Page 59 - TD-4-1

Tumor Discovery Drug repurposing for pancreatic cancer via AI

R w S y U y V y
w
y
n pn
ln
n
tn
ln
p n wr p r w PPIN w PPIN (I) ln ys s yu u yv mn
w
v
y

r1 s1 u1 v1
n (III)

for w = 1,2…,W-1,W，n = 1,2…,N-1,N y y
among which p w [n] and p r [n] denote the expression for y = 1,2…,Y-1,Y, n = 1,2…,N-1,N
levels of the w-th protein and the r-th protein in the n-th
sample, respectively; π w r represents the interaction ability where l y [n] indicates the expression level of the y-th
−
between the r-th protein and the w-th protein; R w is the lncRNA in the n-th sample; S y, U y, and V y represent the total
total number of proteins interacting with the w-th protein; numbers of TFs, lncRNAs, and miRNAs binding to the y-th
W denotes the total number of proteins in the candidate lncRNA, respectively; t s [n], l u [n], and m v [n] denote the
PPIN; N is the number of data samples (PDAC or non- expression levels of the s-th TF, the u-th lncRNA, and the
PDAC); β w PPIN indicates the basal expression level of the v-th miRNA in the n-th sample, respectively; ζ y s symbolizes
−
−
w-th protein, reflecting changes due to interactions such the transcriptional regulatory ability of the s-th TF on the
as acetylation, phosphorylation, or unknown histone y-th lncRNA; ψ y u signifies the transcriptional regulatory
−
modifications that cannot be modeled in (1); δ w PPIN [n] ability of the u-th lncRNA on the y-th lncRNA; k y v > 0
−
−
accounts for random noise affecting the w-th protein in represents the post-transcriptional regulatory ability of the
the n-th sample due to modeling residuals, experimental v-th miRNA in degrading the y-th lncRNA’s miRNA; Y is the
measurement errors, or environmental interference. total number of lncRNAs in the candidate GWGEN; N is the
number of data samples (PDAC or non-PDAC); β y reflects
After establishing the PPI system model, we also the expression basal level of the y-th lncRNA, influenced
developed a regulatory system model to describe the by modifications such as phosphorylation, acetylation, or
relationships between genes and their regulators, including unknown gene regulatory effects; δ y [n] captures the random
TFs, miRNAs, and lncRNAs. The transcriptional regulation noise affecting the y-th lncRNA in the n-th sample due to
system model for the x-th gene in the n-th sample can be modeling residuals and measurement errors.
expressed as: 28
Finally, we established the miRNA regulatory system
S x U x V x model in a similar manner. The transcriptional regulation
x
g n xs s xu u xv mn g x n system model for the z-th miRNA in the n-th sample can
tn
ln
v

s1 u1 v1
x x n (II) be described by the following equation:

S z U z V z
z
ln
tn
v
for x = 1,2…,X-1,X, n = 1,2…,N-1,N mn zs s zu u zv mn

s1 u1 v1
where g x [n] indicates the expression level of the x-th mn n (IV)

gene in the n-th sample; S x, U x, and V x represent the total z z z
number of TFs, lncRNAs, and miRNAs binding to the x-th for z = 1,2…,Z-1,Z, n = 1,2…,N-1,N
gene, respectively; t s [n], l n [n], and m v [n] denote the where m z [n] represents the expression level of the z-th
expression levels of the s-th TF, the u-th lncRNA, and the miRNA in the n-th sample; S z, U z, and V z indicate the total
v-th miRNA in the n-th sample, respectively; α x s symbolizes number of TFs, lncRNAs, and miRNAs binding to the z-th
−
the transcriptional regulatory ability of the s-th TF on the miRNA, respectively; t s [n], l u [n], and m v [n] denote the
x-th gene; γ x u signifies the transcriptional regulatory ability expression levels of the s-th TF, the u-th lncRNA, and the
−
of the u-th lncRNA on the x-th gene; εx − y > 0 indicates the v-th miRNA in the n-th sample, respectively; λ z s symbolizes
−
post-transcriptional regulatory ability of the v-th miRNA in the transcriptional regulatory ability of the s-th TF on the
degrading the x-th gene’s miRNA; X is the total number of z-th miRNA; µ z u signifies the transcriptional regulatory
genes in the candidate GWGEN; N is the number of data ability of the u-th lncRNA on the z-th miRNA; ρ z v > 0
−
samples (PDAC or non-PDAC); β x represents the basal represents the post-transcriptional regulatory ability of the
−
expression level of the x-th gene, influenced by modifications v-th miRNA in degrading the z-th miRNA’s miRNA; Z is
such as methylation, phosphorylation, acetylation, or the total number of miRNAs in the candidate GWGEN; N
unknown gene regulatory effects; δ x [n] accounts for the is the number of data samples (PDAC or non-PDAC); β z
random noise affecting the x-th gene in the n-th sample due indicates the change in the expression of the z-th miRNA
to modeling residuals and measurement errors. due to phosphorylation, acetylation, or unknown gene
Next, we established the regulatory system model for regulatory effects; δ z [n] accounts for the random noise
lncRNA. The transcriptional regulation system model for affecting the z-th miRNA in the n-th sample due to model
the y-th lncRNA in the n-th sample is described as: residuals and experimental measurement errors.
Volume 4 Issue 1 (2025) 51 doi: 10.36922/td.4709