Kamada-filehhhhhhhhhhhhhhhhhhhhhhhhhhhh.ppt

Clustering the Temporal Sequences of
3D Protein Structure
Mayumi Kamada+*
, Sachi Kimura,
Mikito Toda‡
, Masami Takata+
, Kazuki Joe+
+：Graduate School of Humanities and Science,
Information and Computer Sciences,
Nara Women’s University
‡：Departments of physics, Nara Women’s University

Outline
• Motivation
• Flexibility Docking
• Feature Extraction using Motion
• Analysis
• Conclusions and Future Work

Motivation
• Protein in biological molecules
“Docking”
– Transform oneself and Combine with other
materials
• Prediction of Docking
 Prediction of resultant functions

Existing Docking Simulation
Predicted structures
from docking
structure
A
structure
B
Docking simulation
PDB*
Rigid
structures
* Protein Data Bank
Fluctuating in living cells
 Low prediction accuracy
Docking simulation
Considering fluctuations

Flexibility Docking
Predicted structures
from docking
structure
A
structure
B
Docking simulation
PDB
Flexibility handling
• Considering fluctuation of proteins in living cells
Extraction of fluctuated
structures
Consideration of
structural fluctuation of proteins

Flexibility Handling
Flexibility handling
MD
Filter
・・・
output
file
Representative
structure
・・・
・・・
・・・
Filtering
• Selection of representative structures
from similar structures
Molecular dynamic
simulation(MD)
• Simulation of motion of
molecules in a polyatomic system
output
file
output
file
output
file
output
file
Representative
structure
Create filters by using RMSD

Filters using RMSD
• RMSD(Root Mean Square Deviation)
– Comparison of the similarity of two structures
• Propose two filtering algorithms
<Filter-1> Maximum RMSD selection filter
<Filter-2> Below RMSD 1Å deletion filter
• Result
– Useful for the heat fluctuation condition
– RMSD
Unification of topology information
Lapse of information
Feature extraction
focusing on Protein Motion
not Structure

Capture Protein Motion
MD
・・・・・・
Wavelet transform
・・・・・・
Clustering
・・・・・・
Continuous wavelet
transform:
Morlet wavelet
Clustering algorithm:
Affinity Propagation
Selection of representative motions
Feature extraction
The frequency
may change
momentarily!

Target Protein
• 1TIB
– Residue length: 269
• MD simulation
– Software: AMBER
– Simulation run time: 2 nsec
– Result data files: 200
• Space coordinates of Cα atoms

Singular Value Decomposition
• SVD(Singular value decomposition)
• Definition:
*
V
U
A 

Unitary matrix U:
Left-singular vectors
Spatial motion
Unitary matrix V:
Right-singular vectors
Frequency fluctuation
Matrix A:
At time step i (ti)
Components column ： Cα
row ： Frequency
★matrix-size of A: 807×199

Verification of Reproducibility
• Singular values and principal components
• N=1 • N=4
• N=6 • N=8
• M=1 • M=4
• M=6 • M=8
2
1
2
2
807
1

 

N
j
j
j
i
'
i u
vs
a 
2
1
2
2
199
1

 

M
j
j
j
i
i v
vs
a 
Left Singular Vectors
(Spatial motion)
Right Singular Vectors
(Frequency fluctuation)

Reproducibility
Using the eight principal components,
the motion expressed by 199 components
can be reproduced !
Almost adjusted !

Examination
(1) Each of singular values
(2)The first singular value
– Accounted for about 30% over
Expression of the original motion
 Possible by the six singular values
The first singular value is useful

Clustering Analysis
• Focus on the first principal component
• Definition
– Similarities and Preference
 Clustering by using the above values

Similarities (1)
• For left singular vectors
– Difference of spatial directs
 Inner products
– Similarity :
Same direction Differential direction
Kij :Value
1 0
)
(
)
( 1
1 j
i
ij t
e
t
e
K 

ij
j
i
j
i K
t
t
S 


)
,
(
Cα

Similarities (2)
• For right singular vectors
– Difference between distributions of spectrum
 Hellinger Distance
– Similarity:
 
 


n
j
i
j
i
i
i
n
P
n
P
P
P
d
n
x
n
P
2
2
)
(
)
(
2
)
,
(
)
(
)
(
)
,
(
)
,
( j
i
j
i P
P
d
P
P
S 


Clustering Method
• Affinity propagation(AP)
– Brendan J. Frey and Delbert Dueck
– “Clustering by Passing Messages Between Data
Points”. Science 315, 972–976.2007
– Obtain “Exemplars”: cluster centers
• Preference
– Left singular vectors
• Average of similarities
– Right singular vectors
• minimum of similarities－（maximum of similarities－minimum）
Data point i
Candidate
exemplar k
Competing candidate
exemplar k’
Supporting
data point i’
)
,
( k
i
r
)
,
( k
i
r 
)
,
( k
i
a 
)
,
( k
i
a
Data point i
Candidate
exemplar k
Competing candidate
exemplar k’
Supporting
data point i’
)
,
( k
i
r
)
,
( k
i
r 
)
,
( k
i
a 
)
,
( k
i
a

Similarities
between Left Singular Vectors

Clustering
of Left Singular Vectors

Similarities
between Right Singular Vectors

Clustering
of Right Singular Vectors

Discussions
• Each of motions
– Spatial motion
• Repetition of several similar spatial motions
in time variation
– Frequency fluctuation
• Repetition of similar frequency patterns
in time variation
• Relationship
Characteristic Frequency fluctuation
Group transition on spatial motion

Conclusions and Future Work
• Flexibility docking
– Flexibility handling: MD and Filter
• Feature extraction based motion
– Wavelet analysis
– Analysis of motions
– Clustering
• Future work
– Collective motion
– Relationship
– Perform the docking simulation

Kamada-filehhhhhhhhhhhhhhhhhhhhhhhhhhhh.ppt

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