Computational Systems Biology Methods and Protocols.7z

are standard deviations of genes X and Y, andσRxandσRyare
standard deviations of rank variablesXandY.
In the recent years, the Gini correlation coefficient (GCC)
measurement is used to detect correlation of genes for network
reconstruction, which can compensate for the shortcomings of the
PCC and SCC measurements and thus provide more reliable cor-
relation of genes [11]. The GCC measurement between genes X
and Y is described by the following equations.

GCC XðÞ¼;Y

Pn

i¼ 1

ðÞ 2 in 1 vxðÞi;y

Pn

i¼ 1

ðÞ 2 in 1 vxðÞi;x

GCC YðÞ¼;X

Pn

i¼ 1

ðÞ 2 in 1 vyðÞi;x

Pn

i¼ 1

ðÞ 2 in 1 vyðÞi;y

ð 2 Þ

wherenis the number of experiment,vx(i,x) is theith expression
value of gene X stored in an increasing order, vx(i,y) is the
corresponding expression value of gene X in the gene pair (X, Y)
for theith expression value of gene Y stored in an increasing order,
whilevy(i,x) andvy(i,y) are defined similarly tovx(i,y) andvx(i,x),
respectively. According to Eq.2, the GCC measurement can be
considered as differences between two curves weighted by the
information deriving from the rank order of gene expression data.
In practice, the GCC measurement between genes X and Y is
designed as the higher value among GCC(X,Y) and GCC(Y, X).
In addition, the measurement of mutual information (MI) is
also utilized to calculate correlation between genes widely. For the
MI measurement, it can detect nonlinear and non-monotonic rela-
tionship [8, 10, 12]. The mutual information between two genes X
and Y is defined as the following equation based on the information
theory.

MI XðÞ¼;Y

X

y∈Y

X

x∈X

pxðÞ;ylog

pxðÞ;y

pxðÞpyðÞ



ð 3 Þ

wherep(x,y) is the joint probability distribution of X and Yp(x) and
p(y) are the marginal probability distribution of X and Y, respec-
tively. According to information theory, assuming that the gene X is
similar to gene Z, which is similar to gene Y simultaneously, then a
similar conclusion between genes X and Y is drawn easily. Actually,
whether the genes X and Y are similar or not should consider the
gene Z. Therefore, in the recent years, the conditional mutual
information (CMI) measurement is proposed to reduce false-posi-
tive rate of the MI measure in correlation computing [13, 14]. The

The Reconstruction and Analysis of Gene Regulatory Networks 139