MINING THE GENE EXPRESSION MATRIX: INFERRING GENE RELATIONSHIPS FROM LARGE SCALE GENE EXPRESSION DAT

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MINING THE GENE EXPRESSION MATRIX INFERRING GENE
RELATIONSHIPS FROM LARGE SCALE GENE EXPRESSION
DATA

• Patrik D'haeseleer, Xiling Wen, Stefanie Fuhrman,
  and Roland Somogyi
• Information Processing in Cells and Tissues, pp.
  203-212, 1998
• Presented by Bin He

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Motivations

• it is necessary to determine large-scale temporal
  gene expression patterns
• to decipher the logic of gene regulation, we
  should aim to be able to monitor the expression
  level of all genes simultaneously

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Gene time series

• assay the expression levels of large numbers of
  genes in a tissue at different time points
• Gene time series
• the relative amounts of mRNA produced at these
  time points provide a gene expression time series
  for each gene

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Gene Expression Matrix

• Wen, X., Fuhrman, S., Michaels, G.S., Carr, D.B.,
  Smith, S., Barker, J.L., and Somogyi, R., 1997,
  Large-scale temporal gene expression mapping of
  CNS development, Proc. Natl. Acad. Sci., in press

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Previous Approach

• Euclidean distance and information theoretic
  measures to cluster the genes into related
  expression time series
• A significant problem with this approach is the
  variety of measures that can be used
• Each measure produces a unique clustering of gene
  expression patterns

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Contributions

• determining significant relationships between
  individual genes, based on
• linear correlation
• rank correlation
• information theory

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Linear correlation ------positive
correlation

• positive linear correlation

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Linear correlation ------negative
correlation

• negative linear correlation

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Linear correlation
------restriction

• for 112 different genes, 112x111/2 6216 pairs
  of expression time series need to be examined
• to restrict the number of relationships, we might
  want to test which correlations are significantly
  larger than a certain value

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Linear correlation
------restriction

• For instance, to find those relationships in
  which at least 50 of the variance is explained
  by the correlation, i.e. rho2gt0.5, we need
  rgt0.96 to reject at the 1 significance level
  the null hypothesis that rholt0.7071

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Linear correlation
------visualization

• residual variance based distance measurment
• d1-r2
• d0 if perfectly correlated, d1 if uncorrelated
• multidimensional scaling
• map time series into a two-dimensional plane

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Linear correlation
------visualization

• Multidimensional scaling of 34 time series with
  high correlation

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Nonlinear correlation
------Model

• Spearman rank correlation, rs
• measurement for monotonic relationships
• can be used for non-Gaussian distributions
• 491 pairs of expression time series, involving 98
  genes, which have a significant rs, ranging from
  -0.979 to 0.996

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Nonlinear correlation ------Example

• High rank correlation but low linear correlation
  between mGluR1 and GRa2

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Information Theory ------mutual
information

• if H(A) and H(B) are the entropies of sources A
  and B respectively, and H(A,B) the joint entropy
  of the sources, then M(A,B) H(A) H(B) -
  H(A,B)
• discrete form is much easier to use
• We need discretize the time series by
  partitioning the expression levels into bins

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Information Theory
------Bin size

• The fewer bins we use to discretize the data, the
  more information about the original time series
  we ignore.
• On the other hand, too fine a binning will leave
  us with too few points per bin to get a
  reasonable estimate of the frequency of each bin

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Information Theory
------Mapping

• Some time series map to the same discretized
  series
• In total, from 112 unique continuous-valued time
  series we get 91 discretized time series

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Information Theory
------Mapping
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Information Theory
------Mapping

• eliminate one-to-one mapping by permuting the bin
  numbers
• H(A)H(B)M(A,B)
• row 3 and row 4
• replace such time series by one single series,
  leaving us with a set of 77 unique,
  non-equivalent time series.

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Information Theory
------Measurement

• symmetric measures
• M(A,B)/max(H(A),H(B))
• M(A,B)/H(A,B)
• asymmetric measures
• Relative mutual information
• R(A,B) M(A,B)/H(B)
• R(A,B) 1.0, means that all the information
  about time series B is contained in time series A

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Conclusion

• Linear correlation can be used very effectively
  to detect linear relationships
• detect relationships not captured by Euclidean
  distance, such as high negative correlations
• Rank correlation can be used to detect non-linear
  relationships
• much more robust with respect to the distribution
  of expression levels
• Information theory can be used to detect genes
  whose (binned) expression patterns share
  information
• It will detect any mapping from time series A to
  B