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Outline: The Lymn-Taylor cycle PCA method (theory & applications) Individual involvement coefficient (theory & applications) Summary Future work. http://www.sciencemag.org/feature/data/1049155s1.mov. The Lymn-Taylor cycle. Myosin is bound to actin - PowerPoint PPT Presentation
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Outline:
• The Lymn-Taylor cycle
• PCA method (theory & applications)
• Individual involvement coefficient (theory & applications)
• Summary
• Future work
http://www.sciencemag.org/feature/data/1049155s1.mov
The Lymn-Taylor cycle
(1) Myosin is bound to actin
(2) ATP binds to myosin and then myosin dissociates from actin
(3) Hydrolysis of ATP to ADP and Pi leads to a change in conformation for myosin
(4) Myosin rebinds to actin and actin is “rowed” past myosin with the release of the hydrolyzed products (ADP and Pi)
Geeves & Holmes : Annu. Rev. Biochem. 1999. 68:687–728
Pow
er-S
trok
e
Rec
over
y-S
trok
e
OPEN
(3)
(2)
CLOSED
Principal Component Analysis
100
1
1
b
jj
a
ii
a – number of the first principal components
b – the total number of the principal components
% - the contribution to the total variance of the data
PC1
PC2
we want to simplify the problem by reducing the dimension of the system
we want to preserve as much as possible of the original information content
MD-OPEN
0
20
40
60
80
100
0 10 20 30 40 50
mode nr.
%
MD of S1-Myosin head in OPEN conformation
15 eigenvectors 80% Good projection of data
MD of S1-Myosin head in CLOSED conformation
ATP ADP+Pi
MD-CLOSED-ATP
0
20
40
60
80
100
0 10 20 30 40 50
mode nr.
%
Total nr. of eigenvectors = more than 2200 (only Cα atoms)
MD-CLOSED-ADP+Pi
0
20
40
60
80
100
0 10 20 30 40 50
mode nr.
%
Are we choosing the right eigenvectors?!
R P
PC1
PC2
PC1
PC2
d1d2
PC1=L1
PC2=L2
R P
displacementvectorI2
I1
Individual involvement coefficient
kk LXX
XXI
21
21 )(
n
kkk IC
1
2
Ik - individual involvement coefficient
(X1-X2) – displacement vector
Ck – the cumulative involvement coefficient
Li & Cui : Biophysical Journal 2004. 743-763
MD-CLOSED-ADP+Pi
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 500 1000 1500 2000 2500
mode nr.
Ck
Involvement coefficient-MD-CLOSED-ADP+Pi
0.000.020.040.060.080.100.120.140.16
1
149
297
445
593
741
889
1037
1185
1333
1481
1629
1777
1925
2073
2221
mode nr.
Ik
Md-myosin-OPEN
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 500 1000 1500 2000 2500
mode nr.
Ck
Involvement-coefficient-MD-myosin-OPEN
00.020.040.060.080.1
0.120.140.16
1
149
297
445
593
741
889
1037
1185
1333
1481
1629
1777
1925
2073
2221
mode nr.
Ik
MD-myosin-CLOSED
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 500 1000 1500 2000 2500
mode nr.
Ck
Involvement-coefficient-MD-myosin_CLOSED
00.020.040.060.080.1
0.120.140.16
1
149
297
445
593
741
889
1037
1185
1333
1481
1629
1777
1925
2073
2221
mode nr.
IkIndividual involvement coefficient for different MD trajectories
„Important modes“ ????
“Important” elements of S1-Myosin head in CLOSED conformation
(ATP)
“Important” elements:
Relay-helix : cyan
Switch2-Loop: white
Converter Domain: green
SH1-Helix : pink
Lever Arm : yellow
calculate the % from the total variance (PCA)
calculate the individual involvement coefficients
for some of them visualize the first mode (VMD)
Switch2: blue
P-Loop: red
All “Important” elements
MD-Impres-all
0
20
40
60
80
100
120
0 100 200 300 400 500
mode nr.
%
MD-impres
0
0.2
0.4
0.6
0.8
1 28
55
82
109
136
163
190
217
244
271
298
325
352
379
406
mode nr.
Ik
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1 5 9 13 17 21 25 29 33 37 41 45 49
mode-nr.
Ik MD-Impres
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50 60
mode nr.
Ck
„Important“ element: Relay-helix
MD-relay_helix
0
0.2
0.4
0.6
0.8
1
1 8 15 22 29 36 43 50 57 64 71 78 85 92 99
mode nr.
Ik
MD-relay_helix
0
0.2
0.4
0.6
0.8
1
1.2
0 5 10 15 20
mode nr.
Ck
MD-relay_helix
0
20
40
60
80
100
120
0 20 40 60 80 100
mode nr.
%
MD-relay_helix
0
0.2
0.4
0.6
0.8
1
1 3 5 7 9 11 13 15 17 19
mode nr.
Ik
„Important“ element:
Converter-domain + lever-arm
MD-converter
0
20
40
60
80
100
120
0 50 100 150 200 250
mode nr.
%
MD-converter
0
0.2
0.4
0.6
0.8
1 15 29 43 57 71 85 99 113
127
141
155
169
183
197
mode nr.
Ik
MD-converter
0
0.2
0.4
0.6
0.8
1
1.2
0 5 10 15 20 25 30 35
mode nr.
Ck
„Important“ element: Switch2
MD-sw2p
0
20
40
60
80
100
120
0 5 10 15 20
mode nr.
%
MD-sw2p
0
0.2
0.4
0.6
0.8
1 3 5 7 9 11 13 15 17 19 21 23
mode nr.
Ik
MD-sw2p
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8
mode nr.
Ck
„Important“ element : Switch1
MD-sw1
0
20
40
60
80
100
120
0 5 10 15 20
mode nr.
%
MD-Switch1
0
0.10.2
0.3
0.4
0.50.6
0.7
1 3 5 7 9 11 13 15 17 19 21 23
mode nr.
Ik
MD-Switch1
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10
mode nr.
Ck
„Important“ element : Ploop
MD-Ploop
0
20
40
60
80
100
120
0 2 4 6 8 10 12 14
mode nr.
%
MD-Ploop
00.10.20.30.40.50.60.7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
mode nr.
Ik
MD-Ploop
0
0.2
0.4
0.6
0.8
1
1.2
0 5 10 15 20
mode nr.
Ck
Summary:
a good projection of the data is obtained with PCA
the mode with the largest contribution functionally relevant motion
to analyze the conformational change Individual Involvement Coefficient
the conformational change was decomposed into the motion of some structural elements.
![IMA Preprint Series # 2251 · a segmentation functional optimizing the parameters of the representation with the first deformation modes. Cootes and Taylor [8] compute, using PCA,](https://img.dokumen.tips/doc/110x75/5e8270ebead1592887661085/ima-preprint-series-2251-a-segmentation-functional-optimizing-the-parameters-of.jpg)
