19BIO201
Intelligence in Biological Systems - 3
Linear Neighbourhood Propagation method for predicting Long Non-Coding RNA-Protein Interactions
19BIO201
Intelligence in Biological Systems - 3
Aadharsh Aadhithya - CB.EN.U4AIE20001
Anirudh Edpuganti - CB.EN.U4AIE20005
Madhav Kishor - CB.EN.U4AIE20033
Onteddu Chaitanya Reddy - CB.EN.U4AIE20045
Pillalamarri Akshaya - CB.EN.U4AIE20049
Team-1
Non Coding DNA
Non Coding DNA
- Non coding regions in dna are regions which do not code for proteins
- only about 1% of DNA is estimated to be coding
- However, It is of importance as it contains sequences that can act as regulatory elements
Non Coding DNA
- Promoters
- Enhancers
- Silencers
- Insulators
Non Coding DNA
Other Regions Code for RNA's like tRNA's and rRNA's
Non Coding DNA
- Recent studies have proved that only one-fifth of transcription across the human genome is associated with protein-coding genes
- Expressed in Tissue Specific contexts
- long non-coding RNAs, which consist of more than 200 nucleotides, have gained wide attention because of their large number and their essential functions
Non Coding DNA
- lncRNAs play an important role in regulating many biological processes, such as transcription, splicing and gene expression
- Because of the high cost of experimental identification for lncRNA– protein interactions, a great number of computational methods have been developed.
Features
Features
l1
l_1
l1
l_1
l2
l_2
l3
l_3
.
.
.
.
.
.
ln
l_n
p1
p_1
p2
p_2
pm
p_m
.
.
.
.
.
.
eij=1pi intereacts with lj
e_{ij} = 1 \,\, p_i \text{ intereacts with } l_j
Features
l1
l_1
l1
l_1
l2
l_2
l3
l_3
.
.
.
.
.
.
ln
l_n
p1
p_1
p2
p_2
pm
p_m
.
.
.
.
.
.
Interaction
Profile of l1
Interaction
Profile of p1
Expression Profiles
li
l_i
1,2,⋯24
1 , 2 , \cdots 24
24 Types of Human Tissues
Expression Profile vector
liACGAATCGAAGT
l_i \,\,\,\, ACGAATCGAAGT
A%
A\%
C%
C\%
G%
G\%
T%
T\%
AA%
AA\%
AG%
AG\%
⋯
\cdots
1,2,3⋯20
1,2,3 \cdots 20
Long Noncoding RNA Sequence Composition
Features for Proteins
- Interaction Profile
- Composition,Transition,Destruction Vectors
- Interaction Profile
- Expression Profile
- Sequence Composition
- Interaction Profile
- CTD
lncRNA
Proteins
Linear Neighbourhood Similarity
Linear Neighbourhood Similarity
- Local Neighbourhood of a manifold in feature space can have a linear approximation
- Hence, A datapoint can be a linear combination of its neighbouring points
Linear Neighbourhood Similarity
wij
w_{ij}
Reconstructive
Contribution of j
Xi
X_i
Xi1
X_{i1}
Xi2
X_{i2}
Xij
X_{ij}
wij
w_{ij}
Linear Neighbourhood Similarity
Xi2
X_{i2}
∑j∈N(Xi)wij=1
\sum_{j\in N(X_i)} w_{ij} =1
Xi
X_i
Xi1
X_{i1}
Xi2
X_{i2}
Xij
X_{ij}
wij
w_{ij}
Linear Neighbourhood Similarity
Xi
X_i
Xi1
X_{i1}
Xi2
X_{i2}
Xij
X_{ij}
wij
w_{ij}
∑j∈N(Xi)wij=1
\sum_{j\in N(X_i)} w_{ij} =1
∣Xi−Xij∣2
| X_i - X_{ij}|^2
Linear Neighbourhood Similarity
Xi
X_i
Xi1
X_{i1}
Xi2
X_{i2}
Xij
X_{ij}
wij
w_{ij}
∑j∈N(Xi)wij=1
\sum_{j\in N(X_i)} w_{ij} =1
∣Xi−∑wijXij∣2
| X_i - \sum w_{ij}X_{ij}|^2
Linear Neighbourhood Similarity
Xi
X_i
∑j∈N(Xi)wij
\sum_{j\in N(X_i)} w_{ij}
∑j∈N(Xi)wij=1
\sum_{j\in N(X_i)} w_{ij} =1
∣Xi−∑wijXij∣2
| X_i - \sum w_{ij}X_{ij}|^2
Linear Neighbourhood Similarity
Xi
X_i
∑j∈N(Xi)wij
\sum_{j\in N(X_i)} w_{ij}
∑j∈N(Xi)wij=1
\sum_{j\in N(X_i)} w_{ij} =1
min∣Xi−∑wijXij∣2
min | X_i - \sum w_{ij}X_{ij}|^2
Linear Neighbourhood Similarity
Xi
X_i
∑j∈N(Xi)wij
\sum_{j\in N(X_i)} w_{ij}
∑j∈N(Xi)wij=1
\sum_{j\in N(X_i)} w_{ij} =1
min∣Xi−∑wijXij∣2
min | X_i - \sum w_{ij}X_{ij}|^2
wij≥0
w_{ij} \geq 0
The number of nearest neighbors is a hyperparameter
In Matrix Representation,
Gjk=(Xi−Xj)T(Xi−Xk)
G_{jk} = (X_i - X_j)^T (X_i - X_k)
min∣Xi−∑wijXij∣2=∑Xj,Xk∈N(Xi)wijGj,kwik
min | X_i - \sum w_{ij}X_{ij}|^2 = \sum_{X_j,X_k \in N(X_i)} w_{ij} G_{j,k} w_{ik}
In Matrix Representation,
Gjk=(Xi−Xj)T(Xi−Xk)
G_{jk} = (X_i - X_j)^T (X_i - X_k)
ϵ=∑Xj,Xk∈N(Xi)wijGj,kwik
\epsilon = \sum_{X_j,X_k \in N(X_i)} w_{ij} G_{j,k} w_{ik}
To avoid over-fitting, penalty parameter can be used
ϵ=∑Xj,Xk∈N(Xi)wijGj,kwik+λ∣wi∣2
\epsilon = \sum_{X_j,X_k \in N(X_i)} w_{ij} G_{j,k} w_{ik} + \lambda |w_i|^2
wi=[wi1wi2⋯wik]T
w_i = \begin{bmatrix}
w_{i1} & w_{i2} \cdots w_{ik}
\end{bmatrix}^T
wi=[wi1wi2⋯wik]T
w_i = \begin{bmatrix}
w_{i1} & w_{i2} \cdots w_{ik}
\end{bmatrix}^T
wij→Similarity Between i and j
w_{ij} \rightarrow \text{Similarity Between i and j}
Linear Neighbourhood Similarity
Xi
X_i
Xi1
X_{i1}
Xi2
X_{i2}
Xij
X_{ij}
wij
w_{ij}
∑j∈N(Xi)wij=1
\sum_{j\in N(X_i)} w_{ij} =1
∣Xi−∑wijXij∣2
| X_i - \sum w_{ij}X_{ij}|^2
Label Propagation
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31
w_{31}
w21
w_{21}
w12
w_{12}
w32
w_{32}
w23
w_{23}
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31
w_{31}
w21
w_{21}
w12
w_{12}
w32
w_{32}
w23
w_{23}
If a protein Pi Is known to be Interacting
with lncRNA l1
pi
p_i
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31
w_{31}
w21
w_{21}
w12
w_{12}
w32
w_{32}
w23
w_{23}
If a protein Pi Is known to be Interacting
with lncRNA l1
pi
p_i
if l2 is Similar to l1
It is more likely that Pi interacts with l2 as well
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31
w_{31}
w21
w_{21}
w12
w_{12}
w32
w_{32}
w23
w_{23}
That depends on the Similarity Score
pi
p_i
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31
w_{31}
w21
w_{21}
w12
w_{12}
w32
w_{32}
w23
w_{23}
That depends on the Similarity Score
pi
p_i
How to use what we know, to infer about what we don't?
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31
w_{31}
w21
w_{21}
w12
w_{12}
w32
w_{32}
w23
w_{23}
pi
p_i
How to use what we know, to infer about what we don't?
What do we know?
100
\begin{bmatrix}
1 \\
0 \\
0
\end{bmatrix}
Protein pi interacts with
lncRNA l1
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31
w_{31}
w21
w_{21}
w12
w_{12}
w32
w_{32}
w23
w_{23}
pi
p_i
How to use what we know, to infer about what we don't?
What can we Infer?
100
\begin{bmatrix}
1 \\
0 \\
0
\end{bmatrix}
w11w21w31w12w22w32w13w23w33
\begin{bmatrix}
w_{11} & w_{12} & w_{13} \\
w_{21} & w_{22} & w_{23} \\
w_{31} & w_{32} & w_{33} \\
\end{bmatrix}
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31
w_{31}
w21
w_{21}
w12
w_{12}
w32
w_{32}
w23
w_{23}
How to use what we know, to infer about what we don't?
Protein pi interacts with
lncRNA l2
1w11w21w31+0w12w22w32+0w13w23w33
1 \begin{bmatrix} w_{11} \\ w_{21} \\ w_{31} \end{bmatrix} + 0 \begin{bmatrix} w_{12} \\ w_{22} \\ w_{32} \end{bmatrix}
+0 \begin{bmatrix} w_{13} \\ w_{23} \\ w_{33} \end{bmatrix}
Select Information
About lncRNAs similar to
l1
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31=0.2
w_{31}=0.2
w21=0.8
w_{21}=0.8
w12
w_{12}
w32
w_{32}
w23
w_{23}
How to use what we know, to infer about what we don't?
Protein pi interacts with
lncRNA l2
1w11w21w31+0w12w22w32+0w13w23w33
1 \begin{bmatrix} w_{11} \\ w_{21} \\ w_{31} \end{bmatrix} + 0 \begin{bmatrix} w_{12} \\ w_{22} \\ w_{32} \end{bmatrix}
+0 \begin{bmatrix} w_{13} \\ w_{23} \\ w_{33} \end{bmatrix}
Select Information
About lncRNA similar to
l1
If l2 is similar l1, more likely
it should interact with pi
110
\begin{bmatrix}
1 \\
1\\ 0
\end{bmatrix}
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31=0.2
w_{31}=0.2
w21=0.8
w_{21}=0.8
w12
w_{12}
w32
w_{32}
w23
w_{23}
How to use what we know, to infer about what we don't?
Protein pi interacts with
lncRNA l2
00.80.2
\begin{bmatrix} 0 \\ 0.8 \\ 0.2 \end{bmatrix}
Information About
Closeness of l1 to l2 is
incorporated
If l2 is similar l1, more likely
it should interact with pi
110
\begin{bmatrix}
1 \\
1\\ 0
\end{bmatrix}
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31=0.2
w_{31}=0.2
w21=0.8
w_{21}=0.8
w12
w_{12}
w32
w_{32}
w23
w_{23}
How to use what we know, to infer about what we don't?
Protein pi interacts with
lncRNA l2
00.80.2
\begin{bmatrix} 0 \\ 0.8 \\ 0.2 \end{bmatrix}
Information About
Closeness of l1 to l2 is
incorporated
If l2 is similar l1, more likely
it should interact with pi
110
\begin{bmatrix}
1 \\
1\\ 0
\end{bmatrix}
However, Our Initial Knowledge that Pi intreacts with l1 is lost
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31=0.2
w_{31}=0.2
w21=0.8
w_{21}=0.8
w12
w_{12}
w32
w_{32}
w23
w_{23}
How to use what we know, to infer about what we don't?
Protein pi interacts with
lncRNA l2
00.80.2
\begin{bmatrix} 0 \\ 0.8 \\ 0.2 \end{bmatrix}
If l2 is similar l1, more likely
it should interact with pi
110
\begin{bmatrix}
1 \\
1\\ 0
\end{bmatrix}
However, Our Initial Knowledge that Pi intreacts with l1 is lost
We can Impart this knowledge by
Adding the Ground Truth
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31=0.2
w_{31}=0.2
w21=0.8
w_{21}=0.8
w12
w_{12}
w32
w_{32}
w23
w_{23}
How to use what we know, to infer about what we don't?
Protein pi interacts with
lncRNA l2
00.80.2
\begin{bmatrix} 0 \\ 0.8 \\ 0.2 \end{bmatrix}
If l2 is similar l1, more likely
it should interact with pi
110
\begin{bmatrix}
1 \\
1\\ 0
\end{bmatrix}
However, Our Initial Knowledge that Pi intreacts with l1 is lost
We can Impart this knowledge by
Adding the Ground Truth
+100
+ \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31=0.2
w_{31}=0.2
w21=0.8
w_{21}=0.8
w12
w_{12}
w32
w_{32}
w23
w_{23}
How to use what we know, to infer about what we don't?
What we Infer?
Protein pi interacts with
lncRNA l2
00.80.2
\begin{bmatrix} 0 \\ 0.8 \\ 0.2 \end{bmatrix}
If l2 is similar l1, more likely
it should interact with pi
110
\begin{bmatrix}
1 \\
1\\ 0
\end{bmatrix}
100
\begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}
+
+
α
\alpha
Can be used to select
between inference and ground
truth
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31=0.2
w_{31}=0.2
w21=0.8
w_{21}=0.8
w12
w_{12}
w32
w_{32}
w23
w_{23}
How to use what we know, to infer about what we don't?
What we Infer?
Protein pi interacts with
lncRNA l2
00.80.2
\begin{bmatrix} 0 \\ 0.8 \\ 0.2 \end{bmatrix}
If l2 is similar l1, more likely
it should interact with pi
110
\begin{bmatrix}
1 \\
1\\ 0
\end{bmatrix}
100
\begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}
+
+
α
\alpha
1−α
1-\alpha
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31=0.2
w_{31}=0.2
w21=0.8
w_{21}=0.8
w12
w_{12}
w32
w_{32}
w23
w_{23}
How to use what we know, to infer about what we don't?
What we Infer?
Protein pi interacts with
lncRNA l2
00.80.2
\begin{bmatrix} 0 \\ 0.8 \\ 0.2 \end{bmatrix}
If l2 is similar l1, more likely
it should interact with pi
110
\begin{bmatrix}
1 \\
1\\ 0
\end{bmatrix}
100
\begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}
+
+
α
\alpha
1−α
1-\alpha
Yt+1=α(WYt)+(1−α)Y0
Y^{t+1} = \alpha (WY^t) + (1-\alpha)Y^0
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31=0.2
w_{31}=0.2
w21=0.8
w_{21}=0.8
w12
w_{12}
w32
w_{32}
w23
w_{23}
How to use what we know, to infer about what we don't?
What we Infer?
Protein pi interacts with
lncRNA l2
If l2 is similar l1, more likely
it should interact with pi
110
\begin{bmatrix}
1 \\
1\\ 0
\end{bmatrix}
Yt+1=α(WYt)+(1−α)Y0
Y^{t+1} = \alpha (WY^t) + (1-\alpha)Y^0
Y=(1−α)(I−αW)−1Y0
Y = (1-\alpha)(I-\alpha W)^{-1} Y^0
In Matrix Form
limt→infYt=Y
\lim_{t\rightarrow \inf} Y^t = Y
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31
w_{31}
w21
w_{21}
w12=0.8
w_{12} = 0.8
w32=0.2
w_{32} = 0.2
w23
w_{23}
pi
p_i
How to use what we know, to infer about what we don't?
What do we know?
Protein pi interacts with
lncRNA l2
0w11w21w31+1w12w22w32+0w13w23w33
0 \begin{bmatrix} w_{11} \\ w_{21} \\ w_{31} \end{bmatrix} +1 \begin{bmatrix} w_{12} \\ w_{22} \\ w_{32} \end{bmatrix}
+0 \begin{bmatrix} w_{13} \\ w_{23} \\ w_{33} \end{bmatrix}
Select Information
About lncRNA similar to
l2
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31
w_{31}
w21
w_{21}
w12=0.8
w_{12} = 0.8
w32=0.2
w_{32} = 0.2
w23
w_{23}
pi
p_i
How to use what we know, to infer about what we don't?
What do we know?
Protein pi interacts with
lncRNA l2
0.800.2
\begin{bmatrix} 0.8 \\ 0 \\ 0.2 \end{bmatrix}
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31
w_{31}
w21
w_{21}
w12=0.8
w_{12} = 0.8
w32=0.2
w_{32} = 0.2
w23
w_{23}
pi
p_i
How to use what we know, to infer about what we don't?
What do we know?
Protein pi interacts with
lncRNA l2
0.800.2
\begin{bmatrix} 0.8 \\ 0 \\ 0.2 \end{bmatrix}
Label Propagation
1
1
2
2
3
3
w13
w_{13}
w31
w_{31}
w21
w_{21}
w12
w_{12}
w32
w_{32}
w23
w_{23}
If a protein Pi Is known to be Interacting
with lncRNA l1
if l2 is Similar to l1
It is more likely that Pi interacts with l2 as well
Zij=∑kωkYijk
Z_{ij} = \sum_k \omega_k Y^k_{ij}
k→Number of Features
k \rightarrow \text{Number of Features}
li,pj
l_i , p_j
Thank you sir!
References
Text
[1] Zhang, Wen; Qu, Qianlong; Zhang, Yunqiu; Wang, Wei (2017).
The linear neighborhood propagation method for
predicting long non-coding RNA–protein interactions. Neurocomputing
, (), S0925231217313899–. doi:10.1016/j.neucom.2017.07.065
19BIO201 Intelligence in Biological Systems - 3 Linear Neighbourhood Propagation method for predicting Long Non-Coding RNA-Protein Interactions
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