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

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

• Michael Moran
• CMSC 838T Presentation
• May 9, 2003

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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

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Talk Overview

• Introduction
• Talk Overview
• Genetic Linkage Problem
• Previous Work
• Parallel Genehunter
• Evaluation
• Observations

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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/
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Genetic Linkage Problem

• Recombination occurs in two ways
• Random segregation of chromatids
• 2 x 23 human chromosomes
• gt
• 223 possible haploid combinations
• Genes on different chromosomes
• recombine with probability

www.gen.umn.edu/faculty_staff/hatch/1131/
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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

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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

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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

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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 pedigrees inheritance
• pattern can be summarized by a
• 2n bits

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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 grandfathers chromatid 1 grandmothers
chromatid Pr(0,0) .5 Pr(0,1)
.5 Pr(1,0) 0 Pr(1,1) 0
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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

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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 ij
• P1 , P2 probability vectors for every
  inheritance pattern given markers 1 and 2
  respectively
• P21 P2 (M P1)
• Calculate the probabilities of each markers
  inheritance conditional on all others by Markov
  Chain or FFT convolution

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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 ii1, p PD
  Px1...i Pxi1...m
• Space Requirement
• O(22n) O(22n-f) exploiting symmetry of f
  founders
• Time Requirement
• O(m22n) O(m22n-f) with f founders

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Parallel Genehunter

• Approach
• Parallelize the 3 Genehunter steps separately
• Divides each 22n-sized marker vector evenly among
  the P processors
• allows greater distribution of memory than
  assigning O(m/P) entire vectors to each processor

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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

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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, 22n x 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 P21 P2 (M P1)
• trivially parallelized each processor has the
  same
• portion of each vector.

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Parallel Genehunter

• Parallelization of step 3
• For each marker, calculate the probability of
  unknown
• gene being located at specific locations
• computing Px1...i and Pxi1...m
• FFTs parallelized as in step 2
• Final dot product p (PD Px1...i
  Pxi1...m)
• parallelized as in step 2
• each processor holds all the same portion of each
  vector

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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

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Evaluation

• Runtimes For 19,21 and 24 bit problems

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Evaluation

• Runtimes For 19,21 and 24 bit problems

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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

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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.

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• Questions?