1. Of Sea Urchins, Birds and Men

2. Introduction
SNPs, HAPLOTYPES

3. Genome Assembly (Ch. 5) Hidden Markov Models (Ch
Genome Assembly (Ch. 5) Hidden Markov Models (Ch. 4) Phylogenetic Trees (Ch. 3) Sequence Alignment (Ch. 1)

4. Single Nucleotide Polymorphism (SNP)
GATTTAGATCGCGATAGAG
GATTTAGATCTCGATAGAG
A SNP is a position in a genome at which two or more different bases occur in the population, each with a frequency >1%.
The most abundant type of polymorphism
The two alleles at the site are G and T

5. Human Genome contains ~ 3 G basepairs arranged in 46 chromosomes.
tttctccatttgtcgtgacacctttgttgacaccttcatttctgcattctcaattctatttcactggtctatggcagagaacacaaaatatggccagtggcctaaatccagcctactaccttttttttttttttgtaacattttactaacatagccattcccatgtgtttccatgtgtctgggctgcttttgcactctaatggcagagttaagaaattgtagcagagaccacaatgcctcaaatatttactctacagccctttataaaaacagtgtgccaactcctgatttatgaacttatcattatgtcaataccatactgtctttattactgtagttttataagtcatgacatcagataatgtaaatcctccaactttgtttttaatcaaaagtgttttggccatcctagatatactttgtattgccacataaatttgaagatcagcctgtcagtgtctacaaaatagcatgctaggattttgatagggattgtgtagaatctatagattaattagaggagaatgactatcttgacaatactgctgcccctctgtattcgtgggggattggttccacaacaacacccaccccccactcggcaacccctgaaacccccacatcccccagcttttttcccctgctaccaaaatccatggatgctcaagtccatataaaatgccatactatttgcatataacctctgcaatcctcccctatagtttagatcatctctagattacttataatactaataaaatctaaatgctatgtaaatagttgctatactgtgttgagggttttttgttttgttttgttttatttgtttgtttgtttgtattttaagagatggtgtcttgctttgttgcccaggctggagtgcagtggtgagatcatagcttactgcagcctcaaactcctggactcaaacagtcctcccacctcagcctcccaaagtgctgggatacaggtgtgacccactgtgcccagttattattttttatttgtattattttactgttgtattatttttaattattttttctgaatattttccatctatagttggttgaatcatggatgtggaacaggcaaatatggagggctaactgtattgcatcttccagttcatgagtatgcagtctctctgtttatttaaagttttagtttttctcaaccatgtttacttttcagtatacaagactttgacgttttttgttaaatgtatttgtaagtattttattatttgtgatgttatttaaaaagaaattgttgactgggcacagtggctcacgcctgtaatcccagcactttgggaggctgaggcgggcagatcacgaggtcaggagatcaagaccatcctggctaacatggtaaaaccccgtctctactaaaaatagaaaaaaattagccaggcgtggtggcgagtgcctgtagtcccagctactcgggaggctgaggcaggagaatggtgtgaacctgggaggcggagcttgcagtgagctgagatcgtgccactgcattccagcctgcgtgacagagcgagactctgtcaaaaaaataaataaaatttaaaaaaagaagaagaaattattttcttaatttcattttcaggttttttatttatttctactatatggatacatgattgatttttgtatattgatcatgtatcctgcaaactagctaacatagtttattatttctctttttttgtggattttaaaggattttctacatagataaataaacacacataaacagttttacttctttcttttcaacctagactggatgcattttttgtttttgtttgtttgtttgctttttaacttgctgcagtgactagagaatgtattgaagaatatattgttgaacaaaagcagtgagagtggacatccctgctttccccctgattttagggggaatgttttcagtctttcactatttaatatgattttagctataggtttatcctagatccctgttatcatgttgaggaaattcccttctatttctagtttgttgagattttttaattcatgtgattgcgctatctggctttgctctca g c t a t c g a g a c
Human Genome contains ~ 3 G basepairs arranged in 46 chromosomes.
Two individuals are 99.9% the same. I.e. differ in ~ 3 M basepairs.
SNPs occur once every ~600 bp
Average gene in the human
genome spans ~27Kb
~50 SNPs per gene

6. C A G T T G G C T C G A C A A C A G G T T C G T C A A C A G
Haplotype
C A G
Haplotypes
T T G
G C T C G A C A A C A G
G T T C G T C A A C A G
SNP
SNP
SNP
Two individuals

7. Mutations
Infinite Sites Assumption:
Each site mutates at most once

8. Haplotype Pattern C A G T T T G A C A T G C T G T 0 0 0 0 1 1 0 1
At each SNP site label the two alleles as 0 and 1.
The choice which allele is 0 and which one is 1
is arbitrary.

9. Recombination
G T T C G A C A A C A T
A C G T A T C T A T T A
G T T C G A C T A T T A

10. Recombination G T T C G A C A A C A T A C G T A T C T A T T A
The two alleles are linked, I.e.,
they are “traveling together”
G T T C G A C A A C A T
A C G T A T C T A T T A
Recombination
disrupts the linkage ?
G T T C G A C T A T T A

11. Linkage Disequilibrium (LD)
Common Ancestor
Emergence of Variations Over Time
time
present
Variations in Chromosomes Within a Population
Disease Mutation

12. Extent of Linkage Disequilibrium
2,000 gens. ago
Disease-Causing Mutation
1,000 gens. ago
Time = present

13. A Data Compression Problem
Select SNPs to use in an association study
Would like to associate single nucleotide polymorphisms (SNPs) with disease.
Very large number of candidate SNPs
Chromosome wide studies, whole genome-scans
For cost effectiveness, select only a subset.
Closely spaced SNPs are highly correlated
It is less likely that there has been a recombination between two SNPs if they are close to each other.
Goal of talk
Want to study genomic variation, the particular type of variations we are interested in are single nucleotide polymorphisms.
This may be useful for instance when one is doing an association study – will be implemented as a part of Applera assays on Demand and iScience initiatives.
A large number of SNPs are known to exists, when one does an association study one would like to minimize the cost of doing the study. Selecting only a subset of the informative set of SNPs
We are considering the case when there is a large number of SNPs to use for our study, such as when doing chromosomal wide or genomewide scans. For practical reasons, such as costeffictiveness we would like to limit the number of SNPs that we use. The main guidance that we have in this pursuit is the fact that closely spaced SNPs are highly correleated.

14. Disease Associations

15. Marker A is associated with Phenotype
Association studies
Disease
Responder
Control
Non-responder
Allele 0
Allele 1
Marker A is associated with Phenotype
Marker A:
Allele 0 =
Allele 1 =

16. Association studies T A G C
Evaluate whether nucleotide polymorphisms associate with phenotype T A G C
Spend a lot of time on this slide

17. Association studies C G A C G T A T A G T A C G T G A T G A
Spend a lot of time on this slide T A C G T G A T G A

18. Association studies 1 1
Spend a lot of time on this slide 1 1 1

19. Real Haplotype Data A region of Chr. 22 45 Caucasian samples
We see that in this region has significant overlap in blocks
Our block-free algorithm
Two different runs of the Gabriel el al Block Detection method +
Zhang et al SNP selection algorithm

20. A Data Compression Problem
The Minimum Informative Subset

21. A Data Compression Problem
Select SNPs to use in an association study
Would like to associate single nucleotide polymorphisms (SNPs) with disease.
Very large number of candidate SNPs
Chromosome wide studies, whole genome-scans
For cost effectiveness, select only a subset.
Closely spaced SNPs are highly correlated
It is less likely that there has been a recombination between two SNPs if they are close to each other.
Goal of talk
Want to study genomic variation, the particular type of variations we are interested in are single nucleotide polymorphisms.
This may be useful for instance when one is doing an association study – will be implemented as a part of Applera assays on Demand and iScience initiatives.
A large number of SNPs are known to exists, when one does an association study one would like to minimize the cost of doing the study. Selecting only a subset of the informative set of SNPs
We are considering the case when there is a large number of SNPs to use for our study, such as when doing chromosomal wide or genomewide scans. For practical reasons, such as costeffictiveness we would like to limit the number of SNPs that we use. The main guidance that we have in this pursuit is the fact that closely spaced SNPs are highly correleated.

22. Marker A is associated with Phenotype
Association studies
Disease
Responder
Control
Non-responder
Allele 0
Allele 1
Marker A is associated with Phenotype
Marker A:
Allele 0 =
Allele 1 =

23. Association studies T A G C
Evaluate whether nucleotide polymorphisms associate with phenotype T A G C
Spend a lot of time on this slide

24. Association studies C G A C G T A T A G T A C G T G A T G A
Spend a lot of time on this slide T A C G T G A T G A

25. Hypothesis – Haplotype Blocks?
The genome consists largely of blocks of
common SNPs with relatively little recombination
within the blocks
Patil et al., Science, 2001;
Jeffreys et al., Nature Genetics, 2001;
Daly et al., Nature Genetics, 2001

26. Haplotype Block Structure LD-Blocks, and 4-Gamete Test Blocks
200 kb
Sense genes
DNA
Antisense genes
SNPs
Haplotype
blocks 1 2 3 4

27. Dynamic programming framework
Partitioning a chromosome into blocks
Zhang et al. (PNAS, 2002).
Zhang et al. RECOMB, 2003
H. I. Avi-Itzhak et al. PSB, 2003
Sebastiani et al. PNAS 2003
Patil et al., PNAS 2002.
Parametric in block test
Solve a dynamic program
Optimal block partition requires
the minimal number of blocks.
Within blocks one can select the SNPs
that maximize entropy, diversity or
r2 correlation

28. Data Compression A------A---TG-- ACGATCGATCATGAT G------G---CG--
A------G---TC--
A------G---CC--
G------A---TG--
ACGATCGATCATGAT
GGTGATTGCATCGAT
ACGATCGGGCTTCCG
ACGATCGGCATCCCG
GGTGATTATCATGAT
Given this definition we can select one tagging SNP for the first block, two for the second and one for the third
Given the value of the tagging SNPs the value of all the other SNPs can be predicted. Hence it suffices only to type only the tagging SNPs in order to infer all the haplotype blocks.
Alternate objective functions exists so as to capture a significant fraction of the information.
Selecting Tagging SNPs in blocks
Haplotype Blocks based on LD
(Method of Gabriel et al.2002)

29. Informativeness 1 1 1 1 I({s1,s2}, s4) = 3/4 s1 s2 s3 s4 s51
I({s1,s2}, s4) = 3/4 1
Spend a lot of time on this slide 1 1
s s s s s5

30. Informativeness 1 1 1 1 I({s3,s4},{s1,s2,s5}) = 31
I({s3,s4},{s1,s2,s5}) = 3 1
Spend a lot of time on this slide 1
S={s3,s4} is a Minimal Informative Subset 1
s s s s s5

31. Informativeness Edges SNPs Graph theory insight
Minimum Set Cover = Minimum Informative Subset e4 s4 e3 s3 1 s1 s2 s3 s4 s5 s2 e2
Spend a lot of time on this slide s1 e1
Edges
SNPs

32. Informativeness SNPs Edges Graph theory insight
Minimum Set Cover {s3, s4} = Minimum Informative Subset e4 s4 e3 s3 1 s1 s2 s3 s4 s5 s2 e2
Spend a lot of time on this slide s1 e1
SNPs
Edges