Summarization of Oligonucleotide Expression

Arrays

BIOS 691-803 Winter 2010

What is Summarization?

• Some expression arrays (Affymetrix, Nimblegen) use multiple probes to target a single transcript – a ‘probe set’

• Typically probes have different fold changes between any two samples

• How to effectively summarize the information in a probe set?

Many Probes for One Gene

GeneGeneSequenceSequence

Multiple Multiple oligo probesoligo probes

Perfect MatchPerfect MatchMismatchMismatch

5´5´ 3´3´

How to combine signals from multiple probes into a single gene abundance estimate?

Probe Variation

• Individual probes don’t agree on fold changes

• Probes vary by two orders of magnitude on each chip– CG content is most important factor in signal strength

Signal from 16 probes along one gene on one chip

Probe Measure Variation

•Typical probes are two orders of magnitude different!•CG content is most important factor•RNA target folding also affects hybridization

3x104

0

Bioinformatics Issues

• Probes may not map accurately

• SNP’s in probes

• Affymetrix places most probes in 3’UTR of genes– Alternate Poly-A sites mean that some probe

targets may really be less common than others

Probe Mapping

• Early builds of the genome often confused regions or genes and their complements

• Probe sets at right represent probe sets for rRNA gene and its complement

Alternate Poly-Adenylation Sites

Poly-A marks mRNA ‘tail’

Many genes have alternatives

3’ UTR may be longer or shorter

Alternate Polyadenylation of MID1

Many Approaches to Summarization

• Affymetrix MicroArray Suite; PLiER • dChip - Li and Wong, HSPH• Bioconductor:

– RMA - Bolstad, Irizarry, Speed, et al– affyPLM – Bolstad– gcRMA – Wu

• Physical chemistry models – Zhang et al• Factor model• Probe-weighting

Critique of Averaging (MAS5)

• Not clear what an average of different probes should mean

• Tukey bi-weight can be unstable when data cluster at either end – frequently the conditions here

• No ‘learning’ based on cross-chip performance of individual probes

Motivation for multi-chip models:

Probe level data from spike-in study ( log scale ) note parallel trend of all probes

Courtesy of Terry Speed

Model for Probe Signal

• Each probe signal is proportional to – i) the amount of target sample – a – ii) the affinity of the specific probe sequence to the target – f

• NB: High affinity is not the same as Specificity– Probe can give high signal to intended target and also to

other transcripts

a1

a2

Probes 1 2 3

chip 1

chip 2 f1 f2 f3

Multiplicative Model

• For each gene, a set of probes p1,…,pk

• Each probe pj binds the gene with efficiency fj

• In each sample there is an amount ai.

• Probe intensity should be proportional to fjxai

• Always some noise!

Robust Linear Models

• Criterion of fit– Least median squares– Sum of weighted squares– Least squares and throw out outliers

• Method for finding fit– High-dimensional search – Iteratively re-weighted least squares– Median Polish

• For each probe set, take log of PMij = ai fj:

• then fit the model:

• where caret represents “after pre-processing”• Fit this additive model by iteratively re-

weighted least-squares or median polish

ijjiijMP )ˆ(log

Bolstad, Irizarry, Speed – (RMA)

Critique: Model assumes probe noise is constant (homoschedastic) on log scale

)log()log()(log jiij faPM

Comparing Measures

20 replicate arrays – variance should be smallStandard deviations of expression estimates on arraysarranged in four groups of genesby increasing mean expression level

Green: MAS5.0; Black: Li-Wong; Blue, Red: RMA

Courtesy of Terry Speed

Background

• 25-mers are prone to cross-hybridization

• MM > PM for about 1/3 of all probes

• Cross-hybridization varies with GC content

• Signal intensity varies with cross-hybe

The gcRMA Approach

• Estimate non-specific binding using either:– True null assay (non-

homologous RNA)– Estimates from MM

• Subtract background before normalization and fitting model

Evaluating gcRMA

• On AffyComp data sets, gcRMA wins– Replicates with 14 spike-ins done by Affy

• Many investigators get crappy results (and don’t write it up)

• gcRMA does very well on highly expressed genes, not nearly so well on less expressed genes

• Gharaibeh et al. BMC Bioinformatics 2008 9:452

Factor Model• Assume relation between p observations x

and true value z: x = z + where i are independent

• Use factor analytic methods to estimate – Depends on assuming z ~ Normal– Differs from RMA in relaxing assumption of

IID errors – some probes can have more random error than others

Weighting Probes• It is clear that some probes are more

reliable than others

• How to assess this in a simple fashion?

• If a gene really changes across arrays, then a responsive probe will change more than a noisy probe

• Weight by relative ranges

• Best performance on AffyComp!

Summary and Evaluation

• No one best solution for all situations

• gcRMA and DFW seem to do very well on AffyComp data– May need weights for DFW by tissue

• Leading methods seem to rely on probe weighting