A Bayesian Statistical Approach to Modeling Gene Regulatory Pathways in
Human Placental Data
Elinor VelasquezDept. of Biology
San Francisco State University
Outline of talk
• Introduction• The experimental approach: Obtaining
placenta data• The experimental approach: Modeling gene
regulatory networks• Results from experiments• Conclusions and future work• Acknowledgements
Introduction
Overall goal
http://www.biotechnologycenter.org/hio/assets/hisimages/placenta/placenta44.jpg
To use a bioinformatics model for which to better understand the human placenta
The human placenta
http://www.uchsc.edu/winnlab/index.html
The basal plate in the placenta
Site of known anatomical abnormalities in preeclampsia
http://www.uchsc.edu/winnlab/projects.html
EGFR pathway
• EGFR, cell surface receptor for epidermal growth factors
• Potentially important gene for the placenta
British Journal of Cancer (2006) 94, 184 – 188
EGFR regulates gene expression
EGFR
ANGPT2 CSPG2 DCN
Causal relationships
EGFR
ANGPT2 CSPG2 DCN
Example of a gene regulatory network
Gene 1
Gene2
Gene 3
Gene 5
Gene 6Gene
4
Definition of a Bayesian network
• There exist nodes (disks)
• There are edges (arrows) between some of the nodes
• Causality is implied by the edges
• Acyclic
Gene 1
Gene2
Gene 3
Gene 5
Gene 6Gene
4
The experimental approach: Obtaining placenta data
Data collected from microarrays• Data comes from 36
experiments conducted by Virginia Winn et al. at the SJ Fisher lab, UCSF
• Gene expression profiling experiments
45000 dots (25-mer oligo probe sets)
representing the human genome
cRNA
hybridization
Traditional “spotted” arrays
What is a probe set?
• Several oligonucleotides designed to hybridize to various parts of the mRNA generated from a single gene
Probe set
mRNA
gene
Affymetrix GeneChips
Microarray data
The normalized log 2 intensity values were centered to the median value of each probe set, by Virginia Winn et al.
A probe set x1 ... x6 y1 ... y9 z1 ...z6 w1...w6 s1 ... s9
1 2 3 4 5
5 time segments:
36 data points per probe set
Microarray data• Red denotes the up regulated expression and green denotes
the down regulated expression relative to the median value• Genes differentially expressed in the basal plate of
placentas: Rows contain data from a single basal plate cRNA sample and columns correspond to a single probe set.
http://www.uchsc.edu/winnlab/index.html
Summary of data used in bioinformatics experiments
• 36 placentas• 45, 000 probe sets
• Time-series data from
14-16 weeks to term
Gene egfr
The experimental approach: Modeling gene regulatory
networks
Outline of bioinformatics experimental design
Step 1. Create a naïve Bayesian network using the probe set dataStep 2. Score the naïve Bayesian networkStep 3. Randomly add/delete an edge and rescore the Bayesian
networkStep 4. Continue until best score reachedStep 5. Combine probe sets to create the gene regulatory network
PS1
PS 2 PS
3
PS4
Four probe sets (Three genes)
Define naïve Bayesian network
• Choose a root node• All other nodes branch
off of the root node• PS1 is the parent node
PS1
PS 2 PS
3
PS4
Step 1: Create a naïve Bayesian network using probe set data
• Use data from one time segment• Choose Weeks 23-24 data (6 placentas)• Choose 4 probe sets
PS1
PS2 PS3 PS4
Placenta data for Weeks 23-24
PS1 corresponds to 201984 which corresponds to EGFR
PS2 corresponds to 236034, PS3 corresponds to 211148: PS2 and PS3 both correspond to ANGPT2
PS4 corresponds to 204620 which corresponds to CSPG2
Step 2: Score the naïve Bayesian network
• We want to score this network:
PS1
PS2 PS4 PS3
The network score is a function of conditional probabilities
• Conditional probability, Prob(N | Pa(N)), is the probability of child node N given parent of N
• Example: Given a parent PS1’s node has an associated expression value 10, what is the probability that its child node, PS4, has an expression value of 8?
PS1
PS4
Conditional probability
• EGFR (PS1) is the parent node and has value 10. • CSPG2 (PS4) is the child node and has value 8 two times• Conditional probability = 2/6
PS1
PS4
Score for a Bayesian network
The score of the naive network equals the product of all the nonzero conditional probabilities associated with the network:
P(N1, N2, N3, N4) = Π P(Ni | pa(Ni))i=1
4
Score for the naïve Bayesian network
P(N1, N2, N3, N4) = 1/3966
= 2.54 x 10-5
PS1
PS4PS2 PS3
Step 3: Randomly add/delete an edge and rescore the Bayesian network
The score becomes 1/78732 = 1.27 x 10-5.
PS1
PS2
PS4
PS3
Step 4. Continue until best score reached
• Since the score is a probability, we want the score to be high.
• The naïve network is the better choice between the two networks, so we pick it as our final network.
PS1
PS4PS2 PS3
Step 5. Combine probe sets to create the gene regulatory network
CSPG2ANGPT2
EGFR
40 probe sets (26 genes)
Gene regulatory pathwayfor 26 genes
Step 1. Create a naïve Bayesian network using 40 probe sets for each time segment
Step 2. Score the naïve Bayesian networkStep 3. Randomly add/delete an edge and rescore the Bayesian
networkStep 4. Continue until best score reachedStep 5. Combine probe sets to create the gene regulatory
network for the placenta
Step 1. Create a naïve Bayesian network using 40 probe sets for each time segment
Create a naïve Bayesian network
PS1
PS 2 PS
3
PS4
PS5
PS9
PS6
PS8
PS7
Step 2. Score the naïve Bayesian network
Score for a Bayesian network
The score of the naive network equals the product of all the nonzero conditional probabilities associated with the network:
P(N1, N2, N3, N4) = Π P(Ni | pa(Ni))
40
i=1
Step 3. Randomly add/delete an edge and rescore the Bayesian network
Step 4. Continue until best score reached
With four probe sets, at least two Bayesian networks were constructed:
PS1
PS4PS2 PS3
PS1
PS2
PS4
PS3
Exhaustive search
• To be certain that we have the best scoring network, we need to construct all possible networks from our naïve networks
• With four probe sets, we only constructed one other network than the naïve network
• How to construct all possible networks?
How do we construct all possible networks?
• 1 probe set 1 Bayesian network• 2 probe sets 2 possible Bayesian networks• 3 probe sets 12 possible Bayesian networks• 4 probe sets 144 possible Bayesian networks• 5 probe sets > 4800 possible Bayesian networks!• 6 probe sets … ??• And so on…
Welcome to “Modern Heuristics”• Step 1. Representation of a model• Step 2. The scoring function • Step 3. Defining the search problem• Step 4. Consider local optima
score
local
change
Step 1: Representation of the model
• The model is a gene regulatory pathway.• We are going to assume a Bayesian model for our probe
set:
• The number of possible pathways is so large as to forbid an exhaustive search for the best Bayesian network.
PS1
PS 2 PS
3
PS4
Step 2: The scoring function
• The fair coin, p(X = heads) = ½• What happens if the coin is unfairly weighted?• We need to re-think probability:
p(X) = ∫p(x) r(x) dx
• r(x) is a weight function.
Step 2. The scoring function
• The scoring function is a probability
• Assume the network has a Dirichlet distribution which is the weight function used to weight the conditional probabilities.
www.wikipedia.com
Step 2. The scoring function
Probability of a fixed network equals product of conditional probabilities times the Dirichlet distribution:
P(N) = Π P(Ni | pa(Ni)) D(Ni)40
i = 1
D(Ni) = ∏ Θiάi-1(N i)
such that
Step 3: Defining the search problem
What it means to search: a. Construct a first network (Use a naïve
Bayesian network) b. Score the first network using the scoring
function c. Perform the Hill-climbing algorithm.
Step 3. Defining the search problem The Hill-climbing Algorithm:
• Randomly choose a node• “Search” in the neighborhood of that node for
the best scoring network
Step 4. Consider local optima
• Hill-Climbing is a traditional method for search techniques
• Can get caught on local maxima
• Step 4 is to keep choosing random nodes.
From http://content.answers.com/
score
local
change
randomly chosen node is the origin
Software • Weka software package written by members of the University of
Waikato, New Zealand, http://www.cs.waikato.ac.nz/~ml/people.html
• DEAL, R package, written by Susanne G. Bøttcher, Claus Dethlefsen, http://www.math.auc.dk/novo/deal
• BayesNet Toolbox, Matlab package, written by Kevin Murphy, http://www.cs.ubc.ca/~murphyk/Software/BNT/bnt.html
• ExpressionNet, written by Jingchun Zhu, http://expressionnet.sourceforge.net/
Results from experiments
26 genes
IGFBP1
PLAU
MRC2
ATP5E
ERG
PECAM1IL2RB CECAM1 CYP19A1
USP6NL
EGFR
ADAM9
GLB1
CCNG2
RAP2B
P4HA1
BAMBI
INHBA
CSPG2
DCNCOL5A2COL5A1
COL3A1
COL1A2
SPP1
ANGPT2
SFRP1
Ingenuity network
Results for 26 genes
• 40 probe sets (26 genes)• Data comes from five different time intervals: 1. 14 – 16 gestational weeks 2. 18 – 19 gestational weeks 3. 21 gestational week 4. 23 – 24 gestational weeks 5. 37 – 40 gestational weeks
Time Segment:
Week 14-16 weeks
IGFBP1
PLAU
MRC2
ATP5E
ERG
PECAM1IL2RB CECAM1 CYP19A1
USP6NL
EGFR
ADAM9
GLB1
CCNG2
RAP2B
P4HA1
BAMBI
INHBA
CSPG2
DCNCOL5A2COL5A1
COL3A1
COL1A2
SPP1
ANGPT2
SFRP1
IGFBP1
PLAU
MRC2
ATP5E
ERG
PECAM1IL2RB CECAM1 CYP19A1
USP6NL
EGFR
ADAM9
GLB1
CCNG2
RAP2B
P4HA1
BAMBI
INHBA
CSPG2
DCNCOL5A2COL5A1
COL3A1
COL1A2
SPP1
ANGPT2
SFRP1
Time segment:
18 – 19 weeks
IGFBP1
PLAU
MRC2
ATP5E
ERG
PECAM1IL2RB CECAM1 CYP19A1
USP6NL
EGFR
ADAM9
GLB1
CCNG2
RAP2B
P4HA1
BAMBI
INHBA
CSPG2
DCNCOL5A2COL5A1
COL3A1
COL1A2
SPP1
ANGPT2
SFRP1
Time segment:
21 weeks
IGFBP1
PLAU
MRC2
ATP5E
ERG
PECAM1IL2RB CECAM1 CYP19A1
USP6NL
EGFR
ADAM9
GLB1
CCNG2
RAP2B
P4HA1
BAMBI
INHBA
CSPG2
DCNCOL5A2COL5A1
COL3A1
COL1A2
SPP1
ANGPT2
SFRP1
Time segment:
23 – 24 weeks
IGFBP1
PLAU
MRC2
ATP5E
ERG
PECAM1IL2RB CECAM1 CYP19A1
USP6NL
EGFR
ADAM9
GLB1
CCNG2
RAP2B
P4HA1
BAMBI
INHBA
CSPG2
DCNCOL5A2COL5A1
COL3A1
COL1A2
SPP1
ANGPT2
SFRP1
Time segment:
37 – 40 weeks
How to display data
• One of the most pressing questions in bioinformatics research is how to display the data effectively
• We have two solutions 1. An interaction map 2. Geometrical considerations
An interaction map for 26 genes
Geometrical considerations
• Will illustrate with the gene egfr• egfr is an epidermal growth factor Functions on the cell surface Activated by binding of its specific ligands Responsible for many pathways in animal
models
Gene egfr regulated by:
Genes on a dodecahedron: Gene regulatory network for egfr
Adapted from http://www.math.cornell.edu/~mec/2003-2004/geometry/platonic/dodecahedron.jpg
PLAU
CCNG2 COL1A2
CSPG2
INHBA
DCN
On backside:PECAM1ANGPT2IGFBP1MRC2 SPP1USP6NL
Conclusions
• We can predict gene regulatory networks using Bayesian networks as an intermediate step
• When we leave arrows in network, we are able to show causal relationships between the genes
• Interaction maps and use of geometry are novel ways to display gene behavior
Future Directions
• A three-dimensional viewer with numerical values will be implemented to use with the Weka software
• Use molecular genetics techniques to validate a portion of the results
• Design a genetic programming algorithm (evolutionary algorithm) to create a Bayesian network
Acknowledgements San Francisco State University: Leticia Márquez-Magaña, Chris Smith, Frank Bayliss, Juan Castellon, Ernesto
Flores, Rebecca Garcia, Alba Gutierrez, Jainee Lewis, Rebecca Mendez, Cylyn Cruz, Jasmin Reyes, Jackie Robinson, Peter Thorsen, My family
UC San Francisco:Susan Fisher, Matthew Gormley
M.B.R.S.-R.I.S.E. Grant 5 - R25-GM59298
Top Related