consensus gene connections from different networks are identified
based onp-value calculated by the Fisher’s inverse^2 test. Perfor-
mance investigation by the Dialogue on Reverse Engineering
Assessment and Methods (DREAM) project shows that the com-
bining approach outperforms each of single methods [23].2.2 Methods
for Dynamic Networks
In previous section, we have discussed inferring methods for static
networks, which are not limited to a certain physiological condi-
tion. Actually, many gene regulatory networks are conducted in a
specific biological system with a certain physiological condition, in
which gene expression data is generated at some discrete time
points dynamically. In this scenario, GRNs inferred with these
expression data are dynamic and present stochastic characteristics
for a specific biological system. For dynamic GRNs, two types of
equations are adopted to depict characteristics of these networks
commonly. One type of formula is expression equation, which
presents expression function for genes under a certain physiological
condition (regarded as a state in mathematics) [24]. Another type
of formula is regulation equation, which provides regulatory links
between genes. According to mathematical forms of expression and
regulation function, the dynamic networks can be categorized into
linear and nonlinear state-space models.2.2.1 Linear State-Space
Models
In these models, the expression and regulation functions are
depicted with the simplest linear function as follows.xi∗ðÞt ¼xiðÞt þuiðÞt, i¼1, 2,...m, t¼1, 2,...kxiðÞ¼tþ 1Xmj¼ 1ai,jxjðÞþt viðÞt ð^8 Þwheremis the number of total genes (these genes are measured at
kdiscrete time points);xi(t) is the actual expression value of theith
gene at timet, whilex∗iðÞt is corresponding measure value of theith
gene at timet;ui(t) andvi(t) are the measurement and system noise
of theith gene at timet; andai,jpresents relationship between
genesiandj. Through an expectation maximization algorithm,
both the model parameters (i.e., the A matrix and U, V vectors) and
actual expression value X can be estimated effectively [25].2.2.2 Nonlinear State-
Space Models
It is imperative to inflect nonlinear effects on the expression and
regulation function for dynamic GRNs since there is complex reg-
ulatory relationship between genes. Particularly, the sigmoid func-
tion is employed to capture these complex regulations between
gene pairs.142 Guangyong Zheng and Tao Huang