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2-D and 3-D Coordinates For M-Mers And Dynamic Graphics For Representing Associated Statistics. By Daniel B. Carr [email protected] George Mason University. Overview. Background Encoding and self-similar coordinates Examples Rendering software – GLISTEN Closing remarks. Background. Task - PowerPoint PPT Presentation
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2-D and 3-D Coordinates For M-Mers And
Dynamic Graphics For Representing Associated Statistics
By
Daniel B. Carr
[email protected] Mason University
Overview
• Background
• Encoding and self-similar coordinates
• Examples
• Rendering software – GLISTEN
• Closing remarks
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
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
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
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
ACDE
FGHI
KLMN
PQRS
TVWY
Pos 1
50
Pos 2
50 150 250
Pos 3
50
Pos 4
50
Pos 5
50
Pos 6
50
Pos 7
50
Pos 8
50
Pos 9
50 150
HLA-A2 MoleculePeptide Docking Counts By Amino Acid Given Position
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
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
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)
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)
Sliding hexamer window 300 letters upstream from open reading frames– 300 ATATGA
– 299 TATGAG
– 298 ATGAGT
– 297 TGAGTA
Nucleotides ExampleYeast Gene Regulation
29 Genes in a cluster– YBL072c
– YDL130w
– YDR025w
– …
– YCL054w
Statistics
• Number of genes with hexamer– TTTTTC 22– GAAAAA 21– TTTTTT 19– AAAAAT 19– TTTTCA 18– ATTTTT 17
• Total number of appearances, etc.
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.
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)
• ComputationPosition weights: 3.8(2,1,0) scaled to sum to 1. Letters HIT => (-1.26, -1.08, .180)
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.
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
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
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
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
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?
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 …
Docking Statistics
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
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.
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
Graphics Reference
• Lee, et al. 2002, “The Next Frontier for Bio- an Cheminformatics Visualization,” IEEE Computer Graphics and Applications, Sept/Oct pp,. 6-11.
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.
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.