Analyzing Time Series Gene Expression Data

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Analyzing Time Series Gene Expression Data
Ziv Bar-Joseph Center for Automated Learning and
Discovery Carnegie Mellon University
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Expression Experiments
Time series Multiple arrays at various temporal
intervals
Static Snapshot of the activity in the cell
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Abundance of time series expression datasets

• Over 30 of the 170 papers perform time series
  experiments.
• A total of 220 time series datasets.
• More arrays used for time series than for static
  expression experiments.

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Unique features of time series expression
experiments

• Autocorrelation between successive points.
• Can identify complete set of acting genes.
• Allows to infer causality.

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Time Series Examples Development
Development of fruit flies Arbeitman, Science 02
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Time Series Examples (cont)
Function
Infectious diseases, response to external stimulus
Interactions and Systems
Transcription factors knockouts

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Time Series Examples Systems
The cell cycle system in yeast Simon et al, Cell
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Computational challenges
Computational
Biological
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Sampling Rates

• Non uniform
• Differ between experiments

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Cell Cycle Datasets
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Networks
Pattern Recognition
Data Analysis
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Representing time series expression data

• We are capturing a continuous process with a few
  samples.
• We need a way to convert our samples for each
  gene to an expression profile.
• Some simple techniques
• - Linear interpolation
• - Spline interpolation
• - Functional assignment

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Standard interpolation
If we have missing values and noise linear
interpolation will fail to reproduce an accurate
representation.
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Splines

• Instead of linear interpolation, we can use
  splines piecewise polynomials.
• Still, will overfit when faced with missing
  values and noise.

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The power of co-expression

• We can modify our splines to take into account
  the fact that many genes are co-expressed.

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Avoiding overfitting

• Require that for each gene ? N(0, ?j)
• Add noise term

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Class Assignment

• In some cases the biological classes are known
  in advance.

The algorithm can be modified and combined with a
Gaussian mixture algorithm to perform clustering
of the continuous representation of the
expression data.
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Missing values
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Interpolation
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Alignment
FKH1

• Difference in the timing of similar biological
  processes

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Continuous Alignment
Using the estimated splines, we continuously
align two expression datasets by minimizing a
global error function
RECOMB 2002
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Identifying differentially expressed genes
Wild Type
Knockout

• Hard to perform manual comparison.
• Sampling rates and different timing prevent
  direct comparison.

Zhu et al, Nature 2000
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Using Global Error to Determine Significance
Key idea Combine individual noise model with a
global error (area between curves) that correctly
captures the temporal difference between the two
profiles.
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Comparing the continuous representation
WT
Knockout
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Enrichment for the Cell Cycle Factors
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Overcoming population effects
Smc3 observed values

• Microarray experiments profile population of
  cells.
• Initially cells are synchronized, but they lose
  their synchronization over time.
• Need to compensate for synchronization loss in
  order to recover single cell values.

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Networks
Pattern Recognition
Individual Gene
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Pattern recognition and clustering

• Identifying relationships between genes based on
  expression profiles.
• Handling non uniform sampling rates.
• Determining relationships between clusters.

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Time Shifted and Inverted Profiles
Qian et al Journal of Molecular Biology 2001
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Results
Simultaneous expression profile relationships
Inverted expression profile relationships
Time delayed expression profile relationships
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Hierarchical clustering

• For n leaves there are n-1 internal nodes
• Each flip in an internal node creates a new
  linear ordering
• There are 2n-1 possible linear ordering of the
  leafs of the tree

1
2
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Determine Relations Between Clusters
Optimal leaf ordering selects the ordering that
maximizes the sum of the similarities of adjacent
leaves in the clustering tree.
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Results Synthetic Data
Input
Hierarchical clustering
Optimal ordering
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24 cell cycle experiments
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Short Time Series

• 60 of the time series datasets are short (lt7).
• Over 40000 signals are measured, data is very
  noisy and experiments are compared across all
  time points.
• Most clustering algorithms will miss small sets,
  and in addition, cannot be used to compare
  datasets.

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Taking advantage of the small number of points
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Networks
Pattern Recognition
Individual Gene
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Systems Biology

• Different types of data provide partial
  information about the activity in the cell.
• By integrating these data sources we can obtain a
  better picture of the activity in the cell.
• A lot of current interest though relatively few
  methods construct temporal models.

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Dynamic Bayesian Networks

• Bayesian networks are graphical models which can
  account for the stochastisity in the data.
• Can be extended to handle time series data
  (dynamic Bayesian networks).
• So far have been used for small scale modeling.

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Modeling tryptophan metabolism on E. coli
Ong et al Bioinformatics 2002
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Genetic RegulAtory Modules (GRAM)

• Gene Modules
• Set of genes that are co-regulated and
  co-expressed.
• Functional Module
• Collection of gene modules with related function.

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Assembly of the Cell Cycle Transcriptional Regul
atory Network
Blue boxes gene modules
We combine GRAM with our continuous alignment
algorithms to construct a dynamic model for a
sub-network
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Assembly of the Cell Cycle Transcriptional Regul
atory Network
Blue boxes gene modules
Individual regulators ovals, connected to their
modules Dashed line extends from module
encoding a regulator to the regulator protein oval
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Comparing the Continuous Representation
WT
Knockout
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Assembly of the Cell Cycle Transcriptional Regul
atory Network
Blue boxes gene modules
Individual regulators ovals, connected to their
modules Dashed line extends from module
encoding a regulator to the regulator protein oval
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Summary

• Time series expression data can be used to answer
  important biological questions.
• Pros Autocorrelation, allows for casual
  inference, provides a better view of cellular
  activity
• Cons Large number of signals but small number of
  time points, noise, lack of repeats
• By using methods specifically developed for this
  data we can overcome the above problems and take
  advantage of its unique properties

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Want to know more ?

• Z. Bar-Joseph, Analyzing time series gene
  expression data Bioinformatics, in press.
• www.cs.cmu.edu/zivbj
• zivbj_at_cs.cmu.edu