1. The informatics of SNPs and haplotypes Gabor T. Marth Department of Biology, Boston College marth@bc.edu Cold Spring Harbor Laboratory Advanced Bioinformatics course October 17, 2005

2. Why do we care about variations? underlie phenotypic differences cause inherited diseases allow tracking ancestral human history

3. How do we find sequence variations? look at multiple sequences from the same genome region use base quality values to decide if mismatches are true polymorphisms or sequencing errors

4. Steps of SNP discovery Sequence clustering Cluster refinement Multiple alignment SNP detection

5. Computational SNP mining – PolyBayes 2. Use sequence quality information (base quality values) to distinguish true mismatches from sequencing errors sequencing errortrue polymorphism 1. Utilize the genome reference sequence as a template to organize other sequence fragments from arbitrary sources Two innovative ideas:

6. SNP mining steps – PolyBayes sequence clustering simplifies to database search with genome reference paralog filtering by counting mismatches weighed by quality values multiple alignment by anchoring fragments to genome reference SNP detection by differentiating true polymorphism from sequencing error using quality values

7. genome reference sequence 1. Fragment recruitment (database search) 2. Anchored alignment 3. Paralog identification 4. SNP detection SNP discovery with PolyBayes

8. Polymorphism discovery SW Marth et al. Nature Genetics 1999

9. Genotyping by sequence SNP discovery usually deals with single-stranded (clonal) sequences It is often necessary to determine the allele state of individuals at known polymorphic locations Genotyping usually involves double-stranded DNA  the possibility of heterozygosity exists there is no unique underlying nucleotide, no meaningful base quality value, hence statistical methods of SNP discovery do not apply

10. Het detection = Diploid base calling Homozygous T Homozygous C Heterozygous C/T Automated detection of heterozygous positions in diploid individual samples (visit Aaron Quinlan’s poster)

11. Large SNP mining projects Sachidanandam et al. Nature 2001 ~ 8 million EST WGS BAC genome reference

12. Variation structure is heterogeneous chromosomal averages polymorphism density along chromosomes

13. What explains nucleotide diversity? G+C nucleotide content CpG di-nucleotide content recombination rate functional constraints 3’ UTR5.00 x 10 -4 5’ UTR4.95 x 10 -4 Exon, overall4.20 x 10 -4 Exon, coding3.77 x 10 -4 synonymous 366 / 653 non-synonymous287 / 653 Variance is so high that these quantities are poor predictors of nucleotide diversity in local regions hence random processes are likely to govern the basic shape of the genome variation landscape  (random) genetic drift

14. Where do variations come from? sequence variations are the result of mutation events TAAAAAT TAACAAT TAAAAAT TAACAAT TAAAAATTAACAAT TAAAAAT MRCA mutations are propagated down through generations and determine present-day variation patterns

15. Neutrality vs. selection selective mutations influence the genealogy itself; in the case of neutral mutations the processes of mutation and genealogy are decoupled functional constraints 3’ UTR5.00 x 10 -4 5’ UTR4.95 x 10 -4 Exon, overall4.20 x 10 -4 Exon, coding3.77 x 10 -4 synonymous 366 / 653 non-synonymous287 / 653 the genome shows signals of selection but on the genome scale, neutral effects dominate

16. Mutation rate accgttatgtaga accgctatgtaga MRCA actgttatgtaga accgctatataga MRCA higher mutation rate (µ) gives rise to more SNPS there is evidence for regional differences in observed mutation rates in the genome CpG content SNP density

17. Long-term demography small (effective) population size N large (effective) population size N different world populations have varying long-term effective population sizes (e.g. African N is larger than European)

18. Population subdivision unique shared geographically subdivided populations will have differences between their respective variation structures

19. Recombination acggttatgtaga accgttatgtaga acggttatgtaga accgttatgtaga acggttatgtaga

20. Recombination acggttatgtaga accgttatgtaga acggttatgtaga accgttatgtaga recombination has a crucial effect on the association between different alleles

21. Modeling genetic drift: Genealogy present generation randomly mating population, genealogy evolves in a non- deterministic fashion

22. Modeling genetic drift: Mutation mutation randomly “drift”: die out, go to higher frequency or get fixed

23. Modulators: Natural selection negative (purifying) selection positive selection the genealogy is no longer independent of (and hence cannot be decoupled from) the mutation process

24. Modeling ancestral processes “forward simulations” the “Coalescent” process By focusing on a small sample, complexity of the relevant part of the ancestral process is greatly reduced. There are, however, limitations.

25. Models of demographic history past present stationaryexpansioncollapse MD (simulation) AFS (direct form) history bottleneck

26. 1. marker density (MD): distribution of number of SNPs in pairs of sequences Data: polymorphism distributions “rare” “common” 2. allele frequency spectrum (AFS): distribution of SNPs according to allele frequency in a set of samples Clone 1 Clone 2# SNPs AL00675AL009828 AS81034AK430010 CB00341AL432342 SNPMinor alleleAllele count A/GA1 C/TT9 A/GG3

27. Model: processes that generate SNPs computable formulations simulation procedures 3/5 1/52/5

28. Models of demographic history past present stationaryexpansioncollapse MD (simulation) AFS (direct form) history bottleneck

29. best model is a bottleneck shaped population size history present N 1 =6,000 T 1 =1,200 gen. N 2 =5,000 T 2 =400 gen. N 3 =11,000 Data fitting: marker density Marth et al. PNAS 2003 our conclusions from the marker density data are confounded by the unknown ethnicity of the public genome sequence we looked at allele frequency data from ethnically defined samples

30. present N1=20,000 T1=3,000 gen. N2=2,000 T2=400 gen. N3=10,000 model consensus: bottleneck Data fitting: allele frequency Data from other populations?

31. Population specific demographic history European data African data bottleneck modest but uninterrupted expansion Marth et al. Genetics 2004

32. Model-based prediction computational model encapsulating what we know about the process genealogy + mutations allele structure arbitrary number of additional replicates

33. African dataEuropean data contribution of the past to alleles in various frequency classes average age of polymorphism Prediction – allele frequency and age

34. How to use markers to find disease?

35. Allelic association allelic association is the non- random assortment between alleles i.e. it measures how well knowledge of the allele state at one site permits prediction at another marker site functional site by necessity, the strength of allelic association is measured between markers significant allelic association between a marker and a functional site permits localization (mapping) even without having the functional site in our collection there are pair-wise and multi-locus measures of association

36. Linkage disequilibrium LD measures the deviation from random assortment of the alleles at a pair of polymorphic sites D=f( ) – f( ) x f( ) other measures of LD are derived from D, by e.g. normalizing according to allele frequencies (r 2 )

37. strong association: most chromosomes carry one of a few common haplotypes – reduced haplotype diversity Haplotype diversity the most useful multi-marker measures of associations are related to haplotype diversity 2 n possible haplotypesn markers random assortment of alleles at different sites

38. Haplotype blocks Daly et al. Nature Genetics 2001 experimental evidence for reduced haplotype diversity (mainly in European samples)

39. The promise for medical genetics CACTACCGA CACGACTAT TTGGCGTAT within blocks a small number of SNPs are sufficient to distinguish the few common haplotypes  significant marker reduction is possible if the block structure is a general feature of human variation structure, whole-genome association studies will be possible at a reduced genotyping cost this motivated the HapMap project Gibbs et al. Nature 2003

40. The HapMap initiative goal: to map out human allele and association structure of at the kilobase scale deliverables: a set of physical and informational reagents

41. HapMap physical reagents reference samples: 4 world populations, ~100 independent chromosomes from each SNPs: computational candidates where both alleles were seen in multiple chromosomes genotypes: high-accuracy assays from various platforms; fast public data release

42. Informational: haplotypes the problem: the substrate for genotyping is diploid, genomic DNA; phasing of alleles at multiple loci is in general not possible with certainty experimental methods of haplotype determination (single-chromosome isolation followed by whole-genome PCR amplification, radiation hybrids, somatic cell hybrids) are expensive and laborious A T C T G C C A

43. Haplotype inference Parsimony approach: minimize the number of different haplotypes that explains all diploid genotypes in the sample Clark Mol Biol Evol 1990 Maximum likelihood approach: estimate haplotype frequencies that are most likely to produce observed diploid genotypes Excoffier & Slatkin Mol Biol Evol 1995 Bayesian methods: estimate haplotypes based on the observed diploid genotypes and the a priori expectation of haplotype patterns informed by Population Genetics Stephens et al. AJHG 2001

44. Haplotype inference http://pga.gs.washington.edu/

45. Haplotype annotations – LD based Pair-wise LD-plots Wall & Pritchard Nature Rev Gen 2003 LD-based multi-marker block definitions requiring strong pair-wise LD between all pairs in block

46. Annotations – haplotype blocks Dynamic programming approach Zhang et al. AJHG 2001 333 1. meet block definition based on common haplotype requirements 2. within each block, determine the number of SNPs that distinguishes common haplotypes (htSNPs) 3. minimize the total number of htSNPs over complete region including all blocks

47. Haplotype tagging SNPs (htSNPs) Find groups of SNPs such that each possible pair is in strong LD (above threshold). Carlson AJHG 2005

48. Focal questions about the HapMap CEPH European samples 1. Required marker densityYoruban samples 4. How general the answers are to these questions among different human populations 2. How to quantify the strength of allelic association in genome region 3. How to choose tagging SNPs

49. Samples from a single population? (random 60-chromosome subsets of 120 CEPH chromosomes from 60 independent individuals)

50. Consequence for marker performance Markers selected based on the allele structure of the HapMap reference samples… … may not work well in another set of samples such as those used for a clinical study.

51. Sample-to-sample variability? 1. Understanding intrinsic properties of a given genome region, e.g. estimating local recombination rate from the HapMap data 3. It would be a desirable alternative to generate such additional sets with computational means McVean et al. Science 2004 2. Experimentally genotype additional sets of samples, and compare association structure across consecutive sets directly

52. Towards a marker selection tool 2. generate computational samples for this genome region 3. test the performance of markers across consecutive sets of computational samples 1. select markers (tag SNPs) with standard methods

53. Generating data-relevant haplotypes 1. Generate a pair of haplotype sets with Coalescent genealogies. This “models” that the two sets are “related” to each other by being drawn from a single population. 3. Use the second haplotype set induced by the same mutations as our computational samples. 2. Only accept the pair if the first set reproduces the observed haplotype structure of the HapMap reference samples. This enforces relevance to the observed genotype data in the specific region.

54. Generating computational samples Problem: The efficiency of generating data- relevant genealogies (and therefore additional sample sets) with standard Coalescent tools is very low even for modest sample size (N) and number of markers (M). Despite serious efforts with various approaches (e.g. importance sampling) efficient generation of such genealogies is an unsolved problem. N M We are developing a method to generate “approximative” M-marker haplotypes by composing consecutive, overlapping sets of data-relevant K-site haplotypes (for small K) Motivation from composite likelihood approaches to recombination rate estimation by Hudson, Clark, Wall, and others.

55. M-site haplotypes as composites of overlapping K-site haplotypes 1. generate K-site sets 2. build M-site composites M

56. Piecing together K-site sets 000 100 001 101 010 110 011 111 000 001 010 011 100 101 110 111 this should work to the degree to which the constraint at overlapping markers preserves long-range marker association

57. Building composite haplotypes A composite haplotype is built from a complete path through the (M-K+1) K-sites.

58. 3-site composite haplotypes a typical 3-site composite 30 CEPH HapMap reference individuals (60 chr) Hinds et al. Science, 2005

59. 3-site composite vs. data

60. 3-site composites: the “best case” “short-range” “long-range”

61. Variability across sets The purpose of the composite haplotypes sets … … is to model sample variance across consecutive data sets. But the variability across the composite haplotype sets is compounded by the inherent loss of long-range association when 3-sites are used.

62. 4-site composite haplotypes 4-site composite

63. “Best-case” 4 site composites Composite of exact 4-site sub-haplotypes

64. Variability across 4-site composites

65. … is comparable to the variability across data sets.

66. Utility for association studies? No matter how good the resource is, its success to find disease causing variants greatly depend on the allelic structure of common diseases, a question under debate Regardless of how we describe human association structure, many questions remain about the relative merits of single-marker vs. haplotype-based strategies for medical association studies

67. http://clavius.bc.edu/~marthlab/MarthLab

68. How to use markers to find disease? problem: genotyping cost precludes using millions of markers simultaneously for an association study genome-wide, dense SNP marker map depends on the patterns of allelic association in the human genome question: how to select from all available markers a subset that captures most mapping information (marker selection, marker prioritization)

69. The determinants of allelic association recombination: breaks down allelic association by “randomizing” allele combinations demographic history of effective population size: bottlenecks increase allelic association by non-uniform re- sampling of allele combinations (haplotypes) bottleneck

70. PopGen predictions – extent of LD

71. Software engineering aspects To do larger-scale testing we must first improve the efficiency of generating composite sets. Currently, we run fresh Coalescent runs at each K-site (several hours per region). Total # genotyped SNPs is ~ 1 million -> 1 million different K-sites to match. Any given Coalescent genealogy is likely to match one or more of these. Computational hap sets can be databased efficiently. 4 HapMap populations x 1 million K-sites x 1,000 comp sets x 50 bytes < 200 Gigabytes

72. Un-phased genotypes (AC)(CG)(AT)(CT) A G A C C C T T http://pga.gs.washington.edu/ the primary data represent diploid genotypes one has the choice to “reconstruct” the haplotypes with statistical methods as shown (e.g. the PHASE program); this may be inaccurate or one may account for all possible reconstructions when evaluating data-relevance; this is computationally very expensive