Page 61 - TD-4-1

Tumor Discovery Drug repurposing for pancreatic cancer via AI

Next, with N representing microarray data samples, we constraints to ensure that the degrading effects of miRNAs
can express these as linear Equations V–VIII: on post-transcriptional genes, lncRNAs, and miRNAs
are negative. The parameter estimation problem for the

GWGENs of PDAC and non-PDAC can be solved by the
1
1
w
p 1 w w following constrained least-squares parameter estimation

p 2 2 2 (IX) problem equations:
w w w w
   ˆ 1 2
Θ = argmin Φ ⋅Θ − P w 2 (XVII)
w
w
w
N
N

N N
w
p w Θ w 2
w
for w =1,2…,W-1,W, n = 1,2…,N-1,N ˆ 1 2
Θ = argmin Φ ⋅Θ −G x 2 (XVIII)
x
x
x
Θ x 2

1
1
g 1 x x
x

g 2 2 2 X) 0

x x x x 0 0 0 0 1 0 0
  

0 x

N

N
x
g NN x subject to
x
0 0
0 0
0 1 0

for x = 1,2…,X-1,X, n = 1,2…,N-1,N
S x U x V x

1
1
ˆ
y
l 1 y y Θ = argmin 1 Φ ⋅Θ − L 2 (XIX)

l 2 2 2 (XI) y Θ y 2 y y y 2

y y y y
   0

N
N

y
y
l NN y 0 0 0 0 1 0 0

for y =1,2…,Y-1,Y, n = 1,2…,N-1,N subject to 0 0 0 0 0 1 0 y

0

S y U y V y
1
1
z
m 1 z z

m 2 2 2 (XII) 1

ˆ
z z z z Θ = argmin Φ ⋅Θ − M 2 (XX)
   z Θ z 2 z z z 2

N

z
z
mN NN z 0

for z = 1,2…,Z-1,Z, n = 1,2…,N-1,N 0 0 0 0 1 0 0

Further Equations IX–XII can be represented by the subject to 0 z

following algebraic equations individually: 0 0 0 0 0 1 0

P w w for w 12, , W 1, W (XIII) S z U z V z
w
w
G for x 12, , X 1, X (XIV)
x
x
x
x
Given that the regulatory effects of miRNAs on post-
L y y for y 12, , Y 1, Y (XV) transcriptional genes, lncRNAs, and other miRNAs must
y
y
be negative, we utilized the MATLAB Optimization
M z z for z 12, , Z 1, Z (XVI) Toolbox to solve the constrained least-squares parameter
z
z
where Φ w is the linear regression matrix for proteins, estimation problems with their added constraints in
Φ x is the linear regression matrix for genes, Φ y is the Equations XVII–XX. This approach allowed us to derive
linear regression matrix for lncRNAs, and Φ z is the linear optimal estimated parameter vectors for PPIs, as well
regression matrix for miRNAs. as for gene, lncRNA, and miRNA regulations within the
Next, we employed a constrained linear least-squares GWGENs for both PDAC and non-PDAC.
parameter estimation method to estimate parameter To address the issue of numerous false positive
vectors Φ w, Φ x, Φ y and Φ z. Specifically, we imposed interactions identified among the candidate GWGENs, we
Volume 4 Issue 1 (2025) 53 doi: 10.36922/td.4709