Simulation and Application on learning gene causal relationships

1
Simulation and Application on learning gene
causal relationships

• Xin Zhang

2
Introduction

• High-throughput genetic technologies empowers to
  study how genes interact with each other
• Simulation to evaluate how well IC algorithm
  learns gene causal relationships
• We present an algorithm (mIC algorithm) for
  learning causal relationship with knowledge of
  topological ordering information, and apply it on
  Melanoma dataset
• Apply mIC algorithm on Melanoma dataset

3
Steps for Simulation Study

• Construct a causal network N
• Generate datasets based on the causal network
• Learning the simulated data using causal
  algorithms (e.g. IC algorithm) to obtain network
  N
• Compare the original network N with obtained
  network N w.r.t precision and recall

4
Modeling and simulation of a causal Boolean
network (BN)

• Boolean network

• Constructing a causal structure
• Assign parameters (proper functions) for each
  node with casual parents
• Assign probability distribution

5
Constructing Boolean Network

• 1. Generate M BNs with up to 3 causal parents for
  each node
• 2. For each BN, generate a random proper function
  for each node
• 3. Assign random probabilities for the root
  gene(s)
• 4. Given one configuration, get probability
  distribution
• 5. Collect 200 data points for each network
• 6. Repeat above steps 3-5 for all M networks.

6
Constructing Causal Structure
7
Steps for constructing causal structure
8
Proper function (1)
Proper function The function that reflects the
influence of the operators. Example
By simplifying f, c is a function of a with c
a b is a pseudo predictor of c, and has no
effect on c.
f is not a proper function.
9
Proper function (2)

• Definition

• With n predictors, the number of proper function
  is given by

10
Probability Distribution
11
Generating dataset
12
Steps of learning gene causal relationships

• Step1 obtain the probability distribution and
  data sampling
• Step2 apply algorithms to find causal relations
• Step3 compare the original and obtained networks
  based on the two notions of precision and recall
• Step4 repeat step 1-3 for every random network

13
Comparing two networks
A
B
A
B
D
C
D
C
Original Network
Obtained Network
14
Precision and Recall

• Original graph is a DAG, while obtained graph has
  both directed and undirected edges

Orig Graph Obt. Graph
FN
TP
TN
FP
PFN, PTP
PTN, PFP
Recall ATP/(AFNATP), Precision ATP/(ATP
AFP)
15
Observational equivalence and Transitive Closure

• Two DAGs are said to be observational equivalent
  (OE) if they have the same skeleton and the same
  set of v-structure

OE

• Transitive closure (TC)
• A -gtB -gt C with A -gt C
• cc(x,y) is true if there is a directed or an
  undirected edge from x to y
• pcc(x,y) is true if there is a path from x to y
  consisting of properly directed and undirected
  edges
• pcc(x,y) cc(x,y) pcc(x,z) ? pcc(z,y)

16
Result for IC algorithm
17
How to improve IC algorithm

• The original IC algorithm did not have good
  results on learning gene causal relationships
• A possible way to improve the performance is to
  incorporate extra information
• If we know the topological ordering of the
  regulatory network, it would be helpful to
  improve the learning result

18
Gene topological ordering

• If a specific gene is the causal parent of
  another gene
• In a pathway, if one gene appears before another
  gene
• If one gene is at the beginning or at the end of
  the pathway

IC algorithm topological ordering information
19
mIC algorithm

• mIC algorithm based on IC, but incorporates both
  topological ordering information with steady
  state data to infer causality
• 3 Steps of mIC algorithm
• Find conditional independence
• For each pair of gene gi and gj in a dataset,
  test pairwise conditional independence. If they
  are dependent, search for a set
• Sij gk gi and gj are independent given gk,
  with iltkltj, or jltklti.
• Construct an undirected graph G such that gi and
  gj are connected with an edge if an only if they
  are pairwise dependent and no Sij can be found
• Find v-structure
• For each pair of nonadjacent genes gi and gj
  with common neighbor gk, if gk ?Sij, and kgti,
  kgtj, add arrowheads pointing at gk, such as
  gi -gtgk lt- gj
• Orientate more directed edges according to rules
• Orientate the undirected edges without creating
  new cycles and v-structures

20
Results from mIC algorithm
21
Melanoma dataset

• The 10 genes involved in this study chosen from
  587 genes from the melonoma data
• Previous studies show that WNT5A has been
  identified as a gene of interest involved in
  melanoma
• Controlling the influence of WNT5A in the
  regulation can reduce the chance of melanoma
  metastasizing

22
Applying mIC algorithm on Melanoma Dataset
Partial biological prior knowledge MMP3 is
expected to be the end of the pathway
23
Conclusion

• Evaluated IC algorithm using simulation data
• We presented mIC algorithm that can infer gene
  causal relationship from steady state data with
  gene topological ordering information
• Performed simulation based on Boolean network to
  evaluate the performance of the causal
  algorithms
• We applied mIC algorithm to real biological
  microarray data Melanoma dataset
• The result showed that some of the important
  causal relationships associated with WNT5A gene
  have been identified using mIC algorithm.