Parallel Genehunter : Implementation of a linkage analysis package for distributed memory architectures

1. Parallel Genehunter: Implementation of a linkage analysis package for distributed memory architectures Michael Moran CMSC 838T Presentation May 9, 2003

2. Introduction • Goals • Link Genes to specific loci in the genome • Decrease time and memory requirements through parallelization • Motivation • Locate genes for specific phenotypes • Test for inherited diseases and risk factors • Gene therapy CMSC 838T – Presentation

3. Talk Overview • Introduction • Talk Overview • Genetic Linkage Problem • Previous Work • Parallel Genehunter • Evaluation • Observations CMSC 838T – Presentation

4. Genetic Linkage Problem • Sexual Reproduction • Offspring created by two haploid gametes • Gametes are produced from diploid/polyploid cells during meiosis www.blc.arizona.edu/courses/181gh/rick/genetics1/ CMSC 838T – Presentation

5. Genetic Linkage Problem • Recombination occurs in two ways • Random segregation of chromatids 2 x 23 human chromosomes => 223 possible haploid combinations Genes on different chromosomes recombine with probability www.gen.umn.edu/faculty_staff/hatch/1131/ CMSC 838T – Presentation

6. Genetic Linkage Problem • Recombination occurs in two ways • Random segregation of chromatids • Crossover between homologous pairs of chromosomes Genes on the same chromosome recombine with probability depending on their distance and location on the chromosome CMSC 838T – Presentation

7. Genetic Linkage Problem Given • This model of recombination • Data for a particular pedigree (family) • Phenotype information for each individual • Genetic markers for each individual • Recombination frequencies for each pair of markers Can we apply probabilistic methods to • Reconstruct the inheritance patterns • Link phenotypes to the markers CMSC 838T – Presentation

8. Previous Work • Fisher, Haldane, Smith, Morton (1935 - 1955) Methods to infer genetic maps using maximum likelihood estimators • Elston, Stewart (1971) Genetic Linkage Algorithm • Linear in pedigree size • Exponential in number of markers • Lander, Green (1987) Genetic Linkage Algorithm • Linear in number of markers • Exponential in pedigree size CMSC 838T – Presentation

9. Previous Work • Genehunter (2001) • Implementation of Lander & Green • Analyzes a pedigree containing n non-founders • The inheritance of a gene by one non-founder can be summarized by two bits • The entire pedigree’s inheritance pattern can be summarized by a 2n bits CMSC 838T – Presentation

10. Previous Work • 3 steps of Genehunter: Step 1 : For each marker, calculate the probability of each of the possible inheritance pattern. Store probabilities in a vector of size 22n 0: grandfather’s chromatid 1: grandmother’s chromatid Pr([0,0]) = .5 Pr([0,1]) = .5 Pr([1,0]) = 0 Pr([1,1]) = 0 CMSC 838T – Presentation

11. Previous Work • 3 steps of Genehunter: Step 2 : For each marker, calculate the conditional probably of each inheritance pattern conditional on all of the markers to the left, and to the right • For two markers’ inheritance vectors, each disagreeing bit requires a crossover event • The probability of transitioning between inheritance vectors i, j differing in d bits is CMSC 838T – Presentation

12. Previous Work • 3 steps of Genehunter: Step 2 :For each marker, calculate the conditional probably of each inheritance pattern conditional on all of the markers to the left, and to the right • Mi,j = cost of transitioning between inheritance vectors i&j • P1 , P2 = probability vectors for every inheritance pattern given markers 1 and 2 respectively • P2|1 = P2 • (M P1) • Calculate the probabilities of each marker’s inheritance conditional on all others by Markov Chain or FFT convolution CMSC 838T – Presentation

13. Previous Work • 3 steps of Genehunter: Step 3 : For each marker, calculate the probability of unknown gene being located at specific locations • Hypothesizes phenotype has a gene located at a particular location. • By default tries 5 evenly-spaced locations between consecutive pairs of markers • Calculates PD, the probabilities of each inheritance pattern for based on this phenotype (as in step 1) • For a location between markers i&i+1, p= PD • Px|1...i • Px|i+1...m • Space Requirement: O(22n) O(22n-f) exploiting symmetry of f founders • Time Requirement: O(m22n) O(m22n-f) with f founders CMSC 838T – Presentation

14. Parallel Genehunter • Approach • Parallelize the 3 Genehunter steps separately • Divides each 22n-sizedmarker vector evenly among the P processors • allows greater distribution of memory than assigning O(m/P) entire vectors to each processor CMSC 838T – Presentation

15. Parallel Genehunter • Parallelization of step 1 For each marker, calculate the probability of each of the possible inheritance pattern Each processor calculates the probabilities for a particular 22n / P inheritance patterns for ever marker CMSC 838T – Presentation

16. Parallel Genehunter • Parallelization of step 2 For each marker, calculate the conditional probably of each inheritance pattern conditional on all of the markers to the left, and to the right • FFT convolution • As in serial genehunter, 22nx 22n matrix-vector multiplication is replaced FFT-based convolution: • 2 forward 1D FFTs on 22n-length vectors • element-by-element multiplication • inverse FFT • Each 1D FFT is equivalent to a 2D FFT on a P x 22n / P matrix • There are well-known distributed algorithms for this FFT using all-to-all communication. • Dot Product in P2|1 = P2 • (M P1) • trivially parallelized: each processor has the same portion of each vector. CMSC 838T – Presentation

17. Parallel Genehunter • Parallelization of step 3 For each marker, calculate the probability of unknown gene being located at specific locations • computing Px|1...i and Px|i+1...m • FFTs parallelized as in step 2 • Final dot product p = (PD • Px|1...i • Px|i+1...m) • parallelized as in step 2 • each processor holds all the same portion of each vector CMSC 838T – Presentation

18. Evaluation • Experimental Environment • Input data sets • 51 family member pedigree • {19,21,24}-bit data sets (# bits = 2n-f ) • Computing Facilities • Cplant Cluster (Sandia National Laboratories) • DEC Alpha EV6 processors • Myrinet connection CMSC 838T – Presentation

19. Evaluation • Runtimes For 19,21 and 24 bit problems CMSC 838T – Presentation

20. Evaluation • Runtimes For 19,21 and 24 bit problems CMSC 838T – Presentation

21. Observations Pro: Performs Genehunter computation exactly Pro: Effective for “multipoint linkage” of phenotypes Con: Old-fashioned compared to protein-based methods (?) Pro: Distributes memory requirements Pro: More computers allows larger feasible inputs Con: Experiments based on 1 pedigree Pro: Efficient parallelization up to 32 or 64 processors Con: Only allows pedigrees to grow by only 3 or 4 individuals in equal time CMSC 838T – Presentation

22. References • Genetic Recombination Dr. Craig Woodworth, Genetic Recombination in Eukaryotes, Lecture Notes, (www.clarkson.edu/class/by214/powerpoint) • Genehunter K. Markianos, M.J. Daly, & L. Kruglyak. Efficient Multipoint Linkage Analysis Through Reduction of Inheritance Space. American Journal of Human Genetics 68, 2001. • Parallel Genehunter G. Conant, S. Plimpton, W. Old, A. Wagner, P. Fain, & G. Heffelfinger. Parallel Genehunter: Implementation of a Linkage Analysis Package for Distributed-Memory Architectures,  Proceedings of the First IEEE Workshop on High Performance Computational Biology, International Parallel and Distributed Computing Symposium, 2002. CMSC 838T – Presentation

23. Questions? CMSC 838T – Presentation