Bayesian processbased modeling of gene expression data: estimating absolute mRNA concentrations

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Bayesian process-based modeling of gene
expression data estimating absolute mRNA
concentrations

• Arnoldo Frigessi, University of Oslo
• Mark van de Wiel, Technische Universiteit
  Eindhoven
• Marit Holden, Norwegian Computing Center
• Ingrid K. Glad, University of Oslo
• Heidi Lyng, The Norwegian Radium Hospital

Bricks dag 29-11-2005
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cDNA microarray
DNA
transcription
mRNA
translation
amino acid
organism phenotype
protein
cell phenotype

• Microarrays measure gene expression at the
  transcription level
• Microarray technology 40,000 spots cDNA
  microarray, hybridized with a sample labelled
  with a green fluorescent colour (Cy3) and a
  reference sample, labelled in red (Cy5).

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Adapted fromChristina Kendziorski
http//www.biostat.wisc.edu/kendzior
Data
log2(rj/gj)

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• Efficient production of spotted glass-slide
  arrays has made the microarray technology to a
  widespread technique.
• Spotted microarrays provided valuable
  information on relative transcript levels in
  tissues, but
• differences in experimental protocols make
  direct comparison of results between microarray
  studies very difficult.

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• Can we get information about absolute transcript
  levels from
• standard spotted microarray data?
• Extraction of absolute transcript levels is
  complicated due to experimental variation and
  noise originating in the production and
  hybridisation processes.
• Main difficulty Probes (to which the transcripts
  bind) have different properties.

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• Is information about absolute transcript levels
  useful?
• Absolute concentrations of mRNA are universal
  and can be included in further analysis with
  similar estimates obtained with different
  techniques in other labs.
• A first step towards building an annotated data
  base of transcript levels of cells.
• It is possible to detect significant
  concentration differences between two different
  genes within the same tumor, comparisons that are
  not possible with standard intensity ratios.

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Sample 1
Sample 3
Sample t
Sample 2
K1g
K2g
K1g
Ktg
Estimates
TransCount counting the number of transcripts of
each gene in each sample.
K1g
K2g
K3g

Ktg
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Propagating uncertainty

• Current practice
• Divide the experiment into separate steps
• microarray production
• transcription labelling hybridisation
• image analysis
• normalisation
• imputation
• estimation of intensities
• testing / clustering
• Do inference inside each task and plug-in
  results into the next step.

We do a coherent statistical analysis and
propagate uncertainties.
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• We use available covariates describing the
  various steps of the
• experiment, from target preparation to laser
  scanning of the images.
• We try to keep the model as close as possible to
  the biology, physics,
• bio-chemistry of the experiment.
• MCMC converges (slowly, as usual in complex
  models).

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• Some genes must be spotted at least twice on
  some arrays
• the number of such genes does not depend on
  the total number
• of genes in the study but on the design.
  Currently 50 genes
• in duplicate.
• Our method succeeds in obtaining absolute
  concentrations
• because it makes explicit use of probe and
  spot related covariates
• like probe length and quantity, to describe
  probe-dependent
• hybridisation efficiency. By means of
  duplicate spotting,
• we have many transcripts with more than one
  probe, and the
• effect of probe-dependent covariates can be
  estimated.

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• We follow the mRNA molecules
• through the whole experiment.
• At each step, some molecules
• survive, according to a Binomial
• process with a success probability
• depending on appropriate covariates.
• At the end, some molecules are
• scanned, and produce our data,
• i.e. the raw measured intensities.

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• Two off-line experiments are needed to determine
  two
• covariates which are technology dependent
• Hybridisation factor c is used to scale the
  estimated values
• to the true number of transcripts. Estimated
  using two control
• samples (spikes) with known concentrations.
• Amplification factor f is a measure of the
  increase in intensity per unit
• of increase in PMT voltage during laser
  scanning. Estimated once for
• each dye and scanner.
• Under ordinary stable experimental settings
  it is sufficient to estimate these
• factors once.

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MODEL
1 scaling and selection of target molecules 2
inclusion of covariate information 3 scanning 4
imaging
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• Reparametrisation principle
• Approximate Binomial with Poisson
• Hgt,a Poisson (c nas qta Ktg pst,a )
• and find the parameters that are
  identifiable.
• Reparametrise Ktg to include all other
  remaining parameters
• Next approximate Binomial with Normal
• Parameters that were not Poisson identifiable (
  )
• do not occur in the mean, but only in the
  variance.
• (a is the ratio of the two dye parameters)

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• Validate estimated concentrations in a dye swap
  experiment with
• control samples at known concentrations.
• 17 genes spotted each 6 times on 2 arrays.
• 2 control samples (spikes) each with 17
  different
• mRNA sequences at specific
• concentrations.
• Hyb. Factor 0.001

Low concentrations are overestimated.
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• Validate estimated concentrations with results
  from quantitative
• real-time PCR.
• 12 cervix tumor samples and a pool of ten cancer
  cell lines
• 24 arrays, each with one tumor and the pool,
  dye-swapped
• 10000 genes

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TransCount
Log-ratios
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• Clear linear relation between the PCR data and
  estimated concentrations
• The best agreement for intermediate and high
  concentrations, reflecting the increased
• uncertainties of both methods in
  quantification of low abundant transcripts.
• Good positive correlation between estimated
  concentration and PCR data for some
• individual genes, despite a limited
  within-gene variability and few data points.
• Standard log-ratio expressions also showed a
  significant correlation to PCR data,
• BUT much lower
• Many genes had approximately the same log-ratio
  although their absolute transcript
• concentrations differed considerably. This
  shows the additional information of
• absolute measures.

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Cervix tumor samples and pooled cell lines

• Estimated absolute transcript concentrations
• 12 cervix tumor samples and a pool of ten cancer
  cell lines
• 24 arrays, each with one tumor and the pool, dye
  swapped
• 10000 genes

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• Estimate both parameters in a binomial (which
  allows for estimating gene-dependent effects)
• Use scaling to focus hybridization process
• Do not use single observations to estimate its
  variance.
• Use conditional independence in hierarchical
  models to model
• complex dependencies in a flexible way.
• Start MCMC runs with central initial values.

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• Four main ideas
• we use covariates explicitly, incl. some
  describing hybridisation
• efficiency of each spot
• we treat unequal number of replicates per gene
• we use the binomial process, which better
  describes the experimental
• dynamics and allows estimation of gene and
  dye effects
• we build a bottom-to-top coherent stochastic
  model, avoiding
• plug-ins and propagating fully uncertainty.

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Publications Arnoldo Frigessi, M.A. van de
Wiel, M. Holden, D.H. Svendsrud, I.K Glad and H.
Lyng (2005), Genome-wide estimation of transcript
concentrations from spotted cDNA microarray data,
Nucleic Acids Research - Methods Online, 33,
e143 M.A. van de Wiel, M. Holden, I.K Glad, H.
Lyng and Arnoldo Frigessi (2006), Bayesian
process-based modeling of two-channel microarray
experiments estimating absolute mRNA
concentrations In Bayesian Inference for Gene
Expression and Proteomics (Mueller Do,
eds) Tech report available here
http//www.nr.no/files/samba/smbi/Transcount/repor
t999.pdf
TransCount a prototype and quite-user-friendly
version of the MCMC sampler is available here
http//www.nr.no/pages/samba/area_emr_smbi_transco
unt
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