Computational methods for genetic mapping of quantitative traits

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Computational methods for genetic mapping of
quantitative traits

• Kajsa Ljungberg
• February 17, 2006

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Kajsa Ljungberg

• M.Sc. Biotechnology Engineering (civilingenjör
  Molekylär bioteknik), Uppsala.
• Ph.D. Scientific Computing, Uppsala.
• Various computational projects at e.g.
  AstraZeneca and UC San Francisco

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Overview

• Background of my Ph.D. project Quantitative
  traits, genetics, experiments.
• My work Mathematical problem, methods
  (principles only), results.
• Two related problems in computational biology.
• Lessons learned in industry and academia.

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Heritable traits, examples

• Earlobes Loose or attached
• Blood group A, B, AB or 0

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Qualitative traits

• Can be divided into classes in a natural way.
• Often governed by a single gene, and in such
  cases the genetic basis is relatively easy to
  study
• Examples Earlobes, blood group, Huntingtons
  disease.

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Heritable traits, more examples

• Height
• Hair colour
• Blood pressure

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Quantitative traits

• Vary continuously on some scale.
• Often governed by multiple interacting genes and
  the environment.
• Examples Blood pressure, cholesterol levels,
  growth rate in e.g. farm animals.
• Most traits of economic or medical importance are
  quantitative.

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QTL

• Abbreviation of Quantitative Trait Locus
• Region in the genome where one or several genes
  influencing a quantitative trait are located.
• Can be found using QTL mapping, and is an
  important step in the process of finding the
  individual genes.

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HUGO and QTL mapping

• HUGO project
• Sequence ? Gene ? Function/Trait
• QTL mapping
• Function/Trait ? QTL ( ? Gene)

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Experiments in QTL mapping
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Fit model A(x)by (bb0 b1). b0 denotes the
mean weight and b1 the effect of the genotype.
Experiment? model
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110000000 0000000111111111111 0000000000111111111
1111111111111000111 ...
11 11 11 10 10 11 .. A(x)
1672g 945g 213g 1212g 418g 744g .. y
x
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If 1 QTL only

Residual norm
x
The genome, all chromosomes lined up
Model
Experiment data A(x), y
Least-squares problem
Residual norm
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If 1 QTL only, contd.




Residual norm
















x
The genome, all chromsomes lined up
The genome position with the smallest residual
norm (best model fit) indicates the most likely
position of the QTL.
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If 2 QTL
Searching for two QTL corresponds to a
two-dimensional optimization problem.
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Computational problem
Searching for n QTL corresponds to
an n-dimensional optimization problem, where the
objective function is the residual norm of a
least-squares problem.
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My project

• Minimize f(x), i.e. find the genome positions
  giving the best model fit, faster.
• Two main strategies
• 1) Speed up the computation of the residual norm.
  Linear algebra, updated QR factorizations...
• 2) Speed up the multidimensional search for the
  optimum. DIRECT algorithm

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Results

• 2-3 orders of magnitude speed-up for typical
  problems, even more for complicated models.
  Computational times measured in minutes instead
  of days.
• This allows for more thourough data exploration
  and model testing.

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• PSEUDOMARKER 2.02
• Hao Wu1, Saunak Sen2, Kajsa Ljungberg3, Karl W.
  Broman4, Gary A. Churchill1
• 1The Jackson Laboratory, Bar Harbor, ME
• 2Department of Epidemiology and Biostatistics,
  University of California San Francisco, San
  Francisco, CA
• 3Department of Information Technology, Division
  of Scientific Computing, Uppsala University,
  Uppsala, Sweden.
• 4Department of Biostatistics, Johns Hopkins
  University, Baltimore, MD
• http//www.jax.org/staff/churchill/labsite/softwar
  e/pseudomarker/

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Related problems, 1

• Gene expression levels from microarray
  experiments are also quantitative traits.
• QTL analysis on microarray data can help
  distinguish between covariation and causation.
• Hot topic!

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Related problems, 2

• QTL analysis in human populations (different
  statistical issues).
• Examples at AstraZeneca
• 1) Procardis risk factors heart disease.
• 2) Identify QTL related to adverse side
  effects, e.g liver problems (Exanta).

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Lessons learned

• (as a computational expert among
  experimentalists)
• The importance of visualization
• Differences in language
• Real data is a pain
• People use what they know
• ? Future projects?

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• End of presentation.

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Thanks

• Sverker Holmgren
• Örjan Carlborg
• Kateryna Mishchenko
• Mahen Jayawardena
• Leif Andersson
• Martina Hägglund
• Forskarskolan i Matematik och Beräkningsvetenskap
• Linné-centrum

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Paper 1
Standard method
Genetic info
Experiment data
Computation
Constant info
Prediction
Genetic info
Computa
-tion
Constant info
Prediction
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Paper 1 (Ljungberg, Holmgren, Carlborg)

Model
Experiment data
Computation
Prediction Real value Difference
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Paper 2 (Ljungberg, Holmgren, Carlborg)
Difference between prediction real value


























The genome, all chromosomes lined up
Search carefully in regions with good values, but
only sparsely in regions with bad values.
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Paper 3 (Ljungberg, Mishchenko, Holmgren)
Difference between prediction real value

















The genome
When a region with good values has been found,
use a special algorithm which is efficient in
finding the bottom of the closest valley.
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Paper 4 (Ljungberg)
100, 010, 000, 111 11 00 01 11
2
Model
Experiment data
Computation
Prediction
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Paper 5 (Jayawardena, Holmgren, Ljungberg)

Difference between prediction real value


Model
Model
Model
Data
Computation
Computation
Data
Computation
Data
Perform several computations simultaneously in an
organized and efficient manner.