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Computational Challenges in Analyzing Complex Traits. Jun Zhu Institute of Bioinformatics Zhejiang University . 1. Mendelian Traits. Phenotypes controlled by singular genes No epistasis No GE interaction. Complex Traits. Phenotypes controlled by multiple genes

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computational challenges in analyzing complex traits
Computational Challenges in Analyzing Complex Traits

Jun Zhu

Institute of Bioinformatics

Zhejiang University

1

mendelian traits
Mendelian Traits
  • Phenotypes controlled by singular genes
  • No epistasis
  • No GE interaction

Complex Traits

  • Phenotypes controlled by multiple genes
  • Epistasis (gene-gene interaction)
  • Gene-environment interaction
  • Genetic pleiotropy and heterogeneity
  • Low heritability
  • Limited statistical power
slide4

Human Chromosomes

  • Chromosome to DNS
slide5

From Genome to Genes

  • From Gene to Phenotype
slide6

Partition of Phenotypic Variation

Phenotype

y =  + E + G + GE + e

Genetic Effect: A, D, I

G

GE: AE, DE, IE

GE

Macro Env, Micro Env

E

Genome

QTL Position & Effects

Genetic Effects

3

partitioning of phenotypic variation
Partitioning of Phenotypic Variation

y =  + E + G + GE + e

  • Gene Effects (G):

Addtive (A), Dominance (D)

Gene-Gene Interaction (AA, AD, DD)

  • Environment Effects (E):

Location, Weather, Treatment

  • Gene-Environment Interaction (GE)

AE, DE, AAE, ADE, DDE

  • Random Error (e)

4

partitioning of phenotypic variation8
Partitioning of Phenotypic Variation

y =  + E + G + GE + e

  • Classical quantitative genetics
  • Molecule quantitative genetics

4

method of mapping qtl
Method of Mapping QTL

NATURE REVIEWS 2001

slide10

Presentation of QTL

Multiple QTL

QTL Network

QTL × Env

29

07/11/09

slide11

Populations for Mapping QTL

P1× P2

?

F1

DH

Haploid

P1×F1

P2×F1

BC1

BC2

F2

experimental design observations n 250 12 3 9 000
Experimental Design (Observations n = 250×12×3=9,000)
  • Mapping Population

250 DH lines

  • Environments

4 Location, 3 Years

  • Replications

3 Blocks

slide13

Mixed-model-based Composite Interval Mapping

(Wang & Zhu et al. 1999, TAG, V99)

Mapping QTL with A+AA and QE Interaction (DH, RIL)

Ai

AAij

Aj

31

slide14

Mixed-Linear Model Approaches

The Likelihood Function for QTL Mapping Model

Estimation of QTL Main Effects

Prediction of QTL-Environment Interaction Effects

challenges in computation for inverses of big matrix
Challenges in Computation for Inverses of Big Matrix
  • Rice Map Distance = 2031 cM
  • Step of QTL Searching= 1 cM
  • Steps of Two-dimession Search

= 2031 2030/2 = 2.06 Millions

  • Detecting QTLs for 10 Traits Needs to Calculate 20.6 Millions Inverses of V
slide19

Mapping DevelopmentalQTL for Complex Traits

Time: 0 1 2 …t -1tt +1 … f

Unconditional Model for Phenotypic Value at Time t

y(t) = (t) +GQ(t) + E(t) +GQE(t)

+GM(t) + GME(t)+(t)

Analyzing Q & QE Effects from Time 0t

Conditional Model for Phenotypic Value at Time t

y(t|t-1) = (t|t-1) +GQ(t|t-1) + E(t|t-1)

+GQE(t|t-1) +GM(t|t-1) + GME(t|t-1)+(t|t-1)

Analyzing Net Q & QE Effects From Time t -1 t

slide20

Table 2. Chromosomal regions and estimated genetic effects of QTLs for plant height (cm) at different stages in two environments.

(Yan, et al. 1998, Genetics, V150)

43

challenges in presentation of g g and g e during developmental stages
Challenges in Presentation of G-G and G-E During Developmental Stages
  • For G-G interaction presentation, there needs two-dimension display
  • When Genes express differently across times and spaces, there needs four-dimension display or three-dimension dynamic display
experimental design for microarray testing
Experimental Design for Microarray Testing
  • Array Design:
    • 14112 Genes(84 x 68)/Array
  • Treatment Design( 3 Way Factors):
    • Factor G: 14112 Genes
    • Factor C:8 Cancer Cells
    • Factor M:7 Medicine
  • Replicates: 3

Combining Analysis

challenges in mixed model approaches for array analysis
Challenges in Mixed-Model Approaches for Array Analysis

Prediction of Random Effects

Experiment Size

n = 14112 873 = 2.37 Millions

a two step strategy for detecting differential gene expression of cdna microarray data
A Two-step Strategy for Detecting Differential Gene Expression of cDNA Microarray Data

(Lu, Zhu, &, Liu, 2005, Current Genetics. 47: 121–131)

Choosing a subset of potential genes with differential expression

Combining analysis of multiple genes

Experiment Size Reduced to ≈ 300

n = 300873 ≈ 50,400