Iterative Learning of Single Individual Haplotypes from High-Throughput DNA Sequencing Data

Transcription

1 Iterative Learning of Single Individual Haplotypes from High-Throughput DNA Sequencing Data Zrinka Puljiz and Haris Vikalo Electrical and Computer Engineering Department The University of Texas at Austin 8 th International Symposium on Turbo Codes & Iterative Information Processing Bremen, Germany, August 18-22, 2014 Iterative Learning of Single Individual Haplotypes 1 / 22

2 Overview of the Talk Motivation and background DNA sequencing and studies of genetic variations Haplotype assembly data structure and problem formulation graphical representation of the problem existing methods Communication systems analogy and belief propagation haplotype assembly as a decoding problem belief propagation algorithm performance analysis, comparison with existing methods Conclusions and future work Iterative Learning of Single Individual Haplotypes 2 / 22

3 DNA Sequencing: Discovering Genetic Blueprint Determine the order of nucleotides in a DNA sequence Human Genome Project: mapping the genetic blueprint followed by sequencing more individuals, studies of genetic variations Iterative Learning of Single Individual Haplotypes 3 / 22

4 Study of Genetic Variations in Humans Humans are diploid organism with 23 pairs of chromosomes chromosomes in a pair of autosomes are homologous the most common type of variation are SNPs Iterative Learning of Single Individual Haplotypes 4 / 22

5 Study of Genetic Variations in Humans Cont d Describing variations SNP calling determines locations and type of polymorphisms based on the detected SNPs, perform genotype calling example: A/T, A/C, G/T Genotypes provide only the list of unordered pairs of alleles no association of alleles with one of the chromosomes in a pair The complete information is provided by haplotypes the list of alleles at contiguous sites in a region of a chromosome example: (A,C,G) and (T,A,T) fundamental for many applications (personalized medicine!) Iterative Learning of Single Individual Haplotypes 5 / 22

6 Single Individual Haplotyping Determine a haplotype of an individual using DNA sequencing The SNP rate is low, typically estimated to be 10 3 high-throughput DNA sequencing provides reads that are too short get pairs of fragments at opposite ends of a strand of known length Iterative Learning of Single Individual Haplotypes 6 / 22

7 A Fragment Conflict Graph Interpretation Represent reads by nodes, conflicts by edges fragments are in conflict if they cover a common SNP location but have di erent nucleotides there (so, di erent chromosomes) If data is error-free, conflict graph is bipartite otherwise, the graph contains cycles Iterative Learning of Single Individual Haplotypes 7 / 22

8 Various Formulation of the Haplotype Assembly Problem If the conflict graph is not bipartite, assembly is non-trivial Approach: minimize the number of transformation steps needed to alter the graph so that it becomes bipartite minimum edge removal (MER), minimum fragment removal (MFR), minimum SNP removal Minimum error correction (MEC): find the smallest number of nucleotides in reads whose flipping to a di erent value resolves conflicts among the fragments from the same chromosome essentially, remove cycles in the conflict graph by assuming the fewest possible sequencing errors NP hard, various methods: HapCut [Bansal & Banfa, 2008], HapCompass [Aguiar & Istrail, 2013], HapTree [Berger et al., 2014] Iterative Learning of Single Individual Haplotypes 8 / 22

9 Minimum Error Correction Formulation Label bases in heterozygous sites as h 1 i, h 2 i 2 {1, 0} define h = h 1 = h 2 =[h 1 1 h h 1 n] Each read is as a ternary string with entries 0, 1 and organize reads into a matrix R, rowr i is the i th read 2 x x 0 x x 3 1 x 1 x x 0 x x x 0 x 0 x 0 x x 1 x x R = 6 1 x 1 x x x 7 4 x x 1 x 0 x 5 x 0 x 0 x x x x x 0 x 0 The MEC formulation is concerned with minimizing Z over h, mx nx Z = min(hd(r i, h), hd(r i, h)), hd(r i, h) = d(r i,j, h j ) i=1 j=1 Iterative Learning of Single Individual Haplotypes 9 / 22

10 Structure of the Data Matrix Consider the error-free SNP fragment matrix 2 R = 6 4 x x 0 x x 1 x 1 x x 0 x x x 0 x 0 x 0 x x 1 x x 1 x 1 x x x x x 1 x 0 x x 0 x 0 x x x x x 0 x 0 Let h = [ ], and the origin of the reads in R be s = [ ]. Then for a binary R i,j it holds s i h j R i,j Iterative Learning of Single Individual Haplotypes 10 / 22

11 Haplotype Assembly as a Decoding Problem Collect indices {(i k, j k )} identifying positions where the m n matrix R has binary entries (1 apple k apple M) Define the code generating matrix G, ( 1ifl = j k or l = i k + n, 1 apple k apple M, G(l, k) = 0, otherwise. apple 0 1 Example: for R= G= 6 4, we construct Iterative Learning of Single Individual Haplotypes 11 / 22

12 Haplotype Assembly as a Decoding Problem Cont d Define a message m =[h s] and a codeword c = mg c collects binary entries from an error-free data matrix R Due to sequencing errors, entries in R erroneously flipped this can be interpreted as the e ect of a binary symmetric channel on c = mg formally, y = c + e =[h s]g + e, wherey k = R(i k, j k ) Iterative Learning of Single Individual Haplotypes 12 / 22

13 Graphical Model Graphical representation of the problem Iterative Learning of Single Individual Haplotypes 13 / 22

14 Graphical Model Cont d Haplotyping with MEC criterion min distance decoding using the parity check matrix H: MEC = min H(y+e)=0 kek0 Iterative Learning of Single Individual Haplotypes 14 / 22

15 Belief Propagation for Haplotype Assembly Graphical model for the belief propagation algorithm Iterative Learning of Single Individual Haplotypes 15 / 22

16 Belief Propagation for Haplotype Assembly Cont d Iterative Learning of Single Individual Haplotypes 16 / 22

17 Belief Propagation for Haplotype Assembly Cont d Iterative Learning of Single Individual Haplotypes 17 / 22

18 Belief Propagation for Haplotype Assembly Cont d Stopping criterion: threshold, max # of iterations reached Iterative Learning of Single Individual Haplotypes 18 / 22

19 Computational Complexity Belief propagation algorithm: Allow random restarts, MAXITER iterations Schemes relying on parity-check need preprocessing: Parity check matrix transformation Complexity for each haplotype block: O((#SNP +#Reads) (#entries in R)) This step depends on the locations of the binary entries in the matrix R Iterative Learning of Single Individual Haplotypes 19 / 22

20 Results on 1000 Genomes Project Data Iterative Learning of Single Individual Haplotypes 20 / 22

21 Performance Guarantees Found lower bounds on Pr{ĥ 6= h}, E[ ĥ h 0 ], E[#switch errors] [SVV, ITW 2014] Consider the haplotype of length n, error rate p, and probability of assembly error P e =Pr{ĥ 6= h R}. The number of reads m necessary for the assembly satisfies m (1 P e )n 2[1 H(p)]. If m = (n ln n), one can determine h accurately with high probability. Specifically, given a target small constant > 0, there exists n large enough such that by choosing m = (n ln n) theprobabilityoferror P e apple. Iterative Learning of Single Individual Haplotypes 21 / 22

22 Summary and Future Work Developed a novel framework for haplotype assembly rephrased assembly as a decoding problem belief propagation algorithm as a solution outperforms existing methods on 1000 Genomes Project data Several possible extensions exploit possible prior SNP/genotype information develop joint base/snp/genotype calling and haplotype assembly schemes Explore other suitable methods and techniques sparse low-rank matrix completion, spectral partitioning, correlation clustering Analyze limits of performance, experimental conditions needed to achieve desired accuracy Iterative Learning of Single Individual Haplotypes 22 / 22