The document proposes new tools for analyzing HIV-1 sequences clinically using geometric representations of DNA sequences called W-curves and clustering sequences using the Traveling Salesman Problem. The existing tools for analyzing HIV sequences make assumptions that do not apply to HIV and are not suitable for clinical analysis. The W-curve represents DNA as a geometric curve in 3D space, allowing alignment and comparison without assumptions. Clustering sequences using the TSP problem groups similar sequences and can identify progression towards drug resistance over time.

1. Douglas Cork
Steven Lembark

2. HIV­1, W­curves, & Shoe Leather
● Existing genetics tools fail on HIV­1
● They make assumptions based on “normal” DNA
that fail on HIV – or cancer, or plants.
● Correlation tools look at evolution, not state.
● We are working on tools for clinical analysis.
● The W­curve abstracts DNA into geometry.
● The TSP clusters genenes rather than trying to
impute inheritence.

3. Sequences Inform Treatment
● Treating HIV requires sequencing it to choose
appropriate drugs:
● HIV­1 evolves drug resistence in months.
● Multiple strains in a single pateint are common,
both from multiple sources or evolution.
● Crossover recombination relatively common due to
cross­infected cells.

4. Problem: HIV is Hard to Analyze
● HIV is a non­correcting retrovirus.
● Evolves 10,000 times faster than humans or
influenza – one new strain per patient per day.
● Genomes for wild types range from 8349 to
9829 bases, making localized comparisions
difficult.
● The single FDA approved algorithm directing
treatment from sequence handles only type­B;
the U.S. Army has 15%+ non­B infections.

5. The Current Tools
● Blast, Fasta, ClustalW perform alignment.
● Table­driven analysis of base transitions.
● Score the entire sequence with a single value.
● Graphical tools are designed to display
inheritence rather than state.
● Output is difficult to read in a clinical setting.

6. Phenogram of Drug­
Resistant and Random
Samples
● Tries to show ancestory,
not state.
● Not very good for visual
identification of which
patients are drug
resistant.

7. Trees are not particularly
helpful either.

8. HIVHXB2CG TGATCTGTAGTGCTACAGAAAAATTGTGGGTCACAGTCTATTATGGGGTACCTGTGTGGA
AY736838-gp120_ -------------------------------TACAGTTTATTATGGGGTGCCTGTGTGGA
***** *********** **********
HIVHXB2CG AGGAAGCAACCACCACTCTATTTTGTGCATCAGATGCTAAAGCATATGATACAGAGGTAC
AY736838-gp120_ GAGATGCAGATACCACCCTATTTTGTGCATCAGATGCCAAGGCACATGAGACAGAAGTGC
ClustalW of gp120
** *** ***** ******************** ** *** **** ***** ** *
HIVHXB2CG ATAATGTTTGGGCCACACATGCCTGTGTACCCACAGACCCCAACCCACAAGAAGTAGTAT
AY736838-gp120_ ACAATGTCTGGGCCACACATGCCTGTGTACCCACAGACCCCAACCCACAAGAAATACACC
* ***** ********************************************* **
HIVHXB2CG TGGTAAATGTGACAGAAAATTTTAACATGTGGAAAAATGACATGGTAGAACAGATGCATG
AY736838-gp120_ TGGAAAATGTAACAGAAAATTTTAACATGTGGAAAAATAACATGGTAGAGCAGATGCAGG
*** ****** *************************** ********** ******** *
HIVHXB2CG AGGATATAATCAGTTTATGGGATCAAAGCCTAAAGCCATGTGTAAAATTAACCCCACTCT
AY736838-gp120_ AGGATGTAATCAGTTTATGGGATCAAAGTCTAAAGCCATGTGTAAAGTTAACTCCTCTCT
***** ********************** ***************** ***** ** ****
Difficult to compare
HIVHXB2CG GTGTTAGTTTAAAGTGCAC------TGATTTGAAGAATGATACTAATACCAATAGTAGTA
AY736838-gp120_ GCGTTACTTTAAATTGTACCAATGCTAATTTGACCAATGGCAGTAGCAAAACCAATGTCT
● * **** ****** ** ** * ****** **** * ** * * * *
HIVHXB2CG GCGGGAGAATGATAATGGAGAAAGGAGAGATAAAAAACTGCTCTTTCAATATCAGCACAA
AY736838-gp120_ CTAACATAATAGGAAATATAACAGATGAAGTAAGAAACTGTACTTTTAATATGACCACAG
sequences vis.ually.
* *** ** * ** ** *** ****** **** ***** * ****
HIVHXB2CG GCATAAGAGGTAAGGTGCAGAAAGAATATGCATTTTT
TTATAAACTTGATATAATACCAA
AY736838-gp120_ AACTAACAGATAAGAAGCAGAAGGTCCATGCACTCTTTTATAAGCTTGATATAGTACAAA
*** ** **** ****** * ***** * ******** ********* *** **
● Not useful for large HIVHXB2CG
AY736838-gp120_
HIVHXB2CG
T---AGATAATGATACTACCAGC---TATAAGTTGACAAGTTGTAACACCTCAGTCATTA
TTGAAGATAAGAAGAATAGTAGTGAGTATAGGTTAATAAATTGTAATACTTCAGTCATTA
* ****** * * ** ** **** *** * ** ****** ** **********
CACAGGCCTGTCCAAAGGTATCCTTTGAGCCAATTCCCATACATTATTGTGCCCCGGCTG
numbers of
AY736838-gp120_ AGCAGGCTTGTCCAAAGATATCCTTTGATCCAATTCCTATACATTATTGTACTCCAGCTG
***** ********* ********** ******** ************ * ** ****
HIVHXB2CG GTTTTGCGATTCTAAAATGTAATAATAAGACGTTCAATGGAACAGGACCATGTACAAATG
AY736838-gp120_ GTTATGCGATTTTAAAGTGTAATGATAAGAATTTCAATGGGACAGGGCCATGTAAAAATG
sequences.
*** ******* **** ****** ****** ******** ***** ******* *****
HIVHXB2CG TCAGCACAGTACAATGTACACATGGAATTAGGCCAGTAGTATCAACTCAACTGCTGTTAA
AY736838-gp120_ TCAGCTCAGTACAATGCACACATGGAATTAAGCCAGTGGTATCAACTCAATTGCTGTTAA
***** ********** ************* ****** ************ *********
HIVHXB2CG ATGGCAGTCTAGCAGAAGAAGAGGTAGTAATTAGATCTGTCAATTTCACGGACAATGCTA
AY736838-gp120_ ATGGCAGTCTAGCAGAAGAAGAGATAATAATCAGATCTGAAGATCTCACAAACAATGCCA
Gaps make analysis
*********************** ** **** ******* ** **** ******* *
HIVHXB2CG AAACCATAATAGTACAGCTGAACACATCTGTAGAAATTAATTGTACAAGACCCAACAACA
● AY736838-gp120_ AAACCATAATAGTGCACCTTAATAAATCTGTAGAAATCAATTGTACCAGACCCTCCAACA
************* ** ** ** * ************ ******** ****** *****
HIVHXB2CG ATACAAGAAAAAGAATCCGTATCCAGAGAGGACCAGGGAGAGCATTTGTTACAATAGGAA
difficult AY736838-gp120_
HIVHXB2CG
AY736838-gp120_
ATACAAGAACAAGTATAACTAT------AGGACCAGGACGAGTATTCTATAGAACAGGAG
********* *** ** *** ********* *** *** ** ** ****
A---AATAGGAAATATGAGACAAGCACATTGTAACATTAGTAGAGCAAAATGGAATAACA
ATATAATAGGAAATATAAGAAAAGCATATTGTGAGATTAATGGAACAAAATGGAATAAAG
* ************ *** ***** ***** * **** * ** *************
HIVHXB2CG CTTTAAAACAGATAGCTAGCAAATTAAGAGAACAATTTGGAAATAATAAAACAATAATCT
AY736838-gp120_ TTTTAAAACAGGTAACTGAAAAATTAAAAGAGCACTTT------AATAAGACAATAATCT
********** ** ** ******* *** ** *** ***** **********
HIVHXB2CG TTAAGCAATCCTCAGGAGGGGACCCAGAAATTGTAACGCACAGTTTTAATTGTGGAGGGG
AY736838-gp120_ TTCAACCACCCTCAGGAGGAGATCTAGAAATTACAATGCATCATTTTAATTGTAGAGGGG
** * * * ********** ** * ******* ** *** ********** ******
HIVHXB2CG AATTTTTCTACTGTAATTCAACACAACTGTTTAATAGTACTTGGTTTAATAGTACTTGGA
AY736838-gp120_ AATTTTTCTATTGCAATACAACAAAACTGTTTAATAATATTTGCCTAGGAAATG---AAA
********** ** *** ***** ************ ** *** * * * *
HIVHXB2CG GTACTGAAGGGTCAAATAACACTGAAGGAAGTGACACAATCACCCTCCCATGCAGAATAA
AY736838-gp120_ CCATGGCGGGGTGTAATGACACT---------------ATCACACTTCCATGCAAGATAA
* * **** *** ***** ***** ** ******* ****

9. New Tools
● Clinical vs. evolutionary.
● Avoid assumptions that break current tools.
● Suitable for a repeatable process in clinics or
data mining in research.
● We are using:
● W­curve for analysis.
● TSP for clustering.
● R for data management & display.

10. W­curve
● Geometric abstraction of DNA.
● Manufactured by a simple state machine.
● Alignment at finer scale available using
geometry than character strings.
● Avoids assumptions about transition
probabilities by taking the figure as­is.

11. W­Curve Generator is a State Machine
● C,A,T,G are assigned to corners of a square.
● Successive points move halfway to the next
base's corner.

12. W­curve for “CG”
● Curve shown
in Blue.
● Halfway to C
then G in
X‑Y, single
steps in Z.
● Cyl. storage
simplifies
comparision.

13. W­curve of Wild HIV­1 POL Gene
W­curve of Wild HIV­1 POL

14. W­curves of Wild & Drug Resistant Pol

15. Detail of Wild & Drug Resistant Pol

16. Distance Metric
● Bases are arranged in
square to minimize
effects of SNP's.
● Synonymous SNP's
are usually in the
same quadrant.
● Points within same
quadrant have small
difference, opposite
quad's get larger.

17. Comparison Produces “Chunks”
● Comparison yields a list of chunks.
● Curves are aligned within the chunk.
● Summing chunks gives single value two curves.
● Analyzing them in detail allows mining local
similarities and variations.
● Grouping allows examination of crossover­
recombination events.

18. Clustering: Traveling Salesman Problem
● The TSP is simple to describe, hard to solve:
● Starting and finishing in the same city.
● Visit a list of cities once each.
● Minimize the distance (cost).
● Optimal solutions will cluster the nearby cities.
● The problem was always in defining the
clusters.

19. Take a Walk and Cluster Your Genes
● Climer & Zhang, 2004.
● Method for detecting N clusters:
● Add N dummy cities to the distance map.
● Each one has the same, small distance to all other
cities (we use 2­20).
● Dummy cities end up in the inter­cluster gaps.
● The process is trivial to implement: just add that
many rows and columns to the original
comparison matrix.

20. Displaying the Tour
● Mapping the tour onto a circle gives a good
view of the distances.
● Coloring simplifies inspection.
● Black dots for dummy cities.
● Single type at the top (e.g. wild type).
● Color successive data points using the “rainbow”
sequence with a large number of colors.
● Sequences more alike get more similar colors.

23. Example with 8 D­R, 100 Samples

24. Multiple uses for color sequence.
● Track individual over time.
● Progression through colors shows history.
● Clustering highlights progression towards drug
resistance.
● Track sample population.
● Recycling the colors from one initial tour helps show
changes in successive graphs.
● Simplifies tracking progression in anonymous
populations found in HIV treatment centers.

25. Visualizing W­curves
● We use a WebGL­based package “WebCurve”.
● Developed at IIT as a web­friendly solution for
examining 3D geometry.
● Gracefully handles displaying 100+ sequences
at 10K bases each on a notebook computer.
● Available from github, archive includes a web
server and code to generate files for display.

26. Summary
● W­curve and TSP allow us to cluster genes.
● Provides a more useful output in a clinical
setting.
● Color coding the TSP results allows tracking
changes in a population or progression an
individual over time.