1、Introduction to SNP and Haplotype Analysis,Algorithms and Computational Biology Lab, Department of Computer Science & Information Engineering, National Taiwan University, Taiwan.,Yao-Ting Huang,Kun-Mao Chao,2,Genetic Variations,The genetic variations in DNA sequences (e.g., insertions, deletions, an
2、d mutations) have a major impact on genetic diseases and phenotypic differences. All humans share 99% the same DNA sequence. The genetic variations in the coding region may change the codon of an amino acid and alters the amino acid sequence.,Single Nucleotide Polymorphism,A Single Nucleotide Polymo
3、rphisms (SNP), pronounced “snip,” is a genetic variation when a single nucleotide (i.e., A, T, C, or G) is altered and kept through heredity. SNP: Single DNA base variation found 1% Mutation: Single DNA base variation found 1%,C T T A G C T T,C T T A G T T T,SNP,C T T A G C T T,C T T A G T T T,Mutat
4、ion,94%,6%,99.9%,0.1%,4,Mutations and SNPs,Common Ancestor,Observed genetic variations,5,Single Nucleotide Polymorphism,SNPs are the most frequent form among various genetic variations. 90% of human genetic variations come from SNPs. SNPs occur about every 300600 base pairs. Millions of SNPs have be
5、en identified (e.g., HapMap and Perlegen). SNPs have become the preferred markers for association studies because of their high abundance and high-throughput SNP genotyping technologies.,Single Nucleotide Polymorphism,A SNP is usually assumed to be a binary variable. The probability of repeat mutati
6、on at the same SNP locus is quite small. The tri-allele cases are usually considered to be the effect of genotyping errors. The nucleotide on a SNP locus is called a major allele (if allele frequency 50%), or a minor allele (if allele frequency 50%).,A C T T A G C T T,A C T T A G C T C,C: Minor alle
7、le,94%,6%,T: Major allele,7,Haplotypes,A haplotype stands for a set of linked SNPs on the same chromosome. A haplotype can be simply considered as a binary string since each SNP is binary.,8,Genotypes,The use of haplotype information has been limited because the human genome is a diploid. In large s
8、equencing projects, genotypes instead of haplotypes are collected due to cost consideration.,9,Problems of Genotypes,Genotypes only tell us the alleles at each SNP locus. But we dont know the connection of alleles at different SNP loci. There could be several possible haplotypes for the same genotyp
9、e.,or,We dont know which haplotype pair is real.,10,Research Directions of SNPs and Haplotypes in Recent Years,Haplotype Inference,Tag SNP Selection,Maximum Parsimony,Perfect Phylogeny,Statistical Methods,Haplotype block,LD bin,Prediction Accuracy,SNP Database,11,Haplotype Inference,The problem of i
10、nferring the haplotypes from a set of genotypes is called haplotype inference. This problem is already known to be not only NP-hard but also APX-hard. Most combinatorial methods consider the maximum parsimony model to solve this problem. This model assumes that the real haplotypes in natural populat
11、ion is rare. The solution of this problem is a minimum set of haplotypes that can explain the given genotypes.,12,Maximum Parsimony,or,Find a minimum set of haplotypes to explain the given genotypes.,13,Related Works,Statistical methods: Niu, et al. (2002) developed a PL-EM algorithm called HAPLOTYP
12、ER. Stephens and Donnelly (2003) designed a MCMC algorithm based on Gibbs sampling called PHASE. Combinatorial methods: Gusfield (2003) proposed an integer linear programming algorithm. Wang and Xu (2003) developed a branching and bound algorithm called HAPAR to find the optimal solution. Brown and
13、Harrower (2004) proposed a new integer linear formulation of this problem.,14,Our Results,We formulated this problem as an integer quadratic programming (IQP) problem. We proposed an iterative semidefinite programming (SDP) relaxation algorithm to solve the IQP problem. This algorithm finds a soluti
14、on of O(log n) approximation. We implemented this algorithm in MatLab and compared with existing methods. Huang, Y.-T., Chao, K.-M., and Chen, T., 2005, “An Approximation Algorithm for Haplotype Inference by Maximum Parsimony,” Journal of Computational Biology, 12: 1261-1274.,15,Problem Formulation,
15、Input: A set of n genotypes and m possible haplotypes. Output: A minimum set of haplotypes that can explain the given genotypes.,16,Integer Quadratic Programming (IQP),Define xi as an integer variable with values 1 or -1. xi = 1 if the i-th haplotype is selected. xi = -1 if the i-th haplotype is not
16、 selected. Minimizing the number of selected haplotypes is to minimize the following integer quadratic function:,17,Integer Quadratic Programming (IQP),Each genotype must be resolved by at least one pair of haplotypes. For genotype G1, the following integer quadratic function must be satisfied.,or,S
17、uppose h1 and h2 are selected,18,Integer Quadratic Programming (IQP),Maximum parsimony:We use the SDP-relaxation technique to solve this IQP problem.,to resolve all genotypes.,Find a minimum set of haplotypes,19,The Flow of the Iterative SDP Relaxation Algorithm,Integer Quadratic Programming,Integra
18、l Solution,Semidefinite Programming,Vector Solution,Vector Formulation,SDP Solution,20,Research Directions of SNPs and Haplotypes in Recent Years,Haplotype Inference,Tag SNP Selection,Maximum Parsimony,Perfect Phylogeny,Statistical Methods,Haplotype block,LD bin,Prediction Accuracy,SNP Database,21,P
19、roblems of Using SNPs for Association Studies,The number of SNPs is still too large to be used for association studies. There are millions of SNPs in a human body. To reduce the SNP genotyping cost, we wish to use as few SNPs as possible for association studies. Tag SNPs are a small subset of SNPs t
20、hat is sufficient for performing association studies without losing the power of using all SNPs. There are many definitions of tag SNPs. We will first study one definition of tag SNPs based on haplotype blocks model.,22,Haplotype Blocks and Tag SNPs,Recent studies have shown that the chromosome can
21、be partitioned into haplotype blocks interspersed by recombination hotspots (Daly et al, Patil et al.). Within a haplotype block, there is little or no recombination occurred. The SNPs within a haplotype block tend to be inherited together. Within a haplotype block, a small subset of SNPs (called ta
22、g SNPs) is sufficient to distinguish each pair of haplotype patterns in the block. We only need to genotype tag SNPs instead of all SNPs within a haplotype block.,23,Recombination Hotspots and Haplotype Blocks,24,A Haplotype Block Example,The Chromosome 21 is partitioned into 4,135 haplotype blocks
23、over 24,047 SNPs by Patil et al. (Science, 2001). Blue box: major allele Yellow box: minor allele,25,Examples of Tag SNPs,P1,P2,P3,P4,S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12,SNP loci,Haplotype patterns,Suppose we wish to distinguish an unknown haplotype sample. We can genotype all SNPs to identify th
24、e haplotype sample.,An unknown haplotype sample,: Major allele,: Minor allele,26,Examples of Tag SNPs,P1,P2,P3,P4,S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12,SNP loci,Haplotype pattern,In fact, it is not necessary to genotype all SNPs. SNPs S3, S4, and S5 can form a set of tag SNPs.,P1,P2,P3,P4,S3,S4,S5,
25、27,Examples of Wrong Tag SNPs,P1,P2,P3,P4,S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12,SNP loci,Haplotype pattern,SNPs S1, S2, and S3 can not form a set of tag SNPs because P1 and P4 will be ambiguous.,P1,P2,P3,P4,S1,S2,S3,28,Examples of Tag SNPs,P1,P2,P3,P4,S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12,SNP loci
26、,Haplotype pattern,SNPs S1 and S12 can form a set of tag SNPs. This set of SNPs is the minimum solution in this example.,P1,P2,P3,P4,S1,S12,29,Problem Formulation,(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),S1,S4,There are pairs of patterns.,The relation between SNPs and haplotypes can be formulated as a bi
27、partite graph. S1 can distinguish (P1, P3), (P1, P4), (P2, P3), and (P2, P4). S2 can distinguish (P1, P4), (P2, P4), (P3, P4).,P1,P2,P3,P4,S3,S4,S1,S2,30,Observation,(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),Each pair of patterns is connected by at least one edge.,The SNPs can form a set of tag SNPs if ea
28、ch pair of patterns is connected by at least one edge. e.g., S1 and S3 can form a set of tag SNPs. e.g., S1 and S2 can not be tag SNPs.,31,Problems of Finding Tag SNPs,The problem of finding the minimum set of tag SNPs is known to be NP-hard. This problem is the minimum test set problem. A number of
29、 methods have been proposed to find the minimum set of tag SNPs (Bafna et al., Zhang, et al.). In reality, we may fail to obtain some tag SNPs if they do not pass the threshold of data quality. In the current genotyping environment, the missing rate of SNPs is around 510%. We proposed two greedy alg
30、orithms and one linear programming relaxation algorithm to solve this problem.,32,References:,Huang, Y.-T., Zhang, K., Chen, T. and Chao, K.-M., 2005, “Selecting Additional Tag SNPs for Tolerating Missing Data in Genotyping,” BMC Bioinformatics, 6: 263. Chang, C.-J., Huang, Y.-T., and Chao, K.-M., 2
31、006, “A Greedier Approach for Finding Tag SNPs,” Bioinformatics, 22: 685-691.,33,Research Directions of SNPs and Haplotypes in Recent Years,Haplotype Inference,Tag SNP Selection,Maximum Parsimony,Perfect Phylogeny,Statistical Methods,Haplotype block,LD bin,Prediction Accuracy,SNP Database,34,Linkage
32、 Disequilibrium,The problem of finding tag SNPs can be also solved from the statistical point of view. We can measure the correlation between SNPs and identify sets of highly correlated SNPs. For each set of correlated SNPs, only one SNP need to be genotyped and can be used to predict the values of
33、other SNPs. Linkage Disequilibrium (LD) is a measure that estimates such correlation between two SNPs. We will formally introduce the detailed information of LD later.,35,Linkage Disequilibrium Bins,The statistical methods for finding tag SNPs are based on the analysis of LD among all SNPs. An LD bi
34、n is a set of SNPs such that SNPs within the same bin are highly correlated with each other. The value of a single SNP in one LD bin can predict the values of other SNPs of the same bin. These methods try to identify the minimum set of LD bins.,36,An Example of LD Bins (1/3),SNP1 and SNP2 can not fo
35、rm an LD bin. e.g., A in SNP1 may imply either G or A in SNP2.,37,An Example of LD Bins (2/3),SNP1, SNP2, and SNP3 can form an LD bin. Any SNP in this bin is sufficient to predict the values of others.,38,An Example of LD Bins (3/3),There are three LD bins, and only three tag SNPs are required to be
36、 genotyped (e.g., SNP1, SNP2, and SNP4).,39,Difference between Haplotype Blocks and LD bins,Haplotype blocks are based on the assumption that SNPs in proximity region should tend to be correlated with each other. The probability of recombination occurs in between is less. LD bins can group correlate
37、d of SNPs distant from each other. A disease is usually affected by multiple genes instead of single one. The SNPs in one LD bin can be shared by other bins. The SNPs in a haplotype block do not appear in another block.,40,Introduction to Linkage Disequilibrium,A,b,A, B: major alleles a, b: minor al
38、leles PA: probability for A alleles at SNP1 Pa: probability for a alleles at SNP1 PB: probability for B alleles at SNP2 PB: probability for b alleles at SNP2 PAB: probability for AB haplotypes Pab: probability for ab haplotypes,SNP1,SNP2,41,Linkage Equilibrium,PAB = PAPB PAb = PAPb = PA(1-PB) PaB =
39、PaPB = (1-PA) PB Pab = PaPb = (1-PA) (1-PB),SNP1,SNP2,42,Linkage Disequilibrium,PAB PAPB PAb PAPb = PA(1-PB) PaB PaPB = (1-PA) PB Pab PaPb = (1-PA) (1-PB),SNP1,SNP2,43,An Example of Linkage Disequilibrium,- A - - - G - - -,- C - - - G - - -,- C - - - C - - -,Suppose we have three haplotypes: AG, CG,
40、 and CC. There is no AC haplotype, i.e., PAC = 0. Note that PAC =0, PAPC =1/9, and PAC PAPC. These two SNPs are linkage disequilibrium.,PA=1/3 PC=2/3,PG=2/3 PC=1/3,44,An Example of Linkage Equilibrium,- A - - - G - - -,- C - - - G - - -,- C - - - C - - -,- A - - - C - - -,- A - - - G - - -,- C - - -
41、 G - - -,- C - - - C - - -,Before recombination,After recombination,PA=1/2 PC=1/2,PG=1/2 PC=1/2,After recombination, PAG = PAPG = 1/4, PCG = PCPG = 1/4, PCC = PCPC = 1/4, and PAC = PAPC = 1/4. These two SNPs are linkage equilibrium.,45,Linkage Disequilibrium,There are many formulas to compute LD bet
42、ween two SNPs, and most of them are usually normalized between -11 or 01. LD = 1 (perfect positive correlation) LD = 0 (no correlation or linkage equilibrium) LD = -1 (perfect negative correlation) LD = 0.8 (strong positive correlation) LD = 0.12 (weak positive correlation),46,Linkage Disequilibrium
43、 Formulas,Mathematical formulas for computing LD: r2 or 2:D:Chi-square Test. P value.,47,Correlation Coefficient,The correlation between two random variables A and B can be measured by the correaltion coefficient:,48,Examples of Computing LD,49,Minimum Clique Cover Problem,This problem asks for a mi
44、nimum set of LD bins. The minimum LD value required between two SNPs in one bin is usually set to 0.8. This problem is known to be the minimum clique cover problem (by Huang and Chao, 2005). Consider each SNP as nodes on the graph. There exists an edge between two nodes iff the LD of these two SNPs
45、0.8.,50,Relaxation of This Problem,The minimum clique cover problem is not easy to be approximated. The relaxed problem asks for a minimum set of LD bins such that at least one SNP in an LD bin has r2 0.8 with other SNPs in the same bin. The relaxed problem is known to be the minimum dominating set
46、problem. The minimum dominating set problem is still NP-hard but is easier to be approximated.,51,Minimum Dominating Set Problem,Given a graph G(V, E), the minimum dominating set C is the minimum set of nodes, such that each node in V has at least one edge connecting to nodes in C.Consider each node
47、 as a SNP and each edge as strong LD (r2 0.8) between two SNPs. The minimum dominating set of this graph is the set of tag SNPs. We can only use this set of SNPs to predict other SNPs.,52,Experimental Data Sets,Hinds et al. (2005) identified 1,586,383 SNPs across three human populations. African, Americans of European, and Asian. The database provides both genotype data and inferred haplotype data.,
