • 3 3-mers -> two segment path -> 9 mer • Challenges • Overplotting, path ambiguity, prime sequence lengths • Using translucent triangles for triples is poor, etc.

  16. Letter x Position Coordinates And Paths • Merits • Few points and simple structure • 20 amino acids by 9 positions = 180 points • Challenges • Path overplotting =>filtering • Avoiding path interpretation ambiguity in higher dimensional tables => 3-D layouts

  17. Self-Similarity At The Same Scale:Amino Acids Coordinates • Each point represents a letter and position pair • 9-mers: 20 letter x 9 positions = 180 points • Geometry: icosahedron face centers • Let x1= .539, x2=.873, x3=1.412 • A=(x1,x3,0), C=(0,x1,x3), … Y=(-x3,0,-x1) • Use scale factor for a given position • Scale factors for 9-mers: 2.2, 2.4, 2.6, …, 3.6 • A1 => 2.2*(x1,x3,0) C2=>2.4*(0,x1,x3) • Problem: overplotting of paths

  18. Self-Similarity At The Same Scale:Amino Acids Example • Each point represents a letter and position pair • 9-mers: 20 letter x 9 positions = 180 points • Geometry: hemisphere • Amino acid: longitude, Position: latitude • Amino acid ordering • Group by chemical properties: hydrophobic, etc. • Order to minimize path length in given application • Include gaps for perceptual grouping • Path overplotting still a problem, need filtering

  19. Peptide Docking Example • Immune system molecules combine with peptides to form a complex recognized by T-cell receptors • Problems: • Failure to dock foreign peptides • Docking with “self” peptides • Molecule specific databases of docking peptides • MHCPEP 1997, Brusic, Rudy, and Harrison • Human leukocyte antigen (HLA) A2, class 1 molecule • Small: about 500 peptides of 209 = ½ trillion possibilities • Mostly 9-mers (483) • Positions related to asymmetric docking groove

  20. Peptide Docking Interests • Which amino acids appear in which position? • Characterize the space of • docking, not-docking, unknown • Prediction of unknowns • Focused questions • Is there a docking peptide in a key protein common to all 23 HIV strains?

  21. Docking Statistics Number of the 483 peptides with the amino acid in position 2 M Q P S T F V A L G I K R H E D C W N Y 45 4 1 1 23 2 16 14 294 1 71 5 2 0 2 1 1 0 0 1 Cells from the collection of all 4-position tables: 126 tables of potentially 204 = 160000 cells each G4 F5 V6 F7: 35 L2 A7 A8 V9: 29 …

  22. Graphics Software • GLISTEN • Geometric Letter-Indexed Statistical Table Encoding • Swap out coordinates at will with tables unchanged • NSF research: second generation version in progress • Available partial alternatives • CrystalVision ftp://www.galaxy.gmu.edu/pub/software/ • Ggobi www.ggobi.org/download.html

  23. Hemisphere Plot Versus Parallel Coordinate Plots • PC plots are • Better for the many scientists preferring flatland • Straight forward to publish • Ambiguous when connecting non-adjacent axes • Hemisphere plots • 3-D curvature reduces line ambiguity and provides a general framework for tables involving non-adjacent positions • 3-D provides more neighbor options to group amino acids based on chemical properties: non-polar, etc.

  24. Closing Remarks • Docking applications are still evolving • New procedures for inference and better databases • Graphics still need work • More scientific structure • Work on cognitive optimization • GLISTEN can address many other applications

  25. Graphics Reference • Lee, et al. 2002, “The Next Frontier for Bio- an Cheminformatics Visualization,” IEEE Computer Graphics and Applications, Sept/Oct pp,. 6-11.

  26. Relate Scientific References (1) Spellmen, et al. 1998. “Comprehensive Identification of Cell Cycle-regulated Gened of the Yeast Saccharomyces cervisiae by Microarray Hybridization,” Molecular Biology of the Cell. Vol 9, pp. 3273-3297. Keles, van der Laan, and Eisen. 2002. “Identification of regulatory elements using a feature selection method.” Bioinformatics, Vol. 18. No 9. pp1167-1175.

  27. Related Scientific References (2) • Segal Cummings and Hubbard. 2001. “Relating Amino Acid Sequences to Phenotypes: Analysis of Peptide-Binding Data,” Biometrics 57, pp. 632-643.

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