2-D and 3-D Coordinates For M-Mers And Dynamic Graphics For - - PowerPoint PPT Presentation

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

– 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

A C D E F G H I K L M N P Q R S T V W Y 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 Molecule Peptide 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

• pen reading frames

– 300 ATATGA – 299 TATGAG – 298 ATGAGT – 297 TGAGTA

Nucleotides Example Yeast 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)

• Computation

Position 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.