2-D and 3-D Coordinates For M-Mers And

Dynamic Graphics For Representing Associated Statistics

By

Daniel B. Carr

dcarr@gmu.eduGeorge 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.