Generation of patterns from gene expression by assigning confidence to differentially expressed genes

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Generation of patterns from gene expression by
assigning confidence to differentially expressed
genes

• Elisabetta Manduchi, Gregory R. Grant, Steven
  E.McKenzie, G. Christian Overton, Saul Surrey,
  Christian J. Stoeckert

Presented by Keith Betts
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Goal

• Provide tools to aid in the analysis of data
  collected from highly parallel gene expression
  experiments.
• Generate descriptive and dependable expression
  patterns representing the differential expression
  of genes across cell types.

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• Identify those genes that are most likely to be
  differentially expressed.
• Transform typical raw input into easily
  interpretable list of patterns

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            Patterns from Gene Expression
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What is
???

• PaGE is free downloadable Perl software (tested
  mainly on Unix systems) which can be used as a
  statistical test for differentially expressed
  genes between two experimental conditions, given
  replicated expiriments.
• Available at
• http//www.cbil.upenn.edu/PaGE/

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Methods and Algorithm

• Input consists of normalized data (the
  normalization procedure depends on the kind of
  experiments conducted)
• The input normalized intensities are subjected to
  preprocessing steps.

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Methods and Algorithm Cont.

• In each gene tags expression pattern there will
  be one symbol for each homotypic group (set of
  samples of the same type)
• For each homotypic group and for each gene tag,
  compute the average intensity of that tag over
  the group which have values for that tag.
• This average will represent the intensity of that
  tag at that group.

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Two Stage Approach

• First
• Attach an ordered list of real numbers to each
  tag.
• Second
• Bin the numbers in this list, resulting in a
  pattern of integers.

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First Stage

• Fix an ordering of the groups in the collection.
• Attach to each tag the ordered list of real
  numbers obtained by dividing each of its
  non-reference group intensities by the median of
  its group intensities.
• List of ratios attached to the tag.

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Second Stage

• For each non-reference group, partition the range
  into disjoint subintervals.
• Number the bins using consecutive integers
  m,,0,.m (where 0 corresponds to ratio 1)
• Attach the ordered list of integers to each gene
  tag.

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Example

• For group i Divide the range into mi ni 1
  bins.
• The list of ratios from the first stage for a
  certain gene tag is (r1, r2,., rl)
• Each ri belongs to exactly one of the bins Bi,j.
• The expression pattern associated with this tag
  is then (j1, j2,, jl)

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Choose level cutoffs

• Suppose we are taking ratios to a reference
  homotypic group (group 0) and are focusing on a
  fixed group (group i).
• Suppose also that we have replicate experiments
  for each of the two groups.
• Concentrate on up-regulation

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Goal

• Goal is to achieve a certain degree of confidence
  in the assertion
• this gene is up-regulated at group i as compared
  to the reference group

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• Each gene will have a distribution of intensities
  in a group, whose mean will be called the true
  mean intensity of the gene at that group
• Denote the Random Variable giving the intensity
  of gene g at group j by Xg,j, and denote the Mean
  and Std. Dev as ?g,j, ?g,j

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False Positive Rate

• Prob((Xg,I / Xg,0) gt Ci
• (?g,j / ?g,0 ) lt 1)

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• Claim that
• (Ave.g,I / ?g,j) / (Ave.g,0 / ?g,0) gt Ci )
• And
• (?g,j / ?g,0 ) lt 1
• Are independent events.

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• Seek Ci as small as possible such that
• Prob(
• (Ave.g,I / ?g,j) / (Ave.g,0 / ?g,0) gt Ci )
• lt s

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• Approximate (Ave.g,j / ?g,j) for (j 0, i)
• ((Xg,j,k / Ave.g,j) 1)
• / Sqrt(tj 1) 1

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• Compute the desired Ci through integration
• If fj ( j 0,i) is the density function for
  Ave.g,j / ?g,j , and C is fixed, then evaluate
  using

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• If this is above the desired false positive rate,
  them C is raised and the integral is
  recalculated.
• Repeat process until the desired false positive
  rate is attained.

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Down-regulation

• Proceed in similar manner
• Seek ci as small as possible such that
• Prob(
• (Ave.g,I / ?g,j) / (Ave.g,0 / ?g,0) gt ci )
• lt s

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• Once the Cis and the cis are determined for
  each reference group I, if the ratio of the
  average intensity of a gene tag at group i, and
  the average intensity of the same gene tag at the
  reference group is between Ci and Ci2, we say
  that the gene tag is up-regulated one level at
  this group as compared to the reference group.

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• One can now estimate the probability Prob(not up
  predicted up)
• Prob(not up) Prob(predicted up not up) /
  Prob(predicted up)
• ?
• Prob(predicted up not up) / Prob(predicted up)

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• As a consequence of this approach, when we see a
  level different from 0, we have a certain
  confidence in the gene tag being up-regulated or
  down-regulated as compared to the reference
  group.
• However, when we see a 0 there is no confidence
  implied.
• We can only take 0 to mean that we do not have
  enough evidence to support a change in level.

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Results

• Application to an erythroid development nylon
  filter dataset

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Background

• Erythroid development dataset contains 5
  homotypic groups representing an erythroleukemic
  cell line and normal cells under different
  conditions
• There are repliate data for each of the groups.

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Background Continued

• The groups are
• CD34 positive cells
• Human adult erythroblasts
• Cord erythroblasts
• HEL cells
• HEL cells treated with hemin

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Application

• Available replicates
• Two CD34
• Three adult erythroblasts
• Two cord blood erythroblasts
• Three HEL
• Two HEL hemin

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• The value of d is set at 15
• Only the moderate to highly abundant mRNA classes
  are likely to have given hybridization signals
  above background on the filter array.
• Set the HEL group as reference

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Two approaches

• PaGE was run once merging the adult and the cord
  erythoblasts into one group with five replicates
• PaGe was run a second time keeping the adult and
  cord erythoblasts in separate groups.

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Performance

• Running time always under 90 seconds when run on
  a UltraSPARC Iii CPU at 300MHZ with 128MB RAM.

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Adult and Cord Merged Results

• Total of 18,123 clones
• 540 were above the minimum useful value in every
  group
• 5,063 were above the minimum useful value in at
  least one group.

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Merged Results Cont.

• For s 1 (false positive rate)
• 5 levels for CD-34 (0 to 4)
• 10 levels for erythoblasts (-1 to 8)
• 6 levels for HEL hemen (-1 to 4)

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Findings

• Clones representing the same gene were usually
  found to have identical or very similar patterns.
• Clones representing genes whose expression is
  known in these cells presented patterns
  compatible with what was expected.

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New Application

• Ask what genes are differentially expressed
  between Normal and leukemic cells?
• Ask which genes are induced by hemin to adopt a
  normal expression pattern.

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Findings

• Having more genes available to start with led to
  more genes identified as differentially expressed
  but at lower confidence.
• At similar confidence levels, starting with more
  genes did not necessarily lead to more genes
  identified as differentially expressed between
  normal and HEL cells.