Target Discovery and Validation Reviews and Protocols

Gene Networks 49
network and nonparametric regression model. After determining the threshold,
we compute the conditional probability table of the multinomial distribution. Let
X j be a discrete type random variable. The posterior probability of X j = u k |Pa(X j ) =
u jl conditional on the n sets of data D = {x i ,…,x n } can be written as follows:
π post (X j = u k ⏐Pa(X j ) = u jl ) =
α jkl + N jkl
∑ k′(α
jk′l + N jk ′ l)
If a gene is directly affected by a drug, the expression level of the gene may
be overexpressed or suppressed independently on the expression level of its parent
genes. In contrast, if a gene is not directly affected by a drug, the expression
value should be determined by the expression values of its parent genes. Based
on this assumption, we define a score function called drag-affected score
(DAS)j that determines whether jth gene is affected by a drug or its parents,
DAS j (x,u) = πpost(X j = x⏐Pa(X j ) = u)
,
Pr (X j = x)
where x and u are the observed expression values of jth gene and its parents,
and Pr(Xj ) is the marginal probability given by Pr(Xj ) = ΣXj :i ≠ j Pr(X1 ,…, Xp ).
This marginalization is often referred as the probabilistic inference and takes
exponential time for the number of genes and is infeasible for the large network.
To compute this interference efficiently, several approximation algorithms have
been proposed. In this chapter, we use the loopy belief propagation algorithm.
For additiontal comments on the probabilistic inference based on the Bayesian
networks, see Note 11.
Let xj (t) and pj (t) is the expression values of jth gene and its direct parents
at time t. The procedure for finding drug-active pathways can be performed by
the following steps.
Step 1. Construct the time-expanded network from the estimated gene network.
Step 2. Compute DASj (xj (t), pj (t)) and put the constant c (c>0),
if DASj (xj (t), pj (t)) ≤ c, jth gene at time t is called a drug-active gene,
if DASj (xj (t), pj (t)) > c –1 , jth gene at time t is called a parent-active gene.
We call both drug-active and parent-active genes affected genes.
Step 3. If a direct edge, in the time-expanded network, from Xu (t) to Xv (s), where
Xu (t) is a node corresponding to uth gene at time t, satisfies with a condition
out of three, this direct edge is called a drug-active path.
(i) Xv (s) is a drug-active gene, where s = t + 1 (Fig. 8a).
(ii) Xv (s) is a parent-active gene, where s = t (Fig. 8b).
(iii) Xv (s) is an affected gene, where s = t + 1 and v = u (Fig. 8c).
Step 4. Extract connected components of the drug-active paths from the timeexpanded
network.
.