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Microbes & Immunity Big data and DNN-based DTI model in CHP

profile of 1, indicating that the bindings of TFs, miRNAs, miRNAs binding to the n-th lncRNA. e [i], f [i], and g [i],
z
y
x
lncRNAs, and RNA polymerase to the l-th target gene still respectively, denote the expression levels of the x-th TF, the
exist. The expression level of the l-th gene results from y-th lncRNA, and the z-th miRNA in the i-th sample. o
mx
transcriptional regulations of TFs and lncRNAs, the post- denotes the transcriptional regulatory ability of the x-th
transcriptional regulations of miRNAs, and the basal level TF on the n-th lncRNA. ρ denotes the transcriptional
ny
of the l-th gene with measurement noise in Equation II. regulatory ability of the y-th lncRNA on the n-th lncRNA.
Furthermore, the transcriptional regulations of TFs and τ > 0 represents the post-transcriptional regulatory
nz
lncRNAs, the post-transcriptional regulations of miRNAs, ability of the z-th miRNA and the n-th lncRNA. N is the
and basal expression level (RNA polymerase binding) can total amount of lncRNAs in the candidate GWGEN, and
be influenced by DNA methylation in Equation III. I is the total amount of data samples (fibrosis slice cells
In addition, the miRNA regulatory system model of or non-fibrosis slice cells). u represents the basal level,
n
candidate GRN, describing the transcriptional expression that is, the change in expression of the n-th lncRNA due
of the m-th miRNA of lung slice cells for sample i, is to phosphorylation, ubiquitination, and acetylation. ν [i]
n
constructed by Equation IV: represents the random noise in the i-th sample due to the
residuals of modeling and measurement noise.
X m
Z m
Y m
ei[]+
di[]= ∑ η mx x ∑ κ my fi[]− ∑ λ mz gi di[] []+ c ++ hi[] 2.4. System identification and order detection
m
y
m
m
z
m
x=1 y=1 z=1 in stochastic regression models for real gene
for m = 1,2,…,M and i=1,2,…,I (IV) regulation network of candidate genome-wide and
EINs
where d [i] represents the expression level of the m-th
m
miRNA in the i-th sample. X , Y , and Z , respectively, After constructing the protein interaction regression model
m
m
m
represent the total numbers of TFs, lncRNAs, and for candidate PPINs in Equation I and the regulatory
miRNAs binding to the m-th miRNA. e [i], f [i], and g [i], models of genes/miRNAs/lncRNAs for candidate GRNs in
y
x
z
respectively, denote the expression levels of the x-th TF, the Equations II, IV, and V, we applied system identification
19
17
y-th lncRNA, and the z-th miRNA in the i-th sample. η method and system order detection scheme to identify
mx
denotes the transcriptional regulatory ability of the x-th protein interactions in the protein interaction model in
TF on the m-th miRNA. k denotes the transcriptional Equation I and genetic regulations of genetic regulation
my
regulatory ability of the y-th lncRNA on the m-th miRNA. models in Equations II, IV, and V. Using parameters a , β
kw
k
λ > 0 represents the post-transcriptional regulatory ability for the protein interaction model and δ , k , and τ for the
lx
my
nz
mz
of the z-th miRNA in degrading the m-th miRNA. M is the gene/miRNA/lncRNA regulatory models, we combined
total amount of miRNAs in the candidate GWGEN, and I lncRNA expression data and DNA phosphorylation,
is the total number of data samples (fibrosis slice cells or ubiquitination, and methylation of each lung slice cell
non-fibrosis slice cells). c represents the basal level due to with the protein interaction model and the gene/miRNA/
m
phosphorylation, ubiquitination, acetylation, or other gene lncRNA regulatory models to identify real GWGENs of
regulatory effects that are considered to have unknown CHP and non-CHP using their microarray data. Next, our
effects on the miRNA. h [i] represents the random noise goal was to use system identification and order detection
m
of the m-th miRNA in the i-th sample due to the residuals methods to filter out false-positive interactions and
17
from model establishment and experimental measurement regulations from the candidate GWGENs. In addition,
noise. Equations II, IV, and V can be represented as the following
linear regression equations (Equations VI-IX) to obtain
Furthermore, the lncRNA regulatory system model of the parameter vectors for protein interactions and gene
candidate GRN, describing the transcriptional expression regulations in candidate GWGEN of CHP and non-CHP. 18
level of the n-th lncRNA of lung cells for sample i, is
presented in Equation V: a a  
 k1 
X n Y n Z n  a k2 
qi[]= ∑ oe i[]+ ∑ ρ ny f i[]− ∑ τ nz g iq i[] []+ u ++ vi[] Si   =  Si Si Si Si   Si S  i    ×1  

 
 
 
k  
y
z
n
nx x
n
k  
n
n
x=1 y=1 z=1  k   1   k   2   Kk     
 a Kk 
for n = 1,2,…,N and i=1,2,…,I (V)  
 b k 
where q [i] represents the expression level of the n-th +ϕ i   =σ i   β* +ϕ i  
n
lncRNA in the i-th sample. X , Y , and Z , respectively, k   k   k k  
n
n
n
represent the total amount of TFs, lncRNAs, and for k = 1,2,…,K and i=1,2,…,I (VI)
Volume 2 Issue 2 (2025) 81 doi: 10.36922/mi.4620