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.