A Practical Guide to Cancer Systems Biology

106 A Practical Guide to Cancer Systems Biology

fold change selection are usually applied to gene expression profiles from
the transcriptomics data for global selection of genes of interest. In this
case, the constructed network will represent the global scenario for all the
dynamically regulated genes under the experimental condition. If one-way
ANOVA is employed to detect significant gene expression variations across
different time-points for each gene, the null hypothesis of ANOVA assumes
that the average expression level of a gene would be the same at every time
point.^3 Usually, genes with Bonferroni-adjustedp-values of less than 0.05
are identified as dynamically regulated genes and selected as the genes of
interest. On the other hand, the function-based selection method is applied
only if we want to construct the network for some specific functions. Gene
ontology annotations are useful tools for functional annotation of genes.^4

3.2. Model structure construction

The construction of model structure represents determination of the updat-
ing functiong(m, t) (the right-hand side of the discrete dynamic model (9.3)),
which depends on the prior knowledge about the investigated biological
systems and the experimental data itself. In the case of gene regulation
modeling, we consider a gene regulation relationship as a system block with
several regulatory genes as inputs and a target gene as output. Based on our
knowledge about the transcriptional regulation, for a target geneiamong the
genes of interest, the temporal expression of the target gene can be described
by the following discrete dynamic model:

xi(t+1)=xi(t)+

∑Ni

j=1

aijxj(t)−λixi(t)+ki+εi(t) (9.4)

wherexi(t) represents the gene expression level of target geneiat timet,aij
denotes the regulatory ability of thej-th regulatory gene for the target gene
iwith a positive value indicating activation and a negative value indicating
repression,xj(t) represents the gene expression level for thej-th regulatory
gene that potentially regulates target genei, Ni denotes the number of
genes potentially regulating genei,λiindicates the degradation effect of the
target genei,kirepresents the basal expression level, andεi(t)represents
the stochastic noise due to the model uncertainty. The biological implication
of the discrete dynamic model (9.4) is that the gene expression level of target
geneiat the next timet+ 1 is determined by the present gene expression
level, the regulation ofNiregulatory genes, the degradation effect of the
present time, the basal level of gene expression, and some stochastic noises,^5
which coincides with our realization of transcriptional regulation.