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Normalization Methods for Time-Course DNA Microarray Data
RM Flight, TK Karakach, PD Wentzell
Department of ChemistryDalhousie UniversityHalifax, NS
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About Us
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Sources of measurement error
DNA microarrays
Estimate errors
Incorporate into analysis
Extract curves describing evolution of transcription factor activity over time
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Discover clusters of co-regulated genes
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Karakach et al, Anal. Bioanal. Chem., 389, 2125-2141 (2007)
Wentzell et al, BMC Bioinformatics, 7, 343 (2006)
Wentzell et al, J. Chemomet., 11, 339-366 (1997)
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MCR-WALS
Multivariate curve resolution via weighted alternating least squares
MLPCA
Maximum likelihood principal components analysis
Transcriptome Analysis Using DNA Microarrays
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DNA Microarray
Which genes are different?What do they do?How are they regulated?Organism function?
Objective is to determine which genes change expressionunder different conditions
Comparator Experiments - two or more discrete conditions
Time Course Experiments - a continuum of conditions
DNA Microarray Time-Course Analysis
How does gene expression change as a function of time
Synchronize
Perturb
Time
Ratios (Red / Green)
Genes
Time
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Problem: Differences Between Arrays
Each step potentially introducessystematic variation
Reference
Test
Hybridize
Scan+Analyze
mRNA
cDNA
Extract
RT+Label
mRNA
mRNA
cDNA
Extract
RT+Label
mRNA
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Solution: Normalization!
Normalization
Removal of non-biological sources of variation from the data
Physical Solutions
Spike-in controls, microarray samplepool (MSP)
Low number, low intensity variation
Equal amounts of expression inboth samples
Possible to find genes with equal amount of expression in both samples
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Assumptions
J. Quackenbush, Nat. Genet. 32, 496 (2002)
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Total Intensity
Log Mean / Median
LOWESS
Invariant Set
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Computational Solutions
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These are a problem in time-course studies
Time-Course Experimental Design
Common Reference
Each array uses the same reference sample
Should contain mRNA from all genes of interest
Measurement
Not interested in differential expression!
How the gene expression changes over time
Time
No expression on reference = no measurement
Reference
Test
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VS
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Normalization?
Actual amounts of mRNA
Impossible in practice
Housekeeping genes
Often don't exist in time-course experiments
Total amount of mRNA
Often done in practice, but total mRNA varies between samples
HI: 20% of genes, 6x up-regulatedLO: 80% of genes, 3x up-regulated
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Replicate Arrays
Replicate Normalization
Ratios from replicate arrays (samples) related by a simple scaling factor
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Pseudo-Replicates
Pseudo-Continuum
Individual time-points (arrays) form apseudo-continuum
If the time-points are close enough, theybehave much like replicates
Therefore, is it possible to normalize between subsequent arrays?
Replicate Arrays
Sequential Arrays
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Sequential Normalization
Assumptions
Each array related to next by scaling in ratio space
Slope of log-ratios is 1
Can normalize each to previous, and eventually to the first
Data Sets
Intraerythrocytic development cycle ofmalaria - 55 arrays, 1 hour intervals
Yeast exit from stationary phase, 19 arrays, 5 min intervals
Drosophila life cycle from embryo to adult, 74 arrays, various intervals
Steps
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To normalize array :
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Determine "good" ratios on array and
Bozdech et al, PLoS Biol., 1, 85-100 (2003)
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Martinez et al, Mol. Biol. Cell, 15, 5295-5305 (2004)
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Arbeitman et al, Science, 297, 2270-2275 (2002)
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Calculate intercept from log-log plot of ratios:
Calculate normalization factor for array
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Does it Work?
Before normalization
After normalization
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Validation
Linearity
Assumed that slope in log-space is equal to 1