Outline

1

• Outline
• Biological motivation
• Introduction to graph models and Bayesian network
• Case study
• Module networks identifying regulatory modules
  and their condition-specific regulators from gene
  expression data Segal, Shapira, Regev, Peer,
  Botstein, Koller, Friedman. Nature Genetics. 2003
• Large-scale mapping and validation of E. Coli
  transcriptiional regulation from a compendium of
  expression profiles. PLoS Biology. 2007.

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1. Biological motivation

• cis-regulatory motif A short (6-to-12-ish)
  series of DNA bases that can bind to an
  activator or repressor protein. Illustrated
  at right as activator/repressor binding sites.

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1. Biological motivation

• Module set of genes that participate in a
  coherent biological process
• Module group set of modules that all share at
  least one cis-regulatory motif
• regulator a gene that encodes a protein whose
  concentration regulates the expression of other
  genes
• expression profile concentrations of various
  genes in given bio-experimental circumstances

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1. Biological motivation
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2. Introduction to Bayesian Network
"Graphical models are a marriage between
probability theory and graph theory. They provide
a natural tool for dealing with two problems that
occur throughout applied mathematics and
engineering -- uncertainty and complexity.
..Fundamental to the idea of a graphical model
is the notion of modularity -- a complex system
is built by combining simpler parts. Probability
theory provides the glue whereby the parts are
combined, ensuring that the system as a whole is
consistent. Many of the classical multivariate
probabalistic systems are special cases of the
general graphical model formalism -- examples
include mixture models, factor analysis, hidden
Markov models, Kalman filters and Ising
models...the graphical model formalism provides
a natural framework for the design of new
systems." --- Michael Jordan, 1998.
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2. Introduction to Bayesian Network
P(C)0.5, P(-C)0.5
Cloudy
Sprinkler
Rain
P(SC)0.1, P(-SC)0.9 P(S-C)0.5, P(-S-C)0.5
P(RC)0.8, P(-RC)0.2 P(R-C)0.2, P(-R-C)0.8
Wet Grass
P(WS,R)0.99, P(-WS,R)0.01 P(WS,-R)0.9,
P(-WS,-R)0.1 P(W-S,R)0.9, P(-W-S,R)0.1 P(W-
S,-R)0, P(-W-S,-R)1
From http//www.cs.ubc.ca/murphyk/Bayes/bnintro.
html
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2. Introduction to Bayesian Network

• Graphs in which nodes represent random variables
  (cloudy? sprinkler? rain? wet grass)
• Arrows represent conditional independence
  assumptions. (e.g. P(WS,R,C)P(WS,R))
• Present absent arrows provide compact
  representation of joint probability distributions
• BNs have complicated notion of independence,
  which takes into account the directionality of
  the arrows

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Bayes Rule
2. Introduction to Bayesian Network

• Can rearrange the conditional probability formula
• to get P(AB) P(B) P(A,B), but by symmetry we
  can also get P(BA) P(A) P(A,B) It follows
  that
•  The power of Bayes' rule is that in many
  situations where we want to compute P(AB) it
  turns out that it is difficult to do so directly,
  yet we might have direct information about
  P(BA). Bayes' rule enables us to compute P(AB)
  in terms of P(BA).

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2. Introduction to Bayesian Network
Need prior P for root nodes and conditional Ps,
that consider all possible values of parent
nodes, for nonroot nodes.
Cloudy
P(C)0.5, P(-C)0.5
Sprinkler
Rain
P(RC)0.8, P(-RC)0.2 P(R-C)0.2, P(-R-C)0.8
P(SC)0.1, P(-SC)0.9 P(S-C)0.5, P(-S-C)0.5
Wet Grass
P(WS,R)0.99, P(-WS,R)0.01 P(WS,-R)0.9,
P(-WS,-R)0.1 P(W-S,R)0.9, P(-W-S,R)0.1 P(W-
S,-R)0, P(-W-S,-R)1
From http//www.cs.ubc.ca/murphyk/Bayes/bnintro.
html
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Major benefit of BN
2. Introduction to Bayesian Network

• We can know P(W) based only on the conditional
  probabilities of W and its parent nodes (R and
  S). We dont need to know/include all the
  ancestor probabilities between W and the root
  nodes (C) .

Cloudy
Sprinkler
Rain
Wet Grass
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This BN benefit hugely reduces of numbers and
computations needed for large networks, e.g.
hundreds or thousands of genes
2. Introduction to Bayesian Network

• SSR article many separate Bayesian networks
  generated based on gene expression data. Here one
  activator and one repressor form basic BN, with 3
  corresponding expression contexts shown at
  bottom.

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2. Introduction to Bayesian Network
Cloudy
P(C)0.5, P(-C)0.5
Order of reduction of required numbersReduce
from 24-115 to 9
Sprinkler
Rain
P(RC)0.8, P(-RC)0.2 P(R-C)0.2, P(-R-C)0.8
P(SC)0.1, P(-SC)0.9 P(S-C)0.5, P(-S-C)0.5
Wet Grass
P(WS,R)0.99, P(-WS,R)0.01 P(WS,-R)0.9,
P(-WS,-R)0.1 P(W-S,R)0.9, P(-W-S,R)0.1 P(W-
S,-R)0, P(-W-S,-R)1
From http//www.cs.ubc.ca/murphyk/Bayes/bnintro.
html
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2. Introduction to Bayesian Network
Bayesian network general formulation
Given a graph G, the likelihood of observing the
data D
De Jong (2002)
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Evaluating Bayesian networks
2. Introduction to Bayesian Network

• Generally NP hard!

Where do the numerical estimates of probability
come from?

• Can be, at least initialized with, expert opinion
• Can be learned by system
• Both SSR and BSK articles lay out basics and some
  details of iterative algorithms for finding
  probability numbers.

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Modellinging regulatory network
2. Introduction to Bayesian Network
De Jong (2002)
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3. Case study

• Module networks identifying regulatory modules
  and their condition-specific regulators from gene
  expression data
• Segal, Shapira, Regev, Peer, Botstein, Koller,
  Friedman SSR
• Nature Genetics, June 2003
• Bayesian network-based algorithms are applied to
  gene expression data to generate good testable
  hypotheses.

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3. Case study

• Expression data set, from Patrick Browns lab, is
  for genes of yeast subjected to various kinds of
  stress
• Compiled list of 466 candidate regulators
• Applied analysis to 2355 genes in all 173 arrays
  of yeast data set
• This gave automatic inference of 50 modules of
  genes
• All modules were analyzed with external data
  sources to check functional coherence of gene
  products and validity of regulatory program
• Three novel hypotheses suggested by method were
  tested in bio lab and found to be accurate

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3. Case study
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3. Case study
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3. Case study

• 2 examples of 50 modules inferred by SSR methods
• Respiration mostly genes encoding respiration
  proteins or glucose-metabolism proteins. One
  primary regulator predicted Hap4 which is
  known from past experiments to play activation
  role in respiration. Secondary regulators affect
  Hap4 expression.
• Nitrogen catabolite repression 29 genes tied to
  process by which yeast uses best available
  nitrogen source. Key regulator suggested is Gat1,
  due to 26 of 29 genes having Gat1 regulatory
  motif in their upstream regions.

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3. Case study
Respiration Network
Two major motifs found
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3. Case study

• Evaluating module content and regulation programs
• All 50 modules were tested to see if proteins
  coded in same module had related functions
• Scored modules on how many genes are noted in
  current bio databases as being related to the
  predicted function diagram, next slide
• 31 of 50 modules had coherence gt50 only 4 had
  coherence lt30.

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3. Case study

• Colored boxes indicate that known experimental
  evidence validates the predicted regulatory role
  of a regulator (named in one of the Reg
  columns) in a given module (each row of the
  table).
• M, C and G column headers and different colors of
  boxes represent different sorts of experimental
  evidence that validate the models prediction.
• C() functional coherence of module, from
  literature mentions of module genes.
• G number of genes in module

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3. Case study

• To find global relationships between modules,
  graph (next 2 slides) made showing modules
  their motifs. Motifs were found within the 500
  base pairs upstream from each gene.
• Observations from this graph modules with
  related biological functions often shared at
  least one motif, sometimes shared one or more
  regulator genes.

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Module relationships
3. Case study
Yeast mutants of Kin82, Ppt1, Ypl230W were
further tests to validate their relationship with
the module.
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3. Case study
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What does a BN look like here?
3. Case study

• Need to specify two things to describe a BN
• Graph topology (structure)
• Parameters of each conditional probability
  distribution
• Possible to learn both from data
• Learning structure is much harder than learning
  parameters

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What can we learn?Why the Segals paper can be
successful?
3. Case study

• Yeast! Not mouse or human.
• Use gene clustering first. Start from simplified
  hypothesis and a small set of known regulators
  not to attempt a network of thousands of genes.
• Experimental validation.